Grade 2
Mathematics
Grade 2
Mathematics
Table of Contents
Unit 1: Numbers, Numerals, and Data.............................................................................1
Unit 2: Extending Facts and Operations .......................................................................19
Unit 3: Money and Time..................................................................................................37
Unit 4: Place Value and 2-Digit Addition ......................................................................50
Unit 5: Place Value and 2-Digit Subtraction .................................................................64
Unit 6: Shapes and Fractions ..........................................................................................73
Unit 7: Measurement in Our World...............................................................................86
Unit 8: Extending Number Patterns through 100s and 3-Digit Operations ...............99
Louisiana Comprehensive Curriculum, Revised 2008
Course Introduction
The Louisiana Department of Education issued the Comprehensive Curriculum in 2005. The
curriculum has been revised based on teacher feedback, an external review by a team of content
experts from outside the state, and input from course writers. As in the first edition, the
Louisiana Comprehensive Curriculum, revised 2008 is aligned with state content standards, as
defined by Grade-Level Expectations (GLEs), and organized into coherent, time-bound units
with sample activities and classroom assessments to guide teaching and learning. The order of
the units ensures that all GLEs to be tested are addressed prior to the administration of iLEAP
assessments.
District Implementation Guidelines
Local districts are responsible for implementation and monitoring of the Louisiana
Comprehensive Curriculum and have been delegated the responsibility to decide if
 units are to be taught in the order presented
 substitutions of equivalent activities are allowed
 GLES can be adequately addressed using fewer activities than presented
 permitted changes are to be made at the district, school, or teacher level
Districts have been requested to inform teachers of decisions made.
Implementation of Activities in the Classroom
Incorporation of activities into lesson plans is critical to the successful implementation of the
Louisiana Comprehensive Curriculum. Lesson plans should be designed to introduce students to
one or more of the activities, to provide background information and follow-up, and to prepare
students for success in mastering the Grade-Level Expectations associated with the activities.
Lesson plans should address individual needs of students and should include processes for reteaching concepts or skills for students who need additional instruction. Appropriate
accommodations must be made for students with disabilities.
New Features
Content Area Literacy Strategies are an integral part of approximately one-third of the activities.
Strategy names are italicized. The link (view literacy strategy descriptions) opens a document
containing detailed descriptions and examples of the literacy strategies. This document can also
be accessed directly at http://www.louisianaschools.net/lde/uploads/11056.doc.
A Materials List is provided for each activity and Blackline Masters (BLMs) are provided to
assist in the delivery of activities or to assess student learning. A separate Blackline Master
document is provided for each course.
The Access Guide to the Comprehensive Curriculum is an online database of
suggested strategies, accommodations, assistive technology, and assessment
options that may provide greater access to the curriculum activities. The Access
Guide will be piloted during the 2008-2009 school year in Grades 4 and 8, with
other grades to be added over time. Click on the Access Guide icon found on the first page of
each unit or by going directly to the url http://mconn.doe.state.la.us/accessguide/default.aspx.
Louisiana Comprehensive Curriculum, Revised 2008
Grade 2
Mathematics
Unit 1: Numbers, Numerals, and Data
Time Frame: Approximately five weeks
Unit Description
This unit focuses on extending students’ command of place value, estimation, and
collecting and using data to make decisions.
Student Understandings
Students will demonstrate their understanding of place value using numbers up to 99.
They will model, write, compare, and round numbers through 99. They will count
forward or backwards from a given number. Using a benchmark, they will be asked to
make estimates. Students will also collect, graph, interpret, and analyze data.
Guiding Questions
1. Can students count, show expanded and standard notation, and use cardinal
number skills through 99?
2. Can students compare and order a set of numbers?
3. Can students round a number to the nearest 10?
4. Can students count forward and backwards from a given number?
5. Can students make reasonable estimates for group sizes through 99 and know
when estimations are appropriate?
6. Can students collect and organize data from questionnaires, surveys, and
experiments?
7. Can students make and interpret bar graphs, pictographs, and line plots
including choice of scale and title?
8. Can students make classifications involving and, or, and is/is not statements
and represent outcomes on one- and two-circle Venn diagrams?
Unit 1 Grade-Level Expectations (GLEs)
GLE # GLE Text and Benchmarks
Number and Number Relations
1.
Model, read, and write place values for numbers through 999 in word,
standard, and expanded form (N-1-E)
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3.
Make reasonable estimates of the number of objects in a collection with fewer
than 100 objects (N-2-E)
5.
Read, write, compare, and order whole numbers through 999 using words,
number lines, and models (N-3-E) (N-1-E)
6.
From a given number, count forward and backward and count to 100 by 2s
(N-3-E) (N-1-E) (N-4-E)
10.
Round numbers to the nearest 10 or 100 and identify situations in which
rounding is appropriate (N-7-E) (N-9-E)
Data Analysis, Probability, and Discrete Math
25.
Collect and organize data using observations, surveys, and experiments
(D-1-E)
26.
Construct and read line plots and tables (D-2-E)
27.
Interpret pictographs in which each picture represents more than one object
(D-2-E)
28.
Generate questions that can be answered by collecting and analyzing data (D3-E)
29.
Solve logic problems involving two sets by using elementary set logic (i.e.,
and, or, and is/is not statements) (D-3-E)
Sample Activities
Activity 1: Counting the Days (GLEs: 1, 5, 6, 10)
Materials List: adding machine tape, black marker, monthly calendar, Post-it® notes,
Base 10 ® blocks; paper; pencil; a Ziploc® bag containing scissors and a copy of Base
10 Blocks BLM for each student
If Base 10® blocks are not available, copy the Base 10 Blocks BLM for each student and
have them cut out each piece. Have students use the pieces to model the number of days
they have been in school. Store the scissors and the BLM in a Ziploc® bag for future
activities.
Use a black marker to write the numbers representing the number of school days on
adding machine tape and attach it to the walls around the classroom. Circle every
multiple of ten. Underline every multiple of 5.
Post a monthly calendar. Have students write the date each day. Model the number of
days in school with Base 10 ® blocks. Also, have students write the number of days in
school in expanded and word form. Each day select an activity from the list below, and
have students use the counting tape to locate their answers.
 Have students practice counting using the counting tape.
 Cover a number on the counting tape with a Post-it® note. Have students identify
the missing number.
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Choose a number and have students count up or down from that number.
Select two numbers and have students find the missing number between the two
numbers selected.
Select a number and have students identify the number that comes before or after
the number.
Select a number and ask students which ten is closer to it.
Select two numbers on the counting tape and have students identify which number
is greater and explain why it is greater.
Skip count by 2s, 5s, and 10s using the counting tape.
Activity 2: Bundles of Ten (GLE: 1)
Materials List: Jumbo Popsicle® sticks with each student’s name on one, rubber bands,
paper, pencil
Write each student's name on a Jumbo Popsicle® stick. Provide each student with his/her
stick, and have class members count-off to see how many students are present. Once the
number is determined, write “ ________students are present in our class today.” on the
board. Tell students they are going to bundle the sticks into groups of ten. Ask students:
“How many bundles of ten do you think we will have? How many sticks will we have
that can not be bundled?”
Have students count-off again. This time as students count to10, have the10 students
come to the front of the class and use a rubber band to make a bundle of ten sticks. Place
the bundle where all students can see it. Have the next student start over with 1 while
students continue counting-off until another bundle of 10 can be made. Continue this
procedure until students cannot make another bundle. Place the unbundled sticks to the
right of the bundles. Have students write the sentence, “We have ______students
present.” Then have them draw a model to represent the number.
See if students can transfer knowledge by asking them, “How many bundles would we
need to represent the number 42?” Have them draw the model.
Teacher Note: These sticks may be unbundled and placed in a cup/can and pulled one at
a time to identify a student who should answer a question during the day’s activities. Do
not return the stick to the cup/can unless all the sticks are used. This procedure assures
that each student will be given a chance to answer questions throughout the day.
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Activity 3: Modeling Numerals (GLEs: 1, 5)
Materials List: Place Value Mat BLM, 40 Popsicle® sticks, rubber bands, Ziploc® bags,
Digit Cards BLM, math learning log
Teacher Hint: Cut out 2 sets of digit cards for each student prior to the lesson. Put the
Popsicle® sticks, rubber bands and 2 sets of digit cards in a Ziploc® bag prior to the
lesson.
Give each pair of students a Place Value Mat BLM, 40 Popsicle® sticks, and two sets of
0-9 digit cards. Call out the number 13 and have students count out 13 sticks. Have
students place three sticks on the ones side of the mat. Have them count how many sticks
they have left (10). Have students place the 10 sticks on the mat under the tens side of the
mat. Have them group the 10 sticks into 1 bundle. Instruct students to use digit cards to
represent the number. Ask students what each digit represents.
Have students clear their mats and repeat the procedure using the numbers 12, 18, and 16.
Ask students what the 1 represented in 13, 12, 18, and 16? (1 group of 10) Ask students
to represent the number 32 on their mats. Have students explain what each digit in the
number 32 represents. Repeat the procedure modeling numbers under 41. Give each
student a two-digit number between 10 and 40. (Make sure to give someone a multiple of
10.) Have them model the number with Popsicle® sticks and digit cards. Have students
compare their number to their neighbor’s number. Encourage students to use the
vocabulary greater than and less than. Make them explain why their number is greater
than/less than their neighbor’s number. Example: One student models 27 and the other
models 31. The first student might say, “The number 27 is less than 31 because 27 has 2
tens and 31 has 3 tens. Three tens are more than two tens.”
Have students use their math learning logs (view literacy strategy descriptions) to
compare and contrast the numbers 23 and 32. A math learning log is a notebook students
use to record a problem of the day or an open- ended problem that you want them to
solve and explain.
Activity 4: Number Words (GLE: 1)
Materials List: Vocabulary Self-Awareness Chart BLM, Number Words Chart BLM,
scissors, two sets of 0-9 digit cards (see Activity 3-Digit Cards BLM), paper, pencil
Introduce students to a vocabulary self-awareness (view literacy strategy descriptions)
chart to access their understanding of the meaning of number words. Give each student a
Vocabulary Self-Assessment Chart BLM and direct him/her to rate his/her understanding
of each word/symbol with either a “+” (understands well), “√ ”(limited understanding), or
a “ – ” (don’t know). Over the course of the activity, students are to return to their chart
and add new information. The objective is that students will replace all the check and
minus marks with plus signs.
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Give each student a Number Words Chart BLM. Have him/her cut the chart apart and
sort words into groups [teens (13-19), ty numbers (20-90), zero-twelve (0-12)]. Review
that the word teen means plus ten, and the ending ty stands for ten.
14 - fourteen means 4 plus 10
42 - forty-two means 4 tens plus 2
60 – sixty means 6 tens
Flip two digit cards and have students find the number words to represent the two-digit
number. Make a big deal about the hyphen. This will help students with expanded form.
Twenty-three means 2 tens plus 3 more or, 20 + 3. Repeat the procedure. Circulate to
assess students’ needs. Repeat as many times as possible.
Have students reassess their understandings of number words using the self-awareness
chart. If any students are still unsure about how number words are connected to
numerals, provide the remediation that is necessary.
Activity 5: Order It! (GLEs: 5, 6)
Materials List: pocket chart, hundreds-chart poster, clock-timer, paper, pencil
Cut apart a hundreds chart poster, and allow students to place the cards in correct order in
a pocket chart. After about 30 cards have been placed, discuss patterns that are emerging
(i.e., skip counting). Play the game, Make 100 Fast.
 Deal the number cards to the students. Tell the students that they will have 3
minutes (or a specified time determined by you) to fill the 100s chart with
their cards. When you say “Go,” the student holding the card with the number
1 places it in the pocket chart; then the student with number 2, and so on. The
goal is for students to place all of the cards (1–100) in order as quickly as
possible.
 Remind students to stay seated until the number ahead of theirs is placed in
the chart. Allow them to walk fast but not to run.
 Repeat at various times during the unit as a review with the goal of shortening
the time to fill the chart.
 Take out just the even numbers from 2-100. Give each student an even
number and have him/her skip count by 2s to 100 by placing their numbers in
the chart.
 As students become proficient with the numbers through 100, create cards for
the numbers from 100 – 999 in sets of 100 (e.g., 201-300).
 Put students into groups of 4. Give each student a card with a numeral on it.
Each member of the group will contribute to a story chain (view literacy
strategy descriptions) for each student’s number. The student writes the first
clue for his/her numeral on the back of the card and then passes the card to
his/her left. The next student writes another clue for the numeral on the card.
Continue passing the card until the card returns to “owner.” The “owner”
checks the clues for validity and makes adjustments to false statements.
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Finally, each group exchanges cards and tries to guess the numeral on the card
according to the clues that the students listed.
Example of a story chain:
47
My number has 4 tens.
My one’s digit is less than 8.
My one’s digit is greater than 6.
What am I?
Activity 6: Forward – Backwards (GLEs: 1, 5, 6)
Material List: Spinner BLM and Hundreds Chart BLM copied on tagboard, large paper
clip, pencil
Use the Spinner BLM.
1. Place the point of a pencil through a large paper clip. 2. Place the point of the pencil on
the center of the spinner. 3. Adjust the paper clip so that the end of the paper clip is on the
center of the spinner. 4. “Flick” the paper clip to spin it.
Cut apart the Hundreds Chart BLM. Turn the numbers over so that students cannot see
the number. A student is selected to come up and choose a number and spin the spinner.
According to the spinner he/she must count forward or backwards from his/her number.
(You determine if you want him/her to count 1 or 2 numbers forward or backwards.) Play
as many rounds as time will permit. A variation is to divide the class in half and make
this into a game format, rewarding points to each team when a member completes the
task correctly.
Teacher note: If the numbers are too small for the students to handle, write the numerals
1-100 on index cards, and substitute them for the Hundreds Chart BLM in the activity.
Play a modified version of this game by using just the even numbers. Have students
select an even number, and always count forward 2 numbers to find the next even
number.
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Activity 7: What’s Missing? (GLEs: 1, 5, 6)
Materials List: Hundreds Chart BLM per group, 10 x 10 grid BLM, Ziploc® bags, glue
sticks
Cut apart as many Hundreds Chart BLMs as there are groups. As charts are cut apart,
place the numerals in a Ziploc® bag. Remove five numerals from each group’s bag. Give
each group a 10 x 10 grid, a bag, and a glue stick. Have students fill in the grids with
numerals to find the five missing numerals on their chart. Let each group share their
findings. After students have mastered cards from 1-100, create cards for numbers 101200, 201-300, and so on.
Website of an interactive game
http://www.bbc.co.uk/schools/numbertime/games/mend.shtml
Activity 8: Families (GLE: 5)
Materials List: numeral cards 0-99, word cards 0-19, word cards twenty– ninety, index
cards that fit pocket chart, pocket chart, Number Words Chart BLM (see Activity 4
BLM)
Make a set of numeral cards representing the numbers 0–99 and set aside. Make a set of
word cards for the numerals 0–9. Place the cards for the words for zero to nine
horizontally in a pocket chart. Write the words for the multiples of 10 (through 90) on
cards. Place them vertically along the left side of the pocket chart.
zero
one
two
three
four
five
six
ten
twenty
etc
…
twentythree
thirty
Tell the students that when you point to them, they are to call out any number at random
such as 54, 79, etc. Write the students’ numbers (in word form) on the corresponding
numeral card, and ask the students to put them in the pocket chart where they belong.
After all students have had a turn, ask them to decide if each number word card has been
placed correctly. Make adjustments, as needed.
For the numbers that are not yet represented, pass out the number cards (that were set
aside) to the students until all cards are distributed, and ask them to write the number
words on the back of the card. Check for correct spelling, including the use of the hyphen
between words. Direct students to a resource for correct spellings (Number Words Chart
BLM from Activity 4).
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When cards are checked and completed, have students place them in the 100-pocket chart
correctly.
Activity 9: Base 10® Blocks (GLEs: 1, 5)
Materials List: Base 10® blocks, overhead Base 10® blocks, transparency of Place Value
Chart BLM, set of cards with numerals 0 – 9 per student, Place Value Chart BLM per
student
If Base 10® blocks are unavailable, use the Activity 1 BLM to create student sets and
transparency of Base 10® blocks.
Use the transparency of the Place Value Chart BLM to demonstrate how to use the Base
10® blocks to model a 2-digit number. Give each student a copy of a Place Value Chart
BLM. Model a number with the Base 10® blocks on the overhead, and then write the
number for your model in standard form, word form, and expanded form. Model about
five numbers. Then ask students to choose two numbers to model and write in standard,
word and expanded form.
Partners can play the High Card game.
 Give each player a set of cards with the numerals 0–9.
 Shuffle both sets of cards together.
 Have each student draw two cards and form the greatest possible number.
 The student with the greatest number wins a point if he/she can correctly read
the number. If the student with the highest number fails to correctly read the
number, the next student may earn a point if he/she reads his number
correctly.
Observe partners playing and discuss strategies they have discovered for making the
greatest number. After students have been exposed to 3-digit numbers, let students play
High Card using three cards.
Activity 10: Spinning Numbers (GLEs: 1, 5, 10)
Materials List: Spinners - Number Line BLM and Recording Sheet BLM per pair of
students, pencil, large paper clip, 2 counters, (See Activity #6 for explanation of how to
make a spinner.)
Have students work in pairs. Instruct player 1 to spin a spinner marked 1–8 two times.
Record the digits spun on the Recording Sheet BLM. Next, spin a spinner marked
larger/smaller to determine if the student is to make the larger or smaller number that can
be formed with the two digits. Record the results of spinner on the recording sheet. The
student then records the 2-digit number on the recording sheet. Player 2 repeats the
process. Next, have students plot their numbers on the number lines at the bottom of the
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Spinners – Number Line BLM using counters. Compare numbers using greater than and
less than. Finally, have students round their numbers to the nearest ten. Repeat the
process. Collect Recording Sheet BLMs and use them as an informal assessment of what
students know about rounding numbers. Rounding numbers will be taught in Activity 12.
Activity 11: Order Those Numbers! (GLE: 5)
Material List: number line, hundreds chart, 3 x 5 cards
Use a number line and a hundreds chart to review how to use the location of two numbers
on a number line or on a hundreds chart to tell which number is greater than or less than.
When shown three or four 1-digit numbers, have students order the numbers from least to
greatest, using the hundreds chart as a reference. To practice putting numbers in order,
instruct each student to write a number from 0 through 40 on a 3” x 5” card. Ask two or
three students to bring their cards and line up in order from least to greatest. Next, choose
three or four students to stand with their cards and put themselves in the correct
designated order (greatest to least or least to greatest). Keep index cards for Activity 12.
Activity 12: Rounding to Nearest 10 (GLE: 10)
Materials List: 0, 10, 20, 30, 40 written on colored index cards, 3 x 5 cards made in
Activity 11, clothesline, clothespins, math learning logs
Prior to class write the numbers 0, 10, 20, 30, and 40 on colored index cards. Hang the
multiples of 10 on a clothesline. Pass out index cards used in Activity 11. Have each
student determine which two tens his/her number is between and then determine which
10 the number is closer to. As each student discovers which ten the number rounds to
have him/her pin the number to the bottom of the appropriate colored index card. Repeat
until all students have had a chance.
Ask if students can determine why numbers are rounded a certain way. Students should
be able to reason that 32 is rounded to 30 because on a number line 32 is closer to 30 than
to 40. In the same way, 36 is rounded to 40 because it is closer to 40 than to 30. Explain
the rule for a number ending in 5.
At the completion of this activity, ask students to list the numbers that would round to 50
(45, 46, 47, 48, 49, 50, 51, 52, 53, 54). It is very important when teaching rounding to
always ask which two tens the number is between or which ten the number is closer to.
Have students explain to a younger sibling the rules for rounding with examples in their
math learning logs (view literacy strategy descriptions). Have them give an example of
when you round up, round down or when a number ends in 5 what rule applies.
Teacher Note: For students that have trouble with this activity, have them use a hundreds
chart to help them determine the closest ten.
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Activity 13: Round About! (GLE: 10)
Materials List: number line, newspaper advertisement or school supply list with items
priced less than $1, paper, pencil
Explain that a rounded number tells about how many instead of exactly how many. Use a
number line to round 14, 12, and 16 to the nearest 10. Allow the students to brainstorm
(view literacy strategy descriptions) ideas about when to round numbers in real-life
situations. Explain how to round money amounts to the nearest 10 cents. Have small
groups (2–4 students) use a newspaper advertisement or a list of school supplies to list
prices of items and round the cost to the nearest 10 cents.
Example: Eraser 87¢ rounds to 90¢
Sticker 13¢ rounds to 10¢
Activity 14: Place Value Word Grid (GLEs: 1, 5, 6, 10)
Material List: Number Sense BLM, pencil
After students have learned how to round numbers and skip count by 5’s and 10’s have
them fill out the Number Sense BLM that utilizes a word grid (view literacy strategy
descriptions) that demonstrates their mastery of place value, rounding, counting forward
and backwards. After the word grid is filled in, allow time for students to quiz each other
on the information in preparation for class activities and quizzes.
Word Grid
Numeral
21
47
70
57
35
62
Tens
Ones
2
1
Number Number
Before
After
20
Nearest
Ten
22
20
Multiple
of 10
yes or no
no
Multiple
of 5
yes or no
no
Activity 15: Professor Know-It-All (GLEs: 1, 5, 6, 10)
Materials List: cards with 2-digit numbers, Place Value Certificate BLM
Ask for a volunteer to be professor know-it-all (view literacy strategy descriptions). The
student is given a two-digit number. He/she is expected to model the number with
manipulatives, write the number in words, write it in expanded form, state a number that
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comes directly before it and after it, and round it to the nearest ten. When the task is
complete, give the student a certificate that states he/she has earned the status of being a
Professor of Place Value.
Activity 16: The Guessing Jar (GLEs: 3, 26)
Materials List: 2 glass jars that are the same size, some sort of filler for jars, Post-it®
notes, poster, pencil
Introduce the terms estimate and exact. Show students a jar (the same size as the
Guessing Jar) with only 10 or 20 jellybeans or other small yummy treats. This will give
the students a point of reference for making estimates.
Ask the students to guess how many items are in the Guessing Jar. Have each student
write a guess on a sticky note and place it on a poster. Arrange their guesses into a line
plot. Discuss how students decided on their guesses and how they might determine how
close their estimates might be.
Count the items to find the exact number. Talk about which were good estimates. Do not
emphasize or reward the student that got the closest to the exact number. This goes
against the reason we estimate. Using the line plot, discuss how many students
overestimated vs. how many underestimated the number of items in the jar.
Teacher Note: There is an example of a line plot in the assessment section of this unit.
Activity 17: Estimate (GLEs: 3, 5, 10, 26)
Materials List: Popscicle® sticks, Post-it® notes, poster, pencil, marker
Count out 62 Popsicle® sticks before class. Have students estimate how many sticks they
think there are. Count out 10 sticks and ask students if they would like to adjust their
estimates. Have students record their estimates on a sticky note.
Ask students to round their estimate to the nearest ten. Construct a line plot after
determining the range of the estimates. Use multiples of ten on the line plot. Have
students place their sticky notes above the multiple of ten that corresponds to their
rounded estimate. Ask questions relating to the line plot. Finally, count out sticks in
bundles of ten.
Website of an interactive estimation game with place value blocks
http://www.learningbox.com/base10/Estimation.html
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Activity 18: Exactly! (GLE: 3)
Materials List: T-chart, chalk
Discuss the difference between exact and estimated numbers using items in the classroom
and vocabulary such as more than, almost, nearly, and about to describe and compare
numbers of items. For example, “There are about fifty books on the bookshelf” is an
estimate. “We have fifteen boys and nine girls in our classroom” is an exact number.
Provide students with opportunities throughout the year to practice and give examples of
estimated and exact numbers. Lead discussions about situations that would require exact
numbers and those in which only estimates are required. Record situations on a T-chart
labeled estimate – exact.
estimate exact
Activity 19: Responding to a Venn Diagram (GLEs: 25, 26, 28, 29)
Materials List: Venn diagram poster, overhead pen, tally chart, linking cubes, pencil
Make a graphic organizer (view literacy strategy descriptions) of a single Venn diagram
poster and laminate it. Post a statement each day and have students sign their names in
the location of the poster that represents their responses. Point out that everyone has a
place on the Venn diagram. Students who do not agree with the statement place their
signatures outside the box containing the statement.
Suggested statements: I like chocolate ice cream.
I have a sister.
I have a brother.
I have a sister.
Teacher Note: It is important for students to realize that if a signature is placed outside
of the statement box, it could mean that the student has only brothers or he/she is an only
child.
Transfer results to a tally chart. Review how to record tally marks. Represent the data
using linking cubes. Have students write two questions that could be answered using the
data.
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Have a sister
Don’t have a sister
Activity 20: Playing Around with Vennie! (GLEs: 25, 29)
Materials List: colored chalk, paper, pencil
Draw a large graphic organizer (view literacy strategy descriptions) of a Venn diagram
that has two overlapping circles on the playground. Choose students to act out various
combinations to demonstrate the correct use of the two-circle Venn diagram.
For example, label the circles “I like to read.” and “I like to play video
games.” Call up students that like to read and have them stand in the first
circle. Then call up those that like to play video games and have them stand
in the other circle. Ask if there are any students that like to both read and
play video games. Those students should stand in the overlapping part. Have those who
don’t like reading or playing video games stand outside the circles. Dramatize other
comparison situations using the large Venn diagram.
Have students brainstorm (view literacy strategy descriptions) to identify animals that
live on land and animals that live in water. Have students draw or cut out two pictures to
represent animals that live on land and those that live on water. Next, show the students
an example of an empty two-circle Venn diagram which has been drawn on a large chart
or bulletin board. Label the circles “land animals” and “water animals.” Ask students
which type of animals would go in the overlapping part of the circles; discuss and
conclude that it would be those that live on both land and water. Have the students glue
their animal pictures in the correct position in the two-circle Venn diagram, explaining
why they should be placed there. Ask questions to show student understanding of the data
posted on the Venn. Use and, or, and is/is not statements to describe the information
represented in the diagram.
Activity 21: Graphs (GLEs: 25, 26, 28)
Materials List: My Predictions Worksheet BLM, Bar Graph BLM, overhead of Bar
Graph BLM, red marker, blue marker, pencil, paper
Students will use an anticipation guide (view literacy strategy descriptions) during class.
The purpose of the guide is to have students anticipate answers -use their estimation skills
in mathematics. After estimating, they will find the actual numbers and compare them to
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their estimates. The emphasis is on students’ ability to estimate and not the “exactness”
of their estimates.
1. Give each student the anticipation guide entitled My Predictions Worksheet
BLM. Count how many students are present in class today, and record that
number on the My Predictions Worksheet BLM. Instruct students to predict how
many of their classmates were born in each month. The sum of their predictions
should equal the number of students in attendance.
2. Give each student a Bar Graph BLM. Have them use the red marker to color in
the number of squares above each month that represents their predictions.
3. Next, have students come up and color a square blue on the overhead
transparency to show the month that they were born. Ask the students to help title
the graph. A possible title is Birthday Months.
4. Have students use their blue marker to fill in the second bar next to each month to
show the actual number of birthdays in each month.
5. Have students count the number of blue squares above each month. Record this
information on their My Predictions Worksheet BLM.
6. Have students fill in the last column of the My Predictions Worksheet BLM. They
can compare the number, or they can look at the bars on their graph to determine
if their predictions were over, under, or exact in relation to the actual number of
birthdays each month. Have students share information about how close they were
on their predictions. Also ask which method they used to compare their prediction
to the actual number - the chart or the bar graph.
Finally, talk about the information they can learn from the graph. Ask questions that can
be answered by looking at the graph, such as, “Which month has the most/least
birthdays?” and “How many more birthdays does March have than April?” Remind
students to look at the blue bars when asking the questions.
Activity 22: Favorite Type of Cookie (GLEs: 25, 26, 27)
Materials List: pictograph poster, cut out circles, table with cookies listed, graph paper,
pencil
Before class begins, make a pictograph outline and cut out circles to represent 4 types of
cookies. Make a table with the types of cookies listed. Have each student vote for his/her
favorite type of cookie by placing a tally mark next to the name of the cookie.
After students have voted, count the votes for each type of cookie. Tell students they are
going to construct a pictograph to display their data. Have students group themselves
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according to their favorite type of cookie. Tell students that you have paper cookies and
that each paper cookie represents two votes.
Have students line up in pairs and give each pair of students one paper cookie to place on
the pre-made pictograph outline. If there is an odd number of students, have students
decide how to represent that student’s vote on the graph (i.e., place a half cookie to
represent one vote). Ask students to make up questions that could be answered using the
data on the graph. Have students transfer data to a bar graph. Challenge them to set up the
vertical scale, horizontal axis, and title.
Activity 23: Using technology to Create a Class Graph (GLEs: 25, 28)
Materials List: computer, graphing program Graph Club® or Excel®, paper, pencil, list of
survey questions
Have students respond to a question. Collect the data and show them how to create a
graph using a program like Graph Club® or Excel®. Show students how the same data
can be used in different types of graphs.
Have students work in pairs to create a survey question. Each pair should ask 20 students
to respond to their survey. Have students use a computer program to input their data and
create a graph. Have students write 2 questions that could be answered using their graph.
Activity 24: Daily Graph (GLEs: 6, 25, 26, 27, 28)
Materials List: students pictures pasted on a magnet, laminated sentence strip, laminated
index cards with magnets, graph paper, paper, pencil
Each day, write a question that students must respond to on a sentence strip. Use a
magnetic board or your filing cabinet to set up the graph. Use index cards attached to
magnets to be the horizontal axis. Have students place their picture above the index cards
that indicates their response to the question. Have students transfer the data to a chart or
create a pictograph with each picture representing 2 responses. Also challenge them to
write questions that could be answered using the data. Throughout the year have students
use a key of 2 when transferring the data to a pictograph.
Which of the days listed do you like to watch TV the
most?
Monday
Wednesday
Friday
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Sample Assessments
Performance and other types of assessments can be used to ascertain student
achievement. Observation and performance based assessments will be used whenever
possible. Following are some examples:
General Assessments



