Accomack County Public Schools
Elementary Mathematics
Third Grade
Curriculum Guide
STANDARD 3.1
3.1
STRAND: NUMBER AND NUMBER SENSE
GRADE LEVEL 3
The student will
a) read and write six-digit numerals and identify the place value and value of each digit;
b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and
c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal
to).
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)





The structure of the Base-10 number system is
based upon a simple pattern of tens, where each
place is ten times the value of the place to its right.
This is known as a ten-to-one place value
relationship.
The structure of the Base-10 blocks is based on
the ten-to-one place value relationship (e.g., 10
units make a long, 10 longs make a flat, 10 flats
make a cube).
Place value refers to the value of each digit and
depends upon the position of the digit in the
number. In the number 7,864, the eight is in the
hundreds place, and the value of the 8 is eight
hundred.
Flexibility in thinking about numbers — or
“decomposition” of numbers (e.g., 12,345 is 123
hundreds, 4 tens, and 5 ones) — is critical and
supports understandings essential to multiplication
and division.
Whole numbers may be written in a variety of
formats:
– Standard: 123,456;
– Written: one hundred twenty-three thousand,
four hundred fifty-six; and
– Expanded: (1  100,000) + (2  10,000) + (3
 1,000) + (4  100) + (5  10) + (6  1).
All students should

Understand that knowledge of place value is
essential when comparing numbers.

Understand the relationships in the place value
system, where each place is ten times the value of
the place to its right.

Understand that rounding gives an estimate to use
when exact numbers are not needed for the
situation.

Understand the relative magnitude of numbers by
comparing numbers.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Investigate and identify the place and value for
each digit in a six-digit numeral, using Base-10
manipulatives (e.g., Base-10 blocks).

Use the patterns in the place value system to read
and write numbers.

Read six-digit numerals orally.

Write six-digit numerals that are stated verbally or
written in words.

Round a given whole number, 9,999 or less, to the
nearest ten, hundred, and thousand.

Solve problems, using rounding of numbers, 9,999
or less, to the nearest ten, hundred, and thousand.

Determine which of two whole numbers between
0 and 9,999 is greater.

Determine which of two whole numbers between
0 and 9,999 is less.

Compare two whole numbers between 0 and
9,999, using the symbols >, <, or =.

Use the terms greater than, less than, and equal to
when comparing two whole numbers.
STANDARD 3.1
3.1
STRAND: NUMBER AND NUMBER SENSE
GRADE LEVEL 3
The student will
a) read and write six-digit numerals and identify the place value and value of each digit;
b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and
c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal
to).
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)

Numbers are arranged into groups of three places
called periods (ones, thousands, millions, and so
on). Places within the periods repeat (hundreds,
tens, ones). Commas are used to separate the
periods. Knowing the place value and period of a
number helps students find the value of a digit in
any number as well as read and write numbers.

To read a whole number through the hundred
thousands place,
– read the digits to the first comma;
– say the name of the period (e.g., “thousands”);
then
– read the last three digits, but do not say the
name of the ones period.

Reading and writing large numbers should be
related to numbers that have meanings (e.g.,
numbers found in the students’ environment).
Concrete materials, such as Base-10 blocks may
be used to represent whole numbers through
thousands. Larger numbers may be represented on
place value charts.

Rounding is one of the estimation strategies that is
often used to assess the reasonableness of a
solution or to give an estimate of an amount.

Students should explore reasons for estimation,
using practical experiences, and use rounding to
solve practical situations.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS
STANDARD 3.1
3.1
STRAND: NUMBER AND NUMBER SENSE
GRADE LEVEL 3
The student will
a) read and write six-digit numerals and identify the place value and value of each digit;
b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and
c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal
to.)
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)

The concept of rounding may be introduced
through the use of a number line. When given a
number to round, locate it on the number line.
Next, determine the multiple of ten, hundred, or
thousand it is between. Then identify to which it
is closer.

A procedure for rounding numbers to the nearest
ten, hundred, or thousand is as follows:
– Look one place to the right of the digit to
which you wish to round.
– If the digit is less than 5, leave the digit in the
rounding place as it is, and change the
digits to the right of the rounding place to
zero.
– If the digit is 5 or greater, add 1 to the digit in
the rounding place, and change the digits
to the right of the rounding place to zero.

A procedure for comparing two numbers by
examining may include the following:
– Line up the numbers by place value by lining
up the ones.
– Beginning at the left, find the first place
value where the digits are different.
– Compare the digits in this place value to
determine which number is greater (or
which is less).
– Use the appropriate symbol > or < or the
words greater than or less than to
compare the numbers in the order in which
they are presented.
If both numbers are the same, use the symbol = or
the words equal to.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
Page
3.1a
1
3
3.1a
--
-7
10
3.1a
1
1
Checkpoint
Extra Practice
Chapter Test
6-8
*SBG supports to 3digits only.
*SBG does not support
place value to 6-digits.
20, 21
28, 29
34
36-38
39
*Note: SBG Grade 4 text supports SOL 3.1 to the 6-digits. See Chapter 1, Lesson 2, pp. 4-6 and
Checkpoint p. 14.
Saxon Math References (Second Edition):
SOL Number
3.1a
Lesson
3, 27, 41, 68, 103 (up to five-digit numbers)
Everyday Counts: Teacher’s Guide p. 6
Math At Hand: 004-006
Aims: “A Pumpkin Caper”, magazine Volume 6, Issue 3; “Zip, Zap, Zorp,” Magazine Volume 8,
Issue 1; “Flip”, Magazine Volume 8, Issue 1
Other Books: Marilyn Burns, About Teaching Mathematics- A K-8 Resource, p. 173-182: Marilyn
Burns and Bonnie Tank, A Collection of Math Lessons from Grades 1-3, p.167-172; Lola J. May and
Shirley M. Frye, Down to Earth Mathematics, p. 5-16; Cuisenaire Math Manipulative Kit, “Learning
with Base Ten Blocks”, p. 2-8; Marilyn Burns, Math By All Means: Place Value, Grade 2
Technology: Math Blaster: In Search of Spot, Davidson
Visit: www.teacher.mathsurf.com, www.mathsurf.com/3/ch2
Children’s Literature: The Chicken Stew By Keiko Kasza, How Much is a Million? By David
Schwartz, The Hundred Dresses by Eleanor Estes, Zipping, Zapping, Zooming Bats By Ann Earle
Standard 3.1a continued
Instructional Vignette: (Alternate Teaching Strategies)
 Use base ten materials to show numbers and identify specific values of digits.
 Have students show the numbers called out by the teacher using number tiles 0-9 or place value mats and
base 10 materials. For example: Show me a number that is less than 4,570. Show me a number greater that
91,000 but less than 98,765. Show me an odd number that is greater than 6,032 but less than 6,097. Show
me a number that is one less than 75, 830. Notice that some “show me” statements have one correct answer
while others are more open-ended.
 Draw lines for a six-digit number on the chalkboard. Pass out cards for students to fill in a
six-digit number such as: forty, eleven thousand, six hundred, seven, one hundred thousand.
Let children pick a number and call on a friend to do the same.
 Have four to six students stand at the front of the class. Randomly give each student a large
one-digit number. The teacher or student leader will ask the class specific questions about the
number
such as “Which student is in the thousands place? What is the place value of a specific student? Who can
read the number that has just been created? Who can come to the chalk board and write the number in
expanded form? How can the students be rearranged to show the smallest possible number? How can they
be rearranged to show the largest possible number?
 SWAT: Write a six-digit number on the board and have a student stand on either side of the number
holding a fly swatter. Call out a place value such as hundreds or ten thousands. The first child to swat the
number in that place earns a point for his team.
Additional Vocabulary:
digit- Any one of these ten symbols:
0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
standard- A number written with one digit for each place value.
Released Test Items:
1
A news story reported that 713,298 people
watched the play-off game. What is the
value of the 3 in 713,298?
A
B
C
D
300
3,000
30,000
300,000
2 Last February, a card shop sold two
hundred thousand, one hundred greeting
cards. Which shows this number?
F
G
H
J
2,000,100
200,100
20,100
2,100
Released Test Items:
1
A news story reported that 713,298 people
watched the play-off game. What is the
value of the 3 in 713,298?
A
B
C
D
2 Last February, a card shop sold two hundred
thousand, one hundred greeting cards. Which shows
this number?
F
G
H
J
300
3,000
30,000
300,000
2,000,100
200,100
20,100
2,100
3.1a continued
Released Test Items
3.
Last month, 104,629 people went
to the circus.
4. Last year, 345,129 people watched a parade.
Which of the following shows 345,129
written in words?
What is the value of the 6 in 104,629?
A
B
C
D
6
60
600
6,000
F
G
H
J
Three thousand, four hundred twenty-nine
Three hundred forty-five, one hundred twentynine
Three hundred forty-five, one hundred twentynine
Three hundred forty-five thousand, one hundred
twenty-nine
Standard 3.1b
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
Page
1
4
10-12
Checkpoint
16
3
9
100
1
4
10-12
Checkpoint
16
3
9
100
*SBG text does not support VA SOL 3.2 rounding to the
thousand’s place (supports only to hundred’s place).
3.1bSa
3.1bSb
REFERENCES: Saxon Math Second Edition
SOL Number
Lesson
3.1bSa
3.1bSb
18, 19, 72, 130
18, 19, 72, 130
Everyday Counts: Teacher’s Guide p. 50-51, 60-61, 74
Math At Hand: 095, 101, 103 (to 6-digits)
Other Books: Lola J. May and Shirley M. Frye, Down to Earth Mathematics, p.5-16
Technology: Math Blaster: In Search of Spot, Davidson
http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Number & Operations and then find activities)
Children’s Literature: Margie’s Diner by Gail Gibbons; Charlotte’s Web by E. B. White
Instructional Vignette: (Alternate Teaching Strategies)
 Group students in pairs and give each student nine cards. The students will write a number
between 100 and 999 on each of the nine cards. The cards are mixed up and placed in a pile.
Each player then draws two cards and estimates the sum to nearest tens or hundreds by rounding
the numbers. One partner keeps all the cards, the sum of which is less than 1,000. The other
partner will keep all cards, the sum of which is greater than 1,000. The student who has the most
cards after all are drawn wins a point. Reshuffle the cards and continue to play until one student
wins the game by getting ten points first.
♦ Set up a pretend restaurant or store in the classroom. Have children create menus for the restaurant
or price tags for the store. Give children pretend money and have them make purchases by estimating
what they can buy by rounding the prices of the items in the restaurant or store. Let everyone take
turns being the store or restaurant workers and the purchasers.
Additional Vocabulary:
Rounding-- To find the nearest ten, hundred, thousand (and so on).
Estimation-- A number close to an exact amount; an estimate tells about how much or about how
many.
Released Test Items:
Standard 3.1c continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.1cSa
3.1cSb
3.1cSc
3.1cSd
Chapter
Lesson
1
Checkpoint
Extra Practice
1
Checkpoint
Extra Practice
1
Checkpoint
Extra Practice
1
Checkpoint
Extra Practice
8
8
9
8
9
8
9
Page
22-24
34
37
22-24
34
37
22-24
34
37
22-24
34
37
REFERENCES: Saxon Math Second Edition
SOL Number
3.1c
Lesson
47-135
Math At Hand: 008-010
Aims: “Math with M&M Candies”, Primarily Bears; “Getting the Hang of It”, Magazine Volume
11, Issue 2
Other Books: Lola J. May and Shirley M. Frye, Down to Earth Mathematics, p.13-16
Technology: http://mati.usu.edu/nlvm/nav/vlibrary.html (choose Number & Operations then find
activities)
Standard 3.1c continued
Instructional Vignette: (Alternate Teaching Strategies)
 Encourage students to work in pairs to model two three-digit numbers such as 308 or 380
using base 10 materials. The students will compare their numbers to determine which is
greater or less. Have students practice saying their numbers aloud to one another. Have
children write the numbers they create on a sheet of paper for the other student to check.
 Ask students to use number tiles to create numbers. Ask the students to make a number that
is less than 3,674 or a number that is greater than 1,857. Next ask for a number that is greater
than 2,567 but less than 3,692. Assign table leaders to help you quickly check the answers.
 Play “War” with a deck of student generated cards with whole numbers up to 9,999.
Students shuffle the cards and split the cards into two stacks. Each student turns over a card.
The highest number takes both cards and the winning student places all those cards at the
bottom of their pile. Play continues until one player has no cards left.
 Bring in empty food containers that are similar such as canned vegetables or boxes of cereal.
Review the nutritional labels with the children pointing out where calories, sodium, etc. are
located. Have students take turns putting the labels in order from least amount of calories to
greatest amount of calories. Repeat using a different measure such as sodium. A variation on
this activity might be to cut out advertisements of similar items such as clothes from the
newspaper and have students arrange the advertisements in order from least expensive to
most expensive.
 Give groups of students a number card and ask the groups to arrange themselves in order
from least to greatest and greatest to least without talking. Choose other students to check.
 Play “Hi-Lo”. Students work with a partner. Ask one student to think of a number between 1
and 1,000 and the other students to guess the number. The student who knows the number
states “higher” or “lower” while the other students are trying to guess.
Standard 3.1c continued
Additional Vocabulary:
Inequality-- A mathematical sentence that compares two amounts using the symbols; ≠, < or >.
3.1c Released Test Items:
STANDARD 3.2
3.2
STRAND: NUMBER AND NUMBER SENSE
GRADE LEVEL 3
The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic
fact sentences. The student will use these relationships to solve problems.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)

Addition and subtraction are inverse operations, as
are multiplication and division.

In building thinking strategies for subtraction, an
emphasis is placed on connecting the subtraction fact
to the related addition fact. The same is true for
division, where the division fact is tied to the related
multiplication fact. Building fact sentences helps
strengthen this relationship.

Addition and subtraction should be taught
concurrently in order to develop understanding of the
inverse relationship.

Multiplication and division should be taught
concurrently in order to develop understanding of the
inverse relationship.
All students should

Understand how addition and subtraction are related.

Understand how multiplication and division are
related.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Use the inverse relationships between
addition/subtraction and multiplication/division to
solve related basic fact sentences. For example,
5
+ 3 = 8 and 8 – 3 = __;
4  3 = 12 and 12 ÷ 4 = __.

