Chapter Resources
Grade 4, Chapter 6
Contents
Unit 3: Multiplication and Division
• Unit 3 Prerequisite Skills Test
• Unit 3 Pretest
• Family Letter/Carta a la familia
Individual and Class Record Sheets
Resources for Chapter 6: Relate Multiplication and Division
• Lesson Quizzes Lessons 6.1–6.5
Daily Routines
Reteach
Practice
Enrichment
Leveled Problem Solving
Homework
• Chapter 6 Test
Individual and Class Record Sheets
B
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Booklet 6 of 29
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Name
Unit 3 Prerequisite
Skills Test
Date
Unit 3 Prerequisite Skills Test
Show the expressions using addition.
1
2×4
2
3×5
Solve.
3
How can 7 × 4 be solved using addition?
4
What division does 12 – 3 – 3 – 3 – 3 = 0 show?
5
Mary wants to show 20 ÷ 5 using subtraction. How can she show this?
-
6
What is the product of 7 × 8?
Assessment Resources 4
-
-
7
-
What is the product of 6 and 3?
6–3
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73744_U3_US.indd 6–3
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Name
Unit 3 Prerequisite
Skills Test
Date
8
What is 0 × 5?
9
What is 6 ÷ 2?
10
What is 5 ÷ 5?
11
What is 9 ÷ 3?
12
Kenesha has 9 boxes of crayons with 8 crayons in each box. What multiplication
sentence shows how many crayons she has?
13
Each of Erik’s 4 friends gave him 9 marbles. How many marbles did Erik receive?
14
Lian decides to plant a vegetable garden. Her garden looks like this:
What multiplication sentence shows how many plants Lian has in her garden?
Assessment Resources 4
6–4
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73744_U3_US.indd 6–4
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Name
Unit 3 Prerequisite
Skills Test
Date
Find the missing number in each number sentence.
15
17
6×
= 24
16
42 ÷
=7
Lee had a bag of buttons. She divided the buttons into 7 groups. If each group had
7 buttons in it, how many buttons did Lee have?
Solve.
18
Find the missing number. What property does this number sentence show?
×8=8×5
19
Michelle needs to find the missing number in a number sentence. What property
does she need to use? 2 × (5 × 7) = (2 × 5) ×
20
Find the missing number. What property does this number sentence show?
4×1×8=8×
×1
Assessment Resources 4
6–5
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73744_U3_US.indd 6–5
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Name
Date
Unit 3 Prerequisite
Skills Test
Individual Student Record Form
Unit 3 Prerequisite Skills Test
Use the Prerequisite Skills Test to identify your students’
mastery of the skills prerequisite to the unit. The item
analysis below will help you recognize strengths and
weaknesses.
Item
Number
Correct
Response?
Indicate whether the student’s response was correct in the
column to the right of the item number.
California State Standards
1.
3NS2.2
Memorize to automaticity the multiplication table for numbers between 1 and 10.
2.
3NS2.2
3.
3NS2.2
4.
3NS2.2
5.
3NS2.2
6.
3NS2.2
7.
3NS2.2
8.
3NS2.2
9.
3NS2.2
10.
3NS2.2
11.
3NS2.2
12.
3AF1.1
Students select appropriate symbols, operations, and properties to represent,
describe, simplify, and solve simple number relationships.
13.
3NS2.2
Memorize to automaticity the multiplication table for numbers between 1 and 10.
14.
3AF1.1
Students select appropriate symbols, operations, and properties to represent,
describe, simplify, and solve simple number relationships.
15.
3AF1.2
Solve problems involving numeric equations or inequalities.
16.
3AF1.2
17.
3NS2.2
Memorize to automaticity the multiplication table for numbers between 1 and 10.
18.
3AF1.5
19.
3AF1.5
Recognize and use the commutative and associative properties of multiplication
(e.g., if 5 × 7 = 35, then what is 7 × 5? and if 5 × 7 x 3 = 105, then what is
7 × 3 × 5?).
20.
3AF1.5
out of 20
Assessment Resources 4
6–6
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73784_IRF_US_U3.indd 6–6
1/31/08 10:32:35 AM
Name
Date
Unit 3 Prerequisite
Skills Test
Class Record Form
Unit 3 Prerequisite Skills Test
Use the Prerequisite Skills Test to identify your students’
mastery of the skills prerequisite to the unit.
Item
Number
The record below will allow you to group students for
differentiated instruction.
Groups for Differentiated Instruction
California State Standards
1.
3NS2.2
Memorize to automaticity the multiplication table
for numbers between 1 and 10.
2.
3NS2.2
3.
3NS2.2
4.
3NS2.2
5.
3NS2.2
6.
3NS2.2
7.
3NS2.2
8.
3NS2.2
9.
3NS2.2
10.
3NS2.2
11.
3NS2.2
12.
3AF1.1
Students select appropriate symbols,
operations, and properties to represent,
describe, simplify, and solve simple number
relationships.
13.
3NS2.2
Memorize to automaticity the multiplication table
for numbers between 1 and 10.
14.
3AF1.1
Students select appropriate symbols,
operations, and properties to represent,
describe, simplify, and solve simple number
relationships.
15.
3AF1.2
16.
3AF1.2
Solve problems involving numeric equations or
inequalities.
17.
3NS2.2
Memorize to automaticity the multiplication table
for numbers between 1 and 10.
18.
3AF1.5
19.
3AF1.5
20.
3AF1.5
Recognize and use the commutative and
associative properties of multiplication (e.g., if
5 × 7 = 35, then what is 7 × 5? and if 5 × 7 ×
3 = 105, then what is 7 × 3 × 5?).