Maintain portfolios which contain copies of individual and group projects
completed successfully during this unit: one- and two-circle Venn diagrams, a
student-made game using the hundreds chart, tables, charts, graphs, or pictures
made by the student, and teacher-made tests on specific topics studied.
Using data from the class, the student will create a two-circle Venn diagrams
showing statements such as I have a bike, I have a Playstation 2®, Game
Cube®, or X-box®. The teacher will observe the finished product and ask
questions to check for understanding.
Given a bar graph, pictograph, or line plot, the student will interpret and
write/answer questions pertaining to the data.
Activity-Specific Assessments

Activities 1-4: Given several models, students write the numeral, number
word, and expanded form of the number.

Activities 5, 7: Students fill in ten missing numbers in a hundreds chart.

Activities 1, 2, 3, 4, 9, 10, 11,: Students draw models of 30, 67, 42, 59, 29,
and 15, write them in word form and expanded form and then arrange them in
order from least to greatest. They will also complete statements such as these:
29 is more than__________
59 is less than___________
_______is the greatest number listed
What number would be on the left of 42 on a number line? __________
What number would be on right of 29 on a number line?_________

Activities 12 and 13: Students solve problems such as this: Paul said he had
about $20. What amounts could he have that would round to $20? Do you
know exactly how much money he has?
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
Activities 17: Given a line plot, students transfer information to a table using
tally marks and answer questions related to the information given.
x
x
x
x
grapes

x
x
x
x
x
x
strawberries
x
x
x
x
x
x
cherries
apples
Activities 19 and 20: Students place numbers in their proper places on a Venn.
Example: 21, 27, 29, 26, 23, 25, 40, 15, 35
Numbers that Round to 30

Activities 16, 17, 18: Students complete this Performance Assessment.
Label four identical jars as A, B, C, and D. Fill jars A and B with the same
number of Cheerios®. Fill a third jar with the least amount of cereal. Fill the
fourth jar with the greatest amount of cereal. The student will come to the
table and estimate the number of Cheerios® in the jars. The teacher will tell
the class how many Cheerios® are in Jar A and then each student will compare
the contents of jars B, C and D to that of Jar A, estimating the number of
Cheerios® in each jar.
Use a checklist to evaluate the student’s estimation skills.
_____Student determined which jars were filled with the same amount.
_____Student identified the jar with the least amount.
_____Student identified the jar with the greatest amount.
_____Estimates were reasonable when compared to Jar A

Activities 16, 17, and 18: Students complete the following self-assessment.
Each student will bring a personal collection of objects (e.g., stamps, pins,
marbles) numbering fewer than 100 in a plastic zip-lock bag or appropriate
see-through container. Students will place all the collections on a long table
and number the collections and number a piece of paper with the correct
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number of collections. The student will guess/estimate the number of objects
in each collection and record the estimates by the correct numbers on his/her
paper. (Give the students only a few seconds at each collection by ringing a
bell to signal that they should move to another collection.) The students will
check his/her estimates as owners of the collections give the correct numbers.

Activity 21-24: Pairs of students will survey their classmates on assigned
topics (favorite color or snack, lunchbox or lunch tray, how they get to school,
and so on). Each pair will create a bar graph to show the data collected and
correctly title and label the graph. Students will use a computer program to
graph the data if one is available.
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Grade 2
Mathematics
Unit 2: Extending Facts and Operations
Time Frame: Approximately five weeks
Unit Description
This unit focuses on basic addition and subtraction facts.
Student Understandings
Students use basic addition and subtraction facts to help them solve real-life problems.
They recognize when a situation calls for addition or subtraction and use facts and related
fact families to solve such settings. Students will write number sentences using the
correct symbols.
Guiding Questions
1. Can students give all addition and subtraction facts through 9 + 9 with ease
and apply related family facts?
2. Can students apply facts to solve real-life problems and complete 1- and 2digit addition and subtraction problems without regrouping?
3. Can students locate sums and differences on the number line?
4. Can students use appropriate symbolism for operations and number
sentences?
5. Can students use number sentences to model problems and find missing
values in fact-related equations?
Unit 2 Grade-Level Expectations (GLEs)
GLE # GLE Text and Benchmarks
Number and Number Relations
1.
Model, read, and write place values for numbers through 999 in word, standard,
and expanded form (N-1-E)
5.
Read, write, compare, and order whole numbers through 999 using words, number
lines, and models (N-3-E) (N-1-E)
6.
From a given number, count forward and backward and count to 100 by 2s
(N-3-E) (N-1-E) (N-4-E)
7.
Know all basic facts for addition and subtraction and use them to solve real-life
problems (N-5-E) (N-6-E) (N-7-E) (N-8-E) (N-9-E)
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GLE #
8.
GLE Text and Benchmarks
Recognize, select, connect, and use operations, operational words and symbols
(+, ) for addition (join, part/part/whole) or subtraction (take away, comparison,
missing addend, and set/subset) situations (N-6-E) (N-5-E)
Add and subtract 1- and 2-digit numbers (N-6-E) (N-7-E)
9.
Algebra
12.
Use number sentences to represent real-life problems involving addition and
subtraction (A-1-E) (A-2-E)
13.
Find the missing number in an equation involving addition or subtraction
(e.g., # + 4 = 7, 8 - # = 3) (A-2-E) (N-4-E)
Data Analysis, Probability, and Discrete Math
25.
Collect and organize data using observations, surveys, and experiments (D-1-E)
Patterns, Relations, and Functions
30.
Recognize, extend, create, and explain patterns of addition and subtraction as
represented in charts and tables and in varied forms of skip-counting (P-1-E)
(P-2-E)
32.
Recognize and apply patterns in problem-solving in other content areas and reallife situations (P-3-E) (N-9-E)
Sample Activities
Activity 1: Addition Strategies (GLE: 7)
Materials List: paper, pencil, fact practice sheets, addition fact flashcards
Write the following problems on the board.
 5 boys + 0 boys =____boys
 6 girls + 1 girls = ____girls
 6 cats + 6 cats = _____cats
 7 rings + 6 rings + _____rings
 9 candies + 4 candies = ________candies
Ask students to share how they solved each problem. Listed below are strategies that
might help a student who has yet to learn the facts.
+0 Adding Zero – When 0 is added to a number, the number doesn't change.
5 boys plus 0 boys is 5 boys because the amount doesn't change when I add zero
boys.
+1 or +2 Counting On – To add 1 or 2 to a number, start with the larger number and
count forward.
6 girls plus 1 more girl is 6 and 1 more = 7.
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6 + 6 is a Double – When students are learning facts for the first time, teaching them all
the doubles is a strategy that can be used.
7 + 6 is a Double + 1 – Have students use what they know about doubles to help them
find sums that are a double plus one more. It helps to think 7 + 6 = 6 + 6 +1 which is 12
and 1 more = 13.
9 + 4 Compensation – To add these numbers, have students make a 10 by taking 1 from
the 4 and put it with the 9 to make 10 so 10 + 3 = 13.
Facts they must memorize: 3 + 5, 3 + 6, 3 + 7, 3 + 8, 4 + 6, 4 + 7, 4 + 8, 5 + 7, 5 + 8,
6+8
Target a strategy each week, and practice facts the first 5-10 minutes of your lesson. Use
fact practice sheets. Have students write the facts, and use flashcards to practice facts.
Activity 2: Digit Run (GLE: 7)
Materials List: 2 sets of enlarged digit cards (0-9) each digit written on a 8 x 11 sheet of
paper, addition flashcards
Divide the class into two teams. Give each student a digit from 0-9 that has been enlarged
to fit on an 8 12 x 11 piece of paper. Have the students on each team line up in order
according to the digit they are holding. The teacher uses the flashcards to call out an
addition fact. Ask the student (s) holding the digit(s) on each team that represents the sum
to walk quickly to the front and turn toward their team.
Example: 6 + 7 = ?
The student that has the 1 digit card and the student that has the 3 digit card must
walk quickly and position themselves so that the 1 is on the left and the 3 is on the
right.
The first team to represent the answer is awarded a point. Students return to their team.
Then another problem is called out. After students learn their subtraction facts, play the
game using subtraction facts.
Activity 3: Addition Sentences (GLEs: 7, 8, 12)
Materials List: 10 books, paper, pencil, vocabulary cards, 10 counters per pair of
students, math learning log
Gather ten books. Place two books in the first pile and three books in the second pile. Ask
students how many books there are in all. Write the number sentence, 2 books + 3 books
= 5 books, on the board. Ask the students to make a generalization about addition.
Grade 2 MathematicsUnit 2Extending Facts and Operations
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part + part = total
Rearrange the book piles so that there are three books in the first pile and two books in
the second pile. Write the number sentence, 3 books + 2 books = 5 books, on the board.
Ask the students if the total number of books has changed.
Make vocabulary cards (view literacy strategy descriptions) for: addend, sum, addition
sign and equal sign. Each card should resemble and include the information on the
following sample card:
Characteristics:
Found in addition
problems.
Definition:
The numbers
being added in
an addition
problem.
addends
Term/Concept
Examples:
Illustration:
3+4=7
3 and 4 are the
addends.
When students create vocabulary cards, they see connections between words, examples
of the word, and the critical attributes associated with the word. This vocabulary strategy
also helps students with their understanding of word meanings and key concepts by
relating what they do not know with familiar concepts. Vocabulary cards require
students pay attention to words over time, thus improving their memory of the words. In
addition, vocabulary cards can become an easily accessible reference for students as they
prepare for tests, quizzes, and other activities with the words.
Repeat the process using a different number of books. Guide students to the conclusion
that the order in which the numbers (addends) are added does not affect the total number
of books (sum). So it doesn’t matter which part you start with – when you put the two
parts together, they equal the total.
Have students work in pairs. Give each pair of students 10 counters. Have them write a
number sentence and its commutative number sentence (turn around fact) for 8 counters,
4 counters, and 10 counters. Allow students to share their sentences. Ask students to
write 7 + 1 = 8 in the math learning logs (view literacy strategy descriptions). Have them
identify the addends, addition sign, and sum.
Grade 2 MathematicsUnit 2Extending Facts and Operations
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Activity 4: Addition Battle (GLE: 7)
Materials List: deck of cards with face cards and 10s removed for each pair of students
Give each pair of students a deck of cards. Have them remove all the face cards and the
10s from the deck. The ace will represent 1. Have one student in each pair deal all the
cards.
Play begins as both students flip over one card at the same time. The student who says the
sum of the two cards faster gets both cards. Play continues until all cards have been
played. Have students count their cards to see who won the game.
A variation of this game is to play with three students with students adding three numbers
to find the sum.
Teacher Note: Four sets of digit cards may be used for each pair instead of using playing
cards.
Activity 5: Modeling Number Sentences (GLEs: 7, 8, 12 )
Materials List: paper bags, marker, two different colors of cubes or tiles, paper, pencil
Prior to class use marker to number paper bags 1-15. Start with bag #1 and put some (19) cubes of the same color in each bag. Repeat the process using a different color of
cubes. Do not put more than 18 cubes in a bag.
Use two different color linking cubes to model addition and subtraction sentences. Make
sure students use correct terminology (addends, sum, difference), the operation symbols
for addition (+) and subtraction (–), and the equal (=) sign. The objective is to
demonstrate the relationship between addition and subtraction.
Model the four related addition and subtraction sentences using 8 of one color and 4 of
the other color cube. While modeling, have a student write the math sentences on the
board. Also, have students use a modified version of split page notetaking (view literacy
strategy descriptions) to record the related sentences as in the example below. This is
done by drawing a line down the page. The page should be split into one-thirds/two thirds
format. Students will list the total number of cubes on the left and write all the related
number sentences on the right. The strategy has been modified by using numbers instead
of words.
Example: 8 cubes + 4 cubes = 12 cubes
Bag #12
Related Sentences
4 cubes + 8 cubes = 12 cubes
12 cubes
12 cubes – 8 cubes = 4 cubes
8 + 4 = 12
12 cubes – 4 cubes = 8 cubes
4 + 8 = 12
12 – 4 = 8
12 – 8 = 4
Grade 2 MathematicsUnit 2Extending Facts and Operations
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Ask students if it makes a difference which number (addend) they write first in an
addition statement. Then ask if it makes a difference which number they write first in a
subtraction statement.
Put students into pairs. Give each pair a bag with 2 different color cubes. Have them
record the number of cubes on the bag. Then have them model and write the addition and
the related subtraction sentences using their cubes using the modified version of splitpage notetaking. Then have students share their related facts on the board. Have students
exchange bags and repeat the activity.
Demonstrate for students how they can study their split-page notes by covering
information in one column and recalling information in the other. Allow them time to
quiz each other on the information in their notes in preparation for tests and other class
activities.
Activity 6: Single Out (GLEs: 7, 9, 30)
Materials List: calculator, Single Out 3 x 3 Grid BLM, transparency of Single Out 3 x 3
Grid BLM, pen, paper, pencil, die per pair of students, math learning log, calculator
(optional)
Play Single Out.
Single Out


The object of the game is to get as many equal sums as possible.
Handout Single Out 3 x 3 Grid BLM. Model a game using the overhead
transparency. Have students record the numbers on their BLM as you record
them on the transparency.

Roll a die and call out a number. Have a student go to the overhead and place
the number on the grid. Repeat the process until all the squares are filled.
Have a student find the sums of the three numbers on each row and each
column, writing each sum on the blank outside the grid.
Examine all the sums. Have a student cross out the sums that appear only once
and add up the remaining sums to find the score. (Students could use a
calculator to check the sums.) Students will soon learn that there is a strategy
to the game and then they will carefully place the numbers on the grid so that
they can get multiple representations of the same sum.
Put students into pairs. Repeat the game this time letting students play against
one another on the extra boards on their recording sheets.