Write three related basic fact sentences when given
one basic fact sentence for addition/subtraction and
for multiplication/division. For example, given
3  2 = 6, solve the related facts __ 3 = 6,
6 ÷ 3 = __, and 6 ÷ __ = 3.
Standard 3.2 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.2Sa
3.2Sb
Chapter
Lesson
2
Checkpoint
Extra Practice
9
Checkpoint
Extra Practice
Chapter Test
9
10
1
1
Page
66-67
70
74
324-327
70
74
75
324-327
REFERENCES: Saxon Math Second Edition
SOL Number
3.2Sa
3.2Sb
Lesson
20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,
105, 110, 115, 120, 125
20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,
105, 110, 115, 120, 125
Everyday Counts: Teacher’s Guide p. 9 – 11, p. 31 - 32
Math At Hand: 128, 145
Aims: “Counting Combinations”, Magazine Volume 10, Issue 7; “Matching Tops and Bottoms”,
Magazine Volume 10, Issue 8; “Goody Goody Gumballs”, Fall Into Math and Science; “Counting
on Combinations”, Magazine Volume 10, Issue 7
Other Books: Lola J. May and Shirley M. Frye, Down to Earth Mathematics, p. 13-16
Technology: www.teacher.mathsurf.com , http://matti.usu.edu/nlvm/nav/vlibrary.html (choose
Number & Operations then find activities)
Children’s Literature: The Lamplighter by Robert Stevenson; “Little Bits” from You Read to Me,
I’ll Read to You by John Ciardi, Hershey’s Milk Chocolate Multiplication Book by Jerry Pallotta,
Hershey’s Kisses Addition Book by Jerry Pallotta, Hershey’s Kisses Subtraction Book by Jerry
Pallotta
Virginia Department of Education Training Module: Patterns, Functions & Algebra: Section 3,
Activity 3 “Open Sentences” ; Section 4, Activity 3 “Build the Rule” ; Section 4, Activity 11
“Reflections on Functions”
Standard 3.2 continued
Instructional Vignette: (Alternate Teaching Strategies)
 Use counters or other manipulatives such as Cheerios, M & Ms or buttons to invite children to
explore “fact families”. Facilitate their exploration by demonstrating how inverses can be
viewed. For example say, “Count out 12 Cheerios. Now divide them into 2 groups. Who can
make an addition sentence out of what you are showing?” (e.g. 3 + 9 = 12) Ask the children if
they can create another addition sentence using the same numbers. Model for the students a
subtraction sentence and ask them to do the same. Encourage the children to write down their
groups of sentences on paper. Duplicate this activity with multiplication and division facts.
 Model for the children how inverses can be written and numbers can be rearranged for
addition/subtraction and multiplication/division facts. Encourage students to physically
manipulate their own fact sentences by using number tiles. Again model for the class that the
same can be done with large cards that have been magnetized for use on the chalkboard.
Standard 3.2 continued
Instructional Vignette continued
 Have children select dominoes from a container and create fact sentences from the numbers
shown on both sections of the domino. Make sure the related facts are written as well. For
example, if a domino is chosen with six dots on one section and three dots on the other section,
the sentence 3 + 6 = 9, and the related fact sentences can be written. The same can be done for
multiplication/division. The sentence 3 x 6 = 18 can be written and the related facts as well.
This same activity can be done by rolling two dice.
 Play the game “If the answer is _________, what can the question be?” Students will list all
the possible answers including the inverse relationship.
Additional Vocabulary:
addition- An equation which shows a sum.
subtraction- An operation that gives the differences between two numbers.
multiplication- The operation of repeated addition of the same number.
division- The operation of making equal groups and finding the number in each group or the
number of groups.
fact family- Number sentences that relate addition and subtraction or multiplication and division.
Each number sentence in the fact family has the same numbers.
addend- Any number being added.
sum- Total; the result of addition.
factor- When you multiply two whole numbers to get a given number, then the two whole
numbers are factors of the given number.
product- The result of multiplication.
quotient- The result of division.
divisor- The number by which another number is divided.
Standard 3.2 continued
Released Test Items:

Harold can use the fact, 3 x 4 = 12, to help
him solve a related problem. Which of the
following could be the problem he is trying
to solve?
A
B
C
D
•÷3=4
• - 4 = 12
•+3=4
• - 3= 4
STANDARD 3.3
3.3
STRAND: NUMBER AND NUMBER SENSE
The student will
a) name and write fractions (including mixed numbers) represented by a model;
b) model fractions (including mixed numbers) and write the fractions’ names; and
c) compare fractions having like and unlike denominators, using words and symbols (>, <, or =).
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)


A fraction is a way of representing part of a whole
(as in a region/area model or a length/measurement
model) or part of a group (as in a set model).
Fractions are used to name a part of one thing or a
part of a collection of things. Models can include
pattern blocks, fraction bars, rulers, number line, etc.
In each area/region and length/measurement model,
the parts must be equal-sized (congruent). Wholes
are divided or partitioned into equal-sized parts. In
the set model, each member of the set is an equal part
of the set. The members of the set do not have to be
equal in size.

The denominator tells how many equal parts are in
the whole or set. The numerator tells how many of
those parts are being considered.

Provide opportunities to make connections among
fraction representations by connecting concrete or
pictorial representations with oral language and
symbolic representations.

GRADE LEVEL 3
Informal, integrated experiences with fractions at this
level will help students develop a foundation for
deeper learning at later grades. Understanding the
language of fractions (e.g., thirds means “three equal
1
parts of a whole,” represents one of three equal3
size parts when a pizza is shared among three
students, or three-fourths means “three of four equal
parts of a whole”) furthers this development.
All students should
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Understand that the whole must be defined.

Understand that the denominator tells the number of
equal parts that represent a whole.


Understand that the numerator is a counting number
that tells how many equal size parts are being
considered.
Name and write fractions (including mixed numbers)
represented by a model to include halves, thirds,
fourths, eighths, tenths, and twelfths.

Use concrete materials and pictures to model at least
halves, thirds, fourths, eighths, tenths, and twelfths.

Compare fractions using the terms greater than, less
than, or equal to and the symbols ( <, >, and =).
Comparisons are made between fractions with both
like and unlike denominators, using models, concrete
materials and pictures.

Understand that the value of a fraction is dependent
on both the number of parts in a whole (denominator)
and the number of those parts being considered
(numerator).

Understand that a proper fraction is a fraction whose
numerator is smaller than its denominator.

Understand that an improper fraction is a fraction
whose numerator is greater than or equal to the
denominator and is one or greater than one.

Understand that an improper fraction can be
expressed as a whole number or a mixed number.

Understand that a mixed number is written as a
whole number and a proper fraction.
STANDARD 3.3
3.3
STRAND: NUMBER AND NUMBER SENSE
GRADE LEVEL 3
The student will
a) name and write fractions (including mixed numbers) represented by a model;
b) model fractions (including mixed numbers) and write the fractions’ names; and
c) compare fractions having like and unlike denominators, using words and symbols (>, <, or =).
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)
 Comparing unit fractions (a fraction in which the
numerator is one) builds a mental image of fractions
and the understanding that as the number of pieces of
a whole increases, the size of one single piece
1
1
decreases (e.g., of a bar is smaller than of a bar).
5
4
Comparing fractions to a benchmark on a number
1
1
line (e.g., close to 0, less than , exactly , greater
2
2
1
than , or close to 1) facilitates the comparison of
2
fractions when using concrete materials or pictorial
models.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS
Standard 3.3a &b
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.3aSa
3.3aSb
Chapter
Lesson
11
11
11
Checkpoint
Extra Practice
Chapter Test
11
11
11
Checkpoint
Extra Practice
Chapter Test
1
4
7
1
4
7
Page
402-403
408-409
414-415
418
436-437
439
402-403
408-409
414-415
418
436-437
439
REFERENCES: Saxon Math Second Edition
SOL Number
3.3aSa
3.3aSb
Lesson
10, 12. 15, 15, 17, 21, 24, 26, 37, 61
10, 12. 15, 15, 17, 21, 24, 26, 37, 61
Everyday Counts: Teacher’s Guide p.71
Math At Hand: 028-033
Aims: Jelly Belly, Pieces and Patterns
Technology: www.mathsurf.com/3/ch10
http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Numbers & Operations then find activities)
Children’s Literature: The Pie Makers by Helen Cresswell, Eating Fractions by Bruce
McMillan, Wayside School is Falling Down by Louis Sacher, Apple Fractions by Jerry Pallotta,
The Hershey’s Milk Chocolate Fraction Book by Jerry Pallotta, Fraction Action by Loreen Leedy,
Spaghetti and Meatballs for All by Marilyn Burns
Virginia Department of Education Training Module: Fractions, Decimals, Proportion and
Percent: Section 1, Activity 1 “Vignettes: Children’s Mathematical Thinking About Fractions” ;
Section 1 Activity 2 “What are the Goals of the Institute?” ; Section 1, Activity 3 “Three
Categories of Fraction Models” ; Section 1, Activity 4 “Area or Region Modes” ; Section 1,
Activity 5 “Building Fraction Strips” ; Section 1, Activity 6 “Length or Measurement Models” ;
Section 1, Activity 7 “Set or Discrete Models” ; Section 1, Activity 10 “Why are Representations
Important? (Part One)” ; Section 2, Activity 1 “Tree Problem” ; Section 2, Activity 2 “Why Are
Representations Important (Part Two)” ; Section 2, Activity 4 ‘Three Interpretations of Fractions” ;
Section 2, Activity 5 “Part-Whole Interpretation” ; Section 2, Activity 8 “Egg Carton Fractions”
Instructional Vignette: (Alternate Teaching Strategies)
 Allow students time for free exploration with groups of blocks. Guide the class using pattern
blocks to explore the idea of equal parts making up a whole. Begin by facilitating a discussion
about how many pieces of one particular block would make up a whole. An example might
include: "Two blue trapezoids would make 2 halves of a yellow hexagon whole." Have
children record their findings on a piece of paper to share in small groups.
 Use M & M candies to explore fractions as sets. Give each child a specific number of M & Ms
in a small cup. Ask the children to record the fractions they discover with their candy on a
piece of paper. Explain that the total number of candy is the denominator and each color of
candy is a different numerator. Emphasize that the colors together make up a set of fractions.
Let the children eat their explorations!
Standard 3.3a &b continued
Additional activities continued
 Read Eating Fractions by Bruce McMillan. Bring in some of the food mentioned in the story
and help children divide the food into equal parts to make fractions. Have children draw
pictures and write the fractions that they create with the food. Eat the results!! This activity
can also be done by reading The Hershey’s Milk Chocolate Fraction Book by Jerry Pallotta and
by giving each child a chocolate bar with which to make fractions.
 Have children go on a fraction scavenger hunt around the school with a partner. Have the
children take notebooks, draw pictures and record the fractions that they discover in their
surroundings. "Our windows have 4 equal panes" might perhaps be an excellent example to
share with the students to initiate the hunt.
Additional Vocabulary:
fraction- A way to describe a part of a whole or a part of a group by using equal parts.
Whole number- Any of the numbers 0, 1, 2, 3, 4, 5, and so on.
3.3a&b Released Test Items:
3.3c
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
3.3cSa
11
11
11
Checkpoint
Extra Practice
Chapter Test
11
11
Checkpoint
Extra Practice
Chapter Test
3
2
3
3.3cSb
3.3cSc
2
3
Page
406-407
404-405
406-407
418
436
439
404-405
406-407
418
436
439
REFERENCES: Saxon Math Second Edition
SOL Number
3.3cSa
3.3cSb
3.3cSc
Lesson
93, 94
94
94
Math At Hand: 038 - 041
Aims: “Clock Wise Fractions,” Magazine 11 Issue 4; “Proportionality,” Magazine 3 Issue 9
Other Books: Robert Baratta-Lorton, Mathematics, A Way of Thinking, Lessons 11-16, 11-17, 1120, and 11-21; Lola J. May and Shirley M. Frye, Down to Earth Mathematics, p. 13-16
Technology: Math Blaster: In Search of Spot, Davidson
http: //matti.usu.edu/nlvm/nav/vlibrary.html (choose Number & Operations then find activities)
Children’s Literature: The Hershey’s Fraction Book by Jerry Pallotta, Apple Fractions, by Jerry
Pallotta, Fractions Are Parts of Things by Dennis
Virginia Department of Education Training Modules: Fractions, Decimals, Proportion and
Percent: Section 1, Activity 1 “Vignettes: Children’s Mathematical Thinking About Fractions” ;
Section 1, Activity 2 “What Are the Goals of the Institute?” ; Section 1, Activity 5 “Building Fraction
Strips” ; Section 1, Activity 10 “Why are Representations Important? (Part One)” ; Section 2, Activity
8 “Egg Carton Fractions” ; Section 3, Activity 2 “Which is More?”
Instructional Vignette: (Alternate Teaching Strategies)
 Have the children create a fraction bar set using construction paper strips with the following
fractions: 1 whole, 1/2, 1/4, 1/3, 1/8, and 1/10. Cut out the strips and compare.
 Use Cuisenaire Rods to compare fractions with like denominators. For example compare 2/8
and 4/8 by using the brown 8 cm rod for the denominators and the white1 cm rod to represent
the numerator. Two white rods over 1 brown rod would equal 2/8 and 4 white rods over 1
brown rod equals 4/8. Facilitate a discussion by asking children questions. "Which is greater?
Which is less?"
 Place pictures of fractions into a paper bag. Each child chooses a picture from the bag. The
student who chooses the greatest fraction from the paper bag scores a point. The first child to
score a certain number of points wins. This activity will work well when students work with a
partner.
Additional Vocabulary:
equivalent—Having the same value.
Inequality – Having a different value, not the same. (≠)
Released Test Items:
STANDARD 3.4
3.4
STRAND: COMPUTATION AND ESTIMATION
The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole
numbers, each 9,999 or less, with or without regrouping.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)


GRADE LEVEL 3
Addition is the combining of quantities; it uses the
following terms:
addend 
423
addend  + 246
sum 
669
Subtraction is the inverse of addition; it yields the
difference between two numbers and uses the
following terms:
minuend  7,698
subtrahend  – 5,341
difference  2,357

An algorithm is a step-by-step method for
computing.

An example of an approach to solving problems is
Polya’s four-step plan:
– Understand: Retell the problem; read it twice;
take notes; study the charts or diagrams; look
up words and symbols that are new.
– Plan: Decide what operation(s) and sequence of
steps to use to solve the problem.
– Solve: Follow the plan and work accurately. If
the first attempt does not work, try another
plan.
– Look back: Does the answer make sense?

Knowing whether to find an exact answer or to make
an estimate is learned through practical experiences
in recognizing which is appropriate.