6–7
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73784_CRF_US_U3.indd 6–7
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Name
Unit 3 Pretest
Date
Unit 3 Pretest
Solve.
1
Write a division fact that is in the same family as 6 × 7 = 42.
2
What multiplication fact is represented by the array below?
3
What is any number multiplied by 1?
4
Rewrite 6 × (3 × 7) using the associative property.
5
What are the factors of 12?
7
What is the remainder when 39 is divided by 5?
8
What is 48 ÷ 6?
9
What is the remainder of 9 ÷ 2?
6
What are two multiples of 12?
6–9
Assessment Resources 4
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73744_U3_UP.indd 6–9
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10483
Nets Gr4 CA Math ‘08 Reprint
73744_U3_UP
ljc 05-02-07 edit ds 05-08-07
1pp
Name
Unit 3 Pretest
Date
Solve using the order of operations.
10
5 × (3 + 1) - 8
11
28 ÷ 4 × 6 - 3
12
( (7 × 4) - 15 ) ÷ 13
13
(9 + 1) × 7 - 3 × (6 + 2)
14
Adita played violin for 80 minutes. Hana played for less than half this time. Write
an expression that could be used to find the number of minutes Hana played.
15
Ramon can fold 30 shirts in 1 hour. Carla can fold 15 more shirts in 1 hour than
Ramon. What expression shows how many shirts Carla can fold in 1 hour?
Use the figure below for questions 16 and 17.
=
16
How many squares would equal
3 stars?
17
What sign belongs in the oval
below?
18
Eno bought 4 movie tickets for
$4 each. What shows the cost of
all the tickets?
19
Luz has 7 more hair clips than Maria.
Together, they have 19 clips. How
many clips does Luz have?
20
Pedro’s truck can hold 20 crates of berries. Each crate contains 12 baskets of berries.
How many baskets of berries can Pedro’s truck hold?
Assessment Resources 4
6–10
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73744_U3_UP.indd 6–10
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Name
Date
Unit 3 Pretest
Individual Student Record Form
Unit 3 Pretest
Use the Unit Pretest to identify your students’ knowledge
of the skills in the upcoming unit. The item analysis below
will help you recognize strengths and weaknesses.
Item
Number
Correct
Response?
Indicate whether the student’s response was correct in the
column to the right of the item number.
California State Standards
1.
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and
division of whole numbers and understand the relationships among the
operations.
2.
4NS3.0
3.
4NS3.0
4.
4AF1.2
Interpret and evaluate mathematical expressions that now use parentheses.
5.
4NS4.0
Students know how to factor small whole numbers.
6.
4NS4.0
7.
4NS3.4
8.
4NS3.4
9.
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and
division of whole numbers and understand the relationships among the
operations.
10.
4AF1.2
Interpret and evaluate mathematical expressions that now use parentheses.
11.
4AF1.2
12.
4AF1.2
13.
4AF1.2
14.
4AF1.0
15.
4AF1.0
16.
4AF1.1
17.
4AF1.1
18.
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and
division of whole numbers and understand the relationships among the
operations.
19.
4AF1.1
Use letters, boxes, or other symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an understanding and the use of the
concept of a variable).
20.
4MR2.2
Apply strategies and results from simpler problems to more complex problems.
Solve problems involving division of multidigit numbers by one-digit numbers.
Students use and interpret variables, mathematical symbols, and properties to
write and simplify expressions and sentences.
Use letters, boxes, or other symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an understanding and the use of the
concept of a variable).
out of 20
Assessment Resources 4
6–11
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73784_IRF_UP3.indd 6–11
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Name
Date
Unit 3 Pretest
Class Record Form
Unit 3 Pretest
Use the Unit Pretest to identify your students’ knowledge
of the California Mathematics Contents Standards in the
upcoming chapter.
Item
Number
The record below will allow you to group students for
differentiated instruction.
California Mathematics Contents Standards
1.
4NS3.0
2.
4NS3.0
3.
4NS3.0
4.
4AF1.2
Interpret and evaluate mathematical expressions that now use
parentheses.
5.
4NS4.0
Students know how to factor small whole numbers..
6.
4NS4.0
7.
4NS3.4
8.
4NS3.4
9.
4NS3.0
Students solve problems involving addition, subtraction,
multiplication, and division of whole numbers and understand the
relationships among the operations.
10.
4AF1.2
11.
4AF1.2
Interpret and evaluate mathematical expressions that now use
parentheses.
12.
4AF1.2
13.
4AF1.2
14.
4AF1.0
15.
4AF1.0
16.
4AF1.1
17.
4AF1.1
18.
4NS3.0
Students solve problems involving addition, subtraction,
multiplication, and division of whole numbers and understand the
relationships among the operations.
19.
4AF1.1
Use letters, boxes, or other symbols to stand for any number in
simple expressions or equations (e.g., demonstrate an understanding
and the use of the concept of a variable).
20.
4MR2.2
Apply strategies and results from simpler problems to more complex
problems.
Groups for differentiated
instruction
Students solve problems involving addition, subtraction,
multiplication, and division of whole numbers and understand the
relationships among the operations.
Solve problems involving division of multidigit numbers by one-digit
numbers.
Students use and interpret variables, mathematical symbols, and
properties to write and simplify expressions and sentences.
Use letters, boxes, or other symbols to stand for any number in
simple expressions or equations (e.g., demonstrate an understanding
and the use of the concept of a variable).
Assessment Resources 4
6–12
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73784_CRF_UP3.indd 6–12
11/30/07 3:31:02 AM
Family Letter for Unit 3
Dear Family,
Vocabulary
During the next few weeks our math class will
be learning how to multiply and divide whole
numbers. We will also continue to work with
expressions, equations, and inequalities.