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
Have students describe what they think the strategy is for Single Out in their
math learning log (view literacy strategy descriptions).
Teacher Note: After the students have played this game with the teacher, provide pairs of
students with grids and die and have them play against each other.
Activity 7: Subtraction Number Sentences (GLEs: 7, 8, 12)
Materials List: 10 counters, connecting cubes, Subtraction Sentences BLM, paper, pencil
Place 10 counters on the overhead. Remove 2 counters. Ask students to identify the
operation being modeled when they have a total amount and then take something away.
Review with the students how to write a subtraction number sentence.
total - part = part
10 counters – 2 counters = 8 counters
Use connecting cubes to make a tower that has 7 cubes and one that has 3 cubes. Ask
students how many more cubes does the 7-cube tower have than the 3-cube tower?
Remind students that when we compare two things, we take away the amount that the
things have in common, and the amount that is left is how they are different. When
comparing 7 to 3, first take away what they have in common (3 cubes) then what is left is
how they are different – 4 cubes. Ask students to identify the operation that is being
modeled when we compare two things to find their difference. Write the subtraction
number sentence.
7 cubes – 3 cubes = 4 cubes
Model several problems for them using the total and removing a part model and the
comparison type problem that requires subtraction.
Give each student a Subtraction Sentences BLM. Have him/her model the subtraction
problem to find the solution. If the situation is a comparison problem, have him/her
model both numbers and remove what the numbers have in common. If the problem is a
total with a part removed, have him/her start with an amount and remove the necessary
counters to solve the problem.
Add difference, subtrahend, subtraction sign and minuend to vocabulary cards (view
literacy strategy descriptions).
Grade 2 MathematicsUnit 2Extending Facts and Operations
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Activity 8: Number Line Subtraction (GLEs: 7, 8, 12)
Materials List: masking tape, chalk, paper, pencil, Number Line Sentences BLM, two
counters per student
Make a large number line on the floor with masking tape and chalk. Number the line 0
through 12. Have one student start at 0 and walk 7 spaces forward and then hop back
three spaces. Ask, Where are you are now? (4) Write the number sentence to show what
happened. (7 spaces– 3 spaces =4 spaces)
Have a student walk to 9 and another student walk to 2. Ask what did the students that
are standing on 9 and 2 do alike? (They both walked to 2.) Then ask what did the students
standing on 9 and 2 do differently? (9 is 7 spaces ahead of 2 on the number line.)
(9 – 2 = 7)
Allow students to return to their desks and make up story problems that can be modeled
on the Number Line Sentences BLM using a counter(s). When students are finished, have
them return to the number line and chose other students to dramatize their story on the
number line. Record the number sentence on the board that matches the story problem.
Assign students a RAFT (view literacy strategy descriptions) writing assignment. Once
students have acquired new content information and concepts, they need opportunities to
rework, apply, and extend their understandings. RAFT writing is uniquely suited to do
just that (Santa & Havens, 1995). This form of writing gives students the freedom to
project themselves into unique roles and look at content from unique perspectives. From
these roles and perspectives, RAFT writing has been used to explain processes, describe a
point of view, envision a potential job or assignment, or solve a problem (Fisher & Frey,
2003). It’s the kind of writing that when crafted appropriately should be creative and
informative.
RAFT is an acronym that stands for:
R – Role (role of the writer)
A – Audience (to whom or what the RAFT is being written)
F – Form (the form the writing will take, as in letter, song, etc.)
T – Topic (the subject focus of the writing)
Next tell students to pretend that they are a number line and some one is walking on
them. Have them write a story problem from the view point of the number line using the
following guide:
R- Number Line
A- Students in the class
R- Word problem
T – Number sentence
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Example:
Someone was standing on me and walked 4 steps forward from 0. Then he hopped back
two spaces. What number of mine is he standing on?
4 steps forward - 2 steps backwards = standing on 2
Allow time for students to share their RAFT writing with a classmate or the whole class.
Ask students to listen for accuracy and logic.
Activity 9: Which Operation is Needed? (GLEs: 7, 8, 9, 12)
Materials List: paper, pencil, calculators
After solving two or three addition or subtraction story problems, discuss with the
students how they will decide if they should add or subtract (add when joining sets and
subtract when separating sets or comparing numbers). Have students brainstorm (view
literacy strategy descriptions) examples of times when they might need to add or subtract.
Make a T-chart with columns labeled "Times I would Add” and “Times I would
Subtract" to display students' examples. List key words in the problem that help identify
whether students need to add or subtract.
Example: I am playing a game with 3 friends and 2 more friends come to play.
What is the total number of people playing the game?
Have students write story problems. Have students read their problems. The class must
determine whether they would add or subtract to find the solution. List words in their
problems on the T-chart that help identify whether to add or subtract. Have a student
write the number sentence for each problem on the board, and then have students use a
calculator to check the solution to the problem.
Activity 10: Color Counter Problems (GLEs: 7, 12)
Materials List: counters – 4 different colors (9 of each color), Spinner 0-8 BLM, paper,
pencil, calculators, large paper clip
Model the following activity for students. Then put students into groups and have them
make sets and write problems.
 In small groups, give students red, yellow, blue, and green counters and a
Spinner 0 – 8 BLM.
 Have each group spin four different numbers and make sets showing each
number with the different color counters.
 Have students make up addition or subtraction sentences using the piles of
counters. Example: 6 yellow counters plus 7 green counters is 13 counters. All
students in the group record the sentence.
Grade 2 MathematicsUnit 2Extending Facts and Operations
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


Ask the next student to make up a sentence that hasn’t been used by their
group members.
Continue playing until all addition/subtraction sentences have been listed.
Have students check their problems using a calculator.
Activity 11: Picture Problems (GLEs: 8, 9, 12)
Materials List: addition and subtraction flashcards, digital cameras, construction paper,
glue, paper, pencil
Put students into groups and give them a flashcard with a basic addition or subtraction
fact on it. Have them make a model of the fact and take a picture(s) of the model with a
digital camera. Print the pictures and glue them on construction paper and laminate them.
Number the pictures, circulate them among groups, and have each group write the
number sentence that it sees depicted in the picture. If a camera is not available, use
magazine photographs or illustrations showing sets of objects that can be described in an
addition or subtraction story. Hang the “posters” on a bulletin board for all to evaluate.
Example: 3 children + 2 children = 5 children
Activity 12: Number Sentences on the Computer (GLEs: 7, 12)
Materials List: computers for students, Kidpix®, printer
Have students illustrate addition and subtraction sentences using a computer drawing
program. For example, if the program has an autoshape feature, have students select a
shape and copy and paste the shape to illustrate the number sentence. If the students have
access to a program like Kidpix® have them select a stamp and use it to illustrate their
number sentence. Print students’ illustrations and assemble them to make a number
sentence book.
Activity 13: Adding Tens (GLEs: 1, 8, 9, 12)
Materials List: digit cards, paper, pencil
Flip over 2 cards from a set of digit cards and form a 2-digit number using the digits
selected. Each card will represent a number of tens.
Example:
Teacher turns over a 2 and 7
She says and writes: 2 tens and 7 tens = 9 tens
Then she writes: 20 + 70 = 90
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Repeat the process two more times modeling for students how to say and write their
number sentences. If students get numbers that add to more than 9 tens, allow them to
leave it as tens. 9 tens + 4 tens = 13 tens When students share their number sentences
with the class, ask them, “What do you know about 13 tens?”
13 tens = 10 tens and 3 more tens
10 tens = 100 and 3 tens = 30
100 and 30 = 130
Put students into pairs. Have students repeat the activity as many times as time will
allow, writing their number sentences as they go along. Have students share their number
sentences.
Activity 14: Number Puzzles (GLEs: 7, 9, 13)
Materials List: transparency of Number Puzzles BLM, paper, pencil, Blank Number
Puzzles BLM, calculator
Make a transparency of Number Puzzles BLM. Use the transparency to guide students
through how to find the missing digit in the problem. Have students complete the
Number Puzzles BLM. They may use a calculator to check their answers.
1
+
8
7
4 8
+
3
3
+
9 5
2
9
+
5 4
3
5 9
Then, have students create their own puzzles on Blank Number Puzzles BLM. Next, have
students exchange puzzles with classmates and solve. Finally, have students check their
solutions using a calculator.
Activity 15: Missing Addends (GLE: 13)
Materials List: paper cup, cubes, paper, pencil
Place three cubes in a paper cup. Show students the cup and seven cubes which have
been aligned in a row. Tell them that there are ten cubes in all. Ask how many cubes they
see (7) and how many are in the cup (3). Why? (3 + 7 is 10) Have students write the
addition sentence that was described (i.e., _______cubes + 7 cubes = 10 cubes). Explain
that this is a missing-addend problem: one addend is 7 and one is 3, making a sum of 10.
Continue with other examples, including some with 10 and 0 as addends.
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Have a student come to the front of the room, place some cubes in the cup, and make a
row of cubes. He/she must tell the class the total number of cubes that have been used.
Have a volunteer write the addition sentence on the board as each is done. Ask students
to solve the missing addend problem. Ask students how they could use subtraction to find
the missing addend. (Subtract the known addend from the sum)
Put students into groups of 4. Have students then write story chain problems
(view literacy strategy descriptions) that have a missing addend.
Example:
Student 1: I have 6 counters in my left hand.
Student 2: I have some counters in my right hand that I will add to my left hand.
Student 3: I now have 13 counters
Student 4: How many counters did I add? (I added 6 + ? = 13. 13 – 6 = 7 So, I must
have added 7 counters.)
After students have had time to create their story chains, have them read the stories to the
class. Make sure the problem has been solved accurately, and make sure students share
how they solved the problem.
Teacher Note: This is a great bell-ringer activity. Put counters in each of your hands.
Open one hand and show students how many counters are in that hand. Then tell them
the total number you are holding. Have students write the number sentence, and solve for
the missing counters.
Activity 16: What’s Missing? (GLEs: 12, 13)
Materials List: paper, pencil, math learning logs
Have students solve real-life problems with missing addends. Have them write the
number sentences to represent the story using labels. Examples are as follows:
Patrick saved $8. He needs $15 to buy a CD. How much more does he need to
buy the CD?
$8 that Patrick saved + _____money he needs = $15 to buy the CD.
Make the connections between addition and subtraction by showing that the
student can subtract $8 from $15 to find out what the missing addend will be.
$15 to buy CD - $8 Patrick saved = ______money he needs
There were 9 people at the beginning of the birthday party. At the end of the party
there were 16 people. How many more people came to the party?
9 people at the beginning + _________more people = 16 people at the end
16 people at the end – 9 people at the beginning = ________additional
people.
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Jacob and Steven ate some cookies. Jacob ate 5 cookies. Together they ate 12
cookies. How many cookies did Steven eat?
5 cookies Jacob ate + _____cookies Steven ate = 12 cookies together
12 cookies together - 5 cookies Jacob ate = ______cookies Steven ate.
Have students write missing addend problems in their math learning logs (view literacy
strategy descriptions).
Activity 17: Candy Store (GLEs: 5, 9, 12, 13)
Materials List: paper, pencil
Use prices of candy to have students practice adding 2-digit numbers without regrouping.
Write the candy prices on the board (21¢, 35¢, 53¢, 14¢, and 42¢).
Make sure students understand the term "expensive" before beginning.
Write the following questions on the board. Have students write a number sentence for
each problem.
 What is the cost of the two most expensive pieces of candy?
 What is the cost of the two least expensive pieces of candy?
 Which two items have a total cost of 49¢?
 Which two items have a total cost of 56¢?
 If you had 75¢, how many different items could you buy?
 How much did the second item cost if you bought an item for 14¢ and you
spent 56¢?
Tell students that the candy store is interviewing for the head cashier position. It is
looking for a professor know-it-all (view literacy strategy descriptions) that can add
prices correctly. Ask students to submit their papers if they would like to be considered
for a head cashier position. Students that get all the problems right get a sticker (button)
that says “Head Cashier.” This is a modified version of professor know-it-all. Students
normally are questioned by the teacher or fellow classmates to check for understanding of
a concept. Once they have demonstrated that they “know it all,” another group is called
to the front of the class for questioning.
Activity 18: Magic Squares (GLEs: 13, 30)
Materials List: Magic Squares BLM, paper, pencil, calculator, math learning log
The objective of this activity is to fill a square with the digits 1 – 9 so that all the rows,
columns, and diagonals have the same sum. Give each student a copy of Magic Squares
BLM.
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Tell students that they are to use the digits 1 – 9 only once to fill in the puzzle so that all
the rows, columns, and diagonals have the same sum. Have students find the digits that
are missing in the puzzle and write them above the puzzle. (1, 3, 6, and 8). Add the
numbers in the first row with a calculator. (2 + 9 + 4 = 15) 15 is the target number. Now
add 7 + 5 = 12. 12 + ? = 15. (3) Add three to the second row. Continue to find the
missing addends.
2
9
7
5
4
solution
2
9
4
7
5
3
6
1
8
Continue to guide students through each square. They should first list the digits that are
missing from the square. If a row/column/diagonal has two numbers recorded, students
should add those two numbers and subtract that sum from 15 to find the missing addend.
By process of elimination, students will be able to fill in the square. Discuss students’
answers.
Ask students to draw a 3 x 3 grid in their math learning logs (view literacy strategy
descriptions). Tell students to place the digits 6, 5, and 7 in the diagonal. Make sure
students place 5 in the center. Have students determine the magic number. (18) Then ask
them to place the digits from 2, 3, 4, 6, 7, and 10 in the empty squares to find the solution
to the puzzle. Remind students that all the digits must add to the same number in every
row, diagonal, and column. Give students hints if needed. Have students share their
solutions.
example of 1
solution
6
4
8
10
5
3
2
9
7
Activity 19: Write the Questions (GLEs: 12, 25)
Materials List: paper, pencil
Give students situations and have them write an addition and a subtraction question for
each situation. Examples:
Mica has 9 dolls. Joy has 8 dolls.
How many dolls do they have altogether? How many more dolls does Mica have?
Mark has 20¢. Jonathan has 50¢.
How much money do they have together? How much more money does Jonathan
have then Mark?
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A variation of this activity would be to use grocery ads. Be selective in the combination
of items since students have not been introduced to regrouping.
Activity 20: Problem Solving with Patterns (GLE: 30)
Materials List: Hundreds Chart BLM, 20 nickels, 10 dimes, counter, paper, pencil
Put students into pairs. Ask students how they might find the value of 12 nickels.
Students may suggest counting by 5s to find the value. Remind students this is called skip
counting.
Give each pair of students a Hundreds Chart and 12 nickels. Ask students to count out
loud by 5s and place a nickel covering the multiples of 5 on the chart as they count. Have
students check each other’s charts and describe the pattern. Ask students how many
nickels it will take to have 95¢.
Next, give 7 dimes to each pair and have students find the value of 7 dimes by placing
dimes on multiples of 10 on the 100s chart.
Finally, tell students you saw 17 animals in the woods. Ask, “How many eyes did I see?”
This time give students counters to figure out the pattern that will allow them to answer
the question.
Activity 21: Function Machines (GLEs: 7, 30)
Materials List: function machine, index cards with answers, rule card, number cards 0-9
Use a function machine to demonstrate basic facts in addition and subtraction. Choose a
student to be the output coordinator (he/she will send the correct answer card out of the
function machine). Write a rule on a card, and place it in a pocket or tape it to the front of
the machine. Choose a volunteer to enter a number card 0 through 9 into the input slot of
the machine. If the rule card says +2, then the output coordinator must send out the
correct sum through the output slot on the machine.
Directions for making a function machine are as follows:
 Use a box turned on its side and covered with paper or painted to look like a
machine with dials, buttons, windows, and so on.
 Cut a slot on the top and side for input and output, and glue a pocket to the
front for the rule card.
 Make a set of cards to match the numbers you want to practice.
Variation: Mentally determine a rule. Put a card with a number in the function machine,
and mentally apply the rule. Show a card that represents the original number and the
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output. Put several cards through the machine with the same rule being applied to them,
and then ask students to try to determine the rule.
Activity 22: Using a T-chart (GLE: 30)
Materials List: paper, pencil
Draw a T-chart graphic organizer (view literacy strategy descriptions) on the board.
Have students use a T-chart to organize information when skip counting.
Example: How many wheels are on 5 tricycles?
Tricycles
1
2
3
4
5
Wheels
3 wheels
6 wheels
9 wheels
12 wheels
15 wheels
Additional examples:
Number of legs on _____dogs
Number of eyes on _____cats
Number of days in ____weeks
Activity 23: Number Patterns (GLES: 6, 32)
Materials List: paper, pencil
Write the following problems on the board. Have students solve each problem and
explain the pattern.
Customers were standing outside of Best Deal. The manager gave the second person in
line 1 coupon, the fourth person in line 2 coupons, the sixth person in line 3 coupons.
How many coupons did the manager give the 12th person in line?
Yolanda was putting stickers on the corners of each pentagon on her page. How many
stickers did she need if there were 6 pentagons on the page?
Alison looked into the woods and saw 14 eyes. How many animals did she see?
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Paul bought a soda for 65¢. He used only nickels. How many nickels did Paul put in the
machine?
Activity 24: Missing Numbers in Patterns (GLE: 32)
Materials List: paper, pencil
Write the following problems on the board and have students find the missing numbers.
1, 3, 5, _____, ______, _______
10, 20, 30, ______, _______, _______
17, 15, 13, ______, _______, _______
50, 45, 40, ______, _______, ________
Sample Assessments
Performance and other types of assessments can be used to ascertain student
achievement. Following are some examples:
General Assessments



Use portfolio assessment to evaluate the unit. Included in the portfolio will be
samples of Magic Squares, stories and pictures, work samples, and teachermade tests.
Write a journal entry -The student will make up a story problem that goes with
the number sentence, 9 + 5 = 14.
Give an illustration of addition or subtraction problem on a number line.
Students will write the related number sentence.
Activity-Specific Assessments
Fact test should be given weekly throughout this unit after teaching students a strategy.

Activity 5: Students write 2 addition sentences and the 2 related subtraction
sentences using the numbers in the example.
The following colors of crayons were counted in the art center:
5 red
4 orange
1 purple
7 blue
2 yellow
10 green
11 brown
9 black
3 white
6 pink
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Example:
4 orange crayons + 9 black crayons = 13 crayons
9 black crayons + 4 orange crayons = 13 crayons
13 orange and black crayons - 9 black crayons = 4 orange crayons
13 orange and black crayons – 4 orange crayons = 9 black crayons

Activity 8: Give the student a number line from 1 through 20. Direct each
student to start at a given number, and indicate that he/she is to model hopping
so many spaces forward or backwards and state what number he/she landed
on. The student will write the number sentence to show which operation was
used.
Example:
Start on 7, and hop 3 spaces forward. Where are you?_______
7 + 3 = 10
Start on 12, and hop 5 spaces backwards. Where are you?________
12 – 5 = 7

Activities 8, 9, 12: Given different real-life situations, the student will identify
which operation is needed to solve the problem, write a number sentence with
labels, and solve it.