When an exact answer is required, opportunities to
explore whether the answer can be determined
mentally or must involve paper and pencil or
calculators help students select the correct approach.
All students should
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to
 Understand that estimation skills are valuable, timesaving tools particularly in practical situations when
exact answers are not required or needed.

 Understand that estimation skills are also valuable in
determining the reasonableness of the sum or
difference when solving for the exact answer is
needed.
Determine whether an estimate or an exact answer is
an appropriate solution for practical addition and
subtraction problems situations involving single-step
and multistep problems.

Develop and use strategies to estimate whole number
sums and differences to determine the reasonableness
of an exact answer.
Determine whether to add or subtract in practical
problem situations.

Develop flexible methods of adding whole numbers
by combining numbers in a variety of ways, most
depending on place values.
Estimate the sum or difference of two whole
numbers, each 9,999 or less when an exact answer is
not required.

Add or subtract two whole numbers, each 9,999 or
less.

Solve practical problems involving the sum of two
whole numbers, each 9,999 or less, with or without
regrouping, using calculators, paper and pencil, or
mental computation in practical problem situations.

Solve practical problems involving the difference of
two whole numbers, each 9,999 or less, with or
without regrouping, using calculators, paper and
pencil, or mental computation in practical problem
situations.

Solve single-step and multistep problems involving
the sum or difference of two whole numbers, each
9,999 or less, with or without regrouping.


STANDARD 3.4
3.4
STRAND: COMPUTATION AND ESTIMATION
GRADE LEVEL 3
The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole
numbers, each 9,999 or less, with or without regrouping.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)

Determining whether an estimate is appropriate and
using a variety of strategies to estimate requires
experiences with problem situations involving
estimation.

There are a variety of mental mathematics strategies
for each basic operation, and opportunities to practice
these strategies give students the tools to use them at
appropriate times. For example, with addition,
mental mathematics strategies include
– Adding 9: add 10 and subtract 1; and
– Making 10: for column addition, look for
numbers that group together to make 10.

Using Base-10 materials to model and stimulate
discussion about a variety of problem situations helps
students understand regrouping and enables them to
move from the concrete to the abstract. Regrouping
is used in addition and subtraction algorithms.

Conceptual understanding begins with concrete
experiences. Next, the children must make
connections that serve as a bridge to the symbolic.
One strategy used to make connections is
representations, such as drawings, diagrams, tally
marks, graphs, or written comments.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS
Standard 3.4 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
3.4Sa
3.4Sb
3.4Sc
3.4Sd
1
3
3
2
3
3
3
3
3
3
5
2
9
1
1
5
10
2
9
3
3
3
3
3
3
Checkpoint
3
3
3
Checkpoint
Extra Practice
Chapter Test
1
2
3
5
5
3.4Se
3.4f
12
13
14
Page
*SBG does not support 3.8a
14-15
82-85
100-101
44-49
80-81
88-91
102-111
82-85
100-101
80- 81
84-85
88-91
81
83
84-85
91
93
97
109
111
113-115
117
118-120
121
REFERENCES: Saxon Math Second Edition
SOL Number
Lesson
5-135
3.4
Everyday Counts: Teacher’s Guide p. 6, 17, 30-31, 52, 64, 74, 87, 100
Math At Hand: 072-082, 118-123, 127-134, 446-447, 481
Aims: “The Age Game,” Magazine Volume 7, Issue 1; “A Little Cup Will Do It,” Water, Precious
Water; “Chaotic Computing,” Math and Science: A Solution
Other Books: Lola J. May and Shirley M. Frye, Down To Earth Mathematics, p.24-34, 37-38, and 40-48;
Robert Baratta-Lorton, Mathematics: A Way of Thinking, Chapters 4, 7 (lessons 7-1 through 7-13), 8, and
21
Technology: Math Blaster: In Search of Spot, Davidson
http://matti.usu.edu/nlvm/nav/vlibrary.html
(choose Number &Operations then find activities)
Children’s Literature: Kid Power by Susan Beth Pfeiffer; Counting on Frank by Rod Clement; The
329th Friend by Sharmat; Sideway Stories From Wayside School by Sachar
Virginia Department of Education Training Module: Patterns, Functions & Algebra: Section 3,
Activity 4 “Number Magic”
3.4 Continued
Instructional Vignette: (Alternate Teaching Strategies)
 Demonstrate to students how to add and subtract with and without regrouping using base-10
blocks. Have students use the blocks to work out given addition and subtraction problems.
Make sure that students are exchanging and borrowing correctly using the blocks.
 Cooperative groups of students can play the game “Go for Broke.” Starting with a flat surface,
the first player rolls the dice for a number. The student will then subtract that number from
100. The student passes the dice to the next player and that player rolls and subtracts. The
game continues until a player reaches 0.
 Cooperative groups roll number dice and symbol dice to create addition and subtraction
problems for everybody in the group to solve. The students independently solve the problems
and then check each other’s answers. If an answer does not match, the students must determine
where the mistake is.
Standard 3.4 continued
Additional Vocabulary:
addend—Any number being added.
sum—Total; the result of addition.
minuend—In subtraction, the minuend is the number you subtract from.
subtrahend—In subtraction, the subtrahend is the number you subtract.
difference—The amount that remains after one quantity is subtracted from another.
addition—An equation which shows a sum.
subtraction—An operation that gives the difference between two numbers; Subtraction can be
used to compare two numbers, or to find out how much is left after some is taken away.
3.4 Released Test Items:

Lisa learned that the Caribbean Sea is
8,173 feet deep and the Black Sea is
3,826 feet deep. How many feet deeper
is the Caribbean Sea than the Black Sea?
F
G
H
J
5,753
5,357
4,947
4,347
STANDARD 3.5
3.5
STRAND: COMPUTATION AND ESTIMATION
The student will recall multiplication facts through the twelves table, and the corresponding division facts.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)

The development of computational fluency relies on
quick access to number facts.

A certain amount of practice is necessary to develop
fluency with computational strategies; however, the
practice must be motivating and systematic if
students are to develop fluency in computation,
whether mental, with manipulative materials, or with
paper and pencil.

GRADE LEVEL 3
Strategies to learn the multiplication facts through
the twelves table include an understanding of
multiples/skip counting, properties of zero and one as
factors, pattern of nines, commutative property, and
related facts.

In order to develop and use strategies to learn the
multiplication facts through the twelves table,
students should use concrete materials, hundred
chart, and mental mathematics.

To extend the understanding of multiplication, three
models may be used:
– The equal-sets or equal-groups model lends itself
to sorting a variety of concrete objects into
equal groups and reinforces repeated addition
or skip counting.
– The array model, consisting of rows and columns
(e.g., 3 rows of 4 columns for a 3-by-4 array)
helps build the commutative property.

The length model (e.g., a number line) also
reinforces repeated addition or skip counting.
All students should

Develop fluency with number combinations for
multiplication and division.

Understand that multiplication is repeated addition.

Understand that division is the inverse of
multiplication.

Understand that patterns and relationships exist in the
facts.

Understand that number relationships can be used to
learn and retain the facts.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Recall and state the multiplication and division facts
through the twelves table.

Recall and write the multiplication and division facts
through the twelves table.
Standard 3.5 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
3.5Sa
5
5
8
1
5
4
Page
174- 183
184-231
296-345
REFERENCES: Saxon Math Second Edition
SOL Number
3.5Sa
Lesson
45, 55, 70, 85, 90, 95, 100, 103, 109, 110, 112, 115, 115, 118,
120, 122, 124, 125, 132
Everyday Counts: Teacher’s Guide p. 42-44, 53-55, 63, 65-66, 76, 86, 88-90, 100-102
Math At Hand: 136,144-145, 482
Aims: “Building Number Sense”, Magazine Volume 10 Issue 10; “Area Patterns,” Magazine Volume 11
Issue 5; “Heavy Works,” Overhead and Underfoot; “Skip to My Rule,” Magazine Volume 11 Issue 3
Other Books: Robert Baratta-Lorton, Mathematics: A Way of Thinking, Ch. 4, 7 (lessons 7-1 through 713), 8, 21; Marilyn Burns, A Collection of Math Lessons from Grade 3 Through 6, p. 11-35; and Math
By All Means, Multiplication Grade 3; Lola J. May and Shirley M. Frye, Down to Earth Mathematics , p.
5-56, 63-65
Technology: Math Blaster: In Search of Spot, Davidson; http://matti.usu.edu/nlvm/nav/vlibrary.html
(choose Number & Operations then find activities)
Children’s Literature: Anno’s Mysterious Multiplying Jar by Masaichiro Anno; Divide and Ride by
Stuart J. Murphy; The Doorbell Rang by Pat Hutchins; The King’s Commissioner by Aileen Friedman;
What Comes in 2’s, 3’s, 4’s by Suzanne Aker; Bunches and Bunches of Bunnies by Louise Mathews;
One Hungry Monster: A Counting Book in Rhyme by O’Keefe; Zipping, Zapping, Zooming Bats by Ann
Earle; Two Ways to Count by Dee; The Cricket in Times Square by Selden; Reese’s Pieces Count by 5’s
by Jerry Pallotta; Hershey’s Milk Chocolate Multiplication Book by Jerry Pallotta; One Hundred Ways to
Get to 100 by Jerry Pallotta
3.5 Instructional Vignette: (Alternate Teaching Strategies)
 Have children use any type of counters to make arrays for given multiplication/division facts.
Students can pair up and take turns giving multiplication/division facts and making arrays and then
checking their partner's work.
 Students can use a “fun food” counter such as cheerios, small marshmallows, gumdrops, or raisins
to group counters into sets and practice skip counting. Students may also practice continued
addition to find answers to multiplication/division facts.
 Play multiplication or division bingo. Have children make cards with answers on them and have
the caller call the fact out. Children cover their space on the card when they hear a fact called that
they have an answer for.
Standard 3.5 continued
Additional activities continued
 SWAT -- Divide students into two teams. One child from each team comes to the board with a
flyswatter. Write several answers to multiplication/division facts on the board. Call out a problem.
The first student who “swats” the correct answer will win a point for their team.
 WAR-- Divide a deck of cards between two players. Each child lays down their top two cards.
Children then multiply the cards together and who ever has the higher product keeps all of the
cards. This activity could also be done by rolling dice and keeping points or by selecting two
dominoes from a cup and keeping points.
 TWISTER-- Write numbers 0-12 on a twister board on different dots. (There can be more than one
dot with the same number.) Call out an answer to a multiplication problem and have children spin
to see what body part to place on the dot with the correct factor. For multiplication, students will
have to spin twice and put each body part on one of the factors. For division, the problem can be
given and one body would be placed on the correct answer.
Additional Vocabulary:
factors- When you multiply two whole numbers to get a given number, then the two whole
numbers are factors of the given number.
product- The result of multiplication.
array- An arrangement of objects in equal rows.
3.5 Released Test Items:
1
7x8=
A
B
C
D
56
54
32
15
2
36  4 =
F
G
H
J
6
7
8
9
STANDARD 3.6
3.6
STRAND: COMPUTATION AND ESTIMATION
GRADE LEVEL 3
The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that
involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)

The multiplication and division facts through the
twelves tables should be modeled.

Multiplication is a shortcut for repeated addition. The
terms associated with multiplication are listed below:
factor 
54
factor 
3
product 
162
All students should

Understand the meanings of multiplication and
division.

Understand the models used to represent multiplying
and dividing whole numbers.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Model multiplication, using area, set, and number line
models.

Model division, using area, set, and number line
models.

Creating real-life problems and solving them
facilitates the connection between mathematics and
everyday experiences (e.g., area problems).

Solve multiplication problems, using the
multiplication algorithm, where one factor is 99 or
less and the second factor is 5 or less.

The use of Base-10 blocks and repeated addition can
serve as a model. For example, 4  12 is read as four
sets consisting of one rod and two units. The sum is
renamed as four rods and eight units or 48. This can
be thought of as
12 + 12 + 12 + 12 = (SET)

Create and solve word problems involving
multiplication, where one factor is 99 or less and the
second factor is 5 or less.

The use of Base-10 blocks and the array model can be
used to solve the same problem. A rectangle array that
is one rod and two units long by four units wide is
formed. The area of this array is represented by 4 rods
and 8 units.

The number line model can be used to solve a
multiplication problem such as 3  4. This is
represented on the number line by three jumps of four.

The number line model can be used to solve a division
problem such as 6 ÷ 3 and is represented on the
number line by noting how many jumps of three go
from 6 to 0.
STANDARD 3.6
3.6
STRAND: COMPUTATION AND ESTIMATION
The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that
involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)
0
1
2
3
4
5
6
The number of jumps (two) of a given length (three) is
the answer to the question.

GRADE LEVEL 3
An algorithm is a step-by-step method for computing.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS
Standard 3.6 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL
Number
Chapter
Lesson
3.6Sa
12
9
12
12
1
9
11
1
3.6Sb
3.6 Sc, d
REFERENCES:
Page
444-453
344- 345
470-471
444-453
Saxon Math Second Edition
SOL Number
Lesson
3.6Sa
3.6Sb
3.6Sc
3.6Sd
57, 87
Not Supported
112, 116-135
56-135
Math At Hand: 137-138, 146-149
Aims: “Peddle the Medal,” Hardhatting in the GeoWorld; “Space Olympics,” Overhead and Underfoot
Other Books: Lola J. May and Shirley M. Frye, Down to Earth Mathematics, p. 5-16; Marilyn Burns, A
Collection of Math Lessons from Grades 3 through 6, p. 21-35
Technology: Math Blaster: In Search of Spot, Davidson; www.mathsurf.com ;
http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Number & Operations then find activities)
Children’s Literature: Spaghetti and Meatballs by Burns; Each Orange Has 8 Slices by Paul Giganti;
One Hungry Monster, by Susan Heyboer O’Keefe; Zipping, Zapping, Zooming Bats by Ann Earle;
Counting on Frank by Rod Clement; The Doorbell Rang by Pat Hutchins
Virginia Department of Education Training Modules: Patterns, Functions, & Algebra: Section 3,
Activity 4 “Number Magic,”
3.6 Instructional Vignette: (Alternate Teaching Strategies)
 Students can use base 10-blocks to work multiplication and division problems using area and
set models. Ask students to create a set model by creating sets of the manipulative. Model
for the class that 18 x 5 would be 1 long and 8 single units grouped together 5 times. Ask
students to create an area model. Instruct the students to make a rectangle with Base-10
blocks on graph paper that represent the problem. Model for the class 1 long and 8 single
units on one side 5 units high. Ask the class to determine the product by counting the
squares inside.
 Have students create word problems based on their everyday life. "Cameron had 19 students
in his class and he wanted to give each student 3 stickers. How many stickers would he need
in all?" Have students exchange problems to solve.
 Have the class create a quilt together. Each child should create a row of squares and then the
class could solve the problem to decide how many squares in all. "If there are17 students,
each child could make 4 squares for their row. The multiplication problem would be 17 x 4.
Standard 3.6 continued
Additional Vocabulary:
multiplicand— The number multiplied, or to be multiplied by another.
multiplier—The number by which a second number is multiplied.
3.6 Released Test Items:

Sarah bought 3 boxes of crackers.
There were 48 crackers in each box.
How many crackers did she buy in all?
F
G
H
J
45
51
124
144
STANDARD 3.7
3.7
STRAND: COMPUTATION AND ESTIMATION
The student will add and subtract proper fractions having like denominators of 12 or less.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)

A proper fraction is a fraction whose numerator is less
than the denominator. A proper fraction is a fraction
that is always less than one.

