Place Value – Grade Two
Ohio Standards
Connection
Number, Number Sense
and Operations
Benchmark B
Recognize, classify,
compare and order whole
numbers.
Indicator 1
Use place value concepts
to represent, compare and
order whole numbers using
physical models, numerals
and words, with ones, tens
and hundreds. For
example:
a. Recognize 10 can
mean “10 ones” or a
single entity (1 ten)
through physical
models and trading
games.
b. Read and write 3-digit
numerals (e.g., 243 as
two hundred fortythree, 24 tens and 3
ones, or 2 hundreds
and 43 ones, etc.) and
construct models to
represent each.
Mathematical Processes
Benchmark F
Draw pictures and use
physical models to
represent problem
situations and solutions.
Lesson Summary:
In this lesson, students use physical models to represent and
demonstrate place value concepts by using base-ten blocks and
hundreds charts. They compare numbers to see which number is
smaller or larger and put numbers in order from smallest to
largest.
Estimated Duration: Three hours
Commentary:
Place value concepts are introduced in first grade. In second
grade these concepts are expanded by using physical models to
create multiple representations of one number through trading.
Students who understand place value see tens and hundreds as
single entities that are represented by its place in a number. For
example, when finding ten more than 33, they count up by ten
and change the digit in the tens place. Students who are
developing place value concepts will count on by one, ten times
to find ten more than 33. Provide opportunities to develop this
connection through building models and comparing the models to
the number. Develop this understanding over time and with
multiple activities in centers and through class instruction.
Pre-Assessment:
· Have each student write the numerals for (6, 23, 85, 14, and 8)
and then use base-ten blocks to build a model of the number.
· Give a hundreds chart to each student. Read aloud the clues
and directions below to the students.
1. I have a 1 in the tens place and a 5 in the ones place.
Circle it with a red crayon.
2. I have a 3 in the tens place and a 7 in the ones place.
Circle it with a blue crayon.
3. I have an eight in the tens place and a 0 in the ones place.
Circle it with green.
4. I have a 2 in the ones place and a 6 in the tens place.
Circle it with yellow.
5. I have a 9 in the ones place and a 4 in the tens place.
Circle it with a purple crayon.
6. I am one more than 79. Circle the digit in the tens place
with a black crayon.
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Place Value – Grade Two
Scoring Guidelines:
Use Attachment A, Pre-Assessment Checklist, to record assessment results. If the student can
perform the activity, indicate with + and if the student is unable to perform the activity, indicate
with –. Brief anecdotal records are evidence of student learning and can be used as narratives for
interim reports, conferences and grade cards.
Post-Assessment:
· In a whole group, give students self-adhesive notes. Say a group of numbers and have the
students write the digit(s) for the numbers and then put the numbers in order from smallest to
largest. For example, (84, 17, 56), (104, 9, 23), (64, 46, 406).
· Using a set of the previous numbers, students circle the number in the hundreds place with a
green crayon, the number in the tens place with a blue crayon and the number in the ones
place with a red crayon. Students hand-in their papers for evaluation.
· Students take 2 flats, 4 towers and 3 cubes from their self-sealing plastic bag. They write the
digits in a three column format to show the amount of hundreds, tens and ones in the number
and then write the number 243 on their paper.
· Repeat the process for the following numbers.
9 towers, 1 cube
(91)
3 flats, 5 cubes
(305)
4 flats, 6 towers, 7 cubes
(467)
8 towers, 2 cubes
(82)
1 flat, 8 cubes
(18)
· Students write the number 162 and then represent 162 with flats, towers and cubes.
· Repeat with the numbers 75, 329, 260, 38 and 407.
Instructional Tip:
If hundred number blocks are not available, make a worksheet using the hundreds, tens and ones
with ink stamps, or draw the flats, towers and cubes on card stock and cut them out.
Scoring Guidelines:
Use Attachment B, Post-Assessment Checklist, to record assessment results. If the student can
perform the activity, indicate with + and if the student is unable to perform the activity, indicate
with –. Brief anecdotal records are evidence of student learning and can be used as narratives for
interim reports, conferences and grade cards.
Instructional Procedures:
Part One – Blocks Represent Numbers
1. Direct the students to place 15 towers from the base-ten blocks on their desks. Ask questions
about the representation such as;
· What number is represented by the 15 towers? (150)
· How do you know? (Count by tens)
· Can you write the number for the representation?
2. Have the students make multiple representations of 150 using the base-ten blocks. Models
may include: one hundreds flat and five towers, one hundreds flat four towers and 10 unit
cubes, etc. Observe students as they create the models. Challenge students to make multiple
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Place Value – Grade Two
models. Assist students with trading activities to make different models. If students can not
trade one tower for 10 unit cubes or ten towers for a hundreds flat, provide intervention to
develop relationships between the different blocks. Note the different models that students
create.
3. Select several students to share their models on the overhead and explain why the model
represents 150. Choose a variety of models to encourage creative ways to think about
numbers and to develop number sense. Draw pictures of the different representations on the
board and have students draw them in a journal.