You can expect to see work that provides
practice in multiplying and dividing basic facts
as well as in evaluating expressions, solving
equations, and comparing inequalities.
As we learn how to evaluate expressions with
all four operations, you may wish to use the
following sample as a guide.
Evaluating Expressions with all Four Operations
Follow these steps to evaluate 30 - (3 + 2) x 4.
• First, do the operations inside the parentheses.
• Then do any multiplication and division
in order from left to right.
• Finally, do any addition and subtraction in
order from left to right.
Knowing how to evaluate expressions and solve
equations using all four operations will allow
students to solve real-world problems.
dividend The number that is divided
in a division problem.
In 10 ÷ 2 = 5, the dividend is 10.
divisor The number by which a
number is divided. In 10 ÷ 2 = 5, the
divisor is 2.
factor One of two or more numbers
that are multiplied to give a product.
product The answer in a
multiplication problem.
quotient The answer in a division
problem. In 10 ÷ 2 = 5, the quotient
is 5.
30 - (3 + 2) × 4
30 - 5 × 4
30 - 20
10
Education Place
Visit www.eduplace.com/camaf/
for eGlossary, eGames, test-prep
practice, and more.
Sincerely,
Your Child’s Teacher
Chapter Resources 4
6–13
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11/30/07 3:31:56 AM
Carta a la familia: Unidad 3
Estimada familia:
Vocabulario
Durante las próximas semanas, aprenderemos
a multiplicar y dividir números enteros en la
clase de matemáticas. También continuaremos
trabajando con expresiones, ecuaciones y
desigualdades.
Verán que trabajaremos con ejercicios para
practicar la multiplicación y la división
de operaciones básicas y para practicar la
evaluación de expresiones, la resolución de
ecuaciones y la comparación de desigualdades.
Mientras aprendemos a evaluar expresiones
con las cuatro operaciones, pueden utilizar la
siguiente muestra como guía.
dividendo Número que se divide en
un problema de división.
En 10 ÷ 2 = 5, el dividendo es 10.
divisor Número entre el cual se
divide un número. En 10 ÷ 2 = 5, el
divisor es 2.
factor Uno de dos o más números
que se multiplican para obtener un
producto.
producto Resultado de un problema
de multiplicación.
cociente Resultado de un problema
de división. En 10 ÷ 2 = 5, el
cociente es 5.
Hallar el valor de expresiones con las cuatro operaciones 30 - (3 + 2) × 4
Sigan estos pasos para hallar 30 - (3 + 2) x 4.
• Primero, resuelvan las operaciones que
están dentro del paréntesis.
• Luego resuelvan todas las multiplicaciones y
divisiones de izquierda a derecha.
• Por último, resuelvan todas las sumas y
restas de izquierda a derecha.
30 - 5 × 4
30 - 20
10
Al saber cómo hallar el valor de expresiones y
resolver ecuaciones con las cuatro operaciones,
los estudiantes podrán resolver problemas de la
vida real.
Atentamente,
Visiten Education Place en
www.eduplace.com/camaf/,
donde encontrarán el glosario
electrónico, eGames, práctica
para preparación para exámenes
y más.
El maestro de su hijo
Recursos del capítulo 4
6–14
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73744_U03_SP.indd 6–14
11/30/07 3:32:32 AM
Name
Date
Chapter 6, Lesson 1
Lesson Quiz
Lesson 1 Quiz
Greg used 12 counters to make 2 rows of 6.
1.
What multiplication equations can he write for his array?
2.
What division equations can he write?
3.
If he puts 4 counters in each row with the same counters, what
array will he make?
4.
What new equations can he write?
Lesson Quiz
Use with Chapter 6, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 6, Lesson 2
Lesson Quiz
Lesson 2 Quiz
Write a fact family for each set of numbers.
1.
6, 2, 12
2.
10, 8, 80
Lesson Quiz
6–15
Use with Chapter 6, Lesson 2
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CAPEG4_C06_LessonQuiz.indd 6–15
11/30/07 3:33:20 AM
Name
Date
Chapter 6, Lesson 3
Lesson Quiz
Lesson 3 Quiz
Name the property or rule shown by each equation.
1.
5 × (2 × 6) = (5 × 2) × 6
2.
15 × 1 = 15
3.
14 ÷ 14 = 1
4.
8 ÷ 0 has no solution.
Lesson Quiz
Use with Chapter 6, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 6, Lesson 4
Lesson Quiz
Lesson 4 Quiz
Use a multiplication table.
1.
Where are the multiples of 5?
2.
What pattern in the multiplication table is shown by the even
numbers?
Lesson Quiz
6–16
Use with Chapter 6, Lesson 4
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CAPEG4_C06_LessonQuiz.indd 6–16
11/30/07 3:33:41 AM
Name
Date
Chapter 6, Lesson 5
Lesson Quiz
Lesson 5 Quiz
Find the quotient and remainder.
1.
_____________
5)27
2.
31 ÷ 4
3.
50 ÷ 6
Show how to check each answer.
4.
18 ÷ 5 = 3 R3
5.
44 ÷ 8 = 5 R4
Lesson Quiz
Use with Chapter 6, Lesson 5
Copyright © Houghton Mifflin Company. All rights reserved.
Lesson Quiz
6–17
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CAPEG4_C06_LessonQuiz.indd 6–17
11/30/07 3:33:56 AM
Name
Chapter 6, Lesson 1
Daily Routines
Date
Hands On: Relate Multiplication and Division
Problem of the Day
KEY AF 1.3
Kaleigh saw 11 robins and 8 finches in her backyard yesterday
morning. This morning she saw 7 robins and 5 finches.
How many more birds did she see yesterday?
Number Sense Review
KEY NS 3.1
In what place would you need to start regrouping if subtracting
a number from 340,000?