An improper fraction is a fraction whose numerator is
greater than or equal to the denominator. An improper
fraction is a fraction that is equal to or greater than
one.

An improper fraction can be expressed as a mixed
number. A mixed number is written as a whole
number and a proper fraction.


GRADE LEVEL 3
The strategies of addition and subtraction applied to
fractions are the same as the strategies applied to
whole numbers.
Reasonable answers to problems involving addition
and subtraction of fractions can be established by
1
using benchmarks such as 0, , and 1. For example,
2
3
4
1
and are each greater than , so their sum is
5
5
2
greater than 1.
 Concrete materials and pictorial models representing
area/regions (circles, squares, and rectangles),
length/measurements (fraction bars and strips), and
sets (counters) can be used to add and subtract
fractions having like denominators of 12 or less.
All students should

Understand that a proper fraction is a fraction whose
numerator is smaller than its denominator.

Understand that an improper fraction is a fraction
whose numerator is greater than or equal to the
denominator and is one or greater than one.

Understand that an improper fraction can be expressed
as a whole number or a mixed number.


ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Understand that a mixed number is written as a whole
number and a proper fraction. A mixed number is the
sum of a whole number and the proper fraction.
Demonstrate a fractional part of a whole, using
– region/area models (e.g., pie pieces, pattern
blocks, geoboards, drawings);
– set models (e.g., chips, counters, cubes,
drawings); and
– length/measurement models (e.g., nonstandard
units such as rods, connecting cubes, and
drawings).

Understand that computation with fractions uses the
same strategies as whole number computation.
Name and write fractions and mixed numbers
represented by drawings or concrete materials.

Represent a given fraction or mixed number, using
concrete materials, pictures, and symbols. For
example, write the symbol for one-fourth and
represent it with concrete materials and/or pictures.

Add and subtract with proper fractions having like
denominators of 12 or less, using concrete materials
and pictorial models representing area/regions
(circles, squares, and rectangles),
length/measurements (fraction bars and strips), and
sets (counters).
3.7 Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.7Sa
3.7Sb
3.7Sc
3.11Sd
REFERENCES:
SOL Number
3.7Sa
3.7Sb
3.7Sc
3.7Sd
Chapter
Lesson
Page
11
1
402-403
11
2
404-405
11
4
408-409
11
7
414-415
Checkpoint
418
Extra Practice
436-437
Chapter Test
439
11
2
404-405
11
3
406-407
Checkpoint
418
Extra Practice
436
Chapter Test
439
11
1
402-403
11
2
404-405
11
4
408-409
11
7
414-415
Checkpoint
418
Extra Practice
436-437
Chapter Test
439
11
14
441
Silver Burdett Gin text does not correlate with Virginia SOL 3.11d.
Saxon Math Second Edition
Lesson
10, 12, 15, 17, 21, 26
26, 37, 61, 74, 111
98
93, 94
Math Steps: Teacher’s Guide T102- T105, T109; student pages 185-186
Math At Hand: 157-159, 162-164
Other Books: Robert Baratta-Lorton, Mathematics: A Way of Thinking, Lessons 11-11 and 11-12; Marilyn Burns,
About Teaching Mathematics, A K-8 Resource, p. 214-217; Cuisenaire Math Manipulative Kit, “Learning with
Cuisenaire Rods,” p.11-15; “Learning with Two-Color Counters”
Technology: Math Blaster: In Search of Spot, Davidson
http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Number & Operations then find activities)
Children’s Literature: Paddy’s Pat Day by Alexander Day; The Trouble with Money by Jan and Stan Berenstein
Virginia Department of Education Training Modules: Fractions, Decimals, Proportion and Percent: Section 4,
Activity 2 “Using Benchmarks: Which is Closer?” ; Section 4, Activity 3 “Addition with Fraction Strips”; Section
4, Activity 4 “Take One: Subtraction with Fraction Strips” ; Section 4, Activity 5 “Problem Solving with Fraction
Strips” ; Section 4 Activity 6 “Egg Carton Addition”; Section 4, Activity 7 “Playground Problem”
Standard 3.7 continued
Instructional Vignette: (Alternate Teaching Strategies)
 Ask students to use unifix cubes or pattern blocks to practice adding and subtracting fractions
with like denominators. Model for the class that a yellow hexagon represents 1 whole, the tan
parallelograms are fifths, then adding the pieces (2/5 + 2/5) would equal 4/5. Unifix cubes
could be used to add or subtract fractional sets as well.
 Bring in a pizza cut into 10 pieces or other food easily divided such as an orange and show the
students how adding fractional parts with the same denominators follows the same rules as
adding/subtracting whole numbers. Have children draw pictures of their own addition or
subtraction fraction problems. Subtraction should be great fun with food!! Treat your students
with candy bars.
 Have students make fraction collages that show adding or subtraction with fractions. Use art
scraps of construction paper, yarn, sequence, pom-poms, etc. to illustrate sets, area, region, or
length and measurements.
Additional Vocabulary:
numerator-- The number written above the line in a fraction. It tells how many equal parts are
described by the fraction.
denominator-- The quantity below the line in a fraction. It tells how many equal parts are in the
whole.
proper fraction-- A fraction less than 1.
mixed number— A number that has a whole number and a fractional part.
Standard 3.7 continued
Released Test Items:
STANDARD 3.8
3.8
STRAND: MEASUREMENT
The student will determine, by counting, the value of a collection of bills and coins whose total value is $5.00 or less, compare the value
of the bills and coins, and make change.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)


GRADE LEVEL 3
The value of a collection of coins and bills can be
determined by counting on, beginning with the
highest value, and/or by grouping the coins and bills.
A variety of skills can be used to determine the
change after a purchase, including
– counting on, using coins and bills, i.e., starting
with the amount to be paid (purchase price),
counting forward to the next dollar, and then
counting forward by dollar bills to reach the
amount from which to make change; and
– mentally calculating the difference.
All students should

Understand that a collection of coins and bills has a
value that can be counted.

Understand how to make change from $5.00 or less.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Count the value of collections of coins and bills up to
$5.00.

Compare the values of two sets of coins or bills, up
to $5.00, using the terms greater than, less than, and
equal to.

Make change from $5.00 or less.
Standard 3.8 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
3.8Sa
1
1
11
12
30-31
32
3.8 Sb
3.8 Sc
1
1
11
11
30-31
32-35
REFERENCES:
Saxon Math Second Edition
SOL Number
3.8Sa
3.8Sb
3.8Sc
Page
Lesson
23, 36, 79
Not supported
102
Everyday Counts: Teacher’s Guide p. 20-22, 33-34, 45, 55-56, 66-67, 77-78, 103
Math At Hand: 023-026
Aims: “Quick Quilts Part 2”, Magazine Volume 7 Issue 8; “Going Shopping “, Magazine Volume 4 Issue
5; “Back to School”, Magazine Volume 4 Issue 5
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Measurement then find activities)
Children’s Literature: Alexander Who Used to be Rich Last Sunday by Judith Viorst, Pigs Will Be
Pigs by Amy Axelrod, The Go Around Dollar by Barbara Johnston Adams, The Case of the Shrunken
Allowance by Joanne Rocklin
3.8 Instructional Vignette: (Alternate Teaching Strategies)
 Ask students to work with "pretend" money to compare the value of given coins. Each student
reaches in a cup and grabs a handful of coins. Each student then determines the value of his or
her coins. The group then determines who has the largest value of coins and who has the
smallest value of coins.
 Give students a specific amount of money to spend on items of their choosing from catalogs or
advertisements. The students add up their purchases to determine if they stayed within their
price range. The students then make the necessary adjustments. Once the adjustments are
made, the students determine how much change they should receive. The students will also
determine the different coin/dollar combinations they might receive as change.
 Have students generate a list of items that could be sold at a concession stand and their prices.
Ask students to work in groups to select items to be purchased. Each student in the group will
add up the items and determine the total amount due. Students will share and discuss the totals.
Students will then determine the amount of change they should receive back from a given
amount. Groups will then work together to see how many different coin/dollar combinations
they might receive as change. Manipulative money can be used to “act out” the purchases.
 Use restaurant menus to have students plan what they would order and how much change they
would get from a given amount of money.
Standard 3.8 continued
Additional Vocabulary:
Cent- Unit of money; 100 cents = one dollar.
Dollar- A bill or coin worth 100 cents.
Change - Amount of money you receive back when you pay with more money than something
costs.
3.8 Released Test Items:
3.8 Released Test Items: continued
STANDARD 3.9
3.9
STRAND: MEASUREMENT
The student will estimate and use U.S. Customary and metric units to measure
1
a) length to the nearest inch, inch, foot, yard, centimeter, and meter;
2
b) liquid volume in cups, pints, quarts, gallons, and liters;
c) weight/mass in ounces, pounds, grams, and kilograms; and
d) area and perimeter.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)



GRADE LEVEL 3
Weight and mass are different. Mass is the amount
of matter in an object. Weight is determined by the
pull of gravity on the mass of an object. The mass
of an object remains the same regardless of its
location. The weight of an object changes
dependent on the gravitational pull at its location. In
everyday life, most people are actually interested in
determining an object’s mass, although they use the
term weight (e.g., “How much does it weigh?”
versus “What is its mass?”).
The concept of a standard measurement unit is one
of the major ideas in understanding measurement.
Familiarity with standard units is developed through
hands-on experiences of comparing, estimating,
measuring, and constructing.
Benchmarks of common objects need to be
established for each of the specified units of
measure (e.g., the mass of a mathematics book is
about one kilogram). Practical experience
measuring the mass of familiar objects helps to
establish benchmarks and facilitates the student’s
ability to estimate measures.

One unit of measure may be more appropriate than
another to measure an object, depending on the size
of the object and the degree of accuracy desired.

Correct use of measurement tools is essential to
understanding the concepts of measurement.
All students should

Understand how to estimate measures of length,
liquid volume, weight/mass, area and perimeter.

Understand how to determine the actual measure of
length, liquid volume, weight/mass, area and
perimeter.

Understand that perimeter is a measure of the
distance around a polygon.

Understand that area is a measure of square units
needed to cover a surface.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Estimate and use U.S. Customary and metric units
1
to measure lengths of objects to the nearest of an
2
inch, inch, foot, yard, centimeter, and meter.

Determine the actual measure of length using U.S.
Customary and metric units to measure objects to
1
the nearest of an inch, foot, yard, centimeter, and
2
meter.

Estimate and use U.S. Customary and metric units
to measure liquid volume to the nearest cup, pint,
quart, gallon, and liter.

Determine the actual measure of liquid volume
using U.S. Customary and metric units to measure
to the nearest cup, pint, quart, gallon, and liter.

Estimate and use U.S. Customary and metric units
to measure the weight/mass of objects to the nearest
ounce, pound, gram, and kilogram.
STANDARD 3.9
3.9
STRAND: MEASUREMENT
GRADE LEVEL 3
The student will estimate and use U.S. Customary and metric units to measure
1
a) length to the nearest inch, inch, foot, yard, centimeter, and meter;
2
b) liquid volume in cups, pints, quarts, gallons, and liters;
c) weight/mass in ounces, pounds, grams, and kilograms; and
d) area and perimeter.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)

Perimeter is the distance around any twodimensional figure and is found by adding the
measures of the sides.

Area is a two-dimensional measure and is therefore
measured in square units.
Area is the number of square units needed to cover a
figure, or more precisely, it is the measure in square
units of the interior region of a two-dimensional
figure.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS

Determine the actual measure of weight/mass using
U.S. Customary and metric units to measure the
weight/mass of objects to the nearest ounce, pound,
gram, and kilogram.