4. Repeat the first step with 12 towers; 8 towers; 24 towers.
5. Present the problem situations below, have students model the situation with base-ten blocks,
determine the solution and explain how they determined the solution. Observe the models
and provide assistance as necessary. Encourage the use of alternate models that represents
140 and 200.
· Jimmy has 14 pages of baseball cards. There are 10 cards on each page. How many
baseball cards does Jimmy have? (140)
· Suzi has 20 pages of stickers in her notebook. There are 10 stickers on each page. How
many stickers does Suzi have? (200)
6. Give each student a hundreds chart. Have the students point to the number 64 and then build
the number with base-ten blocks. Have students share their models and draw pictures of 64 in
their journals.
7. Ask students to find the number that is 10 more than 64. Observe the methods students use.
Students having a good understanding of place value will automatically count up a ten to 74
or change only the tens digit in the number 64. Students who are developing place value
skills will likely count on by ones to ten. Ask students for the answer and to explain how they
found the answer. Use the base-ten blocks to show that adding one tower, changes only the
digit in the tens place.
8. Select additional numbers and have students identify ten more, ten less, twenty more, etc.
Observe students as they find the answer. Reinforce the idea of adding or subtracting tens,
not adding on or taking away by ones.
9. Now have the students find the number 14 on the chart and compare it to 64. (14 is smaller,
the 4 digit stays the same, the 6 digit decreased to 1, 14 is 5 rows away from the 6, or 50 less
or 10 towers less.)
10. Repeat this process with other numbers for additional student practice.
Part Two
11. On the overhead place two models of 100: a flat and a group of 9 towers and 10 cubes.
Students recognize that these are both models of 100. Ask
· How are the models of 100 alike?
· How are the models of 100 different?
· How many other models of 100 can you demonstrate/describe?
Instructional Tip: Reinforce the relationships between
· the cubes and the tower (10 cubes = 1 tower)
· the towers and the flat (10 towers = 1 flat)
· the cubes and the flat (100 cubes = 1 flat).
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Place Value – Grade Two
12. Show a model of 100 (a flat) and 99 (9 towers and 9 cubes). Ask
· Which model represents a larger number? How do you know?
· Nine is larger that zero and larger than one. Why isn’t 99 larger than 100?
13. Display a model of 291 using 2 flats, 9 towers and 1 cube on the overhead projector. Ask
questions about the representation such as;
· What number is represented by the towers? (90)
· What number is represented by the flats? (200)
· What number is represented by the unit cube? (1)
· How do you know?
· Can you say and write the number for the representation? (291)
· Does 200 + 90 + 1 = 291? Why?
· Does 200 + 80 + 11 = 291? Why?
14. Have the students make multiple representations of 291 using the base-ten blocks. Models
may include: two hundreds flat and eight towers, eleven unit cubes or one hundreds flat
seventeen towers 21 unit cubes, etc. Observe students as they create the models. Challenge
students to make multiple models. Assist students with trading activities to make different
models.
15. Select several students to share their models on the overhead and explain why the model
represents 291. Choose a variety of models to encourage creative ways to think about
numbers and to develop number sense. Draw pictures of the different representations on the
board and have students draw them in a journal.
16. Repeat steps 13 – 15 with additional three-digit numbers as needed.
17. Have the students represent the number 214 with the base-ten blocks (2 flats, 1 tower, 4
cubes). Tell the students to increase 214 by 100. Ask students questions about the models
such as:
· Can you describe ways that 100 could be represented by the blocks? (100 cubes, 10
towers or 1 flat)
· Which way is the easiest to use and why? (One flat is easier that counting out the other
blocks.)
· What blocks do you have now? (3 flats, 1 tower and 4 cubes)
· What number does these blocks represent? (314)
· Which digit changed in the number? (The 2 became a 3)
· Why did the 2 change? (The number was increased by 100.)
18. Have students build additional three-digit numbers with the base-ten blocks. Ask them to
identify numbers that are 100 more, 100 less, 10 more, 50 less, etc.
19. Show 5 flats, 2 towers and 4 cubes on the overhead projector. Students write the number that
represents and explain their answer by focusing on the value of the digits.
20. Distribute calculators to students and place with partners. Have them type in the number 456.
Tell them that to make a new number so there is a zero in the tens place. The other numbers
should remain the same. Have them use what they know about place value to determine
which digit has to change. Observe the methods students use. Students who are still
developing place value skills may identify 5 in the tens place and then try to subtract 5 to get
the zero in the tens place. They will find this does not work. Ask questions to guide them to
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Place Value – Grade Two
understand the 5 actually represents 50. Do not give them the answer. Engage students in
thinking about the place value.
21. Continue to provide additional three-digit numbers and challenge students to use place value
skills to solve tasks like the one in step 20.
Part Three
Make sets a set of digit cards (0-9) for the activity in this part of the lesson.
21. Explain the game to the students.
a. They are to draw three boxes on a sheet of paper. Model this for students on the board.