Activity 20: Students use the 100s chart to:
 find and record the value of 10 nickels
 find and record the value of 9 dimes
 find the value of 27 pennies
 Activity 21: Have each student bring a box (any size) and design his/her own
Function Machine. The student will turn in the box and a card stating the rules
to be used. Use a rubric to grade the project.
Sample rubric:
_____All addends written and coded to sums - 5 points
_____ Rule card - 2 points
_____ Sum cards are correct - 5 points
_____Design of machine - 3 points
Teacher Note: These may be used to practice facts at home, or they may be
shared with other classrooms in a peer-tutoring activity to practice basic
facts. Save them to use for multiplication, too.
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Grade 2
Mathematics
Unit 3: Money and Time
Time Frame: Approximately four weeks
Unit Description
This unit extends number and operation skills to include money (skip counting by 5s) and
time (telling time to the nearest 5 minutes).
Student Understandings
Students should be able to recognize and deal with money situations. They tell time to the
nearest 5 minutes and indicate their understanding of elapsed time by stating time one
hour before and after a given time.
Guiding Questions
1. Can students find and write the value of coins and $1 bills?
2. Can students use one-to-several correspondence to trade single items for a
greater quantity of items with equal value?
3. Can students tell time to the nearest 5 minutes and relate 5s on a clock to skip
counting by 5s?
4. Can students solve problems using elapsed time?
Unit 3 Grade-Level Expectations (GLEs)
GLE # GLE Text and Benchmarks
Number and Number Relations
2.
Model the concepts of thirds, fourths, fifths and sixths using regions, sets, and
fraction words (e.g. one-third, three-fourths, five-sixths) (N-1-3)
4.
Count and write the value of amounts of money up to $1.00 using ¢ and $ (N-2-E)
(N-6-E) (M-1-E) (M-5-E)
6.
From a given number, count forward and backward and count to 100 by 2s
(N-3-E) (N-1-E) (N-4-E)
11.
Use the concept of one-to-several correspondence to trade single items for a
greater quantity of items with unequal value (1 nickel for 5 pennies, 1 dime for 2
nickels) (N-9-E)
Measurement
16.
Tell time to the nearest 5 minutes, and identify the time one hour before or after a
given time (M-1-E) (M-3-E)
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25.
26.
Collect and organize data using observations, surveys, and experiments (D-1-E)
Construct and read line plots and tables (D-2-E)
29.
Solve logic problems involving two sets by using elementary set logic (i.e., and ,
or, and is/is not statements) (D-3-E)
Recognize, extend, create, and explain patterns of addition and subtraction as
represented in charts and tables and in varied forms of skip-counting (P-1-E)
(P-2-E)
30.
Sample Activities
Activity 1: Everything you wanted to Know about Coins (GLE: 4)
Materials List: examples of each type of coin, Word Grid BLM, pencil, transparency of
Word Grid BLM
As a prerequisite to this unit on money, give each student a modified word grid (view
literacy strategy descriptions). Using the Word Grid BLM, have students examine each
coin and fill in as much of the grid as possible. Then go through each coin giving students
the necessary information. Once the grid is complete, quiz the students as to how the
coins are alike and different. Students can also quiz each other in preparation for tests and
other class activities. Review how to count the value of coins by skip counting. Have
students count out the value of pennies, nickels, and dimes.
coin
penny
color
value
front of coin
back of coin
nickel
dime
quarter
half-dollar
dollar
Finally, have students do a rubbing of the front and back of each coin. Have students use
the rubbings to indicate differences in the coins. Using this modified word grid, the
review of information students learned in previous grades and puts the information in a
concise format so that students may reference it later.
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Activity 2: Counting Coins (GLEs: 4, 6)
Materials List: Hundreds Chart BLM, 10 nickels, 10 pennies, transparency of Hundreds
Chart BLM, overhead nickels, pennies
Give each student a Hundreds Chart BLM, 10 nickels, and 10 pennies. Tell students to
take out 2 nickels and 3 pennies (13¢). Have a student demonstrate how he/she would
find the value of these coins. Then question students why it would be appropriate to start
the counting with the nickels.
Next, invite students to discuss how they might use a hundreds chart to help them find the
value of coins. Inquire about where their coins should be placed on the hundreds chart.
Use the transparent 100s chart and coins, and model for students how to place their coins
on the chart (2 nickels and 3 pennies)
 Encourage students to start with the coin that has the greatest value.
 Start with one of the nickels. Ask students, “What is the value of a nickel?” (5
cents). Count five spaces on the 100s chart, and place the nickel on the 5.
 Using the second nickel count 1, 2, 3, 4, 5 from the 5 on the 100s chart, and place
the second nickel on the 10.
 Ask students, “What is the value of a penny?” (1 cent). Start with the 10 on the
100s chart count 1, place the penny on the 11.
 With the next penny count 1, and place it on 12.
 With the last penny count 1, and place it on 13.
Then say, “Let’s see if the value of our coins matches the placement of our coins.” Count
5, 10, 11, 12, 13. Is the value of our coins 13 cents? (yes)
Have students clear their charts. Give them a different combination of nickels and
pennies. Students should make the connection between using nickels and skip counting
by 5s on the 100s chart. Then they should just add on 1 for each penny that they have.
After students have practiced several combinations, give them an amount and have them
find the total number of nickels and pennies it would take to model that amount. This
activity should be practiced throughout the week. Vary the coins that students use each
day. Suggested order: nickels and pennies, dimes and pennies, dimes and nickels, then
dimes, nickels and pennies. Finally, introduce quarters.
Teacher Note: Students entering 2nd grade have counted coins using 1 denomination.
Before they can be expected to make change, they should have many experiences
counting different denominations of coins.
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Activity 3: Which Coins am I Holding? (GLEs: 4, 29)
Materials List: empty film canister, coins, chalkboard, chalk
Place coins in a film canister. Write the number of coins and their value on the board.
Students have 10 tries to guess the combination of coins in the canister. Record each
student’s guess and record your response. You may only reply “yes” or “no” to the
questions. It is important that you record each student’s guess so that students may use
deduction in determining the coins in the canister.
Example: Tell students, “I have 4 coins that have a value of 17¢.” Students might
ask, “Do you have a dime?” You would respond, “Yes.” “Do you have a
quarter?” (no)
This question should be discussed at the end of the activity. Students should
realize that they “wasted” a question because a quarter has a value greater than
17¢.
This is a great informal assessment of what students know about the value of coins.
Questioning continues until they ask 10 questions or they guess the coin combination in
the canister.
Teacher Note: This is a great activity to keep handy. It can be used as a bellringer or as
a filler when you have an extra 5 minutes during the day.
Activity 4: Coin Patterns (GLEs: 4, 6, 30)
Materials List: overhead coins, coins, paper, pencil, math learning log
Create a pattern with coins such as penny, nickel, nickel, penny, nickel, nickel. Have
students identify the elements in the cycle and fill in the next three elements. Then have
students find the value of the coins (33 cents). Repeat the process using different patterns.
Give students coins and have them create patterns and find the value of the pattern.
Finally, give students an amount and have them create a pattern that demonstrates that
amount in their math learning logs (view literacy strategy descriptions).
Activity 5: Rolling in the Money (GLEs: 4, 6, 11)
Materials List: per pair – 2 number cubes, a bag of play coins with nickels and dimes,
play one-dollar bills, Rolling in the Money Recording Sheet BLM
Put students into pairs. Give each group a pair of number cubes, a bag of coins, onedollar bills, and a Rolling in the Money Recording Sheet BLM. Tell students, “Today we
are going to play nickels and dimes. The object of the game is to get the most money.”
One person in each pair will roll a pair of number cubes and record the numbers rolled on
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a recording sheet. Have the students take the number of coins rolled from the bag of coins
and find their value, and then record the value on the Rolling in the Money Recording
Sheet BLM. Instruct their partner to count the coins to verify the partner’s work. The
person who rolled the dice will keep the coins if he/she provides the correct value. If
incorrect, the coins are returned to the bag. The next student rolls the number cubes. Play
continues until all students have had three turns. When everyone has finished his/her
rolls, have students trade their coins in for $1 bills and find their total amount. The person
with the highest amount wins the game. Play two games if time permits.
Roll 1
Roll 2
Roll 3
Dimes
4
Nickels
3
Value
55¢
Total amount
is
___dollar(s)
and ___cents
After you introduce the quarter, make a recording sheet that shows quarters, dimes, and
nickels. When you adjust the game to using 3 coins, have students toss three number
cubes.
Activity 6: In How Many Different Ways Can You Make Fifteen Cents? (GLEs: 4,
11, 25)
Materials List: Money Table BLM, bag of coins-quarters, dimes, and nickels, Money
Table BLM transparency
Put students into groups. Give each student a bag of coins and use Money Table BLM.
The Money Table BLM is to be used as a graphic organizer (view literacy strategy
descriptions) to help students make an organized list of their coin combinations. Ask
students to find all the different ways they could model 20 cents without using pennies.
As they model an example of 20 cents, have them record their findings in the Money
Table. After students think they have found all of the different ways to model 20 cents,
guide them through recording their combinations using an organized list starting with the
largest coin and trading coins as they go. Have students use the second table on their
sheet to find all the different coin combinations of 25 (without using pennies). Continue
to give students different amounts each day to model.
Activity 7: School Supply Shopping (GLEs: 4 , 6)
Materials List: each pair – 2 quarters, 4 dimes, 5 nickels, and 10 pennies, items for school
supply store priced less than $1, chalk, chalkboard, paper, pencil
Put students into pairs. Give each pair 2 quarters, 4 dimes, 5 nickels, and 10 pennies. Set
up a school supply store with items priced less than a dollar. Back to school sale papers
may be substituted for real items. Have students take turns buying items and counting
out the exact amount needed to buy the item from their partner. The partner then returns
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the item to the table and selects something he/she would like to buy. They repeat the
process of using the exact amount needed to buy the item. Students continue to shop as
long as time permits. Back to school sale papers may be substituted for real items.
Use SQPL-Student Questions for Purposeful Learning (view literacy strategy
descriptions) to discuss the role that the penny plays in our currency system. Write the
statement “The U.S. Mint is going to stop producing pennies.” on the board. Put students
into groups and have them write one question that relates to the statement. Call on each
group and record their question. Add your own questions if you see the need. Use all the
questions to talk about what role the penny plays in our current monetary system. Make
sure to include in your discussion what would happen to items that are priced 21¢ and
37¢. Stop periodically to have students check which questions have been answered.
Activity 8: Toy Pictures (GLEs: 4, 6)
Materials List: per group – 20 pennies, 10 dimes, 20 nickels, 4 quarters, and a-dollar bill,
pictures of toys from catalogs, index cards
Give each group a set of coins (20 pennies, 10 dimes, 20 nickels, 4 quarters, and $1 bill
of play money). Have students cut pictures from a toy catalog and put the picture with the
cost on a index card. As cards are displayed, have students show different ways to make
the correct amount. Model how students should start counting with the coin of greatest
value. Later the picture cards can be used as a Toy Store Center with the cashier making
change as needed, as students “buy” from the store. After subtraction with regrouping is
taught, have students check their change by setting up a subtraction problem.
Activity 9: Grocery Store (GLEs: 4, 6)
Materials List: coins, items marked with price less than 25¢
Making change is an extremely difficult skill for 2nd graders. They need to practice this
all year long. First, have students buy items priced under a quarter. Have them pay with a
quarter while another student counts the change. When counting change, have the student
put the item in the customer’s hand and then count up. Students are not expected to do
mental math subtraction at this time of the year. Gradually increase the price of items
several times, and have students buy items and pay with a dollar bill. Have students
continue to put the item in the buyer’s hand and count up to 100 when making change.
The end-of- the year goal is to have students make change for a dollar with the fewest
coins possible. Students enjoy playing “store.” Set up a center and leave it up throughout
the year, varying the cost of items and the coins available. After subtraction with
regrouping is taught, have students check their change by setting up a subtraction
problem.
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Activity 10: Do I have enough Money? (GLEs: 4, 6, 11)
Materials List: pictures with prices less than $1, coins, snack menu
Show pictures and costs of two snacks from a refreshment stand to two- or three-member
teams who have a set of coins equaling less than $1.00. Have students decide which of
the 2 items they can afford to buy. Ask if the listed price is more or less than the amount
they have. Ask students what would happen if a child gave the salesperson more money
than the price of the snack. Display a snack menu listing five or six snack items with
price tags of less than $1.00. Give each team coins totaling less than $1.00. Ask, “How
much does the item cost? Do you have enough money? Should you get change back?”
Have each team model how much change it should get back.
Activity 11: Pocket Full of Money (GLEs: 4, 6)
Materials List: Pocket Full of Money Recording Sheet BLM, bags with coins and bills
Before class begins, make bags of money containing coins less than a dollar and onedollar bills. Label the bags to match the names on the recording sheet. Show students
how to count and record the value of money if they have bills ($1) and change. Make a
big deal about the decimal point separating the whole number of bills and the change.
Set up this scenario: Each time I do the wash, I find a wad of bills and change in
someone’s pocket. Tell students that they are going to count how much they find in a
pocket full of money.
Put students into groups. Give each group a Pocket Full of Money Recording Sheet BLM.
Have students determine the value of the money in the bag, record the value, and then
pass the bag to the next group. After all bags have circulated throughout the groups, have
students report their findings.
Finally, tell students that they found $1.53 in a pocket. Have them record the amount in
their math learning log (view literacy strategy descriptions). Have students list three
different bill and coin combinations that could be in that pocket.
Activity 12: How do they make Money? (GLE: 4)
Materials List: The Go-around Dollar by Barbara Johnston Adams, computer, paper,
pencil
Read a book like The Go-around Dollar by Barbara Johnston Adams and discuss with
students how money is made. Visit the website http://www.ustreas.gov/. Have students
draw several $1 bills and coins. Have students exchange papers and find the value of the
money that is depicted.
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Conclude the activity with a RAFT (view literacy strategy descriptions) writing
assignment.
R – a dollar bill
A – fellow classmates
F – postcard
T – A dollar bill started in their home town and traveled across the United States.
Example: I am a dollar bill sitting in a drawer in a Baton Rouge, Louisiana. Yesterday I
was in Houston, Texas, in a gas station. The day before that I was sunning myself in the
pocket of someone in Los Angeles, California. You would think I would be tired. I am
looking forward to seeing where I end up tomorrow.
Allow students to share their RAFTs with a partner or the class. Students should listen
for accuracy and logic in their classmates’ RAFTs.
Activity 13: That’s a Long Time! (GLE: 16)
Materials List: How Many Can I Do? BLM, Blank Clock BLM, analog clock with second
hand, crayons
Cut apart the How Many Can I DO? BLM and give a chart to each student.
Time the students as they close their eyes for 1 minute. Ask students to raise their hands
when they think 1 minute is up. Signal the end of the minute. Show students how to time
1 minute on a clock with a second hand. Explain that there are 60 seconds in 1 minute.
Have students fill out the modified anticipation guide (view literacy strategy
descriptions) How Many Can I Do? BLM. They are to estimate how many they think
they can do of each listed activity in 1 minute. Then have students take turns doing a
physical activity (hop, clap, close their eyes, and so on) for 1 minute while timing the
minute. Have them record the actual number after each activity. Finally, give students the
Blank Clock BLM, which has a large blank clock face. Have them color between the
“hash” marks of the clock, alternating colors for each minute.
Activity 14: Counting the minutes! (GLE: 16)
Materials List: student clocks, demonstration clock
Distribute student clocks. Go over the parts of a clock (i.e., face, hour hand, minute
hand). Use a demonstration clock to show students how the hour hand moves between the
hours as the minute hand approaches 30 minutes. Set a clock to the hour/half-hour
without showing students, and then call out the time. Have students set their clocks and
then check their clocks with the clock you set. Next, have students count out the minutes
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in an hour going around the clock face. Ask students if they noticed anything special
when they got to a numeral on the clock face (i.e., these are the numbers they say when
they skip count by 5s).
Have students move the minute hand on their clocks skip counting by 5s. Call out
different times using multiples of 5 minutes (e.g., 2:20, 3:45), and have students set their
clocks. Make the connection between a digital clock and an analog clock. Show students
how a digital clock is set by first setting the hour and then holding down the minute
button to watch the minutes change from 01-59 minutes. Ask students why they can’t set
a digital clock to 5:60. Set times to the 5 minutes on the digital clock, and have students
model them on their analog clock.
Activity 15: Time Flashes By! (GLE: 16)
Materials List: time flash cards with clocks showing time to 5 minutes, set of cards from
1-12, chalk, yardstick, ruler
Make a set of time flash cards with minutes written from :00 to :55 in 5 minutes
increments. Also make a set of hour cards numbered from 1-12. (If you label the back of
the cards with minutes or hours, it will be easy to keep them separated.) Put the cards in
two different stacks. Create a clock face on the floor, and have students “walk” the
numbers counting by 5s. Then use a yard stick and a ruler as the hands of the clock. Call
out a time, and have a student model the time. Next, put students into pairs, and have
them select a card from each of the piles. Have pairs work together to model the time
using the large clock hands. Have class members state the time represented on the clock.
Instruct students to make adjustments of the hands on the clock if needed. Continue until
all pairs have had a turn.
Activity 16: Quarters of an Hour (GLEs: 2, 16)
Materials List: Blank Clock BLM (used in activity 13), colors, 4 quarters, Popsicle®
stick, large paper clip, transparency of Blank Clock BLM
On individually designed analog clock faces, have students divide the face into fourths
(quarters), coloring each quarter part a different color. Ask students how many different
parts they have divided their clocks into (4). Lead students to understand that the correct
wording to use is “the clock is divided into fourths” instead of into 4. Have students
mimic you as you travel along the edge of the clock saying 1 fourth, 2 fourths, 3 fourths,
and 4 fourths. Then take out 4 quarters and ask them how quarters are like the parts that
they colored on the clock. (It takes four quarters to make a dollar, and it takes 4 fourths of
an hour to make an hour.) Tell students that people say one-quarter of the hour has passed
instead of saying one-fourth of an hour has passed.
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Use the overhead transparency of Blank Clock BLM to guide students through the
following task. Have students put their fingers on the outer edge and travel along the
clock saying 5, 10, 15, a quarter of an hour has passed; 20, 25, 30, two quarters or 12 of an
hour has passed; 35, 40, 45, three quarters of an hour have passed; and then 50, 55, 60
four quarters or a whole hour has passed.
Give each student a Popscicle® stick and a large paper clip to use as hands on their
clocks. Have students model 3:15, 3:30, 3:45 and 4:00. Ask students what they notice
about those times. Have students model 3:15 again. Ask, “Why do some people say ‘a
quarter after three’ when reading this time?” (Because a quarter of an hour has passed.)
Have students model 6:30 on the clock. Ask students if they have ever heard someone say
two quarters past 6. (No, they usually hear people say half-past the hour.) Emphasize
that two quarters of an hour and half-past the hour are the same thing.
Have students model 7:45 on their clocks. Ask them how they would read this clock
using quarters of an hour. Ask students if they have ever heard anyone say 3 quarters of
an hour past 7. Ask students if they have ever heard someone say a quarter till 8. How are
a quarter till 8 and 7:45 alike? Have students model different quarters of an hour reading
their clock faces two different ways.
Activity 17: Found it! (GLE: 16)
Materials List: 10 index cards that have been stamped with a clock face, baggie, pencil
Give each pair of students 10 index cards that have been stamped with a clock face. If a
stamp is not available, copy a page of blank clock faces and have students cut and paste
them on the index cards. Also give each pair a baggie. Have students draw the hands on
10 clock faces to represent time to 5 minutes. Have them write the time shown on each
face on the back of their card. Instruct students to make 1-2 cards that are incorrect.
Check each groups cards before exchanging them.
Ask students to exchange cards with another group to check the information on the cards.
If pairs disagree with a time, they “challenge” the card and you check the card for
correctness. Students who correctly identify the card or cards with errors receive one
point per card. Have students finish checking the cards, bag them, and then pass them on
to another group.
Activity 18: How Long is an Hour? (GLE: 16)
Materials List: student clocks, timer
Have students set their clocks to the current time to the nearest five minutes. Set a timer
for 60 minutes. When the timer goes off, have students move their minute hand around
the clock counting by 5s as they go. Then have students adjust their hour hand. Continue
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the activity throughout the day to give students a sense of an hour. Next, ask students
questions that pertain to elapsed time.
Example: John got home from school at 3:45. He ate a snack and watched TV for
an hour and then started his homework. What time did he start his homework?
Activity 19: School Routine (GLEs: 16, 25, 26)
Materials List: math learning log, pencil
Have students log their school routine to the nearest 5 minutes in their math learning log
(view literacy strategy descriptions). Have them answer questions according to their
findings.
Example: What time is lunch? What will the class be doing an hour later? Repeat
the activity the next day. Have students compare their findings.
Ask students to log their activities until they go to bed one night to the nearest 5 minutes.
The next day have students come up with categories to represent what they do after
school (e.g., playtime, watch TV, play video games, eat, do homework). Have each
student determine which activity he/she did the longest. Lead the class as it organizes the
information into a table, and then create a bar graph or line plot. Ask students to write
two questions that could be answered by looking at the graph/plot.
Activity 20: Activity Time (GLE: 16)
Materials List: paper, pencil, pictures or drawings, class clock label with time units
Have students brainstorm activities that take 1 minute, 1 hour, or 1 day, and collect or
draw pictures of the activities to include on a class chart or bulletin board. Use a class
clock to demonstrate time passed by counting on to find the elapsed time. Have students
model with their clocks. Ask students to show time in hours (5:00) on their clocks, then
reset the clock to 1 hour later (6:00) or 1 hour before (4:00). Play a time game with the
whole group. Label a die to represent the following:
 1 hour later
 1 hour before
 5 minutes later
 5 minutes before
 30 minutes later
 30 minutes before
Call on a student to call out a time, have students show that time on their clocks, and then
roll the die and set their clocks to the new time. Continue practicing counting up or
counting back on the clocks.
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Activity 21: What Time is it Now? (GLE: 16)
Materials List: demonstration clock, student clocks, elapsed time cards
Prior to class make a set of elapsed time cards using index cards. Make a dozen or more
cards labeled with elapsed time statements such as these: 1 hour later or 1 hour before.
Set a time on your demonstration clock and have students set their clocks. Have a student
select an elapsed time card. The student reads the card and everyone sets his/her clocks
according to the description on the card. The teacher then shows her clock, and students
check their clocks for accuracy. Then another student chooses a card and the class sets
its clocks. This process continues until are cards have been selected.
Sample Assessments
General Assessments


Math Learning Log: If I found a dollar, I could buy____________that costs
_____________. Explain if you would or would not get change back.
Counting Money: Use a checklist to note students that are having difficulty
counting money. Using a large demonstration clock, set time to 5 minute
intervals and assess whether the student can identify the correct time
displayed.
Activity-Specific Assessments

Activity 1 – Give students a double Venn diagram and have them compare
and contrast a penny and a nickel by filling in characteristics of the coins.
penny
penny
1¢
round
copper
color

nickel
nickel
coin
5¢
silver
color
Activity 4: Give students patterns using coins. Have them complete the
pattern and determine the value of the pattern.
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
Activity 6: Provide a money table labeled quarter(s), dime(s), nickel(s) and
pennies. The student will then represent 37 cents as many ways as possible
always using only 2 pennies.

Activity 10: Set up stations with coins and $1 bills, number the stations, and
give each student a recording sheet that corresponds to the numbers on the
stations. The student will circulate throughout the stations counting how much
money is at each station and recording that amount next to the station’s
number on his/her recording sheet.

Activities 13 through 21: Provide the student with a clock and the student
will:
_____ Identify the parts of a clock (minute hand, hour hand, face)
_____ Set the clock to the hour
_____ Set the clock to the nearest half-hour adjusting the hour hand
_____ Count by 5s around the clock
_____ Model 6:45
_____ Model a written time, such as 2:20
_____ Model a quarter past 5
_____ Represent 9:10 and tell what time it would be an hour later

Activity 16: Students make up 5 time riddles for others to solve and to be
made into a class book. (For example: My hour hand points to 3. My minute
hand points to 5. What time is it?) As each student shares his or her riddle,
the student will show the time on his/her individual clock face and count by 5s
from twelve to find the correct answer. Observe students for mastery of this
skill as students create and solve the riddles.