Estimate and use U.S. Customary and metric units
to measure area and perimeter. Determine the
actual measure of area or perimeter using U.S.
Customary and metric units.
3.9 Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.9Sa
3.9Sb
3.9Sc
3.9Sd
REFERENCES:
Chapter
Lesson
4
4
Checkpoint
Extra Practice
4
4
Checkpoint
Extra Practice
6
11
4
4
Checkpoint
Extra Practice
4
4
4
4
4
8
13
6
8
11
12
13
140-143
152-155
164-165
167-168
144-145
156-159
164- 165
167-168
390-391, 393
146-147
158-159
164-165
167-168
140
146-148
152-155
156-157
158-159
Saxon Math Second Edition
SOL Number
3.9Sa
3.9Sb
3.9Sc
7
12
Page
Lesson
85
45
95
Math Steps: Teacher’s Guide T144-T148, T150; student pages 251-254, 259-262
Everyday Counts: Teacher’s Guide 35-37, 68-69, 78-79, 92-93, 104-105
Math At Hand: 294, 313-318, 487
Aims: (LENGTH)—“Mini-Metric Olympics,” Math and Science: A Solution; “How Tall Are You?,” Fall Into Math
and Science; “The Pumpkin Caper,” Overhead and Underfoot; “Student Made Measuring Tools,” “Rulers Line Up,”
“Links to Length,” “Are You a Square?,” and “Bear Facts,” Hardhitting in a Geo-World; “Observe a Tree,” Budding
Botanist
(LIQUID VOLUME)-- “Looking for Liter, “ Magazine 10 Issue 9; “Filling Station,” Hardhitting in a Geo-World;
“Measure Up,” “Make your Own Cup,” “All Bottled Up,” “ A Little Cup Will Do It,” and “Little Sprouts,” Water,
Precious Water
(WEIGHT/MASS)-- “Pet Rock,” Overhead and Underfoot; “Water in Apples” and “Neat Feet,” Jawbreakers and Heart
Thumpers; “Teddy Bear Cubs Go Weighing,” Primarily Bears; “A Weigh We Go,” Fall Into Math and Science
Other Books: Marilyn Burns, About Teaching Mathematics, A K-8 Resource, p. 46-53; Lola J. May and Shirley M.
Frye, Down to Earth Mathematics, p.69-74; Cuisenaire Manipulative Kit
Technology: http://matti.usu.edu/nlvm.nav/vlibrary.html (choose Measurement then find activities)
Children’s Literature: How Big is a Foot? By Rolf Myller, Jim and the Beanstalk by Raymond Briggs, Gravity is
a Mystery by Franklyn M. Bransley, Vegetable Soup by Jeanne Modisett, Cranberries by Diane L. Burn,
Melisande by Nesbit, Mr. Archimedes Bath by Allen, Dad’s Diet by Comber, Hershey’s Milk Chocolate Weights and
Measures by Jerry Pallotta
Standard 3.9 continued
Instructional Vignette: (Alternate Teaching Strategies)
 Instruct the students to use Cuisenaire rods to work on measuring with centimeters. The
students should identify the 1 cm cuisenaire rod before beginning this activity. Ask the
children to locate a rod that is 6 cm in length. Continue by having students locate rods of given
lengths and make comparisons.
 Direct students to work in small groups to measure volume. Supply each group with measuring
cups, pint jars, quart jars, and a gallon milk jug. Ask students to pour colored water from the
cup to the pint jar and record the number of cups needed to make a pint. Then have the students
pour water from the pint jar into the quart jar and record the number of pints needed to fill the
quart jar. This should be repeated until the milk jug is filled.
 Encourage students to make a flip book using different colored paper. Explain that the top flip
will equal 1 gallon, the second flip will be cut into fourths to represent the 4 quarts, the third
flip will be cut into eighths to represent 8 pints, and the final flip will be cut into sixteenths to
represent 16 cups. Upon completion, the students should be able to make a number of
comparisons using the flips, such as how many cups are in one pint.
 Ask students to work in pairs to measure height. Direct the partners to cut a piece of adding
machine tape to match their partner’s height. Explain that each student should discover how
many toothpicks, cubes, or popsicle sticks must be laid end-to-end to equal the length of each
student’s tape. Students will then measure the machine tape with a ruler, yardstick, or meter
stick to get an exact measurement.
 Direct students to hold a wooden ball bat or any other object that weighs 1 kg.. After the
students have handled the 1 kg object, ask them to predict how much they would weigh in
kilograms. Have the students write down their predictions on strips of paper that can be folded
so others can’t see. Have the students weigh themselves on a metric scale and write down their
actual measurement next to their prediction. Once the students have finished, discuss their
predictions and the actual measurements.
Additional Vocabulary:
weight- A measure of how heavy an object is.
mass- The amount of matter in an object. Usually measured by comparing with an object of
known mass. While gravity influences weight, it does not affect mass.
measure- A comparison to some other known unit, or to find the measure of something.
length- The distance along a line or figure from one point to another.
inch- A customary unit of length equal to 1/12 foot.
foot- A customary unit of length equal to 12 inches.
perimeter- the distance around an object
area- the amount of space an object takes up, measured in units square..
Standard 3.9 continued
Additional vocabulary continued
yard- A customary unit of length equal to 3 feet.
centimeter- A metric unit of length equal to 0.01 (1/100) of a meter.
meter- The standard unit length in the metric system.
cup- A customary unit of capacity equal to 8 fluid ounces.
pint- A customary unit of capacity equal to 2 cups.
quart- A customary unit of capacity equal to 2 pints.
gallon- A customary unit of capacity equal to 4 quarts.
ounce- A customary unit of weight equal to 1/16 of a pound.
pound- A customary unit of weight equal to 16 ounces.
gram- The standard unit of mass in the metric system.
kilogram- A metric unit of mass equal to 1000 grams.
Standard 3.9 continued
Released Test Items:
STANDARD 3.10
3.10
STRAND: MEASUREMENT
The student will
a) measure the distance around a polygon in order to determine perimeter; and
b) count the number of square units needed to cover a given surface in order to determine area.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)




GRADE LEVEL 3
A polygon is a closed plane figure composed of at
least three line segments that do not cross. None of
the sides are curved.
Perimeter is a measure of the distance around a
polygon and is found by adding the measures of the
sides.
All students should

Understand the meaning of a polygon as a closed
figure with at least three sides. None of the sides are
curved and there are no intersecting lines.

Understand that perimeter is a measure of the
distance around a polygon.
Area is the number of iterations of a twodimensional unit needed to cover a surface. The
two-dimensional unit is usually a square, but it could
also be another shape such as a rectangle or an
equilateral triangle.

Understand how to determine the perimeter by
counting the number of units around a polygon.

Understand that area is a measure of square units
needed to cover a surface.
Opportunities to explore the concepts of perimeter
and area should involve hands-on experiences (e.g.,
placing tiles (units) around a polygon and counting
the number of tiles to determine its perimeter and
filling or covering a polygon with cubes (square
units) and counting the cubes to determine its area).

Understand how to determine the area by counting
the number of square units.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Measure each side of a variety of polygons and add
the measures of the sides to determine the perimeter
of each polygon.

Determine the area of a given surface by estimating
and then counting the number of square units needed
to cover the surface.
STANDARD 3.11
3.11
STRAND: MEASUREMENT
The student will
a) tell time to the nearest minute, using analog and digital clocks; and
b) determine elapsed time in one-hour increments over a 12-hour period.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)


GRADE LEVEL 3
While digital clocks make reading time easy, it is
necessary to ensure that students understand that
there are sixty minutes in an hour.
Use of a demonstration clock with gears ensures that
the positions of the hour hand and the minute hand
are precise when time is read.

Students need to understand that time has passed or
will pass.

Elapsed time is the amount of time that has passed
between two given times.

Elapsed time should be modeled and demonstrated
using geared analog clocks and timelines.

It is necessary to ensure that students understand
that there are sixty minutes in an hour when using
analog and digital clocks.

Elapsed time can be found by counting on from the
beginning time to the finishing time.
– Count the number of whole hours between the
beginning time and the finishing time.
For example, to find the elapsed time between 7
a.m. and 10 a.m., students can count on to find
the difference between the times (7 and 10), so
the total elapsed time is 3 hours.
All students should

Apply appropriate techniques to determine time to
the nearest minute, using analog and digital clocks.

Understand how to determine elapsed time in onehour increments over a 12-hour period.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Tell time to the nearest minute, using analog and
digital clocks.

Match the times shown on analog and digital clocks
to written times and to each other.

When given the beginning time and ending time,
determine the elapsed time in one-hour increments
within a 12-hour period (times do not cross between
a.m. and p.m.).

Solve practical problems in relation to time that has
elapsed.
Standard 3.11a&b continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
3.11Sa,b
4
4
4
Checkpoint
Extra Practice
1
2
3
REFERENCES:
SOL Number
3.11bSa
3.11bSb
Page
128-129
130-131
132-133
138-139
166
Saxon Math Second Edition
Lesson
1, 39, 71
Not supported
Math Steps: Teacher’s Guide T 25, student pages 25-28
Everyday Counts: Teacher’s Guide p. 23, 34-35, 46, 90-91
Math At Hand: 324
Aims: “Minute Minders,” Hardhatting in a Geo-World; “Polar Bear Pie,” Winter with Math and Science;
“The Melting Ice Cube,” Off the Wall Science; “Just a Minute,” Magazine Volume 10 Issue 10; “Time
Marches On,” Magazine Volume 9 Issue 6; “Talk About Time,” Magazine Volume 11 Issue 1; “A Handy
Timepiece,” Magazine Volume 9 Issue 4
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Measurement then find activities)
Children’s Literature: Pigs on a Blanket by Amy Axelrod, Grouchy Ladybug by Eric Carle,
and More Clocks by Pat Hutchins, The Guy Who Was Five Minutes Late by Bill Grossman
Clocks
3.11 a&b Instructional Vignette: (Alternate Teaching Strategies)
 Use a large demonstration clock to set a specific time without showing the class. Tell the
students to set their small clocks to that time. Allow children to check their clocks by looking
at yours.
 "Show Me the Time." The students should have a stack of time cards to draw from and analog
clocks. The first player will draw a card and all players will set the given time on their clocks.
Once the students have set their clocks, they show their clocks and determine which clocks are
set correctly. Students may be divided into teams and score kept.
 Utilize a stack of teacher-made digital time cards for this ongoing time activity. The digital
time cards should reflect actual times the students will be in the classroom. At the start of each
day, the students will pick up a time card. The students will be responsible for watching the
clock and raising their hand when the analog clock in the room matches the digital time on their
card. If the students remember and the time is correct, a reward of some type could be given.
At the end of the day the cards are collected and put back in the stack.
 Watch the Clock—Ask one student to roll a number and put the minute hands on that number.
A partner rolls two number cubes, adds the numbers and moves the minute hand ahead that
number of minutes. The first student tells how many minutes the minute hand moved. After
three or four turns, partners switch roles.
Standard 3.11a&b continued
Additional Vocabulary:
minute—One sixtieth of an hour or 60 seconds.
hour-- 60 minutes.
half hour-- 30 minutes.
elapsed time – Time that has passed.
3.11 a& b Released Test Items:
STANDARD 3.12
3.12
STRAND: MEASUREMENT
The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and
hours.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)



GRADE LEVEL 3
1
days will
4
help students understand the necessity of adding a full
day every fourth year, called a leap year.
The knowledge that a year has 365 and
The use of a calendar facilitates the understanding of
time relationships between days and months, days and
weeks, days and years, and months and years.
Recognize that students need to know the
relationships, such as if there are 24 hours in one day,
how many hours are in three days? If the date is
January 6, what date would it be in two weeks? How
many weeks are in March, April, and May?
The use of an analog clock facilitates the
understanding of time relationships between minutes
and hours and hours and days.
All students should

Understand the relationship that exists among periods
of time, using calendars, and clocks.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Identify equivalent relationships observed in a
calendar, including the number of days in a given
month, the number of days in a week, the number of
days in a year, and the number of months in a year.

Identify the number of minutes in an hour and the
number of hours in a day.
Standard 3.12 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.12Sa
3.12Sb
Chapter
Lesson
4
Extra Practice
4
Checkpoint
5
1
Page
136-137
166
128
138
*Note that SBG does not support “number of days in a given month” within 3.16Sa.
REFERENCES:
Saxon Math Second Edition
SOL Number
3.12Sa
3.12Sb
Lesson
84
39
Math Steps: Teacher’s Guide T2, student pages 23-24
Math At Hand: 322, 486
Aims: “Wrap Around the Clock,” Magazine Volume 8 Issue 3; “Counting on One Hundred,”
Magazine Volume 8 Issue 7
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Measurement then find activities)
Children’s Literature: The Story of Our Calendar by Ruth Brindze, Cloudy with a Chance of Meatballs
by Barrett
3.12 Instructional Vignette: (Alternate Teaching Strategies)
 Keep a daily calendar on a bulletin board. Let children participate or be in charge of adding
dates, recording weather, and changing a clock to note something special that is going to
happen that day at a particular time.
 Use the weekly calendar of events and ask students to determine how many minutes or hours
they spend at specific resources. Students can use the weekly school schedule to determine
how many minutes or hours they spend in physical fitness, music, library or just simply eating
lunch each week.
 Direct students to play a matching concentration game where they match the number of days to
a week, month, or year as well as hours to minutes.
Additional Vocabulary:
year- The amount of time it takes for the earth to make one complete revolution around the sun,
365.25 days. Since it is more convenient to have a whole number of days each year, each year has
365 days except leap years which have 366.
month- One of the 12 divisions in a year.
Standard 3.12 continued
Released Test Items:

On Saturday, Tad took exactly 60
minutes to finish his chores.
How many hours did it take
Tad to do his chores?
F
G
H
J
1
2
3
4
STANDARD 3.13
3.13
GRADE LEVEL 3
The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real
thermometers and physical models of thermometers will be used.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)

STRAND: MEASUREMENT
Estimating and measuring temperatures in the
environment in Fahrenheit and Celsius require the use
of real thermometers.

A physical model can be used to represent the
temperature determined by a real thermometer.

The symbols for degrees in Celsius (C) and degrees
in Fahrenheit (F) should be used to write
temperatures.

Celsius and Fahrenheit temperatures should be related
to everyday occurrences by measuring the temperature
of the classroom, the outside, liquids, body
temperature, and other things found in the
environment.
ESSENTIAL UNDERSTANDINGS
All students should

Understand how to measure temperature in Celsius
and Fahrenheit with a thermometer.
ESSENTIAL KNOWLEDGE AND
SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Read temperature to the nearest degree from real
Celsius and Fahrenheit thermometers and from
physical models (including pictorial representations)
of such thermometers.
Standard 3.13 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
3.13Sa
4
4
Extra Practice
9
14
REFERENCES:
148-149
160-161
167-168
Saxon Math Second Edition
SOL Number
3.13Sa
Page
Lesson
46 continues
Math At Hand: 319-321
Aims: “When It’s Hot, It’s Hot,” Overhead and Underfoot; “Air Temperature,” Primarily Bears;
“What is the Temperature?” Primarily Physics
Technology: http://matti.usu.edu/nlvm/nlvm/nav/vlibraary.html (choose Measurement then find
activities)
Children’s Literature: Hot and Cold by Seymour Simon, About Temperature by Alma Gilleo
Instructional Vignette: (Alternate Teaching Strategies)
 Encourage students to create their own paper thermometers by cutting a narrow slit on a drawn
thermometer at the top and at the bottom. Model for the children by inserting a long, narrow
half red and half white strip of paper. Ask a specific temperature and have the students show
the temperature on their thermometer.
 Have students check temperatures daily in different locations around the building at different
times of the day. Instruct the children to record their findings on drawn thermometers on paper.
Children can color in the exact temperatures with a red crayon and the class can make graphs to
compare temperatures.
Additional Vocabulary:
temperature—A measure of hotness or coldness.
Farenheit—Temperature scale used in the customary system.
Celsius--The scale used in the metric system to measure temperature. Celsius is sometimes called
Centigrade.
Degrees Celsius—The metric unit of measurement for temperature.
Degrees Farenheit—The customary unit of measurement for temperature.
Standard 3.13 continued
Released Test Items:
STANDARD 3.14
3.14
STRAND: GEOMETRY
GRADE LEVEL 3
The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square, rectangle,
triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics, including the
number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
UNDERSTANDING THE STANDARD


The van Hiele theory of geometric understanding
describes how students learn geometry and
provides a framework for structuring student
experiences that should lead to conceptual growth
and understanding.
– Level 0: Pre-recognition. Geometric figures
are not recognized. For example, students
cannot differentiate between three-sided and
four-sided polygons.
– Level 1: Visualization. Geometric figures are
recognized as entities, without any
awareness of parts of figures or
relationships between components of a
figure. Students should recognize and name
figures and distinguish a given figure from
others that look somewhat the same (e.g., “I
know it’s a rectangle because it looks like a
door, and I know that the door is a
rectangle.”).
– Level 2: Analysis. Properties are perceived,
but are isolated and unrelated. Students
should recognize and name properties of
geometric figures (e.g., “I know it’s a
rectangle because it’s closed, it has four
sides and four right angles, and opposite
sides are parallel.”).
A plane geometric figure is any two-dimensional
closed figure. Circles and polygons are examples
of plane geometric figures.
ESSENTIAL KNOWLEDGE AND
SKILLS
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)
All students should


Understand how to identify and describe plane and
solid geometric figures by using relevant
characteristics.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Identify models and pictures of plane geometric
figures (circle, square, rectangle, and triangle) and
solid geometric figures (cube, rectangular prism,
square pyramid, sphere, cone, and cylinder) by
name.