Number of the Day
KEY NS 1.0
9
Nine is the number of place values in one hundred million.
What are the names of those place values?
Facts Practice
KEY NS 3.1
Add.
1.
94,204 + 25,489
2.
6,673 + 729
3.
14,056 + 8,422
4.
5,241 + 5,967
5.
31,489 + 42,330
6.
121,854 + 48,326
Daily Routines
6–19
Use with Chapter 6, Lesson 1
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73744_C6L1_DR.indd 6–19
12/9/07 11:17:50 PM
Name
Chapter 6, Lesson 1
Reteach
Date
Hands On: Relate Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
An array shows objects arranged in equal rows and columns.
You can use an array to multiply and divide.
2 rows × 3 columns = 6
3 rows × 2 columns = 6
6÷2=3
6÷3=2
Write all the multiplication and division equations for each array.
1.
2.
3.
Writing Math How are the arrays for 5 × 3 and 3 × 5 alike?
Reteach
6–20
Use with text pages 120–121.
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73744_C6L1_RET.indd 6–20
11/30/07 3:36:19 AM
Name
Chapter 6, Lesson 1
Practice
Date
Hands On: Relate Multiplication
to Division
CA Standards
NS 3.0, MR 2.3
Write all the multiplication and division equations for each array.
1.
2.
3.
4.
Test Practice
Circle the letter of the correct answer.
5.
Which equation does not go with the
array?
6.
There are 3 rows of 3 counters each.
Which equation goes with this array?
A
3+3=6
B
3×3=9
A
4 × 3 = 12
C
4 + 3 = 12
C
3÷3=1
B
3 × 4 = 12
D
12 ÷ 3 = 4
D
9-3=6
Writing Math Can you make an array with 23 counters?
Explain your answer.
Practice
6–21
Use with text pages 120–121.
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73744_CH6L1_PRAC.indd 6–21
11/30/07 3:36:52 AM
Name
Date
The Stars and Stripes
Chapter 6, Lesson 1
Enrichment
CA Standards
NS 3.0, MR 2.3
The first official United States flag was flown in 1777. It had 13 stars and 13 stripes, one
star and stripe for each colony. It looked like this:
From 1787 to 1790, the colonies became states. As new states entered the Union,
beginning in 1791 with Vermont and ending in 1959 with Hawaii, stars were added to the
flag. (The number of stripes remains 13, for the original colonies.) The numbers of stars in
the different flags are shown in the table below:
Official Flag of the United States
13 Stars 15 Stars 20 Stars 21 Stars 23 Stars
24 Stars 25 Stars 26 Stars 27 Stars 28 Stars
29 Stars 30 Stars 31 Stars 32 Stars 33 Stars
34 Stars 35 Stars 36 Stars 37 Stars 38 Stars
43 Stars 44 Stars 45 Stars 46 Stars 48 Stars
49 Stars
50 Stars
Look at the table. Which numbers of stars can be arranged in two or more unique
arrays? On separate paper, draw all the possible unique arrays for those flags. Write two
multiplication equations for each set of arrays.
Finally, go to www.usflag.org on the Internet to see pictures of all the U.S. flags. Compare
your arrays to the way the stars were really arranged.
Writing Math Tell how you would arrange 51 stars on the
U.S. flag if another state joined the Union.
Enrichment
6–22
Use with text pages 120–121.
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73744_C6L1_ENR.indd 6–22
11/30/07 3:39:45 AM
Chapter 6, Lesson 1
Name
Leveled Problem Solving
Date
Hands On: Relate Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
Solve each problem.
1.
Tranh has 18 dinosaur statues. He
wants to arrange them in an array.
Write a multiplication equation that
describes one possible array.
2.
3.
Mac has 36 rocks in his collection.
What are all the arrays he can make?
4.
5.
Mr. Hansen has 48 pictures of his
grandchildren. Write division equations
to describe all the different arrays he
can make with the pictures if he wants
at least 3 pictures in each row.
6.
Leveled Problem Solving
6–23
Debra is planting 24 tulip bulbs in
an array. She wants at least 3 bulbs
in each row and column. Write a
multiplication equation to describe one
possible array.
María had her seashells in a 5 × 8
array. Then one shell broke. Write
multiplication equations for all the
arrays she can make using the new
number of shells.
Sue has 50 stickers. She wants to
arrange them in three different square
arrays. Write multiplication equations to
describe the arrays.
Use with text pages 120–121.
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73744_C6L1_PS.indd 6–23
11/30/07 3:40:14 AM
Name
Chapter 6, Lesson 1
Homework
Date
Hands On: Relate Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
An array can show multiplication and division.
3 × 4 = 12
4 × 3 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
Write the multiplication and division equations for each array.
1.
2.
4QJSBM3FWJFX
4.
3.
(Chapter 4, Lesson 3; Chapter 5, Lesson 2) KEY NS 3.0, KEY NS 3.1
Simplify the
expression.
Subtract.
3,614
- 1,509
________
5.
(25 + 13) + (46 - 10)
6.
Ursula gives Julio 23 of her Solar Adventures trading cards and 14 to Suri.
If she started with 85 trading cards, how many does she have left?
Homework
6–24
Use with text pages 120–121.
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73744_CH6L1_HMWK.indd 6–24
11/30/07 3:40:42 AM
Name
Chapter 6, Lesson 2
Daily Routines
Date
Relate Multiplication and Division
Problem of the Day
KEY NS 1.1
Write 4,378,619 in expanded notation.
Number Sense
KEY NS 1.1
Use Workmat 2 to write seventy-three million, eight hundred
sixteen thousand, four hundred forty-five in standard form.