Activities 17 and 21: Give students a test made up of clock faces. On some of
the clocks, have students identify the time to 5 minutes. On the other clock
faces, have students draw in the hands when given the time. Also, give
students problems where they must determine the time that has elapsed when
given a starting or finishing time.
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Grade 2
Mathematics
Unit 4: Place Value and 2-Digit Addition
Time Frame: Approximately four weeks
Unit Description
This unit extends place-value concepts through 999 and includes writing those numbers
in expanded, standard, and word forms. This knowledge is then used to enhance
understanding of 2-digit addition problems by regrouping.
Student Understandings
Students can represent numbers through 999 in expanded, standard, and written/verbal
forms and can use this information to add 2-digit numbers with regrouping. Students
develop capabilities to estimate the number of objects in collections of less than 100
objects.
Guiding Questions
1. Can students represent numbers to 999 with objects and in standard,
expanded, and written/verbal forms?
2. Can students make appropriate order comparisons of numbers through 999 in
all representations?
3. Can students complete 2-digit addition problems with and without regrouping,
including notational work?
4. Can students estimate the number of objects in collections of less than 100
objects?
Unit 4 Grade-Level Expectations (GLEs)
GLE #
GLE Text and Benchmarks
Number and Number Relations
1.
Model, read, and write place values for numbers through 999 in word, standard,
and expanded form (N-1-E)
3.
Make reasonable estimates of the number of objects in a collection with fewer
than 100 objects (N-2-E)
5.
Read, write, compare, and order whole numbers through 999 using words,
number lines, and models (N-3-E) (N-1-E)
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GLE #
8.
9.
10.
30.
GLE Text and Benchmarks
Recognize, select, connect, and use operations, operational words and symbols
(+, ) for addition (join, part/part/whole) or subtraction (take away, comparison,
missing addend, and set/subset) situations (N-6-E) (N-5-E)
Add and subtract 1- and 2-digit numbers (N-6-E) (N-7-E)
Round numbers to the nearest 10 or 100 and identify situations in which
rounding is appropriate (N-7-E) (N-9-E)
Recognize, extend, create, and explain patterns of addition and subtraction as
represented in charts and tables and in varied forms of skip-counting (P-1-E) (P2-E)
Sample Activities
Activity 1: What is 100? (GLE: 1)
Materials List: Base 10® blocks
Show students ten rods (tens) and ask them how many blocks there are. (100) Ask
students what group could be exchanged for the ten rods. (A flat of 100) Ask students
how to write one hundred in standard form. Guide them to understand that this means 0
ones, 0 tens, and 1 hundred. (100) Ask students what the model of 345 looks like. Have a
student model the number. Continue calling on students to model 3-digit numbers using
flats, rods, and unit Base 10® blocks.
Activity 2: Spinning for Numbers (GLEs: 1, 5)
Materials List: Base 10® blocks, 0-9 Spinner BLM, Spinning for Numbers Recording
Sheet BLM, paper clip, pencil
Use the Spinner BLM. 1. Place the point of a pencil through a large paper clip. 2. Place
the point of the pencil on the center of the spinner. 3. Adjust the paper clip so that the end
of the paper clip is on the center of the spinner. 4. “Flick” the paper clip to spin it.
Put students into groups and provide each group with Base 10® blocks, 0-9 Spinner
BLM and 2 copies of Spinning for Numbers Recording Sheet BLM. Have one student in
each group spin the 0-9 spinner three times to make a 3-digit number. Record the number
created. Ask another student to model the number using Base 10® blocks and draw the
model in the Base 10® column on the Spinning for Numbers Recording Sheet BLM. .
Have another student fill in another part of the chart (e.g., the digit in the hundreds place,
the expanded form of the number). Continue passing the chart until all the parts of the
chart are filled in.
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Number Created 213
Place Value Chart
Base 10
Model
H
2
T
1
O
3
Expanded Form
Form
200 + 10 + 3
Standard Form Word
213
Two
hundred
thirteen
Call on each group to share how it recorded one of their numbers. Have students repeat
the process five more times. Collect the recording sheets if you are doing Activity 3 on
another day. Observe students and make note of those students who need more practice
with each part of the chart.
Activity 3: Comparing Numbers (GLEs: 1, 5)
Materials List: paper, glue, Spinning for Numbers Recording Sheet from Activity 2,
scissors
Put students into the same groups used in Activity 2 and return their Spinning for
Numbers Recording Sheets BLM. Have students cut apart their sheets and put the 6
charts in order from least to greatest using the numbers that were created. Have students
glue the charts down after they are sure they have them in the correct order. Ask groups
to explain what part of their charts they used to compare their numbers (i.e., they looked
at the values of the digits in the hundreds place, then the tens place, and so on).
Activity 4: I Have….Who Has? (GLE: 1)
Materials List: I Have..Who Has? Cards BLM
Prior to class, run off cards on cardstock, laminate them and then cut them out.
Play a round of I have…Who has? Provide one clue card for each student. Make sure to
hand out all of the cards. It does matter who starts reading the first clue since the cards
will circulate back to first person from the last clue. Direct the student holding the “I have
140” card to start first.
First clue
reads – Who
has ?
I have 50.
Who has 4
hundreds
and 6 ones?
I have 406.
Who has 3
tens ?
I have 30.
Who has 5
hundreds
and 5 tens?
I have 550.
Who has 5
tens and 0
ones?
Grade 2 MathematicsUnit 4Place Value and 2-Digit Addition
Last clue leads back to
first card.
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Activity 5: Ordering Numbers in the Hundreds (GLEs: 5, 10)
Materials List: index cards, electronic equipment pictures with prices, paper, pencil
Prior to class, glue pictures of electronic equipment with their prices on index cards.
Select items whose prices are in the hundreds. A set of 5 cards per group is needed.
Count out 5 cards and label them Set A. Count out another 5 cards and label them Set B.
Continue until all cards are labeled.
Put students into groups. Give each group a set of cards. Have students order the cards
from least expensive to most expensive. Ask students to record their results by writing
the letter of the set of cards they are using, and then write the prices in order. Have
students exchange cards with a different group. Continue until all sets of cards have
circulated among groups.
Teacher Note: After rounding to the nearest hundred has been taught, use these cards in
a rounding activity. Have students round each price to the nearest hundred. Give
students a limited amount of money to shop with, and have them find how many items
they can buy.
Activity 6: Rounding to the Nearest Hundred (GLEs: 1, 5, 10)
Materials List: Rounding to the Nearest Hundred BLM, marker, tape, pencil, postcard
Prior to class, take 11 BLM patterns houses and number them from 0, 100, 200,
….1,000.
Hand out blank Rounding to the Nearest Hundred BLM house patterns. Have each
student use a marker to write a three-digit number in the large rectangle on the BLM
pattern. Ask students to come to the front of the class in pairs to compare their numbers.
Then have students come up three at a time and compare their numbers. Have the whole
class organize themselves into a number line using their house numbers. Finally, post a
set of house patterns that you have numbered from 0,100, 200,… to 1000 on the bulletin
board/chalkboard. Ask students to determine where their houses would be placed. Have
them indicate which two hundreds their house is between and which “hundreds” house it
would be closer to. Have students post their house patterns in numerical order around the
room.
Conclude the activity with a RAFT (view literacy strategy descriptions) writing
assignment.
R – Role (role of the writer)
A – Audience (to whom or what the RAFT is being written)
F – Form (the form the writing will take, as in letter, song, etc.)
T – Topic (the subject focus of the writing)
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R – a number that has been rounded to 100
A – fellow classmates
F – postcard
T – provide clues on the postcard as to what number they represent that has been
rounded to 100.
Allow time for students to share their RAFT writing with a classmate or the whole class.
Ask students to listen for accuracy and logic.
Activity 7: The Guessing Jar (GLE: 3)
Materials List: 3 jars of the same size, 3 different fillers for jars, baby food jar with
objects, Post-it notes, poster
Bring the students into a math circle and show them three jars that are the same size but
contain 20 each of three different objects. For example, one jar would contain 20 cubes,
one would contain 20 peanuts, and the third would contain 20 paper clips. Lead a
discussion about the fact that there are the same number of objects in each jar, but one jar
may look like it has more. Ask why. Explain that a point of reference for the collection of
objects is a tool that can be used to help them estimate.
Before initiating an estimation activity, provide students with a numerical benchmark (a
collection of 10, 20, or 50 of the object that will be placed in the guessing jar).
The Guessing Jar
Place a number of small objects into a baby food jar. (Always begin the year by using
small jars, and gradually increase the size of the jars and the number of objects that the
students will be estimating.)
Have students guess the number of objects, write their names and estimates on small
sticky notes, and place them on a poster shaped like a big jar. When all have guessed,
have the student with the closest estimate fill the jar for the next guessing game.
After each estimation activity, ask students to bring their estimate to a whole group
discussion area and discuss whether they overestimated or underestimated. Ask them if
they can determine why they guessed too many or too few. Make the activity fun and
yummy by using small food items such as peanuts, M&Ms®, Sweet Tarts®, or raisins.
After guessing, divide the food items among the students, and allow students to eat them.
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Activity 8: How many dots do you see? (GLES: 3, 30)
Materials List: transparency of How Many Dots Do You See? BLM, overhead projector
Five dots are in the rectangle below. Tell students they will use this as their benchmark to
help them estimate how many dots are in the large rectangle. Show students how to
section off the large rectangle into smaller rectangles that are the same size as the
benchmark to help them estimate how many dots are in the large rectangle. Have students
count off the dots in the large rectangle: 5, 10, 15, 20, 25, 30 dots After the activity,
emphasize that counting each grid section by “5” is only an estimate because some of the
grid sections have more than “5” dots in them.
Apply this gridding technique to any situation that asks students to estimate how many
are in a picture.
Activity 9: Ordinal Numbers (GLE: 5)
Materials List: number cards from 1-8, Ordinal Numbers BLM, pencil, number cards (131), ordinal cards (first – thirty-first)
Have eight students stand in line and count off in order using the correct ordinal numbers.
Have these students select the cardinal number card (1-8) that corresponds to their order.
Next, using the Ordinal Numbers BLM, have all students create a chart showing cardinal
numbers for 2-31 and ordinal numbers and ordinal number words (1st-first-1). If ordinal
number words are not posted, give students a word list. Model writing ordinal numbers
and words 21st–31st.
Play the following ordinal memory game: Make as many sets of cards as there are
groups.
1. Write numbers and the corresponding ordinal number words on cards.
(1-31) and (first – thirty-first)
2. Shuffle the cards and turn face down in rows and columns.
3. Have students take turns flipping cards to find a match.
4. The student who finds a match takes the cards.
5. When all cards are matched, the student with the most cards wins the
game.
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Activity 10: The Way We Were Game (GLE: 5)
Materials List: student baby pictures, list of student names alphabetized
Have students bring in baby pictures of themselves; line the pictures along the chalk tray.
Give each student an alphabetical list of student names. Have students guess who they
think is first to last, writing the ordinal number two ways (i.e., 1st and first) by the name
they think is first, second, third, and so on. When all students have made their guesses,
reveal the correct names with pictures.
Have students label a page in their math learning logs (view literacy strategy
descriptions) Being First. Have them divide their page into two sections. On one side,
have students write about situations when it is good to be first. On the other side, have
students write about situations where they might not want to be first. Discuss some
examples before requiring the students to generate their own. Let students share their
writings.
Activity 11: Standing in Line (GLE: 5)
Materials List: Standing in Line BLM, pencil
Hand out Standing in Line BLM. Discuss about where students think the “1st circle” is
and why. Have students label the circles using ordinals. Have them follow directions
given by the teacher such as these: draw a triangle around the 15th person in line; Mark is
9th in line. Put a M on the circle that represents where Mark is standing.
Ticket
Booth
Activity 12: More than 9 (GLE: 1)
Materials List: per group of students – More than 9 BLM, large paper clip, 2 number
cubes, Base 10® flats, rods, and unit cubes
Ask students, “What digit is used to represent a number when there is one more than 9?”
They should say, “There is no single digit that represents ten.” Ask, “What digits are used
to represent ten?” Then remind students that the digits have a meaning according to
where they are placed. Tell students that our number system teaches that when we have
more than 9, we make a group of 10. The number 10 means 1 group of ten and no extra.
When we have 10 tens, we create a group; we call that group a hundred (100).
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Play More than Nine
Put students into groups. Give each group a More than 9 BLM, two number cubes, Base
10® flats, rods, and unit cubes. Player 1 rolls both number cubes and spins the spinner.
The spinner will determine which base 10 block they are to use. The sum of the dice tells
them how many Base 10® blocks to take.
Example:
The first person spins and lands on tens, and the sum of the roll is 6. He/she
counts out six rods. He/she says, “6 tens is sixty.” There is no need to regroup.
He/she returns the Base 10® blocks to the center of the group. The next player
spins, and the spinner lands on ones and he/she rolls a 5 and 6. He/she counts out
11 unit cubes. Then he/she says, “Eleven is more than 9, so I need to regroup. I
need to group 10 unit cubes and trade for a rod. Eleven is 1 ten and 1 one.” Play
continues until all players have had four turns. Points many be awarded each time
a member needs to regroup. The next player rolls 5 and 6, and the spinner lands
on tens. The student must say, “5 tens and 6 tens is 11 tens. 11 tens is more than
9, so I have to regroup 10 tens for a flat.”
Have students respond to “It’s Good to be a 10” in their math learning logs (view literacy
strategy descriptions). Example: 10 is an important number in our number system. Any
time you have a group of 10, a trade for 1 of the next place value can be made. If you
have 10 of something, you can change the way that you look and still have the same
value. 10 units can change to a rod. 10 tens can change to a hundred, and10 dimes can
change to a dollar.
After students have had sufficient time to respond, have them share the reasons why they
think it would be good to be a 10.
Activity 13: Regrouping (GLEs: 1, 9)
Materials List: bills (ones, tens, hundreds) per group of students, Base 10® blocks or
Popscicle® sticks, pencil, chalk, chalkboard, paper
Model this problem using one-dollar and ten-dollar bills.
Patrick had $15 in his wallet. His sister, Natalie, gave him $6 for washing her
car. How much money does he have now?
Display a ten-dollar bill and 5 one-dollar bills. Ask students what operation is needed to
solve this problem. Then add 6 one-dollar bills to the display. Ask students how much
Patrick has now. Model putting like amounts together (5 ones + 6 ones is 11 ones). Ask
students what happens when there are more than 9 ones? (We need to create a group of
10.) Trade 10 ones for a 10-dollar bill. Add the new 10-dollar bill to the existing 10dollar bill. That gives Patrick 2 ten-dollar bills and 1 one-dollar bill. Patrick has $21 after
washing Natalie’s car.
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Model several examples with students and then have them work problems using either
money or Base 10® blocks to help them when they need to regroup. Give students many
examples of this type of problem throughout the year. Have students record the number
sentences as they solve problems. Have the students perform the operations on paper after
each modeling. This will make the connection for them. Have students pay close
attention to how they are lining up their digits. Show students how to record the actions
they went through as they were putting their amounts together.
1
$ 15
+
6
$ 21
5 + 6 = 11
11 is more than 9 so I
need to create a group
of 10. That leaves 1.
Put my new group of
10 in the tens group.
Develop a process guide (view literacy strategy descriptions) to help students with the
steps involved in adding numbers. Process guides scaffold students’ comprehension
within unique formats. They’re designed to stimulate students’ thinking during or after
their reading, listening, or involvement in any content area instruction. Guides also help
students focus on important information and ideas, making their reading or listening more
efficient.
Example:
Step 1 – Record numbers by lining up digits
Step 2 – Look at the digits in the one’s place value. Is their sum over 9? Do I
need to regroup?
Step 3 – Add and record the sum of the digits in one’s place. If you need to
regroup, record a 1 in the ten’s place to represent 1 ten.
Step 4 – Add and record the sum of all the digits in ten’s place.
Have students copy the process guide. They should refer to the steps each time they solve
an addition problem until the steps become a natural thought process.
Activity 14: Do I Need to Regroup? (GLE: 9)
Materials List: worksheet with examples of addition problems that require regrouping,
calculator, chalk, chalkboard
Give students examples of 2-digits plus 1-digit problems, and have them circle the
problems that require regrouping. Call on different students and have them explain why
they circled the problem. Then have students solve the problems they circled.
Examples: 2 7 boys
+ 8 girls
3 5 students
5 8 fish
+ 4 fish
6 2 fish
6 4 students
+ 3 students
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Use an opinionnaire (view literacy strategy descriptions) to poll students about the
following statement:
This is the 21st century. Students should be able to use a calculator to solve all
math problems.
Opinionniares are highly beneficial in promoting deep and meaningful understandings of
content area topics by activating and building on relevant prior knowledge and building
interest in and motivation to learn more about particular topics. Opinionnaires also
promote self-examination, value youths’ points of view, and provide a vehicle for
influencing others with their ideas.
Form 2 groups according to if they agree or disagree with the statement. Provide time for
students to come up with examples as to why calculators should or should not be used.
Record all of the students’ responses. Choose one person from each group to debate the
groups’ statements. Finally, have students come up with a general statement that either
supports or doesn’t support the statement after hearing all the reasons.
Make sure to make the point that if calculators were used all the time students would not
learn their facts and would be unable able to do mental math. Also you want to make the
connection to regrouping. That a calculator automatically regroups. If students use a
calculator they wouldn’t learn how to regroup.
Activity 15: Rods to Flats (Tens to Hundreds) (GLE: 1)
Materials List: number cube, rods, flats
Set up a “bank” of rods and flats. Divide the class into two teams. Have students form
two lines.
Have the first member of each team roll a number cube to indicate how many rods he/she
collects from the “bank.” Have the first person hand the rods to the second person who
must roll and collect more rods. The second person passes the rods to the third person
who either rolls or regroups the rods for a hundreds flat. Inform students that they may
not roll if they need to regroup but must go to the bank, trade 10 rods for a flat, and then
pass the blocks to the next person.
Example:
The first player rolls a 6 and collects 6 rods, then passes them to the second
person in line. The second person must roll because he/she can’t regroup. He/she
rolls a 5 and collects 5 rods from the “bank” and passes all 11 rods to the third
person in line. The third person in line must go to the bank and trade 10 rods for a
flat, then pass the flat and the rods to the fourth person in line who must roll. Play
continues until the last person in line has a chance to roll or trade. If the last
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person collects more than 10, base10 blocks, he/she must regroup before returning
to their line. Each line must announce how much the line collected.
Activity 16: Adding Two-digit Numbers + Two-digit Numbers (GLE: 9)
Materials List: Base 10® blocks, practice problems, pencil
Give students a real-life problem involving regrouping in the ones place only.
Jacob ate two servings of chips. Each serving has 18 grams of carbohydrates.
How many carbohydrates did he eat in all?
Model the problem. Put like items together and make a new package if possible. After
using place value blocks, show students how to do the problem numerically adding ones
to ones and tens to tens, and making a new group if necessary. Make sure students
understand how to line up digits before adding. Model several problems for students.
After modeling problems, put students into pairs and have them work problems.
Materials should be available for modeling problems as long as students need them. Have
students practice problems throughout the year.
Activity 17: Ten Tens (GLE: 1)
Materials List: 17 ten-dollar bills, hundred-dollar bills, per group of students, 2 number
cubes per group, 10 and 100-dollar bills, Ten Tens BLM per student, pencil
Ask students: What is 10 tens? Have them model what happens when they have one
more than 9 tens. Count out 10, ten-dollar bills. Have students count with you saying 10,
20, 30,…100. Ask students what happens if they have 13 tens. Count out 13 ten-dollar
bills and then count the money saying 10, 20, 30, …100, 110, 120, 130. Point out to
students that 10 tens is 100 and 13 tens is 130. Ask students what the value would be of
17 ten-dollar bills.
Play Trading for 100
Put students into groups. Give each group 2 number cubes, 10 and 100-dollar bills, and a
Ten Tens Recording Sheet BLM for each member of the group. Have students roll the
two number cubes, count out that many 10-dollar bills, then trade them for 100-dollar
bills when they can, recording their amounts after each roll. Have students continue
trading money after each roll if they can. Play four rounds and have students find who
has the largest amount of money in their group. Play addition games if time will permit
or leave materials in a center for rainy day activity. The recording sheet has a place for
three games.
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Roll #1 ____tens = _________
Roll #2 ____tens = _________
________ total so far
Roll #3 ____tens = _________
_________ total so far
Roll #4 ____tens = _________
_________ final total
Activity 18: Regrouping in the Tens (GLEs: 1, 8, 9)
Materials List: Base 10® blocks, problem set that requires regrouping into the hundred’s
place
Ask a student to model solving the problem below.
Anne earned 63 points while playing the video game. Jerry earned 45 points while
playing the game. How many points did they earn altogether?
After the student has modeled the problem with Base 10® blocks, review the procedure
for recording the problem numerically. Make sure that students know that 6 tens plus 4
tens is 10 tens or 100. Have students record this example. Give students more problems
to practice. After a student has modeled a problem ask him (or another student) to
demonstrate the problem numerically. Give assistance as needed using questioning to
lead the student to the correct answer.
Activity 19: Flip 4 (GLEs: 5, 9)
Materials List: Flip 4 BLM, 2 sets of digit cards per pair of students, paper, pencil
Prior to playing the game have students fill out an anticipation guide (view literacy
strategy descriptions) -Flip 4 BLM. Before playing the game, students fill in the “top”
half of the BLM. After playing five rounds, have students return to the guide and fill in
the “bottom” half. Discuss students’ answers.
Put students into pairs. Give each pair 2 sets of digit cards, paper and pencil. Each player
turns over 4 digit cards. Have each student create two, 2-digit numbers and find his/her
sum. The object of the game is to create the largest sum possible. Instruct students to
record their numbers and their sum. The student that has the largest sum for that round is
awarded a point. Play continues until one player earns 5 points.
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Activity 20: Estimate or Exact Answer (GLEs: 8, 10, 9)
Materials List: chalkboard, chalk, Estimate or Exact Answer BLM
Model the use of mental math to solve addition problems by using 10s or 100s, and then
use basic facts to solve the problems (for example, 2  4 ; 20  40 ; 200  400 ). When an
estimate is all that is needed, estimate the answer by rounding (for example, 53  68 to
50  70 ). Discuss when estimates might be used instead of exact numbers (when you
need to know about how many or how much). Demonstrate estimating money (rounding
to the nearest dollar) to determine about how much is needed to buy something (for
example, 77¢ rounds to $1.00; $2.35 rounds to $2.00).
Have students fill out the anticipation guide (view literacy strategy descriptions) –
Estimate or Exact Answer BLM. . They are to record how many times a day they
estimate and how many times a day they get exact answers doing the activities listed in
the chart. After they fill out the chart, they are to use the sheet the following next few
days to record the number of times they actually found estimates or exact answers for the
activities listed. Once students have had time to fill out their forms, have students share
their findings. Students need to realize the importance of rounding and mental math.
Sample Assessments
Performance and other types of assessments can be used to ascertain student
achievement. Following are some examples:
General Assessments




Provide a word problem, then the student will use Base 10® blocks to model
the problem. Observe if the student knows when to regroup.
Write ten addition problems in context using 2-digit numbers for the student
to solve correctly using concepts learned. (Notice that the student is lining up
the digits according to the correct place value.)
Students use ordinal number words to describe his/her schedule for the school
day and will share the list with the class (list at least ten activities).
Students write story problems using addition of numbers that are to be
rounded to find an estimated answer. He/she will share the work with a
classmate after explaining the answers to the teacher.
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Activity-Specific Assessments

Activity 2: Provide each student with a chart with column titles, Base10, place
value chart, standard, words, and expanded form. Fill in one representation of
a number in each row and the student will fill in the rest.

Activities: 3, 5, and 6: Provide each student with a list of 5 prices in the
hundreds. The student will list prices in order and round prices to the nearest
hundred. The students will provide list of items that could be purchased when
provided a limit on spending.

Activity 8: Given a benchmark, the student will estimate using the “sectioning
off” method to determine how many items are in a diagram and show the
sections used to get the estimate.