Identify and describe plane geometric figures by
counting the number of sides and angles.

Identify and describe solid geometric figures by
counting the number of angles, vertices, edges, and
by the number and shape of faces.

Compare and contrast characteristics of plane and
solid geometric figures (e.g., circle/sphere,
square/cube, triangle/square pyramid, and
rectangle/rectangular prism), by counting the
number of sides, angles, vertices, edges, and the
number and shape of faces.

Compare and contrast characteristics of solid
geometric figures (i.e., cube, rectangular prism,
square pyramid, sphere, cylinder, and cone) to
similar objects in everyday life (e.g., a party hat is
like a cone).

Identify characteristics of solid geometric figures
(cylinder, cone, cube, square pyramid, and
rectangular prism).
Understand the similarities and differences between
plane and solid figures.
STANDARD 3.14
3.14
STRAND: GEOMETRY
GRADE LEVEL 3
The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square, rectangle,
triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics, including the
number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)

Three-dimensional figures are called solid figures
or simply solids. Solids enclose a region of space.
The interior of both plane and solid figures are not
part of the figure. Solids are classified by the types
of surfaces they have. These surfaces may be flat,
curved, or both.

The study of geometric figures must be active,
using visual images and concrete materials.

Access to a variety of concrete tools such as graph
paper, pattern blocks, geoboards, and geometric
solids is greatly enhanced by computer software
tools that support exploration.

Opportunity must be provided for building and
using geometric vocabulary to describe plane and
solid figures.

A cube is a solid figure with six congruent square
faces and with every edge the same length. A cube
has 8 vertices and 12 edges.

A cylinder is a solid figure formed by two
congruent parallel circles joined by a curved
surface.

A cone is a solid, pointed figure that has a flat,
round face (usually a circle) that is joined to a
vertex by a curved surface.

A rectangular prism is a solid figure in which all
six faces are rectangles with three pair of parallel
congruent opposite faces.

A sphere is a solid figure with all of its points the
same distance from its center.
All students should

Understand how to identify and describe plane and
solid geometric figures by using relevant
characteristics.

Understand the similarities and differences between
plane and solid figures.
ESSENTIAL KNOWLEDGE AND SKILLS
STANDARD 3.14
3.14
STRAND: GEOMETRY
GRADE LEVEL 3
The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square, rectangle,
triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics, including the
number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)

A square pyramid is a solid figure with one square
face and four triangular faces that share a common
vertex.

A face is a polygon that serves as one side of a
solid figure (e.g., a square is a face of a cube).

An angle is formed by two rays with a common
endpoint. This endpoint is called the vertex. Angles
are found wherever lines intersect. An angle can be
named in three different ways by using
– three letters to name, in this order, a point on
one ray, the vertex, and a point on the other
ray;
– one letter at the vertex; or
– a number written inside the rays of the angle.

An edge is the line segment where two faces of a
solid figure intersect.

A vertex is the point at which two lines, line
segments, or rays meet to form an angle. It is also
the point on a three dimensional figure where three
or more faces intersect.

Students should be reminded that a solid geometric
object is hollow rather than solid. The “solid”
indicates a three-dimensional figure.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND
SKILLS
Standard 3.14 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.14Sa
3.14Sb
3.14Sc
3.14Sd
REFERENCES:
Chapter
Lesson
10
Checkpoint
10
Extra Practice
10
10
1
362-365
378
386-387
394, 396
362-365
386-387
SBG does not support 3.18Sd
11
1
11
Saxon Math Second Edition
SOL Number
3.14Sa
3.14Sb
3.14Sc
3.14Sd
Page
Lesson
115 (Does not support all plane figures)
Not supported
115
Not supported
Math Steps: Teacher’s Guide T95, student pages 155-156
Everyday Counts: Teacher’s Guide p. 84-85, 95-97
Math At Hand: 385-392
Aims: “Shaping Out, “Geo-Planes”, and “Playground Geometry”, Hardhatting in a goe-World
Other Books: Marilyn Burns, About Teaching Mathematics, A K-8 Resource, p. 79-99; Marilyn
Burns, Math By All Means; Geometry Grade 3; Lola J. May and Shirley M. Frye, Down to Earth
Mathematics, p. 79-81; Cuisenaire Math Manipulative Kit, “Learning with Geoboards” and
“Learning with Color Tiles”
Technology: http://matti.usu.edu/nlvm.nav/vlibrary.html (choose Geometry then find activities)
Children’s Literature: The Josefina Story Quilt by Eleanor Coerr, Round Buildings, Square
Buildings, and Buildings that Wiggle by Phillip Issagone, Grandfather Tang’s Story by Anne
Tompert, The Greedy Triangle by Marilyn Burns
Virginia Department of Education Training Module: Geometry: Section 1, “Quadrilateral Sort”
Activity; Section 1, “What’s My Rule?” Activity; Section 1, “Quadrilateral Properties Laboratory”
Activity; Section 1 “Meet the Turtle” Activity; Section 3, “Partition the Square” Activity; Section
3, “Cutting Square Puzzles” Activity; Section 3, “Make Your Own Tangrams” Activity; Section 3,
“Spacial Problem Solving/Tangrams” Activity; Section 3, “Origami: Making a Heart” Activity;
Section 4, “Sums of Angles of a Triangle” Activity; Section 4, “Do Congruent Triangles Tessellate?”
Activity; Section 4, “Polyhedron Sort” Activity; Section 4, “What’s My Shape? Ask About Me.”
Activity; Section 4, “Take It Apart” Activity; Section 4, “Building Polyhedra” Activity; Section 5,
“Dominoes & Triominoes” Activity; Section 5, “Tetrominoes” Activity; Section 5, “Pentominoes”
Activity; Section 5, “Areas with Pentominoes” Activity; Section 5, “Hexominoes” Activity;
Section 5, “Perimeters with Hexominoes” Activity
Standard 3.14continued
Instructional Vignette: (Alternate Teaching Strategies)
 Create geometric planes using geoboards.
 Sort geometric solids by the number of faces, bases, corners, and edges.
 Encourage students to participate in a number of tangram activities.
 Have students staple together sheets of paper to make a booklet.
Label the pages triangles, squares, rectangles, and circles.
Have students cut-out pictures of objects from newspapers and magazines that show
these shapes. Paste these shapes onto the appropriate pages of the booklet.
 Ask students to identify plane and solid figures around the classroom.
 Encourage students to create space figures using toothpicks and mini-marshmallows.
The figures can be dipped in a food colored bubble solution in order for the student to see
the faces. Ask the children to identify the number of faces, edges, and corners.
Additional Vocabulary:
square- A parallelogram with four congruent sides and four right angles.
rectangle- A quadrilateral with two pairs of congruent, parallel sides and four right angles.
triangle- A polygon with three sides and three angles.
circle- A plane figure with all points the same distance from a fixed point called a center.
square corner- A corner that forms a right angle.
pyramid- A polyhedron whose base is a polygon and whose other faces are triangles that share a
common vertex.
base of a solid figure- A special face of a solid figure.
congruent figures- Figures with the same size and shape.
Standard 3.14 continued
Released Test Items:
STANDARD 3.15
3.15
STRAND: GEOMETRY
The student will identify and draw representations of points, line segments, rays, angles, and lines.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)



GRADE LEVEL 3
A point is an exact location in space. It has no length
or width. Usually, a point is named with a capital
letter.
A line is a collection of points going on and on in
both directions. It has no endpoints. When a line is
drawn, at least two points on it can be marked and
given capital letter names. The line can also be
named with a single, lower-case letter. Arrows must
be drawn to show that the line goes on in both
directions infinitely.
A line segment is part of a line. It has two endpoints
and includes all the points between those endpoints.
The endpoints are used to name a line segment.

A ray is part of a line. It has one endpoint and
continues on and on in one direction.

An angle is formed by two rays having a common
endpoint. This endpoint is called the vertex. Angles
are found wherever lines and line segments intersect.
An angle can be named in three different ways by
using
– three letters to name, in this order, a point on one
ray, the vertex, and a point on the other ray;
– one letter at the vertex; or
– a number written inside the rays of the angle.

Angle rulers may be particularly useful in developing
the concept of an angle.
All students should

Understand that line segments and angles are
fundamental components of plane polygons.

Understand that a line segment is a part of a line, has
two end points, and contains all the points between
those two endpoints.

Understand that points make up a line.

Understand that a line continues indefinitely in two
opposite directions.

Understand that a ray is part of a line, has one
endpoint, and continues indefinitely in only one
direction.

Understand that an angle is formed by two rays
having a common endpoint.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Identify examples of points, line segments, rays,
angles, and lines.

Draw representations of points, line segments, rays,
angles, and lines, using a ruler or straightedge.
Standard 3.15 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.15Sa
3.15Sb
REFERENCES:
Chapter
Lesson
10
Checkpoint
Chapter Test
10
2
366-367, 394
378
397
367
Saxon Math Second Edition
SOL Number
3.15Sa
3.15Sb
2
Page
Lesson
6, 113 (throughout)
6, 113 (throughout)
Math Steps: Teacher’s Guide T93, student pages 147-148
Math At Hand: 334-341, 345
Aims: “From Wedges to Wangles” and “Waxed Wangles”, Hardhatting in a Geo-World
Other Books: Marilyn Burns, About Teaching Mathematics, A K-8 Resource, “Points Dividing a
Line”
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Geometry then find activities)
Children’s Literature: The Dot and the Line by Norton Juster, The Greedy Triangle by Marilyn
Burns
3.15 Instructional Vignette: (Alternate Teaching Strategies)
 Use a pair of straws to represent line segments. Ask students to form a right angle and to show
angles that are not right angles.
 Instruct students to throw down a handful of toothpicks on their desk and identify lines, rays,
and angles.
 Have students create a "Geo-Picture". Ask the children to make a green point, yellow ray, blue
line, purple parallel lines, orange intersecting lines and red line segments on the top half of a
folded piece of paper. Then ask students to come up with a picture on the bottom half of the
paper using those “lines”.
 Create a geo-rule by joining two pieces of 2” x 12” paper with a paper fastener.
Encourage students to find angles in the classroom using their geo-rule.
 Ask students to carefully cut the radius of two different colors of paper plates.
Slide the paper plates together and rotate the plates to form different angles.
Standard 3.15 continued
Additional Vocabulary:
endpoint- A point at either end of a line segment or arc, or a point at one end of a ray.
3.15
Released Test Items:
STANDARD 3.16
3.16
STRAND: GEOMETRY
The student will identify and describe congruent and noncongruent plane figures.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)


GRADE LEVEL 3
Congruent plane figures are figures having exactly
the same size and shape. Noncongruent plane
figures are figures that are not exactly the same size
and shape. Opportunities for exploring figures that
are congruent and/or noncongruent can best be
accomplished by using physical models.
Have students identify figures that are congruent or
noncongruent by using direct comparisons and/or
tracing procedures.
All students should

Understand that congruent plane figures match
exactly.

Understand that noncongruent plane figures do not
match exactly.

Understand that congruent plane figures remain
congruent even if they are in different spatial
orientations.

Understand that noncongruent plane figures remain
noncongruent even if they are in different spatial
orientations.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Identify examples of congruent and noncongruent
figures. Verify their congruence by laying one on
top of the other using drawings or models.