Word of the Day
AF 1.1
equation
Do equations always have an equals sign?
Facts Practice
Gr3 NS 2.2
Multiply.
1.
3×7
2.
5×6
3.
8×8
4.
7×9
5.
2×9
6.
4×9
Daily Routines
6–25
Use with Chapter 6, Lesson 2
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L2_DR.indd 6–25
1/31/08 10:34:40 AM
Name
Chapter 6, Lesson 2
Reteach
Date
Relate Multiplication and Division
CA Standard
NS 3.0
Arrays can be used to represent fact families.
Find 18 ÷ 6.
Step 1 Think: How many groups of 6 are in 18?
× 6 = 18
3 × 6 = 18
Step 2 There are 3 groups of 6 in 18.
Solution: So, 18 ÷ 6 = 3.
The multiplication and division equations that can be written using the numbers
3, 6, and 18 form a fact family.
6 × 3 = 18
18 ÷ 6 = 3
3 × 6 = 18
18 ÷ 3 = 6
Write the fact family for each array or set of numbers.
1.
2.
3.
5, 7, 35
Writing Math Do the numbers 1, 2, and 3 make a fact family
using multiplication and division? Explain your answer.
Reteach
6–26
Use with text pages 122–123.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L2_RET.indd 6–26
11/30/07 3:42:36 AM
Name
Chapter 6, Lesson 2
Practice
Date
Relate Multiplication and Division
CA Standard
NS 3.0
Write the fact family for each array or set of numbers.
1.
2.
3.
2, 7, 14
Complete the fact family.
4.
3×9=
9 × = 27
÷3 =9
27 ÷ = 3
5.
5×7 =
7 × = 35
÷5 =7
35 ÷ = 5
Test Practice
Circle the letter of the correct answer.
6.
Find the missing number:
7.
× 7 = 63
Find the missing number:
48 ÷
=6
A
6
C
7
A
6
C
7
B
8
D
9
B
8
D
9
Writing Math Give an example of a fact family that contains
only two “members.” Explain why there are two and not four members.
Practice
6–27
Use with text pages 122–123.
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73744_CH6L2_PRAC.indd 6–27
11/30/07 3:43:09 AM
Name
Date
Fact Family Dominoes
Chapter 6, Lesson 2
Enrichment
CA Standard
NS 3.0
Dominoes are tiles that use dots (called pips) for numbers. There are
two sets of pips on each domino, separated by a line. For example,
the 2 | 6 domino is shown below.
You and three friends will play dominoes and practice fact families at
the same time.
What You Need:
• 41 index cards
• markers
• 1 number cube
• 4 books or pieces of cardboard
Get Ready:
1.
Make the dominoes. Divide each card in half. Draw the pips. Make two dominoes for
each combination: 2 | 2, 2 | 3, 2 | 4, 2 | 5, 2 | 6, 2 | 7, 3 | 3, 3 | 4, 3 | 5, 3 | 6, 3 | 7, 4 | 4, 4 | 5,
4 | 6, 4 | 7, 5 | 5, 5 | 6, 5 | 7, 6 | 6, 6 | 7, 7 | 7.
2.
Mix up the dominoes and put them in a pile facedown.
3.
Everyone takes seven dominoes. Leave the rest in the pile. Use a book or a folded
piece of cardboard to hide your dominoes from each other.
How to Play:
The object is to get rid of all your dominoes.
4.
The first person puts a domino in the middle of the table and says all of the members
of the fact family for the two numbers.
5.
The next person puts down a domino that “matches” and says the fact family. For
example, if the first domino is 3 | 6, it can be matched with a domino that has a 3 or
6 on it. If you can’t make a match, take another domino from the pile. If you still can’t
make a match, it’s the next person’s turn.
6.
Continue going around the circle until one player has used all of his or her dominoes.
That player is the winner.
Writing Math Why do you think a set of numbers such as
3, 7, and 21 is called a fact family ?
Enrichment
6–28
Use with text pages 122–123.
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73744_C6L2_ENR.indd 6–28
11/30/07 3:43:39 AM
Chapter 6, Lesson 2
Name
Leveled Problem Solving
Date
Relate Multiplication and Division
CA Standard
NS 3.0
Use the numbers in each problem to write a fact family.
1.
There are 36 buttons in 9 rows, with
4 buttons in each row.
2.
Rusty planted 35 trees in 5 rows, with
7 trees in each row.
3.
There are 4 rows, with 7 T-shirts in
each row.
4.
At Frank’s Football Factory, there are
6 rows of footballs, with 8 balls in
each row.
5.
There are 63 stickers in 7 rows.
6.
There are 56 candles in 8 rows on
Mr. Booth’s birthday cake.
Leveled Problem Solving
6–29
Use with text pages 122–123.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L2_PS.indd 6–29
11/30/07 3:44:04 AM
Name
Chapter 6, Lesson 2
Homework
Date
Relate Multiplication and Division
CA Standard
NS 3.0
Write the fact family for each array or set of numbers.
1.
2.
Some numbers can make
a fact family. You can
write multiplication and
division equations using
those numbers.
3 × 7 = 21
7 × 3 = 21
21 ÷ 7 = 3
21 ÷ 3 = 7
The numbers 3, 7, and
21 are a fact family.
3.
3, 5, 15
4QJSBM3FWJFX
4.
4, 8, 32
5.
4, 7, 28
(Chapter 3, Lesson 4) KEY NS 3.1
Add. Use estimation to verify your answer.
6.
3,478
+ 655
______
_______
8.
Mrs. Fox traveled 338 miles from Chula Vista to Fresno and 295 miles
from Fresno to Crescent City. How far did she travel in all?
Homework
7.
6–30
17,961
+ 4,813
________
Use with text pages 122–123.