Activity 11: Given a line of items, the student will identify each item’s
position.
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Grade 2
Mathematics
Unit 5: Place Value and 2-Digit Subtraction
Time Frame: Approximately three weeks
Unit Description
This unit parallels the previous unit with a focus on place value but with the operational
focus on subtraction of 2-digit numbers.
Student Understandings
Students can subtract 2-digit numbers with and without regrouping during activities.
They exhibit their understanding of the subtraction algorithm by recording what happens
during these activities. Students will recognize when to add and when to subtract in
problem-solving situations.
Guiding Questions
1. Can students complete 2-digit subtraction problems with and without regrouping,
including notational work?
2. Can students distinguish between addition and subtraction situations and work
accordingly?
Unit 5 Grade-Level Expectations (GLEs)
GLE GLE Text and Benchmarks
#
Number and Number Relations
1.
Model, read, and write place values for numbers through 999 in word, standard,
and expanded form (N-1-E)
6.
From a given number, count forward and backward and count to 100 by 2s
(N-3-E) (N-1-E) (N-4-E)
8.
Recognize, select, connect, and use operations, operational words and symbols
(+, ) for addition (join, part/part/whole) or subtraction (take away, comparison,
missing addend, and set/subset) situations (N-6-E) (N-5-E)
9.
Add and subtract 1- and 2-digit numbers (N-6-E) (N-7-E)
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Sample Activities
Activity 1: Subtraction with Regrouping (GLEs: 1, 8, 9)
Materials List: Base 10 ® blocks, overhead Base 10 ® blocks, overhead projector
Write this problem on the board or on a transparency:
Marcus has 23 trading cards. He gives Alonzo 17 cards. How many cards does he
have left?
Guide students through the problem. Ask, “Which operation is needed to solve this
problem?” Instruct students to model the number 23 with their Base 10® blocks and then
to remove 17 blocks. Remind students that seventeen indicates that 7 ones and 1 ten are
to be removed. Ask, “Is that going to be a problem? What must be done in order to
remove 7 ones? Are there enough blocks left to remove 1 ten? How many cards does
Marcus have left?”
Repeat this activity many times using different problems. Give students at least one day
of practice in which they go through the actions without recording their actions. Allow
students access to manipulatives for this entire unit.
Activity 2: Recording what Happens in a Subtraction Problem (GLEs: 1, 8, 9)
Materials List: Subtraction BLM, Base 10 ® blocks, overhead Base 10 ® blocks, overhead
projector
Write the problem on the board or on a transparency:
Paul has 32 cookies in his pack. He and his friends ate 27 cookies. How many
cookies does he have left?
Guide students through the problem. Model the problem first, and make the necessary
regrouping in order to subtract the 7 ones. Then show students how to record their
actions. Write the problem on the board/transparency, and talk through each action
relating it to what just happened when you were modeling.
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Example:
I need to remove 7 ones from 2 ones. Do I have enough ones? No, so I need to
regroup. I take a 10 from 3 tens and that leaves 2 tens. The ten that I took I break
apart into 10 ones and put with my other 2 ones. Now I can remove 7 ones from
12 ones. That leaves 5 ones. Next, I remove 2 tens from 2 tens which leaves 0
tens. Paul has 5 cookies left.
2
3
- 2
12
2 cookies
7 cookies
5 cookies
Put students into pairs. Handout Subtraction BLM. Have students first model the
problem, then have them solve the problem and record their actions.
Observe students and make note of places where students are making mistakes in the
problem modeling process. When everyone has finished, allow students to share their
answers.
Activity 3: Regrouping in Subtraction (GLEs: 1, 8, 9)
Materials List: Place Value Mat BLM, Base 10 ® blocks, overhead Base 10 ® blocks,
overhead projector
Discuss how to decide whether or not to regroup in subtraction. Write 23 – 2 on the board
and ask for a solution. Ask, “Is regrouping needed to solve this subtraction problem?”
(No). Ask, “Why?” Hand out Base 10 blocks and Place Value Mat BLM. Then, write 23
– 4 and have students model the subtraction by using Base 10® blocks (rods and ones)
and their Place Value Mat BLM, as you model on the overhead projector. Point out that
they need to regroup when the 1s they are subtracting (taking away) are more than the 1s
they are subtracting from. Write several 2-digit subtractions on the board (vertical and
horizontal form) and practice solving them together using the Base 10® blocks, deciding
first whether regrouping is needed. Model using the overhead while the students follow
your verbal modeling at their seats. Finally, go over how to record subtracting with
regrouping.
Conclude the activity with a RAFT writing (view literacy strategy descriptions)
assignment.
Role – the digit 9
Audience – fellow classmates
Form – paragraph
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Topic – Why it’s good to be the digit 9 in the one’s place value of a 2-digit
number.
Allow students to share their RAFT writing assignment with a partner or the class.
Students should listen for accuracy and logic in their classmates’ RAFTs.
Activity 4: Flip Three (GLEs: 1, 8, 9)
Materials List: digit cards, math learning logs, Base 10 ® blocks
This is a whole group activity. Divide the class into two teams. Flip over 3 digit cards
and challenge students to make a 2-digit minus a 1-digit problem that requires regrouping
using the digits on the cards. Have a student from one of the teams come to the front of
the room and model the problem he/she has created with the digits. First, have him/her
model with manipulatives and then write and solve the problem on the board. Reward the
team with one point if the member from their team was able to write a problem that
requires regrouping. Next, ask the other team if it was able to create a different problem
that requires regrouping. Have a student share the problem and work it out on the board.
If they were unable to create a different problem, flip over 3 more cards. Repeat as many
times as time will permit.
Have students write and answer the following in their math learning logs (view literacy
strategy descriptions):
Compare and contrast what happens to the number 4 in the problem 34 – 27 and the
number 4 in the problem 34 – 22. How are the problems alike? How are they different?
Allow students time to share their answers.
Activity 5: Can you buy it? (GLEs: 1, 8, 9)
Materials List: play money -10s and 1s, 1-8 Spinner BLM, paper clip, chart with prices
Present the following problem to students:
Molly has $20. She wants to buy a CD that costs $18. Does she have enough money to
buy the CD?
Model $20 with 2 ten-dollar bills. Ask a student to come up and remove $18. When there
are no ones to remove, have student trade a 10-dollar bill for 10 ones. Then have the
student remove 8 ones and 1 ten. Molly has enough money to buy the CD because 20 is
greater than 18. The students will learn how much greater when they see how much
Molly has left.
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Put up a chart that shows toy prices to the nearest dollar. Create a spinner using the
Spinner 1-8 BLM. Have students take turns spinning a spinner. The number they land on
determines how many tens they are able to spend. Ask students to select an item off the
toy chart. Student then models the problem using the play money. Then they write their
problem on the board talking out the steps of subtraction.
Example: Student spins a 6. Student gets $60 to spend at toy store. Student selects a video
game off toy list that cost $57. Student must pay with exact amount. Student trades a 10
for 10 ones. Then the student counts and pays with 7 ones and 5 tens. Student has 3 ones
left over.
Student then records problem on the board.
5 10
$6
0
- 5 7
3
Continue the activity until all students have had a turn. Have students record problems as
students work them on the board.
Activity 6: Subtracting with Regrouping using a 100s Chart (GLEs: 8, 9)
Materials List: 100s Chart BLM, counters
Use a 100s chart and point out that each row has 10 numbers, and the numbers in each
column increase by 10. Provide a subtraction sentence orally, such as 44 – 20. Have the
students find 44 on their 100s Chart BLM, place a counter there, and then subtract 20 by
moving the counter up 2 10s (2 rows), ending on 24. Write and solve other subtraction
sentences that involve subtracting 2-digit numbers using a 100s chart. Have students
place a counter on the first number given in the subtraction sentence. Have students start
with the ones and count backwards the number of spaces that represent the number of
ones being subtracted. Then count up rows of 10s to indicate how many tens need to be
removed. See if students notice a pattern on the 100s chart when they are required to
regroup.
Put students into groups of five. Have each group create a math story chain (view literacy
strategy descriptions) that begins with a 2-digit number that involves addition or
subtraction.
Example:
Student 1: Start at 72 on your hundreds chart.
Student 2: Count back 7 spaces.
Student 3: Count up 3 tens.
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Student 4: What space are you on?
Student 5: (reviews logic in the story problem and provides correct answer)
Have each group ensure logic in its story and accurately solve the problem first, then read
the problem and have the class work the problem out using a 100s chart.
Activity 7: Counting Back (GLEs: 6, 8, 9)
Materials List: Play coins – dimes and pennies, Place Value Mat BLM (see Activity 3
BLM)
Ask students to count by 10s, starting at 10 and stopping at 90 and then ask them to count
back by 10s, starting at other numbers such as 83, 77, 92, and so on. Use dimes and
pennies to demonstrate counting back by dimes. Give a volunteer 9 dimes and 5 pennies
(have students count together to find the total amount [95¢]). Then tell the student, “You
spent 20¢.” Ask: “How much do you have left?” Have the class count back by 10s to
find the answer (75¢). Distribute dimes and pennies to pairs of students and have them
practice counting back by 10s. Ask, “How are dimes and pennies like 10s and 1s?” (1 10
equals 10 1s and 1 dime equals 10 pennies.) Using the Place Value Mat BLM, have
students use pennies and dimes to show 23¢. Ask, “How would you subtract 7¢
(pennies)?” Explain that to subtract 7 pennies (1s), 1 dime will have to be exchanged for
10 pennies. Show that now there are 1 10 (dime) and 13 1s (pennies). Now, 7 1s
(pennies) can be subtracted (taken away) from the 13 1s (pennies) with 1 dime and 6
pennies left. Thus 16¢ is the difference. Have small groups work together to solve other
problems with or without regrouping.
Activity 8: Do I Have Enough Money? (GLEs: 6, 8, 9)
Materials List: Order Please! BLM, calculators, menu
Give students an amount such as $5 to spend on lunch. Have students use the menu of a
local restaurant to “order” a drink, sandwich, and a dessert. Have them find the total cost
of their order using a calculator. Ask students to determine if they have enough money to
pay for the lunch that they ordered and what their change will be. Hand out Order Please!
BLM. Remind students that a ticket is the bill that the waiter wrote down for the items
ordered from the restaurant. Have students list their selections, costs, and total on the
BLM and show that they paid with $5.00 and got ______back in change.
Torrie’s Ticket
Paid with 75¢
Spent
- 62¢
Change
13¢
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Activity 9: Grocery Store (GLEs: 6, 8, 9)
Materials List: Receipt BLM, grocery store items with a sticker priced less than $1, coins
If store items are not available use pictures cut from newspaper grocery ads and glue to
poster boards. A large poster can be cut into 4 pieces and the “grocery store” can have
fruits/vegetables, canned goods, cereals, and snacks.
Set up a mock grocery store with items costing less than a dollar. Have students play
cashier and consumer. This time have students create a receipt using the Receipt BLM
before they can count back change. Have students show the amount paid, minus the cost
of the item, to determine how much change they should get back.
Activity 10: Add or Subtract? (GLEs: 8, 9)
Materials List: index cards
Using an index card, have each student create an addition or subtraction story problem
where one of the numbers is a 2-digit number. Ask students to read their problems to the
class, and let classmates share how they would solve the problem. Have the author of the
problem select a student to set up the problem and solve it. If the student is correct, have
that student read his problem.
Activity 11: Subtraction Story Problems (GLEs: 8, 9)
Materials List: sports page, poster, computer
Show students the sports page from a newspaper and how to find scores. Have small
groups find football or basketball scores (home teams or popular area teams) less than
100 points. Instruct the groups to work together to discover the difference between the
two scores and how many points the winning team won by. Have students write a
subtraction story problem about their findings to share on a poster titled, Sports Math. If
computers are available, have students write their story problems using the computer.
Activity 12: Choosing the Correct Operation (GLEs: 8, 9)
Materials List: math learning log, 10 index cards, 4 strips of paper
Ask students to brainstorm (view literacy strategy descriptions) clues that can be used to
decide whether to add or subtract, and make a list to add to the math center and their
math learning logs (view literacy strategy descriptions). Addition clues include: How
many altogether? How many in all? Subtraction clues include: How many are left? How
many more? How many less?
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To play a math game, prepare 10 index cards with a 2-digit number on each and on 4
separate strips of paper, write questions such as:




How many in all?
How many now?
How many are left?
How many more?
Have small groups or individuals choose two number cards and a question strip and work
together to create a story problem using the numbers and questions. Have students record
their problem in their math learning log, and then share their problems with the class.
Activity 13: Subtract From 99 (GLEs: 8, 9)
Materials List: 1-4 Spinner with Recording Sheet BLM, large paper clips, calculators
Provide each pair of students with the 1 – 4 Spinner with Recording Sheet BLM and large
paper clip. Have them spin the spinner twice to make the smallest 2-digit number
possible; then subtract that number from 99. Next, ask them to spin again and subtract the
new 2-digit number from the first difference. Have them continue spinning and
subtracting from the previous difference until they come to a number they cannot
subtract. Challenge them to get as close to 0 as possible. Allow students to use a
calculator to check their subtraction, if needed.
Sample Assessments
Performance and other types of assessments can be used to ascertain student
achievement. Following are some examples:
General Assessments

Problem Solving Book: Have students make a class problem solving book. Each
student will write a problem in which he/she finds the difference between a 2digit and 1-digit number that requires regrouping and write the answer on the
back of the page. Make a booklet and place it in a center for students to solve each
other’s problems.

Journal Writing: Have students explain how addition and subtraction are alike and
how they are different. Students will explain how they know when to regroup in a
subtraction problem.
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
Students will determine if they would use addition or subtraction to solve
problems as story problems are read to them.
Activity-Specific Assessments

Activity 4: Students write a problem using the digits 2, 7, and 9 that would require
regrouping.

Activity 5: Students match the amounts below so that they can buy each item
listed.
Video game $37
$30
Camera $41
$40
CD $21
$50

Activity 6: Students model the subtraction problem 57 – 29 using a 100s chart.
They will fill in the blanks as the work is done.
I started at ________. I moved back _____spaces. Then I moved up
______rows. I ended up on the numeral _________.

Activity 8: Students calculate how much change is due when provided
information for a restaurant ticket by the teacher.

Activity 12: Students decide which operation to use and then set up and solve
real-life problems provided by the teacher.
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Grade 2
Mathematics
Unit 6: Shapes and Fractions
Time Frame: Approximately four weeks
Unit Description
This unit focuses on geometric and fractional number understandings. In geometry,
students extend their work to compare and contrast figures, and to identify congruent and
similar figures. They also examine the role of fractions in geometric and set contexts.
Student Understandings
Students identify congruent shapes and deal with orientations of 3-dimensional objects.
In the plane, they recognize and use vertical and horizontal references. Students also
model fractional parts of a whole and a set.
Guiding Questions
1. Can students compare and contrast 2- and 3-dimensional shapes and recognize
congruent shapes in space?
2. Can students recognize and draw horizontal and vertical lines?
3. Can students identify a reduction or an enlargement of a figure?
4. Can students identify and discuss thirds, fourths, fifths, and sixths?
Unit 6 Grade-Level Expectations (GLEs)
GLE # GLE Text and Benchmarks
Number and Number Relations
2.
Model the concepts of thirds, fourths, fifths and sixths using regions, sets, and
fraction words (e.g., one-third, three-fourths, five-sixths) (N-1-E)
Geometry
21.
Compare and contrast 3-dimensional shapes (i.e., sphere, cube, cylinder, cone,
prism, pyramid) according to their attributes (e.g., number of faces, shape of
faces) (G-2-E)
22.
Identify a reduction or enlargement of a given shape (G-2-E)
23.
Identify congruent 3-dimensional solids in a variety of positions and
orientations (G-3-E) (G-4-E) (G-2-E)
24.
Identify and draw horizontal and vertical line segments (G-5-E)
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Patterns, Relations, and Functions
31.
Recognize, extend, create, and explain patterns that involve simple rotations or
size changes with geometric objects (P-1-E) (P-2-E)
32.
Recognize and apply patterns in problem-solving in other content areas and
real-life situations (P-3-E) (N-9-E)
Sample Activities
Introduction Activity (GLE: 21)
Materials List: 3-D Vocabulary Self-Awareness Chart BLM, pencil
Prior to beginning Unit 6 hand out the 3-D Vocabulary Self-Awareness Chart BLM. Use
the BLM (view literacy strategy descriptions) to gauge students’ knowledge of the
vocabulary used in Unit 6. Give each student 3-D Vocabulary Self-Awareness Chart
BLM, and direct them to rate their understanding of each word/symbol with either a “+”
(understands well), “√ “(limited understanding), or a “ – “ (don’t know). Over the course
of the unit, students are to return to their chart and add new information. The objective is
that students will replace all the check and minus marks with plus signs. At the end of the
unit, students can utilize the chart to compare and contrast 3-D shapes.
Activity 1: Three Dimensional Shapes (GLE: 21)
Materials List: a set of Geoblocks® or a collection of objects of different shapes: eraser,
crayon box, soup can, ball, alphabet block, tissue boxes, a pointed party hat, chalkboard
or chart paper, pictures of 3-D shapes, glue, scissors
Display a set of Geoblocks® or a collection of objects of different shapes: eraser, crayon
box, soup can, ball, alphabet block, tissue boxes, a pointed party hat. Hold up a cube and
ask if anyone knows the name of the shape (cube). Place it so that everyone can see it.
Ask the students to describe it as you write their descriptions on the board or on chart
paper. When students have completed their descriptions, hold the cube and point to a
corner. Tell them that the corner is called a vertex and that the word vertices is used when
talking about more than one vertex. Have a student point to and count the number of
vertices. Point to a face and say the word face. Ask someone to name the shape of the
face of a cube (square). Count the faces and ask if all of the faces have the same shape.
Now, point to an edge and tell the students that this part of the cube is called an edge.
Count the edges with the students.
Using chart paper create a large modified word grid (view literacy strategy descriptions)
that has 5 columns and 7 rows. This is a modified word grid in that instead of putting
checks, pluses, or minuses in each cell, students must write figure names and numbers.
Label the chart “Characteristics of 3-Dimensional Figures.” Label the columns: Picture
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of Figure, Name of Figure, Number of Vertices, Number of Faces, and Number of Edges.
Draw or glue a paper cutout of a cube or picture of an object that is shaped like a cube
(cubic tissue box), and ask the students to help you fill in the columns. Repeat this
activity with at least one other object, and add the information to the chart. Have students
begin making comparisons between the 3-dimensional objects. Continue to introduce
another shape each day until the chart is filled with the shapes (don’t forget pyramids)
and their descriptions.
Picture of
Figure
Characteristics of 3-Dimensional Figures
Name of Figure
Number of
Number of
Vertices
Faces
rectangular
8
6
prism
Number of
Edges
12
Have students return to their Vocabulary Self-Awareness Chart BLM and make
adjustments to the marks that indicate their understanding of the vocabulary words, faces,
vertices, and edges. Return to the chart throughout the unit to compare and contrast 3-D
shapes as students acquire more knowledge. Allow time for students to review the
information on the grid with a partner in preparation for quizzes and other class activity.
Activity 2: Grab Box (GLE: 21)
Materials List: 3-D shapes, box with hole in the top, math learning logs
Place 3-D shapes in a box which has a hole in the top. Have students grab an object in the
box (but don’t remove it from the box). Have them describe the attributes that they can
feel. After they have described the item, ask them to guess the name of the 3-D shape that
they are holding. After guessing, have them pull the object from the box to see if they
were correct. Repeat the activity several more times.
Have students record the following statements in their math learning logs (view literacy
strategy descriptions). Today I picked a _______________in the grab box. I knew it was
a _________________because I could feel ____________________.
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Activity 3: Digital Scavenger Hunt (GLE: 21)
Materials List: index cards, cameras, computer, PowerPoint® program or paper to make
shape booklet, magazines, scissors, glue
Write the name of 3-D shapes on index cards. Put students into groups. Have a student
from each group draw a card. Go on a walk through the school having each group record
examples of their shape on the back of their card.
If cameras are available, students could take pictures of the examples as they walk. Give
each group a camera (digital, disposable, or instant) and have students in each group
alternate taking pictures of their shape. When students get back to class, have them create
a tally chart of the 3-D shapes they saw. Make a presentation with students' pictures.
Create a class PowerPoint® presentation, or put together a shape book.
Note: If cameras are not available, do the activity using pictures from magazines.
These pictures could be used to assess students’ ability to identify 3-D shapes at a later
date.
Activity 4: Top, Front, Bottom Views (GLE: 21)
Materials List: Top, Front and Bottom Views BLM, 3-D shapes, pencil
Hand out the Top, Front and Bottom Views BLM. Give each student a cube. Have them
stand over the shape and look down. Ask, “What shape do you see?” (square) Have
students record their answer under Top View on their recording sheet. Without moving
the cube, have them look at the cube from the front. Ask, “What shape do you see?”
(square) Students record their answer under the proper heading. Finally, have them lift
the cube and look at the bottom of the cube. Ask, “What shape do you see?” (square).
Students record their answer under the proper heading. Repeat this activity with a cone,
pyramid, rectangular prism and sphere. Have students stop after each view and record
their answer. Have students group 3-D shapes according to common faces. Collect and
check students’ BLM for understanding.
Activity 5: Is it Horizontal or Vertical? (GLE: 24)
Materials List: chalkboard, chalk, toothpicks or short straws of congruent length,
construction paper, overhead
Draw a square on the board. Demonstrate that each side is made of a line segment. Using
toothpicks on the overhead, have volunteers model other plane figures studied. Explain
that the place where the toothpicks meet is the corner of the plane figure. Ask, “What are
the sides called?” (line segments) Model on the board the difference between lines and
line segments.
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Draw some shapes slowly on the overhead, and ask students to identify the number of
line segments used in each. Ask students to find line segments that run straight up and
down (square, rectangle) and introduce the term vertical. Have students find line
segments that are lying down straight (rectangle, parallelogram, square, trapezoid), and
introduce the term horizontal. Ask, “Why are these line segments instead of lines?”
In a math circle, give each student about 10 toothpicks and a piece of construction paper
to serve as a work mat. Tell them that the toothpicks will be their line segments. Give
directions for students to place toothpicks horizontally or vertically on their mat. After a
few minutes of having them randomly place their toothpicks, ask them to clear their mats.
Now, tell them that they will have to make the shape that you describe. Ask if they know
how many vertical and how many horizontal line segments are needed to make a square.
After discussion, give directions for laying toothpicks horizontally and vertically with
tips touching to make a square. Repeat with other shapes.
Revisit the Vocabulary Awareness Chart BLM. Check students’ vocabulary selfawareness (view literacy strategy descriptions) of the terms vertical and horizontal.
Activity 6: Creating a Design (GLE: 24)
Materials List: ruler, paper, pencil, red and blue crayons
Have students use a straight edge to draw a picture made up only of line segments. After
they create the design, have them use a red crayon to trace over all the line segments that
are horizontal and use a blue crayon to trace over all the vertical line segments. If their
picture has symmetry, have them draw a dotted line through the shape(s) to show
symmetry. Have students complete a RAFT (view literacy strategy descriptions) writing
assignment to assess their understanding of horizontal, vertical, and lines of symmetry.
RAFT
Role- Museum director
Audience- guest of the Museum
Form – Museum brochure
T- Draw examples of art that do and do not have lines of symmetry as well as
vertical and horizontal lines that are featured in the museum with a description of
the art piece.
Once RAFTs are completed, allow students to share them with a partner or the whole
class. Students should listen for accuracy and logic in the RAFTs.
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Activity 7: Congruent and Similar Shapes (GLEs: 22, 31)
Materials List: computer, Kidpix®
Use a draw program like Kidpix® to show students how to copy and paste a figure. When
a figure is copied and pasted, it creates two congruent figures. Explain to students that
congruent figures are figures that are exactly alike. Next, have them enlarge the second
figure by holding down the shift key as they “stretch” the figure. Lead students to notice
that the figures look the same except one is larger than the other. Tell them this is called
an enlargement. Repeat the process, this time ‘shrinking” or reducing the figure –
reduction. When teaching about enlargements and reductions, make sure students
understand that the original figure has been stretched or shrunk vertically and
horizontally by the same factor. Show students how to stretch figures on the computer
without holding the shift key. The shape becomes distorted. Show students examples of
what is and is not an enlargement.
Example:
original
figure
only stretched wide
only stretched long
stretched long and
wide – looks same
but bigger
Have students create enlargements on the computer.
Next have students create a pattern using a figure that follows the pattern:
congruent, congruent, enlargement
Example:
Activity 8: Similar Shapes (GLEs: 22, 31)
Materials List: piece of red construction paper, scissors, Geoboards®, rubber bands,
Demonstrate cutting out a symmetrical red heart by folding a piece of paper and cutting
half of a heart shape and then unfolding the paper to make the heart. Ask a volunteer to
point out the line of symmetry and the matching parts. Ask, “How can you be sure the
parts are exactly the same size?” (Cut them apart and place them on top of each other to
match size and shape.)
Define congruent figures as those having the same shape and size. Use a Geoboard® to
model making a simple shape. For example, make a square whose sides are 3 units long
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as students make an identical shape on their Geoboards®. Ask students if their shapes are
congruent to yours. (Yes) Have volunteers make a shape to be copied. Each time ask,
“Are these all congruent shapes?” (Yes) Now ask, “Are all shapes congruent to each
other?” (No) Have students create triangles that have a base 3 units long and are 3 units
tall. Students should note that all triangles are not congruent. Next, create a rectangle that
is 4 units long and 1 unit wide. Have 9 students come to the front of the room with their
geoboards. Challenge students to create and ABB pattern using the rectangles on their
geoboards.
Activity 9: Twin Day (GLE: 22)
Materials List: Shapes BLM-3 pages, glue, Popsicle® sticks, cardstock
Prior to class, run off Shapes BLM on cardstock, cut out each shape, and then glue them
on Popsicle® sticks. Position the shapes in different orientations when gluing them on the
sticks.
Give each student a shape. Have students group themselves. Discuss what attribute they
used to group themselves. Next, have students find their family of shapes. The family
should all be the same shape. Next, have students find identical twins in the family
(congruent figures) and other family members that show an example of an enlargement
and reduction. Talk about what makes a shape a reduction or an enlargement. Ask
students to look in the real world and bring in examples of enlargements and reductions.
Revisit the Vocabulary Awareness Chart BLM. Check students’ vocabulary selfawareness (view literacy strategy descriptions) of the terms congruent, similar, and
enlargement.
Activity 10: Tangram (GLEs: 22, 32)
Materials List: Grandfather Tang’s Story, Tangrams BLM or a set of plastic tangrams per
student, overhead projector, transparency of Tangrams BLM or overhead tangrams,
paper, scissors, glue
Introduce tangram shapes with the book Grandfather Tang’s Story by Ann Tompert or
tell the following story:
According to Chinese legend, a man named Tan had a square tile. The tile
fell and broke into 7 pieces (show overhead tangram pieces) that looked
like this. The pieces are called tans. Identify each piece (triangle,
parallelogram, square). Ask students to find an example of an enlargement
or reduction. Ask, “Are there any pieces that are congruent?”
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Read the story to the students, and model each figure in the book using the overhead
tangrams.
If the book is not available, tell students, “The tans can be used to represent many
different pictures (demonstrate bunny, cat, fish, etc.). Today, you will be able to make a
set of paper tangrams. Cut apart the Tangrams BLM or trace plastic tangrams and cut
them out.” Have students use the pieces to create a figure. Next, have students glue down
the pieces and name their figure. Display students’ figures on a bulletin board.
Website for tangram puzzles: http://pbskids.org/cyberchase/games/area/tangram.html
Activity 11: Repeating Pattern Block Designs (GLEs: 31, 32)
Materials List: pattern blocks, paper, crayons, examples of tessellations, class chart
Have students work in pairs with pattern blocks to create designs on a piece of paper (8 12
x 11 inches) with no space or gaps between the pieces. Everything has to fit together (like
a puzzle). As they create their designs, have them observe whether or not they have to
turn or rotate the shape in any way to make it fit. When completed, instruct students to
trace each shape. When the designs are finished, display the designs along the chalkboard
and allow each pair to explain how they made their design. (Did they have to rotate any
blocks?) Have students identify patterns they used in their designs.
Explain that a design or pattern that fits together exactly is called a “tessellation.” Bring
in some quilts to demonstrate a pattern that tessellates. Bring in as many real examples as
possible (e.g., brick walls, tile floors, stained glass windows, etc.). Use examples of
artwork by M. C. Escher to illustrate tessellating shapes. Take a walk around the school
to look at patterns in the bricks, floors, or windows. Tell the students to watch for these
special patterns in and around their homes and neighborhoods and while they are riding
in the car. Create a class chart with the patterns they observe in their environment.
Activity 12: Young Architects (GLE: 23)
Materials List: wooden building blocks, class chart from Activity 1, paper, pencils
Borrow a set of wooden building blocks of different shapes from the kindergarten
teacher. Have the students name each shape in the set (e.g., rectangular prism, triangular
prism, cube). Allow them to find the shape that it matches on the class chart created in
Activity 1, and compare number of faces, edges, and vertices.
Divide the class into four or five small groups, giving each group a set of wooden blocks
and have them make a building using 6 blocks. Direct them to change the positions of
their shapes in as many ways as possible and to just not stack the blocks.
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Allow students to inspect the structures made by all groups. As they look at a structure,
have students record how many of each block shape they see in the structure. When
groups have looked at all structures, lead a discussion in which the class compares
answers.
Activity 13: Vocabulary Connection (GLEs: 21, 22, 24)
Materials List: Vocabulary Self Awareness Chart BLM from Introduction Activity,
index cards, pencil
Students use their Vocabulary Self Awareness Chart BLM to create vocabulary cards
(view literacy strategy descriptions). This activity is done as a culminating activity on
terms used to describe geometric figures. The cards can be collected and used as an
assessment of students’ understanding. Before testing their understanding of the key
vocabulary, allow time for independent and paired review of the cards.
___________
picture
Horizontal
real example
word
A rectangle has two horizontal lines.
sentence
Activity 14: Letter Rotation (GLE: 31)
Materials List: Patterns for Rotations BLM, Capital F BLM, tape, Finish the Pattern
BLM, paper, pencil
Cut out the arrow from the Patterns for Rotations BLM. Use the arrows and demonstrate
a rotation. Tape each arrow to the board as you rotate it. Next, show students how to
record the rotation.
the figure is turning
down
left
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right
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Give each student a capital F. Have the students draw the F in its original position and
then turn the F and draw it as it rotates.
Hand out and have students complete the Finish the Pattern BLM.
Activity 15: Fractions (GLE: 2)
Materials List: Fractional Squares BLM, ruler, crayons, math learning logs
Draw five large congruent squares on the chalkboard; have a volunteer draw a line to
divide one square into two equal parts and color in one of the parts. Write 12 on the
board, and explain that the 2 on the bottom (denominator) tells how many parts in all, and
the 1 on top (numerator) tells how many parts are colored. One of two parts is colored.
1. Hand out the Fraction Squares BLM. Color in 12 , and write 12 on the side that is not
colored.
2. Continue to divide the squares on the board into equal parts, and label them to
explain 13 , 14 , 15 , and 16 . Have students to continue to color and label squares on
their Fraction Squares BLM and label accordingly.
Have students explain why 12 is greater than
logs (view literacy strategy descriptions).
1
4
of the same object in their math learning
Activity 16: Circular Fractions (GLE: 2)
Materials List: Assorted Fractions BLM, paper plates, scissors, marker, bag
Demonstrate to students how to cut paper plates into halves, thirds, fourths, fifths, and
sixths. Point out that each of the fraction pieces must be the same size as the others.
Demonstrate this by stacking the matching pieces together and/or cutting one plate into
two unequal parts. Ask, “Is this plate divided into halves? Why?” (No, the parts are not
exactly the same size.)
Make another cut for three pieces and then four pieces. Write the appropriate fraction on
each plate piece, and choose one student to put them back together, correctly telling the
number of pieces to make the whole plate. Give Assorted Fractions BLM that have been
divided into equal parts. Have students cut the circles apart, and label each part of the
circle. ( 12 , 13 , 14 , 15 , and 16 ). Put all the pieces in a grocery bag, shake them up, and pour
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them out on the floor. Choose two students to work for one minute to put together as
many circles as possible. Continue choosing pairs of students to work for one minute
until all circles are complete.
Note: If the fraction circles are too small for students to manipulate, use the paper plate
pieces instead.
Activity 17: Edible Fractions: (GLE: 2)
Materials List: raisins, shelled peanuts, M&Ms®, dry cereal (Rice Chex® or Fruit
Loops®), 1-cup measuring cups, bowls, small cups, large spoon
Divide the class into four groups, and have each group measure 1 cup of each ingredient
into a bowl and mix carefully. Draw the illustration on the board.
1 cup of cereal
Ask students, “How many cups did we use for the recipe?
What fraction of the recipe is raisins? What fraction of the
recipe is cereal?”
1 cup of M&Ms
1 cup of peanuts
1 cup of raisins
Divide the mix equally among the students in the group, and then discuss what share of
the whole they got. (1 part to the total number of students in the group)
Activity 18: Set Models (GLE: 2)
Materials List: paper, pencil, magnetic shapes, magnetic board, connecting blocks of two
colors
Have each student draw a picture of his/her family and write a sentence telling what
fractional part of the family he/she represents (e.g., I am 14 of my family). Share the
pictures with the class and save for a class book. Have six students stand at the front of
the class. Have two students raise their hands. Ask, “What fraction of the group has its
hands raised? ( 62 ). What fraction of the group is boys? Girls?”
Ask, “How many days in the school week? (5) How many days do you have art?” (1)
Have students write the fraction that tells the number of art days in the week. Continue
using other activities, such as P.E., music, and lunch. Use magnetic shapes to make
groups on the board; ask students what fraction of the whole group each shape is (e.g.,
the apples are 52 of the group, and the hearts are 53 of the group). Give volunteers a
chance to create a set, and choose someone to make a correct fraction statement about it,
writing the fractions on the board. Play a game: Have one of a pair of students use
connecting blocks of two colors to show fractions (e.g., one child says 54 of the cubes are
blue) while the other student models the fraction and writes it on the board.
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Activity 19: Fraction Towers (GLE: 2)
Materials List: per pair of students 5 red, blue, yellow, and green cubes, index cards
Put students into pairs. Give each pair 5 red, blue, yellow, and green cubes. Have students
build towers according to directions. Example: Build a tower that has six cubes. Twosixths of the tower must be red. Three-sixths of the tower must be green. The rest of the
tower is yellow. How many yellow cubes do I need?_________________
Put students into groups of 4. Have each group make a fraction tower with 8 cubes using
4 colors . Then have each group write a math story chain (view literacy strategy
descriptions) describing their tower on an index card. The first student should say. Our
tower is ___eighths _____. The next student says our tower is ____ eighths _____. The
third student says our tower is _____ eighths _______. The fourth student says our tower
is _____ eighths ______. Display all the towers. Then read the math story chains and
have students identify which tower is being described.
Sample Assessments
Performance and other types of assessments can be used to ascertain student
achievement. Following are some examples.
General Assessments:



Show the student 3-D shapes, and the student will identify them using the correct
terminology.
Students make a Shape Book by pasting pictures of 3-D objects into a booklet.
Students will put puzzles together that involve fractional pieces. (Pizza that has
been cut into fourths.)
Activity-Specific Assessments:

Activity 1: The student will create a list or chart of real-life objects of each
solid shape studied. Give students a word bank, and then hold up a 3-D shape.
The student will write down the shape's name. The student will make up solidshape riddles for others to guess. Example: I have 6 faces that are the same
size, 8 vertices, and 12 edges.

Activity 5: Give students a drawing where they must identify horizontal and
vertical lines within the figure(s).
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
Activities 7 through 10: Design a worksheet with pairs of shapes, some
similar and some congruent. The student will identify the correct category for
each pair of figures. Given a grid sheet with a figure drawn, the student will
model a congruent and a similar figure on the blank grid sheet.

Activity 14: Give students a worksheet where they will complete a pattern that
involves a rotation of a figure.

Activities 15 through 17: Give each student five minutes to do a Fraction
Scavenger Hunt around the room, looking for at least five examples of
fractions (for example, 32 of the balls are red; 13 of the windows are open, and
so on). Set up three examples without the students knowing it.
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Grade 2
Mathematics
Unit 7: Measurement in Our World
Time Frame: Approximately five weeks
Unit Description
Measurement tasks are extended to more precise measures, and standard measures for
capacity and mass are introduced and used. The focus at this grade level is on gaining a
strong feeling for selecting tools and using them to measure length, mass, and capacity.
Some conversions are made within the same system. Area of rectangular regions is
introduced. Celsius/Fahrenheit temperatures and their estimation are also added.
Student Understandings
Students select appropriate tools and units for measuring length, perimeter, capacity,
mass, and temperature. Students use the appropriate tool and measure to the nearest inch,
centimeter, foot, cup quart, liter, pound, and kilogram. They can make simple
conversions within the same system. They differentiate between area and perimeter of
rectangular regions by using the appropriate tools.
Guiding Questions
1. Can students select units and tools for measuring length, perimeter, capacity,
mass, and temperature?
2. Can students measure to the nearest unit to find length, perimeter, capacity,
and weight/mass (i.e., inch, centimeter, foot, cup, quart, liter, pound,
kilogram)?
3. Can students differentiate between and measure perimeter and areas of
rectangular regions?
4. Can students read a thermometer in degrees Celsius/Fahrenheit and interpret
temperature?
5. Can students compare units within the same system (i.e. inch shorter than a
foot, day shorter than a week, cup holds less than a quart)?
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Unit 7 Grade-Level Expectations (GLEs)
GLE # GLE Text and Benchmarks
Measurement
14.
Measure and appropriately label measures of length and perimeter (i.e., inch,
centimeter, foot), capacity (i.e., cup, quart, liter), and weight/mass (i.e., pound,
kilogram) (M-1-E)
15.
Read a thermometer in degrees Fahrenheit and Celsius and interpret the
temperature (M-1-E)
17.
Select and use appropriate tools and units to measure length, time, capacity, and
weight (e.g., scales for pounds and kilograms; rulers for inches and centimeters;
measuring containers for cup, quarts, and liters) (M-2-E)
18.
Use non-standard units to cover a given region (M-2-E)
19.
Estimate length in standard units (inch, foot, and centimeter) (M-3-E)
20.
Compare units within the same system (inch is shorter than a foot, minute is shorter
than an hour, day is shorter than a month, cup holds less than a quart) (M-3-E)
Data Analysis, Probability, & Discrete Math
28.
Generate questions that can be answered by collecting and analyzing data (D-3-E)
Sample Activities
Introduction Activity (GLE: 17)
Materials List: Measuring Tools Self-Awareness Chart BLM, pencil
Prior to beginning Unit 7, hand out the Measuring Vocabulary Self-Awareness Chart
BLM. The vocabulary self-awareness chart (view literacy strategy descriptions) will be
used to gauge students’ knowledge of tools used for measurement in Unit 7. Give each
student a Measuring Tools Self-Awareness Chart BLM and direct him/her to rate his/her
understanding of each word/symbol with either a “+” (have used it before), “√ “(haven’t
used it but know what it is), or a “ – “ (never used it and don’t know what it is). Over the
course of the unit, students are to return to their chart and add new information. The
objective is that students will replace all the check and minus marks with plus signs. At
the end of the unit students can utilize the chart to review tools used in measuring objects.
Activity 1: Measuring to the Nearest Inch (GLEs: 14, 17)
Materials List: bag of items to measure per group, transparent ruler, rulers, overhead
projector, Measuring to the Nearest Inch BLM, math learning log
Use the overhead projector to review with students how to measure to the nearest inch.
Model how to correctly place the object on “zero” of the ruler. Make sure students know
not to start on 1 of the ruler. Put students into groups. Give each group a bag with several
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items to measure to the nearest inch. Give each member in the group an inch ruler and
BLM. Have students measure each item to the nearest inch and record their findings. Go
over the BLM with students.
Have students respond in their math learning logs (view literacy strategy descriptions) to
the question: How do you measure an object with a ruler? Students can compare their
responses with a partner to reinforce their understanding of measuring with a ruler.
Activity 2: How Long is that Road? (GLEs: 14, 17, 19)
Materials List: duct tape, scissors, marker, rulers, How Long is that Road? BLM
Use duct tape to represent roads. Place tape on the floor and label the tape with street
names around the classroom. Put students into groups and have them estimate the length
of the road in feet. Have students write down the name of the street and their estimates on
their BLM. Then have students measure the road’s length to the nearest foot by having
students lay 1-foot rulers end-to-end. Have students record their findings.
Activity 3: Choosing the Best Unit (GLEs: 14, 17)
Materials List: bag of objects, ruler, blank word grid on poster or chart
Model how to use a ruler to measure objects. Prepare a “grab bag” of objects (e.g.,
ribbon, a straw, belt) to measure using a ruler. Discuss with students what would be the
best unit of measure to use to find the length of each item (inches or feet).
Create a word grid (view literacy strategy descriptions) on a poster or chart to be
displayed throughout the unit. As tools are introduced in the unit, list the tool and then
check off the attribute the tool is used to measure.
Tool
Length
ruler
Perimeter
Attribute measured
Capacity
Weight
Temperature
X
After perimeter is taught place an X under perimeter for ruler. Once the grid is
completed, allow time for students to quiz each other over the content in preparation for
tests and other class activity.
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Activity 4: Giant Step (GLEs: 14, 17)
Materials List: None
Outside, have students play the game Giant Steps as follows:
 Line players up shoulder to shoulder on one side of the playground; the leader
stands on the other.
 Show students how to take inch (baby) steps, foot (heel of one shoe to toe of
the other shoe) steps, or yard (giant) steps.
 When the leader gives an instruction, “Take 3 giant steps forward,” the
student must say, “May I?” or lose a turn.
 The leader says, “Yes, you may.”
 And the game continues until someone reaches the teacher.
 Play several rounds.
Activity 5: The Metric System (GLEs: 14, 17, 19)
Materials List: cm rulers, objects to measure, examples of polygons
Ask, “What units have been used to measure length so far?” Discuss other ways to
measure length (e.g., using metrics) and show a centimeter ruler. Give each student a
centimeter ruler and write centimeter (cm) on the board. Show students that 1 centimeter
is about the size of the width of their index fingers. Have students find 1 cm and 10 cm
on their rulers. Model how to measure using the centimeter rulers. Give pairs of students
small objects to measure (e.g., spoon, marker, sponge, comb), and have them try to find
something in the room that is about the same length. Limit metric measurement to
centimeters. Give students examples of polygons. Model how to find the perimeter of a
polygon. Have students find the perimeter of each shape in centimeters.
Activity 6: Equal Weights (GLEs: 14, 17)
Materials List: balance scale, chalkboard eraser, connecting cubes, objects to weigh
Model the use of the balance scale to make equal weights. Put a chalkboard eraser into
one pan and put connecting blocks into the other pan until the scale is balanced. Have
students in small groups estimate and discover the number of connecting cubes needed to
balance with other classroom objects.
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Activity 7: Weighing In! (GLEs: 14, 17, 28)
Materials List: balance scale, 40 beans, 2 markers, boxes marked “Weighs More” and
“Weighs Less,” objects to weigh
Model how to use the balance scale by placing 20 beans on each side of the scale to show
how the scale “balances” when both sides are equal. Next place 20 beans in one pan of
the scale and 2 markers in the other. Discuss how to compare the weight of the beans to
the weight of the markers. Label one box with “Weighs More” (than 20 beans) and label
a second box with “Weighs Less” (than 20 beans). Have students place objects found
around the room on one side of the scale pan to see which weighs more (their object or
the 20 beans), and put the objects in the correctly labeled box. Continue with each student
making predictions (estimating) and then measuring.
Activity 8: What is a Pound? (GLE: 14)
Materials List: Examples of 1-pound objects, balance scale, objects to weigh
Collect several examples of objects weighing one pound (coffee, baking soda, beans,
pasta, and powdered sugar). Allow students to handle the objects and determine what a
pound feels like in their hands. Put students into groups. Give each group several objects,
a pound item, and a balance scale. Have students estimate the weight of each object as
weighing a pound, more than a pound, or less than a pound. Have students check their
estimates using a balance scale.
Activity 9: In Order (GLEs: 14, 17, 28)
Materials List: brown paper bags, objects to weigh, balance scale, math learning logs,
large bowl, small bowls, knife
Place objects of different weight (mass) into numbered brown paper bags (one per bag);
use at least five bags; have students pick up and compare the bags, determining which are
heaviest and lightest, arranging them in that order. Have several students try this and
write down their guesses. Then have a volunteer take the objects out of the bags and put
them into the estimated correct order from heaviest to lightest. Use a balance scale to
determine if the objects are placed in the correct order. For homework, have students
bring in their favorite fruits to weigh. Have students take turns holding their fruit in one
hand and the 1-pound bag of beans in the other, guessing and recording whether the fruit
weighs about a pound. Have them weigh each fruit to check their estimates. Make a class
chart showing results as more than a pound, a pound, or less than a pound. Have students
generate questions that could be answered while looking at the data collected in the chart.
When weighing is complete, chop the fruits to make a fruit salad.
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Students use their math learning logs (view literacy strategy descriptions) to respond to
the following question: How is a see-saw like a balance scale? Allow students to compare
their responses with a partner.
Activity 10: By the Pound (GLEs: 14, 17, 28)
Materials List: 2 booksacks, bathroom scale, newspaper/supermarket flyers, scissors,
glue, chart paper
Show students two different booksacks about the same size. Ask which weighs more or
has more mass. How can they find out? Weigh each booksack using a bathroom scale.
Determine which booksack weighs more. Have students select items around the room,
and weigh them on the scale.
Have students bring in ads cut from newspapers/supermarket flyers showing foods that
are sold by the pound. Paste their ads on a chart labeled “Be A Consumer.” Then ask
questions such as these: Which costs more, one pound of apples or one pound of
bananas? How much will you pay for one pound of potatoes and one pound of carrots?
Have students generate questions that could be answered while looking at the data
collected on the chart.
Activity 11: Kilograms (GLEs: 14, 17)
Materials list: objects to weigh, 1-kilogram objects, balance scale, 1-pound items, bag of
beans
Display six objects on the table, and have a student arrange them in order from heaviest
to lightest. Write the word kilogram on the board. Tell students a kilogram is used to
weigh heavy things in the Metric System. Put an object that weighs 1 kilogram on the
balance scale. Add pound items to the balance. Students should conclude that a kilogram
is between 2 and 3 pounds. Put two pounds on one side of the balance, and then open a
bag of beans and pour about half of the bag into the balance. This should come close to
balancing the kilogram. Tell students that a kilogram is about 2 12 pounds. Give students a
list of objects and their weights in kilograms. Have students determine if the weight listed
for the object is reasonable (i.e., an orange weighs 10 kilograms, a book weighs 1
kilogram).
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Activity 12: Finding Capacity (GLEs: 14, 17, 20, 28)
Materials List: index cards, markers, a set of several containers (all groups should have
identical sets), fillers such as rice, beans, or bird seed, scoop, measuring cups, catch basin
(paper box top), Finding Capacity BLM
Explain that capacity is the amount a container will hold when it is full. Have students
brainstorm (view literacy strategy descriptions) objects that hold liquid (e.g., teapot, mug,
watering can, barrel). Write the words on index cards and have students illustrate the
words. As they finish illustrating, they should line the cards up on the chalkboard tray in
order of smallest capacity to largest capacity. Display several containers of different sizes
(e.g., tablespoon, cup, jar, bowl) and ask which will hold more. Scoop beans, seeds, or
rice into each of the containers, counting scoops as you fill the container. Tell students a
standard scoop is called a cup. Show students a measuring cup. Put students into groups.
Give each group several containers, a cup, a catch basin, and filler. Give each student in
the group a BLM with the items listed. Have students determine how many cups each
container will hold. Have students record their findings. Allow students to share their
results.
Activity 13: From Cups to Quarts (GLEs: 14, 17, 20)
Materials List: cup, quart, and liter containers, scoop, filler, 1-cup measure
Show cup, quart, and liter containers. Ask students to arrange the containers according to
size. Review the definition of capacity. Ask which holds the most and least. Use water or
beans to check predictions. Next, label the containers with the correct word and
abbreviation. Explain that the cup and quart are U.S. units of measure and that the liter is
a metric unit. Have a volunteer use a 1-cup measure to find out how many cups will fill
each container. Measure liquid (water) or dry (beans) capacity. In second grade, students
are only expected to compare units within the same system, but this activity will give
them a foundation for making comparisons between systems. Students should understand
that a liter and a quart are about the same. Have students bring in containers that are
labeled cups, quarts, or liters.
Activity 14: Comparing a Quart to a Liter (GLEs 14, 17, 28)
Materials List: quart of a sport drink, liter of water, 2 clear containers that are the same
size, food coloring
Show students a quart of a sport’s drink and a liter of water. Ask students which
container has more liquid in it. Add food coloring to the water. Find two clear containers
that are exactly alike. Pour the sport’s drink in a container. Then pour the water into the
other container. Ask students if they can tell now which one has more liquid in it. They
should be able to see that a liter is a little more than a quart.
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Use a Venn diagram - graphic organizer (view literacy strategy descriptions) to have
students compare and contrast a quart and a liter. Draw the Venn diagram on the board,
and have students copy and complete the diagram using the following terms: Metric
System, Customary System, is the same as 4 cups, and measures liquids. Once
completed, allow students to quiz each other over the information in the graphic
organizer in preparation for quizzes and other class activity.
Example: Which liquid measure is used in the metric
system, a liter or a quart?
quart
liter
Activity 15: Temperature (GLE: 15)
Materials List: Celsius/Fahrenheit thermometers, glasses, water, ice cubes
Discuss why it is important to know the temperature. Explain how to read a thermometer
by reading the number where the mercury stops. Display a Celsius/Fahrenheit
thermometer. Point out to students where the Fahrenheit scale is. Indicate that it is a
system for measuring temperature in the standard or customary measurement system, and
relate this to the fact that it is the same system as the system that uses feet and inches for
length.
Fill glasses of water at different temperatures. Have students place the thermometer in
different glasses, reading the temperatures. Explain that temperature is measured in units
called degrees and show the symbol. Ask:
 What do you notice about the numbers on the thermometers? Guide students
on how to use the scale on the thermometer, if needed.
 What happens when the temperature is higher? Lower? Be sure to use hot
water and ice water in this discovery activity.
Put a thermometer outside the window to record changes in daily temperature for a week.
Check and record the temperature outside at 8:00 A.M., 12:00 P.M., and 2:30 P.M. Help the
students graph the results.
Activity 16: Introduction to the Celsius Thermometer (GLEs: 15, 20, 28)
Materials List: Celsius/Fahrenheit thermometer
Explain to students that the metric system also has a thermometer. Remind students that
the metric system uses centimeters instead of inches and liters instead of quarts. The
metric thermometer is called a Celsius thermometer. Show students a Celsius
thermometer, and tell them that 0 degrees is freezing and 100 degrees is the temperature
at which water boils when using this type of thermometer. After demonstrations, show a
large theremometer and highlight various points. Example: Point to 35° Celsius and ask
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the students if they think the temperature would be cold or warm; would 65° C be hotter
or colder than 45° C?
Activity 17: Calendars (GLEs: 17, 20)
Materials List: calendar, Blank Calendar BLM, markers
Ask, “What day is today? yesterday? tomorrow? What month is it? Last month? Next
month?” Have each student stand as his/her birthday month is called, and record it on a
chart or calendar for the school year. Point out that a calendar shows months, weeks, and
days and that numbers on the calendar tell how many days in a month and the date of
each day. Ask students questions to have them compare units to time. Example: Which is
a longer time period: a day or a week? a month or a week? a month or a day?
Look at the class calendar and find today’s date. Ask: “What is the difference in the date
and the day? How many Wednesdays this month? What is the date of the second
Thursday? What was the first day of this month?” Distribute Blank Calendar BLM, and
have students fill in the month, year, and dates, being sure they begin on the correct day
of the week. Also, mark special dates (holidays, birthdays, coming events) on the
calendar with words/pictures. They may decorate their calendars in any way they wish to
depict the month or season. Play a riddle game as follows:



One student gives a clue and the others guess the day or date (e.g., I am the
last Friday of the month. What is my date?)
Flip through a year-long calendar, naming and repeating the months in order.
Learn the rhyme: 30 days hath September, April, June, and November; all the
rest have 31, except February, which has 28 unless it is leap year and it has
29. Alternative: Make a fist with both hands with backs of hands facing you;
then, with knuckles being mountains (31 days) and “between knuckles” being
valleys (30 days); start naming months from your left hand to your right hand.
(January is the first mountain, February is the first valley [only 28 days],
March is the second mountain, and so on).
Have students draw pictures for each month, attach a calendar, and use as gifts for
Mother’s Day, Christmas, or another holiday
Activity 18: Perimeter (GLES: 14, 17)
Materials List: rulers, objects to measure, paper, pencil, calculator, Perimeter BLM with
items filled in prior to running off for students
Discuss and explain that perimeter is the distance around the outside edge of a shape. Tell
them to look for the word “rim” inside the word “perimeter” as a reminder that rim means
edge, and perimeter is the measure of the outside edge of a shape. Ask students to name
things in the classroom that would have a perimeter (e.g., windows, chalkboard,
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bookcases, doors). Challenge students to think of a way to measure the perimeter of the
chalkboard, and have them try some of the ways suggested; discuss which units of
measure work best. Have students come up and lay their rulers end-to end to find the
length of the board. Assist students in finding the width of the board. Ask students if they
need to measure all four sides. (No, because the chalkboard is a rectangle opposite sides
must be the same length.) Label the chalkboard with the measurements, and have
students find the perimeter.
Set up stations with objects for which the students can find the perimeter (e.g., poster
board, book, computer disc, index card, piece of construction paper). Put students into
groups. Give each student a BLM with the items listed. Have them use a 12-inch ruler to
find the perimeter of each object. Students should circulate among stations recording
their findings. They may check their sums using a calculator. Discuss students’ findings
after all groups have circulated among all the stations.
Activity 19: Cover Up (GLEs: 18, 28)
Materials List: plain paper, pencil, popped popcorn, 1-inch grid paper, circular counter,
color tiles, Cover Up BLM
Use the Cover Up BLM to guide students through a DR-TA (view literacy strategy
descriptions) to help them evaluate their predictions and estimations. DR-TA is an
instructional approach that invites students to make predictions, and then check their
predictions during and after the assignment. DR-TA (Directed Reading – Teaching
Activity) provides a frame for self-monitoring because students should pause throughout
the assignment to ask students questions. Allow students to adjust their estimations or
predictions as they go through the activity.
Hand out the Cover Up BLM. Have students answer questions 1 and 2. Next, have each
student draw the outline of his/her hand on a piece of plain paper, and then cover the
inside of the outline with popped popcorn. Ask: “How many pieces did you use?”
Compare results. Have students record the actual number on their BLM. Students might
conclude that they used different amounts due to the different sizes of the drawings. Now,
have students draw a 4”x 6” rectangle on 1- inch grid paper. Have students answer
questions 3 and 4. Next cover the rectangle with popcorn. Ask: Did everyone use the
same number of pieces of popcorn? (No) Did you cover the rectangle completely? (No)
Make the connection that this time the drawings were the same, but the amount of
popcorn was still not the same. Have students answer questions 5 and 6. Next, try
covering the rectangle with circular counters and ask the same questions. Have students
answer questions 7 and 8. Last, cover the rectangle with square tiles. First, guess
(estimate) the number of tiles you will need. Ask, “How many tiles did you use?” (24)
How many tiles did the other students use? (24) Which unit covered the rectangle best?
Explain: The number of square units needed to cover a shape is its area. The area is
measured in square units. Have students answer question number 9 and discuss their
answers.
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Activity 20: Cover This (GLEs: 14, 18)
Materials List: index cards, construction paper, color tiles
Have students estimate how many square inch tiles it will take to cover an index card and
a sheet of construction paper. Record their estimates. Next, put students into groups and
have them cover the index card with square tiles. Have students label the length and the
width of the card (3 inches x 5 inches). Discuss students´ results. Ask if anyone would
like to adjust his/her estimate for the piece of construction paper. Ask students to share
different ways they could find the number of tiles it would take to cover the construction
paper (i.e., cover the entire piece with tiles, divide the paper in half, cover 12 , and then
double the number of tiles; use the index card and trace it on the paper since we know it
takes 15 tiles per index card). Have students find the area of the piece of construction
paper. Discuss their results.
Activity 21: Can you create this? (GLE: 14)
Materials List: computer
Using a computer program, create a template of a one-inch square. Teach students how to
copy, paste, paint, and move the square. Have students create designs according to your
specifications. Example: Create a design that has an area of 5 square units and a
perimeter of 12 units. If a computer is not available, give students inch grid paper to
complete the activity.
Activity 22: Professors Know-it-All (GLEs: 14, 17)
Materials List: measuring tools, objects to measure
Put students into groups of 4. Each group will be called to the front of the room to see if
the group can be labeled professors know-it-all (view literacy strategy descriptions). A
member from another group chooses an object. One member of the group must describe
what attribute of the object could be measured then another member chooses the tool that
should be used to measure it. Another member of the group demonstrates how to measure
it. Repeat the process until each group has had a turn. Use simple props such as ties,
mortar boards, and clipboards to give the know-it-alls the look of “experts.”
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Sample Assessments
Performance and other types of assessments can be used to ascertain student
achievement. Following are some examples.
General Assessments



Portfolio: As the student encounters different units of measure, have him/her cut
out pictures and glue them to index cards listing the different attributes that can be
measured. For a picture of a truck, the student could list the length of the truck,
the height of the truck, or the number of scoops of dirt the bed of the truck could
hold.
Journal Entry: The student will explain the difference between the perimeter and
area of an object.
Calendar: Have students make a calendar and put holiday stickers on the
appropriate dates. The student will draw an outfit that he/she could wear during
that month and answer a series of questions pertaining to the calendar.
Activity-Specific Assessments

Activity 2: Prepare a list of classroom objects for the student to measure. There
should be two blanks following the name of each object. First, the student will
estimate the length of the object in inches, centimeters, or feet, and then measure
the objects and record the true measurement. Allow the student to explain his/her
estimates and measurements.

Activity 7: Observe each student’s accuracy as he/she chooses an object which
has the same weight as another object and tests the weights using a balance scale.

Activity 8: Using a food scale, the student will select items he/she thinks weigh
about 1 pound and measure to check. The student will sort the items into groups
of “about the same as,” “more than,” and “less than” a pound.

Activity 9: Observe each student weighing and recording the weight of a chosen
fruit on the chart. The student will write 3 sentences comparing his/her fruit’s
weight with that of others.
Example: My apple is heavier than the banana.
My apple is lighter than the orange.

Activity 18: Provide students with several outlined shapes. The student will
measure the perimeter of each shape in inches and centimeters.
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
Activity 20: The student will use 12 square tiles to form at least 6 different
shapes. The student will trace the shapes and create a “Square Units Zoo” by
elaborating on the shapes, and adding details and color. Save the pictures for a
class mural or book.
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Grade 2
Mathematics
Unit 8: Extending Number Patterns through 100s and 3-Digit Operations
Time Frame: Approximately three weeks
Unit Description
This unit deals with extending the number system through 999, focusing on developing a
deep understanding of 100s, 10s, and 1s in all of their representations. Extensions also
include patterns and 3-digit problems without regrouping.
Student Understandings
Students demonstrate a command of place value and numeration concepts by providing
representations of expanded, standard, written, and verbal forms of numbers. Students
model numbers with concrete materials.
Guiding Questions
1. Can students handle all representations of numbers through 999, including
with objects?
2. Can students make reasonable estimates and perform rounding tasks?
3. Can students perform addition and subtraction with 3-digit numbers without
regrouping?
4. Can students use number sentences to represent real-life problems involving
addition and subtraction?
Unit 8 Grade-Level Expectations (GLEs)
GLE # GLE Text and Benchmarks
Number and Number Relations
1.
Model, read, and write place values for numbers through 999 in word,
standard, and expanded form (N-1-E)
3.
Make reasonable estimates of the number of objects in a collection with fewer
than 100 objects (N-2-E)
5.
Read, write, compare, and order whole numbers through 999 using words,
number lines, and models (N-3-E) (N-1-E)
8.
Recognize, select, connect, and use operations, operational words and symbols
(+, ) for addition (join, part/part/whole) or subtraction (take away,
comparison, missing addend, and set/subset) situations (N-6-E) (N-5-E)
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9.
10.
Add and subtract 1- and 2-digit numbers (N-6-E) (N-7-E)
Round numbers to the nearest 10 or 100 and identify situations in which
rounding is appropriate (N-7-E) (N-9-E)
Algebra
12.
Use number sentences to represent real-life problems involving addition and
subtraction (A-1-E) (A-2-E)
13.
Find the missing number in an equation involving addition or subtraction (e.g.,
# + 4 = 7, 8 - # = 3) (A-2-E) (N-4-E)
Patterns, Relations, and Functions
30.
Recognize, extend, create, and explain patterns of addition and subtraction as
represented in charts and tables and in varied forms of skip-counting (P-1-E)
(P-2-E)
32.
Recognize and apply patterns in problem-solving in other content areas and
real-life situations (P-3-E) (N-9-E)
Sample Activities
Activity 1: Body Math (GLEs: 1, 5)
Materials List: sheets of paper labeled 1s, 10s, 100s, Base 10® blocks, Place Value Mat
BLM, poster paper, 3 bean bags
Have students brainstorm and make a list of 3-digit numbers used in school, at home, and
in the neighborhood (house number, oven temperature, or page number in a book).
Divide the class into two teams. Put three labels (1s, 10s, 100s) about a foot apart on the
floor in front of the room. Write a 3-digit number on the board. Have students on the first
team select Base 10® blocks that represent the number. If the number is 324, three
students stand behind the 100s label holding flats, two stand behind the 10s label holding
rods, and four stand behind the 1s label holding unit cubes. The second team checks their
answer and then takes a turn modeling a different 3-digit number. Continue playing
several more rounds.
Put students in pairs. Use the Place Value Mat BLM and Base 10® blocks to model for
the students forming 2- and 3-digit numbers. Write several numbers on the board, and
have student partners model them on their BLM. Write 3 digits on the board, and have
students use the blocks and place value mats to make as many 3-digit numbers as they
can using those 3 digits. Record results and compare with other partners.
Play a game such as the following:
 Put students into groups of 3 or 4
 Divide a large piece of poster paper into 10 sections (squares) numbered 0–9.
 Label 3 different colored bean bags 1s, 10s, and 100s.
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


Have a volunteer toss each beanbag onto a number on the board.
Have partners write the number and make a model with Base 10® blocks as
quickly as possible.
The first group to build and write their number in word, standard, and
expanded form correctly wins.
Activity 2: Build It! (GLEs: 1, 5)
Materials List: Base 10® blocks, Place Value Mat BLM, paper, pencil
Have students practice using the Base 10® blocks to build numbers according to specific
instructions such as these: Use your mat and blocks to build a number that has more 100s
blocks than 10s blocks. Build a number that has more 1 blocks than 100 blocks. Build a
number that has the same number blocks in the 1s and 100s. Write some of the 3-digit
numbers on the board and point out that the value of the number depends on its place. For
example: a 3 in the 10s place has a value of 30 (3 10s) and a 3 in the 100s place has a
value of 300 (3 100s). Continue building 3-digit numbers with Base 10® blocks and place
value mat, writing the number on their paper and telling the value of each digit of the
number. Then write the number in word and expanded form.
Activity 3: Math Chains (GLEs: 1, 5, 8, 12)
Materials List: Hundreds Chart BLM, transparency of BLM, calculators, paper and pencil
Use the transparency to review how to move on a hundreds chart. Have students use the
Hundreds Chart BLM to practice Mental Math Chains of addition by listening as a series
of instructions are read. They may use a scrap piece of paper to write the final answer.
For example: Start with 36, add 10, subtract 1, and add 20. What is the number? Start
with 73, subtract 20, add 7, take away 50. What is the number?
Put students into groups of 4. Have students compose their own Mental Math story
chains (view literacy strategy descriptions) for others to solve using a hundreds chart.
Each person in the group uses the hundreds chart to follow the clues as each person gives
his/her clue. The first person in the group writes, Start with the number _________. The
second person writes, add/subtract _________. The third person writes, add/subtract
___from the number. The fourth person writes, add/subtract ______ from the number.
The first person writes, What number did you end up on? The group discusses the answer
and writes the answer on a separate sheet of paper. The group then uses a calculator to
check the answer. Groups exchange their math story chains with other groups and solve.
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Activity 4: Play a Game: Make 100 (GLEs: 1, 5, 8, 9, 12)
Materials List: paper, pencil, math learning log
.
Draw a large circle on the board, and place 2-digit numbers randomly inside it so that
when 2 are added, they will equal 100. Be sure to include some pairs of numbers that will
NOT equal 100 and also include three numbers inside the circle so students can discover
using 3 numbers to add up to 100 (Example 30, 20, and 50). Students should work fast
and can use numbers more than once. After two minutes, call time and compare answers.
Play again to increase speed.
Give students 5 minutes to write down as many 2-digit plus 2-digit numbers that have a
sum of 100 in their math learning logs (view literacy strategy descriptions). Have
students share their findings.
Activity 5: Rounding to the Nearest Hundred (GLEs: 5, 10)
Materials List: Place Value Spinner BLM, colored index cards, clothesline, clothespins,
white index cards, markers, spinner, pencil, paper clip, 3-digit number cards with a digit
underlined
Write the numbers 0-1000 counting by 100s on colored index cards. Hang the numbers in
order on a clothesline. Give each student an index card and have them write a 3-digit
number on their card. Call on each student to come up and determine which hundred
his/her number is closest to. Have them pin their number under the hundred it would
round to. Continue until all students have had a turn.
Put students into groups. Hand out the Place Value Spinner BLM. Have a member from
the group choose a 3-digit number card. Another member from the group spins the
spinner. The group must do whatever the spinner indicates.
Example: Student 1 selects the number card with 453 written on the card. The second
student spins expanded form on the spinner. The group gets together and writes out 400 +
50 + 3. The group has 30 seconds to agree, and then someone writes the answer on the
board. If they are correct, they earn the title professor know-it-alls (view literacy strategy
descriptions). Then another group is chosen. Play continues until all groups have had a
turn. Use simple props such as ties, mortar boards, and clipboards to give the know-it-alls
the look of “experts.”
If time permits allow groups to challenge one another. Have each group write 4
challenging questions or statements, one for each of the 4 categories on the spinner
(rounding, word form, expanded form, and place value).
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Examples of challenge statements that students could write:
Round it – Find a number that will round to 500. A member from the know-it-alls
group says, “472.”
Word Form – A member from the challenge group writes the word form of a
number on the board. A member from the know-it-alls group must write the
standard form.
Place Value is spun – A member from the challenge group says, “Write a 3-digit
number where the hundreds place value is 200.” A member from the know-it-alls
group writes 269 on the board as an example.
Expanded Form – A member from the challenge group writes a 3-digit number in
expanded form on the board. A member from the know-it-alls group has to write
the standard form of the number.
Note: If place value is spun on the spinner, the group must identify the value of
the underlined digit.
Select two groups to come to the front of the room. Flip a coin to determine if a group
wants to challenge a group or answer the questions of the other group. If the group
answers all 4 challenges correctly then it gets to stay up in front of the room and another
group may challenge it to see if it is really a group of professor know-it-alls. Play as long
as time will permit. Do not use the spinner for this part of the activity. Groups challenge
each other with their 4 questions.
Activity 6: Round to the Nearest Dollar (GLEs: 5, 8, 10)
Materials List: list of prices
Before doing the activity, discuss with the students situations in which rounding is
appropriate. Rounding may be used in situations such as deciding if they have enough
money to buy something. For example: I am at the grocery store and I pick up three
items priced as follows: $2.22, $.78, and $1.68. If I wanted to know about how much
these items will cost, I could add all the prices with a paper and pencil; try to add them in
my head; or I could estimate by rounding to the nearest dollar, like this: $2.00, $1.00,
and $2.00. Now, I can easily figure that I will need about $5.00 to pay for my items. This
is a good estimate of the exact amount of $4.68. Give students a list of prices and have
them round to the nearest dollar. Then have students find the sum of the list mentally.
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Activity 7: Finding Sums and Differences (GLEs: 5, 8, 10)
Materials List: Base 10® blocks, 60 index cards
Using Base 10® blocks, have a student model 10 + 20 and 100 + 200, as another student
writes the appropriate addition sentences on the board. Repeat the process using
subtraction problems such as 30–20 and 300–200. Explain that rounding makes addition
and subtraction of 3-digit numbers easier.
Example: Patrick has 236 baseball cards and 113 Pokemon cards. About how many cards
does Patrick have in both of his collections? Tell students to add 236 and 113 by
rounding each number to the nearest 100 and then add the numbers.
Demonstrate: Round 236 to 200 and 113 to 100. Now, it’s easy to add 200 and 100
mentally to get 300. So, Patrick has about 300 cards in his collections. Use a number line
to move forward or back when rounding 10s and 100s.
Play The Estimation Game as follows:
 Have two or three students write 2-digit numbers on 20 index cards each.
 Shuffle all the cards and place them face down in a deck.
 Turn the top card over next to the deck.
 Have the students take turns flipping over a card and estimating the sum of
some or all the face-up cards, trying to find a combined estimated sum of 100.
 If correct, the student keeps the cards. If not correct, leave the card face up
with other unused cards.
 The winner is the student with the most cards after all the cards are turned
over.
 As students progress in skill, rewrite the cards with 3-digit numbers to find a
combined estimated sum of 900.
Activity 8: Money Problems (GLEs: 1, 8, 10, 12)
Materials List: play money, Place Value Mat BLM, school supplies with prices marked
(If students do not have access to grocery store circulars, ask other teachers/neighbors to
save their papers.)
Model adding/subtracting money (dollars and cents) to practice 3-digit problem solving.
Use play money and Place Value BLM as well as the standard form with $ and the
decimal to show addition and/or subtraction. Follow the same steps as with other 3-digit
numbers (1s, 10s, 100s).
For homework, assign students 5 grocery items, and have them find the prices from
different stores’ advertisements or by looking at prices at home. Have them bring their
lists to school and compare prices with other students. If the prices are different, subtract
to find how much difference, and decide which is the best deal. Review estimation of
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sums and differences through rounding to the nearest 100 or dollar. Give extra attention
to students who look at the 1s instead of 10s when rounding to the 100s place. Give small
groups of students a list of school supplies with prices noted. For example:
 crayons–$1.98
 ruler–$.49
 glue–$.98
 notebook–$3.95
 pencils–$2.98
 scissors–$2.00
Have students estimate the costs, and then list all the combinations of items that can be
bought for $10.00 or less. Compare their answers with other groups.
Activity 9: All Mixed Up! (GLEs: 8, 13)
Materials List: 2 sets of digit cards per pair
Use two sets of digit cards in small groups to solve a brainteaser like the following
example.
Write 423  650  479 on the board. Explain that the digits of the addends are
mixed-up.
Ask students to see if they can rearrange the cards to make the addition correct.
Activity 10: Twenty-one (GLEs: 8, 13)
Materials List: paper, pencil
Let students play the game, Twenty-one.
 Using the digits 6, 7, 8, or 9, try to find all the ways to get 21 by subtracting
2-digit numbers.
 You may use each digit more than once in a problem (e.g., 99–78=21).
 See if you can find 6 different ways to find the difference of 21.
Activity 11: Place Value Charts (GLEs: 30, 32)
Materials List: Place Value Mat BLM, chart paper, marker
Write three 3-digit numbers on the board, and have partners work together to model the
numbers on the Place Value Mat BLM (e.g., 350, 322, 416). Ask: Which of these
numbers is the greatest? (416). How do you know? (It has 4 in the 100s place and the
others have 3 in the 100s place.) Ask: Which of these numbers is the least? (322). How
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do you know? 350 and 322 both have three hundreds so I go to the next place value. 350
has more tens than 322, so 322 is the smaller number.
Draw a table on a poster with 3-digit numbers listed in the center column (e.g., 158, 256,
783, 809, 540, 428) and a column to the left labeled 100 less and a column to the right
labeled 100 more. Have volunteers fill in the table, writing the correct standard numbers.
Have students look for patterns in the table.
100 less
3-digit number
100 more
Activity 12: Estimate! (GLE: 3)
Material List: poster, marker or stickers
Show students a poster with 100 or fewer circles on it for about 30 seconds (just don’t let
them count the circles). Have students discuss how they could estimate how many circles
are on the poster. Section off one part of the poster by drawing square or rectangle around
a set of circles. Count how many circles are in that section. Use that section as a
benchmark. Give students another brief look at the circles and allow them to adjust their
estimates. Section off the rest of the poster with other squares or rectangles the same size
as the benchmark and estimate the number of circles on the poster.
Activity 13: Solve It! (GLE: 12)
Materials List: paper, pencil, computer
Put students into pairs. Have each student do a RAFT (view literacy strategy descriptions)
writing assignment. Instruct students that they are to write a story problem that involves
adding a 2-digit plus 2-digit number or 3-digit plus 3-digit number.
R- pretend they are the author of a math textbook
A – the audience for the textbook is second grade students
F – write a word problem
T – adding a 2- digit to a 2-digit number or a 3-digit to a 3-digit number should be
task
After students share their RAFTs with the class and their problem is checked for accuracy
and logic, have students type their problem on the computer. They may insert graphics if
they are available and then print their problems. After all problems are printed, copy them
and make a textbook for all.
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Sample Assessments
Performance and other types of assessments can be used to ascertain student
achievement. Following are some examples:
General Assessments



Give the student one representation of a number, and the student will give at least
two other ways to represent the number. Example: Model a number, then the
student will give the standard form, expanded form, or word form of that number.
Observe as the student uses different problem-solving strategies such as guess and
check, draw a picture, make a chart, or phone a friend to find the answers to math
story problems.
Provide the student with a chart or table with some patterns that use addition and
subtraction of a constant (i.e., skip counting forwards and backwards) and have
him/her “find” the patterns.
Activity-Specific Assessments

Activity 4: Place several 2-digit numbers that have a sum of 100 randomly inside
of a rectangle. The student will find as many number pairs with a sum of 100 as
he/she can.

Activities 4 and 5: Give the student a list of items with their prices. The student
will round each price to the nearest dollar. Next, the student will find how many
items he/she could buy for $10.00.

Activity 7: When given 10 addition/subtraction problems with 3-digit numbers by
the teacher, the student will estimate by rounding to find the answer. The student
should round to the nearest hundred.

Activity 11: Observe as the student builds and identifies 3-digit numbers using
Base 10® blocks. The students will write the number in word form and expanded
form. When given a 3-digit number with values underlined, the student will
identify the value of each underlined digit.
Grade 2 MathematicsUnit 8Extending Number Patterns/3-Digit Operations 107