Determine and explain why plane figures are
congruent or noncongruent, using tracing
procedures.
Standard 3.16 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.16Sa
3.16Sb
3.16Sc
3.16Sd
REFERENCES:
Chapter
Lesson
10
Checkpoint
10
10
Checkpoint
10
10
Checkpoint
10
10
Checkpoint
4
4
5
4
5
370-371, 395
378
372-373
374-375
378
370-371
373
378
370-371
373
378
Saxon Math Second Edition
SOL Number
3.16Sa
3.16Sb
3.16Sc
3.16Sd
5
6
Page
Lesson
58
58
12
Not Supported
Math At Hand: 372, 380
Aims: “Dick and Bob are Twins”, Magazine 4 Issue 1; “Halves and Half-Nots”, Pieces and
Patterns; “Mirrors Reflect”, Primarily Physics; “Make a Kaleidoscope”, Magazine Volume 4
Issue 2; “Through the Looking Glass”, Magazine Volume 4 Issue 3
Other Books: Marilyn Burns, About Teaching Mathematics, A K-8 Resource, p. 79-99 and Math
By All Means; Geometry Grade 3, p. 34-35, 89-95, and 104-110; Lola J. May and Shirley M. Frye,
Down to Earth Mathematics, p. 87-88; Cuisenaire Math Manipulative Kit, “Learning with Pattern
Blocks”, p. 10-13
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Geometry then find activities)
Children’s Literature: Grandfather Tang’s Story by Ann Tompert, Reflections by Ann Jonas,
Mirror Magic by Seymour Simon, The Patchwork Quilt by Valerie Flournoy, The Snowy Day by
Ezra Jacks Keats
Virginia Department of Education Training Modules: Geometry: Section 3, “Butterfly
Symmetry” activity; Section 3, “Copy Cat” activity; Section 3, “Recover the Symmetry” activity;
Section 3, “Folded Shapes” activity; Section 3, “Origami: Making a Square” activity; Section 3,
“Origami: Making a Heart” activity; Section 5, “Dominoes & Triominoes” activity; Section 5,
“Tetrominoes” activity; Section 5, “Pentominoes” activity; Section 5 “Areas with Pentominoes”
activity; Section 5 “Hexominoes” activity; Section 5 “Perimeters with Hexominoes” activity
3.16 Instructional Vignette: (Alternate Teaching Strategies)
 Instruct students to work with partners in finding tangram pieces that are congruent.
1 Model for students by folding a piece of paper of a design in half. Ask the children
to cut out the design and open it up. The students will be amazed to have created a
symmetrical figure.
2 Have the students draw a line of symmetry in given pictures and then test the symmetry by
using a mirror or a mira.
3 Have the students fold a sheet of paper and draw a picture on one side of the paper. Ask the
students to exchange papers and draw the other half of the picture to complete a
symmetrical design.
Standard 3.16 continued
Released Test Items:
3.16 Released Test Items:
STANDARD 3.17
3.17
STRAND: PROBABILITY AND STATISTICS
The student will
a) collect and organize data, using observations, measurements, surveys, or experiments;
b) construct a line plot, a picture graph, or a bar graph to represent the data; and
c) read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)




GRADE LEVEL 3
Investigations involving data should occur
frequently and relate to students’ experiences,
interests, and environment.
Formulating questions for investigations is studentgenerated at this level. For example: What is the
cafeteria lunch preferred by students in the class
when four lunch menus are offered?
The purpose of a graph is to represent data gathered
to answer a question.
Bar graphs are used to compare counts of different
categories (categorical data). Using grid paper
ensures more accurate graphs.
– A bar graph uses parallel, horizontal or vertical
bars to represent counts for categories. One
bar is used for each category, with the length
of the bar representing the count for that
category.
– There is space before, between, and after the
bars.
– The axis displaying the scale representing the
count for the categories should extend one
increment above the greatest recorded piece
of data. Third grade students should collect
data that are recorded in increments of whole
numbers, usually multiples of 1, 2, 5, or 10.
– Each axis should be labeled, and the graph
should be given a title.
–
Statements representing an analysis and
interpretation of the characteristics of the data
in the graph (e.g., similarities and differences,
All students should

Understand how data can be collected and
organized.

Understand that data can be displayed in different
types of graphs depending on the data.

Understand how to construct a line plot, picture
graph, or bar graph.

Understand that data sets can be interpreted and
analyzed to draw conclusions.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Formulate questions to investigate.

Design data investigations to answer formulated
questions, limiting the number of categories for data
collection to four.

Collect data, using surveys, polls, questionnaires,
scientific experiments, and observations.

Organize data and construct a bar graph on grid
paper representing 16 or fewer data points for no
more than four categories.

Construct a line plot with no more than 30 data
points.

Read, interpret and analyze information from line
plots by writing at least one statement.

Label each axis on a bar graph and give the bar
graph a title. Limit increments on the numerical axis
to whole numbers representing multiples of 1, 2, 5,
or 10.

Read the information presented on a simple bar or
picture graph (e.g., the title, the categories, the
description of the two axes).

Analyze and interpret information from picture and
bar graphs, with up to 30 data points and up to 8
categories, by writing at least one sentence.
STANDARD 3.17
3.17
STRAND: PROBABILITY AND STATISTICS
The student will
a) collect and organize data, using observations, measurements, surveys, or experiments;
b) construct a line plot, a picture graph, or a bar graph to represent the data; and
c) read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)
–

Statements representing an analysis and
interpretation of the characteristics of the data
in the graph (e.g., similarities and differences,
least and greatest, the categories, and total
number of responses) should be written.
A line plot shows the frequency of data on a number
line. Line plots are used to show the spread of the
data and quickly identify the range, mode, and any
outliers.
Number of Books Read
Each x represents one student

GRADE LEVEL 3
When data are displayed in an organized manner,
the results of the investigations can be described and
the posed question answered.
Recognition of appropriate and inappropriate
statements begins at this level with graph
interpretations.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS

Describe the categories of data and the data as a
whole (e.g., data were collected on four ways to
cook or prepare eggs — scrambled, fried, hard
boiled, and egg salad — eaten by students).

Identify parts of the data that have special
characteristics, including categories with the
greatest, the least, or the same (e.g., most students
prefer scrambled eggs).

Select a correct interpretation of a graph from a set
of interpretations of the graph, where one is correct
and the remaining are incorrect. For example, a bar
graph containing data on four ways to cook or
prepare eggs — eaten by students show that more
students prefer scrambled eggs. A correct answer
response, if given, would be that more students
prefer scrambled eggs than any other way to cook or
prepare eggs.
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.17cSa
3.17cSb
3.17cSc
3.17cSd
3.17c2Se
3.17cSf
3.17cSg
REFERENCES:
Chapter
Lesson
7
Checkpoint
No Information
7
7
Checkpoint
Extra Practice
No Information
No Information
7
7
Checkpoint
Not Supported
3
256-259
266
3
4
256-259
260-262
267
280-281
3
4
258
262-263
266-267
Saxon Math Second Edition
SOL Number
3.17Sa
3.17Sb
3.17Sc
3.17Sd
3.17Se
3.17Sf
3.17Sg
Page
Lesson
2, 40
Not Supported
2, 40
Not Supported
Not Supported
2, 40
Not Supported
Everyday Counts: Teacher’s Guide p.24-25, 47, 56-57, 80-81, 105-106
Math At Hand: 269-282
Aims: “Watching the Weather”, Primarily Bears; “Are You Square?” and “Heavy Work”,
Overhead and Underfoot
3.17
Teacher Resources continued
Other Books: Marilyn Burns, About Teaching Mathematics, A K-8 Resource, p.59-78; Lola J.
May and Shirley M. Frye, Down to Earth Mathematics, p.106-108
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Data Analysis & Probability then
find activities)
Children’s Literature: Gregory, the Terrible Eater by Mitchell Sharmat, 20,000 Baseball Cards
Under the Sea by JonBaller and Susan Schade, “Uganda Near Kabalega Falls” In Market by Ted
Lewin
Virginia Department of Education Training Modules: Probability and Statistics: Section 1,
Activity 1 “Sandwich Problem”; Section 1, Activity 2 “Why is Probability and Statistics
Important?”; Section1, Activity 3 “The Big Ideas of Probability and Statistics”; Section 1, Activity
4 “ What are the Goals of the Institute?”; Section 1, Activity 5 “Sixth Grade Mystery Data”;
Section 1, Activity 6 “Posing Questions”; Section 2, Activity 5 “What’s Missing”; Section 2,
Activity 7 “Bar Graphs”; Section 3, Activity 7 “Graph Detective”; Section 4, Activity 5 “Graphical
Interpretations”; Section 4, Activity 6B “Matching Game: Graphs, Data, Summary”; Section 4,
Activity 8 “Draw the Graph Game”; Section 4, Activity 9 “ Interpreting the Data”
Instructional Vignette: (Alternate Teaching Strategies)
 Collect graphs from newspapers and magazines from which to interpret information. Ask
students to write a minimum of two statements about each of the graphs collected.
 Have students conduct a survey to identify a favorite pet, sport, or food. Ask students to draw a
picture of that item or develop a picture using symbols to represent that item. Instruct students
to put the number of pictures corresponding to the number surveyed of the favorite item.
Remind students to include a title and a key and use the collected information to create a bar
graph using grid paper. Students should then write five questions about the information being
presented on their graphs. Instruct the students to exchange graphs and questions with a
partner. Students will read and interpret the graphs and answer the questions.
 Encourage students to develop their own picture graphs from surveyed information obtained
from classmates. Tell students to use symbols of their choosing to represent multiple students
in the classroom. Direct students to write at least two statements about their completed picture
graphs.
Standard 3.17 continued
Additional Vocabulary:
bar graph- A graph that uses bars to show data.
axis- A reference line from which distances or angles are measures in a coordinate grid.
pictograph- A graph that uses pictures or symbols to show data.
line plots- A graph that shows data along a number line.
cluster- A group of data that appear often on a line plot.
Released Test Items:
3.17 Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
3.17aSa
7
Extra Practice
7
Extra Practice
1
3.17aSb
7
Checkpoint
5
264-265
266-267
3.17aSc
7
7
7
7
Extra Practice
7
6
7
3
5
268- 269, 282
270-271, 282
256-259
264
280
259
3.17bSa
3.17bSb
4
3
Page
252-253
280
260-263
281
SBG does not support construction of a line plot or description of each axis of a bar graph..
REFERENCES:
Saxon Math Second Edition
SOL Number
3.17aSa
3.17aSb
3.17aSc
3.17bSa
3.17bSb
Lesson
Not supported
2
2, 135
2, 55
22
Everyday Counts: Teacher’s Guide p. 24-25, 47, 56-57, 80-82, 105-106
Math At Hand: 269-282
Aims: “Gummy Bears” and “Teddy Bears Playing in the Den”, Primarily Bears; “Cat Scan”, Magazine Volume 7
Issue 7; “Fish Chips”, Mostly Magnets; “I’m Stuck on You” Magazine Volume 9 Issue 5
Other Books: Marilyn Burns, About Teaching Mathematics, A K-8 Resource, p. 59-78; Lola J. May and Shirley M.
Frye, Down to Earth Mathematics, p. 106-108; Roberta Barrata-Lorton, Mathematics, A Way of Thinking, Chapter 15
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Data Analysis & Probability then find activities)
Children’s Literature: A Cache of Jewels by Ruth Heller, Gregory, the Terrible Eater by Mitchell Sharmat, 20,000
Baseball Cards Under the Sea by Jon Baller and Susan Schada, “Uganda Near Kabalega Falls” in Market by Ted Lewin
Virginia Department of Education Training Module: Probability & Statistics: Section 1, Activity 1 “Sandwich
Problem”; Section 1, Activity 2 “Why is Probability and Statistics Important?”; Section 1, Activity 3 “The Big Ideas of
Probability and Statistics”; Section 1, Activity 4 “What are the Goals of the Institute?”; Section 2, Activity 1
“Collecting Data: Count the Ways”; Section 2, Activity 2 “Random Sampling”; Section 2, Activity 3 “Household
Data”, Section 2, Activity 6 “Object Graphs and Picture Graphs”; Section 2, Activity 7 “Bar Graphs”
Standard 3.17 continued
Instructional Vignette: (Alternate Teaching Strategies)
 Give each student his or her own bag of M&Ms or Skittles.
Ask children to display all the colors within the bag using either a bar or picture graph.
 Ask students to create a bar and a picture graph based upon a survey of favorite TV shows of
the students in their third grade class.
 Create a weekly bar graph of daily temperatures to display in the room.
 Observe a grid on an overhead transparency and take turns constructing a bar graph on the
transparency, complete with a title and a key. Share with students possible topics that could be
graphed such as favorite television programs, food, sports, clothing items and soft drinks.
Additional Vocabulary:
bar graph- A graph that uses the height or length of rectangles to compare data.
axis- A reference line from which distances or angles are measured in a coordinate grid.
Standard 3.17 continued
Released Test Items:
3.17 Continued
STANDARD 3.18
3.18
STRAND: PROBABILITY AND STATISTICS
The student will investigate and describe the concept of probability as chance and list possible results of a given situation.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)


GRADE LEVEL 3
A spirit of investigation and experimentation should
permeate probability instruction, where students are
actively engaged in explorations and have
opportunities to use manipulatives.
Investigation of experimental probability is
continued at this level through informal activities
using two-colored counters, spinners, and random
number generators (number cubes).

Probability is the chance of an event occurring.

The probability of an event occurring is the ratio of
desired outcomes to the total number of possible
outcomes. If all the outcomes of an event are
equally likely to occur, the probability of the event =
number of favorable outcomes
.
total number of possible outcomes

The probability of an event occurring is represented
by a ratio between 0 and 1. An event is “impossible”
if it has a probability of 0 (e.g., the probability that
the month of April will have 31 days). An event is
“certain” if it has a probability of 1 (e.g., the
probability that the sun will rise tomorrow
morning).

When a probability experiment has very few trials,
the results can be misleading. The more times an
experiment is done, the closer the experimental
probability comes to the theoretical probability (e.g.,
a coin lands heads up half of the time).

Students should have opportunities to describe in
informal terms (i.e., impossible, unlikely, as likely
as, equally likely, likely, and certain) the degree of
likelihood of an event occurring. Activities should
include real-life examples.
All students should

Investigate, understand, and apply basic concepts of
probability.

Understand that probability is the chance of an event
happening.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Define probability as the chance that an event will
happen.

List all possible outcomes for a given situation (e.g.,
heads and tails are the two possible outcomes of
flipping a coin).

Identify the degree of likelihood of an outcome
occurring using terms such as impossible, unlikely,
as likely as, equally likely, likely, and certain.
STANDARD 3.18
3.18
STRAND: PROBABILITY AND STATISTICS
GRADE LEVEL 3
The student will investigate and describe the concept of probability as chance and list possible results of a given situation.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)

For any event, such as flipping a coin, the equally
likely things that can happen are called outcomes.
For example, there are two equally likely outcomes
when flipping a coin: the coin can land heads up, or
the coin can land tails up.