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73744_CH6L2_HMWK.indd 6–30
11/30/07 3:44:34 AM
Name
Chapter 6, Lesson 3
Daily Routines
Date
Multiplication Properties and Division Rules
Problem of the Day
KEY NS 3.0
If 7 × 9 = 63, what is 63 ÷ 9?
Algebra and Functions Review
KEY AF 1.3
Use Workmat 1 to write down the expression 7 – 2 + 3 – 1.
Add parentheses so the value of the expression is equal to 1.
Word of the Day
MR 1.1
inverse operations
What is the inverse operation of each of the following expressions?
1.
45 + 16
2.
56 ÷ 7
3.
82 – 39
4.
15 × 3
Facts Practice
KEY NS 3.1
Subtract.
1.
7,452 - 2,626
2.
9,386 - 129
3.
16,924 - 3,945
4.
48,391 - 39,733
5.
8,193 - 7,642
6.
56,247 - 485
Daily Routines
6–31
Use with Chapter 6, Lesson 3
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73744_C6L3_DR.indd 6–31
11/30/07 3:46:57 AM
Name
Chapter 6, Lesson 3
Reteach
Date
Multiplication Properties and
Division Rules
Commutative
Property
When you change
the order of the
factors, the product
stays the same
CA Standards
NS 3.0, AF 1.0
Identity Property
Zero Property
When you multilply
any number by 1,
the product is equal
to that number.
When you multiply
any number by 0,
the product is 0.
Associative
Property
When you group
factors in different
ways, the product
stays the same.
3×2=6
4 × 3 = 12
3 × 4 = 12
1×9=9
2×3=6
6 × 3 = 18 3 × 6 = 18
6×0=0
Use properties and rules to solve. If there is no solution, explain why.
1.
1 × 43 =
× 12 = 0
4.
7.
5×3=3×
2.
5.
8.
5 × (4 × 3) = (
÷5=0
28 ÷
= 28
× 4) × 3
3.
4÷4=
6.
9×
9.
4÷0=
=9
Writing Math What is the product of 937,568 × 0 × 622,001?
How do you know?
Reteach
6–32
Use with text pages 124–126.
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73744_C6L3_RET.indd 6–32
11/30/07 3:47:38 AM
Name
Chapter 6, Lesson 3
Practice
Date
Multiplication Properties and
Division Rules
CA Standards
NS 3.0, AF 1.0
Use properties and rules to solve.
1.
1 × 436 =
3.
(10 × 85) × 12 = 10 × (
÷ 1 = 999
5.
7.
× 12)
848 ÷ 0 =
2.
122 × 17 = 17 ×
4.
0 ÷ 125,699 =
6.
5,133 × 0 =
8.
÷ 423 = 1
Test Practice
Circle the letter of the correct answer.
9.
10.
Which is an example of the Identity Property of Multiplication?
A
14 × 0 = 0
C
83 × 0 = 83
B
(6 × 2) × 8 = 6 × (2 × 8)
D
1 × 555 = 555
Which is true about division sentences that include 0?
A
0÷8=8
C
0÷8=0
B
8÷0=0
D
8÷0=8
Writing Math Compare the products of 4 × 0 and
444,444 × 0. Explain.
Practice
6–33
Use with text pages 124–126.
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73744_CH6L3_PRAC.indd 6–33
11/30/07 3:48:14 AM
Name
Chapter 6, Lesson 3
Enrichment
Date
Elementary Math
CA Standards
NS 3.0, AF 1.0
Scientists have discovered 110 elements. You have heard of some of them, such as
oxygen, nitrogen, and hydrogen. Did you know that iron and silver are elements too?
Each element has a number. Here are some of them:
hydrogen
1
sulfur
16
gold
79
helium
2
chromium
24
lead
82
beryllium
4
copper
29
californium
98
carbon
6
krypton
36
oxygen
8
iodine
53
Use the elements and their numbers to solve each problem.
For Problems 1–6, write your answer as a number.
1.
1 × krypton =
2.
0 ÷ copper =
3.
lead × 0 =
4.
gold ÷ 1 =
5.
iodine ÷ iodine =
6.
californium ÷ 0 =
For Problems 7 and 8, write your answer using the element names.
7.
2×8=8×2=
8.
(6 × 4) × 1 = 6 × (4 × 1) =
Writing Math The word commutative means “change” or
“trade.” Why is Commutative Property a good name to describe
4 × 3 = 12 and 3 × 4 = 12?
Enrichment
6–34
Use with text pages 124–126.
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73744_C6L3_ENR.indd 6–34
11/30/07 3:48:52 AM
Chapter 6, Lesson 3
Name
Leveled Problem Solving
Date
Multiplication Properties
and Division Rules
CA Standards
NS 3.0, AF 1.0
Solve each problem.
1.
One billion is 1 followed by 9 zeros.
What is 1 billion × 1?
2.
One trillion is 1 followed by 12 zeros.
What is 1 trillion × 0?
3.
One quadrillion is 1 followed by
15 zeros. What is 1 quadrillion ÷ 1?
4.
One quintillion is 1 followed by
18 zeros. What is 1 quintillion divided
by 1 quintillion?
5.
One septillion is 1 followed by
24 zeros. What is 0 ÷ 1 septillion?
6.
One centillion is 1 followed by
303 zeros! What is 1 centillion
divided by 0?
Leveled Problem Solving
6–35
Use with text pages 124–126.
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73744_C6L3_PS.indd 6–35
11/30/07 3:49:21 AM
Name
Chapter 6, Lesson 3
Homework
Date
Multiplication Properties and
Division Rules
CA Standards
NS 3.0, AF 1.0
Use properties and rules to solve.