Tell them to make the boxes small enough so the game can be played several times on the
sheet of paper.
b. Tell students that three digit cards will be drawn and they are to make a number with the
three digits. The number they make will be based on a challenge. The challenge will be
given before the digit cards are drawn. Sample challenges include; make the largest
number using the three-digits, make the smallest number using the three-digits, make a
number larger than 400, make a number with less than 6 in the tens place.
c. Explain that each digit must be drawn in a box right after it has been drawn. After
everyone has placed the digit in one of the three boxes, the second digit will be drawn.
Do not use the same digit twice in one game.
22. Play the game with students several times. It may be necessary to model the game the first
time. Ask questions about the numbers created, such as:
· What does the 5 in the number represent? How do you know?
· What could you do to the number to get a zero in the hundreds place?
· Can you order the different numbers made by the class from smallest to largest? Allow
the students to use models to prove which number is the largest.
Differentiated Instructional Support:
Instruction is differentiated according to learner needs, to help all learners either meet the intent
of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified
indicator(s).
· In a learning center, students practice what they learned about place value. Flats, towers, and
cubes are put in labeled (numbered) plastic bags. Students determine the number represented
by the hundreds, tens and ones in the bag and record that number on their paper.
· Students play the Hundreds, Tens and Ones Game in pairs. Each student has a worksheet
labeled hundreds, tens and ones. The first player draws a card from the deck of digit cards 09 turned upside down on the desk and decides to put the card in the hundreds, tens or ones
place. The second player takes a turn. Each player continues until the 3-digit number is
complete. The player with the biggest number wins the game.
· After reviewing the spelling of the number words students write a number using digits,
represent the number using blocks, write the number in expanded form and write the number
using words.
· Students play Place Value Concentration. Make cards with the number written in words (two
hundred thirteen), the numeral written (213), the picture for the number 213 (2 flats, 1 tower
and 3 cubes), and the expanded notation (200 + 10 + 3). Students turn over two cards, trying
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Place Value – Grade Two
to make a match. If the two cards represent the same number, this is a match. The student
keeps the cards and takes another turn. If the cards do not match, the cards are returned face
down and the other player takes a turn. Continue playing until all of the cards are used. The
player with the most matches is the winner.
Extensions:
· Have students play the Hit 100 game in pairs. Each student draws six cards from a set of 40
digit cards numbered 0-9. The student uses the cards to make two 2-digit numbers whose
sum is close to 100. The student who is the closest to 100 gets a point. The first student who
gets five points wins.
· Make a chart to represent numbers four different ways.
Number
63
Number word
Sixty-three
Drawing
Expanded Form
60 + 3
Home Connections:
· Students take turns wearing a pedometer. When they get home, the parents ask how many
steps they took. What number is in the tens place? What number is in the ones place? What
number is in the hundreds place?
· Students write a riddle giving clues to the number in the ones, tens and hundreds place.
Parents have to guess the number.
· Paper flats, towers and cubes made from cardstock provide students with a “take-home”
version of the Guess My Number game (explained in Part Two of Instructional Procedures).
Interdisciplinary Connections:
Content Area: Social Studies
Standard:
History
Benchmark: B. Use a calendar. Discuss chronology of the 1700s, 1800s, and 1900s. Make a
time-line. Put the dates in order.
Materials and Resources:
The inclusion of a specific resource in any lesson formulated by the Ohio Department of
Education should not be interpreted as an endorsement of that particular resource, or any of its
contents, by the Ohio Department of Education. The Ohio Department of Education does not
endorse any particular resource. The Web addresses listed are for a given site’s main page,
therefore, it may be necessary to search within that site to find the specific information required
for a given lesson. Please note that information published on the Internet changes over time,
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Place Value – Grade Two
therefore the links provided may no longer contain the specific information related to a given
lesson. Teachers are advised to preview all sites before using them with students.
For the teacher: Overhead projector, set of base-ten blocks, construction paper
For the student:
Set of base-ten blocks for each pair, mathematics journals, hundreds charts
Vocabulary:
· digit
· hundred
· ones
· place value
· tens
Technology Connections:
Have students work in pairs. One student keys a 3-digit number in the calculator. The other
student identifies the digits in the ones, tens or hundreds place.
Research Connections:
Burns, Marilyn. About Teaching Mathematics: A K-8 Resource.. Sausalito Ca.: Math Solutions
Publications, 1992.
Attachments:
Attachment A, Pre-Assessment Checklist
Attachment B, Post-Assessment Checklist
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Place Value – Grade Two
Attachment A
Pre-Assessment Checklist
Student
Writes a
given 1-digit
number.
Writes a
given 2-digit
number.
Writes a
given 3-digit
number.
Points to
correct
number on
100 number
chart.
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Place Value – Grade Two
Attachment B
Post-Assessment Checklist
Student
Writes twodigit
numbers
Writes
three-digit
numbers
Orders
numbers
Identifies
tens place
Identifies
hundreds
place
Identifies
two- and
three-digit
numbers
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