A sample space represents all possible outcomes of
an experiment. The sample space may be organized
in a list, table, or chart.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS
3.18 Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
Chapter
Lesson
3.18Sa
7
7
7
Checkpoint
Chapter Test
7
Checkpoint
8
9
10
3.18Sb
2.18Sc
REFERENCES:
272
274-275
276, 276a
278
283
272-273
278
Saxon Math Second Edition
SOL Number
3.18Sa
3.18Sb
3.18Sc
8
Page
Lesson
90
90
90
Math Steps: Teacher’s Guide T97, student pages 163-164
Math At Hand: 285-292
Aims: “Sharing Birthdays”, Magazine Volume 9 Issue 6; “Gimme a Gimel”, Magazine Volume 8
Issue 5; “Ahlewus” Magazine Volume 4 Issue 10; “Scissors, Rock, or Paper?”, Magazine 3
Volume 5
Other Books: Marilyn Burns, About Teaching Mathematics, A K-8 Resource, p. 59-78 and A
Collection of Math Lessons from Grade 3 through 6, p. 45-56; Cuisenaire Manipulative Kit, “Two
Color Counter Book”
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Data Analysis & Probability
then find activities)
Children’s Literature: Calculations and Chance by Laura Buller, Jesse Bear What Will You Wear
by Nancy White Carlstrom, 100 Hungry Ants by Elinor J. Pinczes
Virginia Department of Education Training Module: Probability and Statistics:
Section 1, Activity 1 “Sandwich Problem”; Section 1, Activity 2 “Why is Probability and
Statistics Important?”; Section 1, Activity 3 “The Big Ideas of Probability and
Statistics”; Section 1, Activity 4 “What are the Goals of the Institute?”; Section 4,
Activity 9 “Interpreting the Data”; Section 5, Activity 1A “Between 0 and 1”; Section 5,
Activity 2 “ What’s In the Bag?”; Section 5, Activity 3 “Fair or Not Fair”
Standard 3.18 continued
Instructional Vignette: (Alternate Teaching Strategies)
 Play coin toss and keep track by tally marks.
 Shake color counter up in a bag and pour out onto table and observe which color is facing up.
Keep track of the number of trials and the results of each trial.
 Use a spinner or dice to participate in probability activities.
 Cut a small hole in the bottom of a shoebox. Put two marbles in the box and replace the lid.
Hold the lid in place with rubber bands. Shake the box. Allow one of the marbles to roll over
the hole, so that the color is visible. Mark the color on a tally sheet. Repeat 20 times and
observe how many times that each color appears. Repeat this procedure with different
combinations of colors, such as 2 of one color and 1 of another, or 3 of one color and 2 each of
two colors.
 Have students play a prediction game with a partner. Student A will get a paper bag and ten
manipulatives such as marbles, counting bears, color tiles, and number cubes. Student A will
determine how many of each color to put in the bag (e.g., 2 blue, 8 red). Student B will reach
in the bag and draw out a manipulative. Student B will record what was drawn and replace the
item in the bag. Student B will repeat this procedure 10 times. When student B has finished,
he/she will make a prediction as to how many of each color are actually in the bag. Once the
prediction is made, Student A will share the actual contents of the bag with Student B. The
students will compare the prediction with the actual contents. The students will switch roles
and continue to practice making predictions.
Additional Vocabulary:
impossible event- An event with a probability of 0.
unlikely event- An event with a probability that is close to zero.
equally likely- Having the same chance, or probability.
certain event- Something that will definitely happen. An event with the probability of 1.
likely event-- An event with a probability that is close to 1.
table- An organized way to list data. Tables usually have rows and columns data.
Standard 3.18 continued
Released Test Items:
3.18 Continued
STANDARD 3.19
3.19
STRAND: PATTERNS, FUNCTIONS, AND ALGEBRA
The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns,
using the same or different forms.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)

Exploring patterns requires active physical and
mental involvement.

The use of materials to extend patterns permits
experimentation or trial-and-error approaches that
are almost impossible without them.

GRADE LEVEL 3
Reproduction of a given pattern in a different
representation, using symbols and objects, lays the
foundation for writing numbers symbolically or
algebraically.

The simplest types of patterns are repeating patterns.
In each case, students need to identify the basic unit
of the pattern and repeat it. Opportunities to create,
recognize, describe, and extend repeating patterns
are essential to the primary school experience.

Growing patterns are more difficult for students to
understand than repeating patterns because not only
must they determine what comes next, they must
also begin the process of generalization. Students
need experiences with growing patterns in both
arithmetic and geometric formats.
 Create an arithmetic number pattern. Sample
numeric patterns include
– 6, 9, 12, 15, 18, (growing pattern);
– 1, 2, 4, 7, 11, 16, (growing pattern);
– 20, 18, 16, 14,…(growing pattern); and
– 1, 3, 5, 1, 3, 5, 1, 3, 5 (repeating pattern).
All students should

Understand that numeric and geometric patterns can
be expressed in words or symbols.

Understand the structure of a pattern and how it
grows or changes.

Understand that mathematical relationships exist in
patterns.

Understand that patterns can be translated from one
representation to another.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

Recognize repeating and growing numeric and
geometric patterns (e.g., skip counting, addition
tables, and multiplication tables).

Describe repeating and growing numeric and
geometric patterns formed using numbers, tables,
and/or pictures, using the same or different forms.

Extend repeating and growing patterns of numbers
or figures using concrete objects, numbers, tables,
and/or pictures.
STANDARD 3.19
3.19
STRAND: PATTERNS, FUNCTIONS, AND ALGEBRA
GRADE LEVEL 3
The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns,
using the same or different forms.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)
 In geometric patterns, students must often recognize
transformations of a figure, particularly rotation or
reflection. Rotation is the result of turning a figure
around a point or a vertex, and reflection is the
result of flipping a figure over a line.
 Sample geometric patterns include
Δ O O Δ Δ O O O Δ Δ Δ ; and
– □□★★□★□□★★□★.
–O
A table of values can be analyzed to determine the
pattern that has been used, and that pattern can then
be used to find the next value.
ESSENTIAL UNDERSTANDINGS
ESSENTIAL KNOWLEDGE AND SKILLS

3.19 Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.19Sa
3.19Sb
3.19Sc
Chapter
1
Checkpoint
5
5
5
5
12
Extra Practice
1
5
5
5
6
Checkpoint
9
1
5
5
5
Lesson
1
6
7
7
11
4
1
6
7
7
2
2
1
6
7
7
Page
2-3
16
187
191
229
198-199
444-445
480
3
187
191
229
216-217
267
328-329
3
187
191
229
Note: SBG does not support geometric patterns strongly.
REFERENCES:
Saxon Math Second Edition
SOL Number
Lesson
2-135
3.19Sa
2-135
3.19Sb
2-135
3.19Sc
Everyday Counts: Teacher’s Guide p. 2-4, 14-15, 27-28, 39-40, 49, 61-62, 71-72, 84-85, 95
Math At Hand: 401-402
Aims: “Taking Turns with Triangles”, Magazine 9 Volume 5; “Teddy Bears Go to the Movies”, “Who’s
Not Home”, and “Bear Soccer”, Primarily Bears; “Now What?”, What’s Next, Volume 3; “In and Out”,
What’s Next, Volume 1; “Picking Apart Patterns”, Magazine Volume 8 Issue 5
Other Books: Marilyn Burns, About Teaching Mathematics, A K-8 Resource, p. 112-123 and A Collection of Math
Lessons from Grade 3 through 6, p. 57-69; Robert Baratta-Lorton, Mathematics: A Way of Thinking, Chapter 2 and 3;
Lola J. May and Shirley M. Frye, Down to Earth Mathematics, p. 105-106
Technology: http://matti.usu.edu/nlvm/nav/vlibrary.html (choose Algebra then find activities), Math Blaster: In
Search of Spot, Davison
Children’s Literature: What Comes in 2’s, 3’s, and 4’s by Suzanne Aker, The King’s Commissioners by Aileen
Friedman, King’s Chessboard by David Birch, Tar Beach by Faith Ringgold, Caps for Sale by Esphyr Slobodkino
Virginia Department of Education Training Module: Patterns, Functions & Algebra: Section 1, Activity 1
“Creating and Identifying Patterns (Warm-Up); Section 1, Activity 2 “The Big Ideas of Algebra”; Section 1, Activity 3
“ Why is Algebraic Thinking Important?”; Section 1, Activity 4 “ Tibby (warm-up) What’s In the Box?”; Section 1,
Activity 5 “Play!”; Section 1 Activity 6 “Missing Pieces”; Section 1 Activity 8 “ Who Am I? Game”; Section1,
Activity 9 “Differences- Train and Games”; Section 2, Activity 1A “I Need A Necktie, Please!”; Section 2, Activity 1B
“Up, Up and Away!”; Section 2, Activity 1C “How High Are My Castle Walls?”; Section 2 Activity 10 “Exactly How
Many Doors Are We Talking About?”; Section 2, Activity 2A “Tons of Tunnels”; Section 2, Activity 3A “The Jeweled
Snake”; Section 2, Activity 4G “Arrow Math”; Section 2, Activity 5A “The King’s Commissioner”; Section 2, Activity
5B “The King’s Chessboard”; Section 4, Activity 6 “Toothpick Patterns”; Section 4, Activity 7 “Graphing Patterns”;
Section 4, Activity 11 “Reflections on Functions”
Standard 3.19 continued
Instructional Vignette: (Alternate Teaching Strategies)
 Use manipulatives or familiar objects such as beads, blocks, cereal, cards, chalk, pattern blocks,
buttons, geometric shapes, colored cubes and colored bears to create and extend a pattern.
Differentiate between growing and repeating patterns and ask the children to create such
patterns.
 Instruct students to work in pairs using interlocking cubes. One student should build a pattern
with cubes by making a succession of cube towers. Ask the students to add a fixed number of
cubes to each succeeding tower (e.g. starting with one cube and adding three cubes each time in
order to form towers of 1, 4, 7, 10, etc.). Direct the partner to read the pattern and determine
what number is being added each time and then continues the pattern. Reverse roles.
 Have students look for patterns in such bathroom and floor tiles, wallpaper, quilts, and clothing
both at home and at school.
 Have students use calculators and the constant function feature to program a skip count. Ask
students to press “+, a number of their choosing, =, =, =, =, “ and the calculator will count by
that number. The students should then predict what the next number will be before they press
the equal key.
Additional Vocabulary:
pattern- A sequence of objects, events, or ideas that repeat.
Released Test Items:
Standard 3.19 continued
Released Test Items continued
STANDARD 3.20
3.20
STRAND: PATTERNS, FUNCTIONS, AND ALGEBRA
The student will
a) investigate the identity and the commutative properties for addition and multiplication; and
b) identify examples of the identity and commutative properties for addition and multiplication.
UNDERSTANDING THE STANDARD
ESSENTIAL UNDERSTANDINGS
(Background Information for Instructor Use Only)




GRADE LEVEL 3
Investigating arithmetic operations with whole
numbers helps students learn about several different
properties of arithmetic relationships. These
relationships remain true regardless of the numbers.
The commutative property for addition states that
changing the order of the addends does not affect the
sum (e.g., 4 + 3 = 3 + 4). Similarly, the commutative
property for multiplication states that changing the
order of the factors does not affect the product (e.g., 2
 3 = 3  2).
The identity property for addition states that if zero is
added to a given number, the sum is the same as the
given number. The identity property of multiplication
states that if a given number is multiplied by one, the
product is the same as the given number.
A number sentence is an equation with numbers (e.g.,
6 + 3 = 9; or 6 + 3 = 4 + 5).
All students should

Understand that mathematical relationships can be
expressed using number sentences.

Understand the identity property for addition.

Understand the identity property for multiplication.

Understand the commutative property of addition.

Understand the commutative property of
multiplication.

Understand that quantities on both sides of an equals
sign must be equal.

Understand that quantities on both sides of the not
equal sign are not equal.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical
communication, mathematical reasoning, connections,
and representations to

Investigate the identity property for addition and
determine that when the number zero is added to
another number or another number is added to the
number zero, that number remains unchanged.
Examples of the identity property for addition are
0 + 2 = 2; 5 + 0 = 5.

Investigate the identity property for multiplication
and determine that when the number one is multiplied
by another number or another number is multiplied by
the number one, that number remains unchanged.
Examples of the identity property for multiplication
are 1 x 3 = 3; 6 x 1 = 6.

Recognize that the commutative property for addition
is an order property. Changing the order of the
addends does not change the sum (5 + 4 = 9 and 4 + 5
= 9).

Recognize that the commutative property for
multiplication is an order property. Changing the
order of the factors does not change the product (2 
3 = 3  2).

Write number sentences to represent equivalent
mathematical relationships (e.g., 4 x 3 = 14 - 2).

Identify examples of the identity and commutative
properties for addition and multiplication.
Standard 3.20 continued
Teacher Resources:
Core Text: Silver Burdett Ginn Math (1999)
SOL Number
3.20aSa
3.20aSb
3.20bSa
REFERENCES:
SOL Number
3.20Sa
3.20Sb
3.20Sc
Chapter
Lesson
Page
Lessons in Silver Burdett Ginn text did not correlate with Virginia
Sol 3.25.
Lessons in Silver Burdett Ginn text did not correlate with Virginia
Sol 3.25.
Lessons in Silver Burdett Ginn text did not correlate with Virginia
Sol 3.25.
Saxon Math Second Edition
Lesson
47
47
Not Supported
Everyday Counts: Teacher’s Guide p. 4-6, 15
Math At Hand: 216-218, 227-229
Technology: http://matti,usu.edu/nlvm/nav/vlibrary.html (choose Algebra then find activities)
Children’s Literature: “Little Bits” by Ciardi
Virginia Department of Education Training Module: Patterns, Functions, & Algebra: Section 1,
Activity 1 “Creating and Identifying Patterns (warm-up)”; Section 1, Activity 2 “The Big Ideas of Algebra”;
Section 1, Activity 3 “ Why is Algebraic Thinking Important?”; Section 1, Activity 4 “Tibby (warm-up)
What’s In the Box?”; Section 2, Activity 1C “How High Are My Castle Walls?”; Section 2, Activity 10
“Exactly How Many Doors Are We Talking About?”; Section 2, Activity 2A “Tons of Tunnels”; Section 2,
Activity 3A “The Jeweled Snake”; Section 2, Activity 5A “The King’s Commissioner”; Section 2, Activity
5B “The King’s Chessboard”; Section 4, Activity 6 “Toothpick Patterns”; Section 4, Activity 11
“Reflections on Functions”; Section 5, Activity 4 “Can You Make The Scale Balance”
Standard 3.20 continued
Instructional Vignette: (Alternate Teaching Strategies)
 Use cubes to create number sentences that show equivalent sides.
(
+
=
+
) (2+2) = (1+3)
 Have children form a circle on the floor. Pass around a ball or some other object while playing
music. When the music stops, the player holding the ball must answer a question generated by
the teacher involving the commutative property. If the player answers incorrectly, he/she is out
of the game. Play continues until only one player remains.
 Play “I am. Who is?” with equivalent mathematical relationships. Create just enough cards for
each student to have and write statements on each card such as:
“I am 8 + 0. Who is equivalent to 4 x 3?”
“I am 2 x 6. Who is equivalent to 4 + 5?”
“I am 6 + 3. Who is equivalent to 2 x 4?” Play should continue until it returns to the
first child.
Standard 3.20 continued
Additional Vocabulary:
commutative property- Changing the order of addends or factors does not change the sum or
product.
Released Test Items:
Lexi had 6 fish in her fish tank. Her
dad bought her some more fish. After
that, Lexi had 14 fish in her tank. How
many fish did Lexi’s dad buy for her?
F
G
H
J
8
9
12
20