1×7=
The Identity Property of Multiplication states that when you multiply
any number by one, the product is equal to that number.
Solution: 1 × 7 = 7
1.
6×5=5×
3.
(3 × 7) × 2 = 3 × (
5.
0 ÷ 71 =
7.
29 ÷
10.
0 × 61 =
4.
1 × 45 =
6.
÷ 23 = 1
= 29
4QJSBM3FWJFX
8.
× 2)
2.
(Chapter 5, Lessons 2–3) KEY AF 1.2, AF 1.0
Simplify the expression.
(38 - 4) + 12
9.
Complete the equation.
20 + 7 = (16 - ) + 14
Perry Porcupine has the sum of 73 and 15 quills. His sister Pamela
has 7 fewer quills than Perry. Write an expression for the number of quills Pamela
has.
Homework
6–36
Use with text pages 124–126.
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73744_CH6L3_HMWK.indd 6–36
11/30/07 3:49:46 AM
Name
Chapter 6, Lesson 4
Daily Routines
Date
Hands On: Patterns in Multiplication
and Division
Problem of the Day
KEY NS 3.0
An array has 5 rows and 4 counters in each row.
Use the array to write multiplication and division equations.
Number Sense
KEY NS 3.1
A hiker climbs 704 feet and then 235 feet before descending 150
feet. How high is she?
Number of the Day
KEY NS 1.1
10
Give an example of when you might need to multiply by 10.
Facts Practice
KEY NS 3.1
Add or subtract.
1.
156 + 72
2.
297 + 13 - 100
3.
837 - 490
4.
(1,023 - 211) + 15
Daily Routines
6–37
Use with Chapter 6, Lesson 4
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73744_C6L4_DR.indd 6–37
11/30/07 3:56:34 AM
Name
Chapter 6, Lesson 4
Reteach
Date
Hands on: Patterns in Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
You can use a multiplication table to help you divide.
To find 42 ÷ 6, you can use a multiplication table.
Step 1 Look down the column for 6 until you find 42.
Step 2 Follow the row to the left to find the quotient.
ⴛ 0 1 2 3 4 5 6 7 8 9
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
2
0
2
4
6
8
10 12 14 16 18
3
0
3
6
9
12 15 18 21 24 27
4
0
4
8
12 16 20 24 28 32 36
5
0
5
10 15 20 25 30 35 40 45
6
0
6
12 18 24 30 36 42 48 54
7
0
7
14 21 28 35 42 49 56 63
8
0
8
16 24 32 40 48 56 64 72
9
0
9
18 27 36 45 54 63 72 81
Solution: 42 ÷ 6 = 7
Use the multiplication table to answer each question.
1.
24 ÷ 6 =
2.
81 ÷ 9 =
3.
32 ÷ 8 =
4.
20 ÷ 4 =
5.
49 ÷ 7 =
6.
56 ÷ 7 =
7.
12 ÷ 3 =
8.
63 ÷ 9 =
9.
72 ÷ 8 =
Writing Math You know that 42 ÷ 6 = 7. How does that
help you solve 42 ÷ 7?
Reteach
6–38
Use with text pages 128–129.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L4_RET.indd 6–38
11/30/07 3:57:17 AM
Name
Chapter 6, Lesson 4
Practice
Date
Hands On: Patterns in
Multiplication and Division
CA Standard
NS 3.0, MR 2.3
Use a multiplication table to answer each question.
1.
List different multiples of 8 that are shown in the table.
2.
Is 42 a square number? Why or why not?
3.
Use the table to find the quotient of 56 ÷ 7. Describe how you found it.
4.
5.
Find 12 in four different places in the table. Write a division sentence for
each 12 you find.
Use the table to find the product of 4 × 7. Describe how you found it.
Test Practice
Circle the letter of the correct answer.
6.
Which number is a square number?
A
15
C
25
B
35
D
48
7.
15 is the product of which factors?
A
B
8 × 7,
7×8
5 × 2,
2×5
C
D
15 × 0,
0 × 15
5 × 3,
3×5
Writing Math What pattern do square numbers form
on the multiplication table?
Practice
6–39
Use with text pages 128–129.
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73744_CH6L4_PRAC.indd 6–39
11/30/07 3:57:59 AM
Name
Chapter 6, Lesson 4
Enrichment
Date
Extend the Pattern
CA Standards
NS 3.0, MR 2.3
Look at the products of the square numbers in the multiplication table.
Do you see the pattern?
ⴛ
0
1
2
3
4
5
6
7
8
9
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
2
0
2
4
6
8
10 12 14 16 18
3
0
3
6
9
12 15 18 21 24 27
4
0
4
8
12 16 20 24 28 32 36
5
0
5
10 15 20 25 30 35 40 45
6
0
6
12 18 24 30 36 42 48 54
7
0
7
14 21 28 35 42 49 56 63
8
0
8
16 24 32 40 48 56 64 72
9
0
9
18 27 36 45 54 63 72 81
1
4
3
9 16 25 36 49 64 81
5
7
9 11 13 15 17
The difference of the products is an odd number. The difference
increases by 2 each time.
Extend the pattern to solve these multiplication problems.
1.
10 × 10
2.
11 × 11
3.
12 × 12
4.
13 × 13
5.
14 × 14
6.
15 × 15
Writing Math It is easy to multiply using a calculator. Why
do you need to memorize products?
Enrichment
6–40
Use with text pages 128–129.
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73744_C6L4_ENR.indd 6–40
11/30/07 3:58:31 AM
Chapter 6, Lesson 4
Name
Leveled Problem Solving
Date
Hands On: Patterns in Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
Use a multiplication table to solve.
1.
Find the number 4 three times in
the table. Write multiplication
sentences and division sentences for
each 4.
2.
Find the number 9 three times in
the table. Write multiplication
sentences and division sentences
for each 9.
3.
Find the number 16 three times in the
table. Write multiplication sentences
and division sentences for each 16.
4.
Find the number 36 in the table. Write
multiplication sentences and division
sentences for each 36.
5.
Name five numbers that are found only
once in the table.
6.
What type of numbers is found an odd
number of times in the table?
Leveled Problem Solving
6–41
Use with text pages 128–129.
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73744_C6L4_PS.indd 6–41
11/30/07 3:59:04 AM
Name
Chapter 6, Lesson 4
Homework
Date
Hands On: Patterns in
Multiplication and Division
CA Standards
NS 3.0, MR 2.3
columns
Multiplication
ⴛ 0 1 2 3 4 5 6 7 8 9
The product of two numbers is shown in
the table in the square where the row and
column of the two factors meet.
Division
To divide, find the column of the number
you are dividing by. Look down the column
to find the number you are dividing. Follow
that row to the left to find the quotient.
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
2
0
2
4
6
8
10 12 14 16 18
3
0
3
6
9
12 15 18 21 24 27
4
0
4
8
12 16 20 24 28 32 36
5
0
5
10 15 20 25 30 35 40 45
6
0
6
12 18 24 30 36 42 48 54
7
0
7
14 21 28 35 42 49 56 63
8
0
8
16 24 32 40 48 56 64 72
9
0
9
18 27 36 45 54 63 72 81
rows
Use the multiplication table to answer each question.
1.
Find the product of 3 and 7 in
two places in the table. Write two
multiplication sentences using
3 and 7 as factors.
2.
Find the product of 5 and 9 in
two places in the table. Write two
multiplication sentences using
5 and 9 as factors.
3.
Find 42 in two places in the table. Write
a division sentence for each 42.
4.
Find 36 in three places in the table.
Write a division sentence for each 36.
4QJSBM3FWJFX
(Chapter 2, Lessons 3–4) KEY NS 1.3
Round each number to the place of the underlined digit.
5.
35,671
7.
The Transamerica Pyramid in San Francisco is 10,236 inches high.
How many inches is that rounded to the nearest thousand?
Homework
6.
6–42
842,105,367
Use with text pages 128–129.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_CH6L4_HMWK.indd 6–42
11/30/07 4:04:17 AM
Name
Chapter 6, Lesson 5
Daily Routines
Date
Division with Remainders
Problem of the Day
KEY NS 3.0
Write a fact family using the numbers 4, 9, and 36.
Algebra and Functions Review
KEY AF 2.1
If 54 + 638 = 54 + (329 + 309), can you find the value of the
expression in the parentheses without adding?
Number of the Day
AF 1.0
1
What is the difference between adding by 1 and multiplying by 1?
Facts Practice
KEY AF 1.3
Simplify each expression.
1.
(22 - 5) + 12
2.
(30 - 14) + 41
3.
(93 - 60) + (36 + 8)
4.
(77 - 52) + (16 - 9)
5.
100 - (33 + 7) + 4
6.
84 - (45 + 27) + 8
Daily Routines
6–43
Use with Chapter 6, Lesson 5
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L5_DR.indd 6–43
11/30/07 4:05:20 AM
Name
Chapter 6, Lesson 5
Reteach
Date
Division with Remainders
CA Standard
NS 3.2
You will divide numbers with remainders.
Find 13 ÷ 4.
Step 1 Think of
multiplication facts that
have products close to 13.
Quotient
Divisor
ⴛ 1 2
3
4
5
1
1
2
3
4
5
2
2
4
6
8
10
3
3
6
9
12 15
4
4
8
12 16 20
5
5
10 15 20 25
Step 2 Find the quotient.
_ _ _ _ _ _ _ _3_ _ _ _ _
4 )13
- 12 ← Multiply. 3 × 4
1 ← Subtract. 13 - 12
Step 3 Show the
remainder.
_ _ _ _ _ _ _ _3_ _ _ _ _ R1
4 )13
- 12
1 ← remainder
There is 1 left over.
16 is too many.
Try 3 as the quotient.
Solution: 13 ÷ 4 = 3 R1.
Divide.
1.
_____________
3 )22
2.
_____________
4 )21
3.
_____________
7 )30
4.
_____________
2 )19
5.
_____________
8 )30
6.
_____________
2 )15
7.
_____________
9 )37
8.
_____________
3 )17
9.
_____________
8 )59
10.
_____________
5 )47
11.
38 ÷ 5 =
12.
25 ÷ 3 =
Writing Math What is a remainder?
Reteach
6–44
Use with text pages 130–132.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L5_RET.indd 6–44
11/30/07 4:05:45 AM
Name
Chapter 6, Lesson 5
Practice
Date
Division with Remainders
CA Standard
NS 3.2
Divide.
1.
____________
4)14
2.
_________
2) 7
3.
_____________
3)20
4.
_____________
6)26
5.
_____________
5)36
6.
_____________
8)34
7.
_____________
7) 40
8.
_____________
9)17
9.
___________
6)32
10.
_____________
3)28
55 ÷ 9 =
15.
41 ÷ 7 =
11.
40 ÷ 6 =
12.
37 ÷ 7 =
13.
80 ÷ 7 =
14.
Find each missing number.
16.
4÷
19.
= 1 R1
17.
÷ 7 = 6 R2
20.
10 ÷ 3 = 3 R
÷ 4 = 7 R3
18.
33 ÷ 9 = 3 R
21.
110 ÷
= 12 R2
Test Practice
Circle the letter of the correct answer.
22.
Mary is packing plates in boxes. She
has 93 plates. Each box holds 8 plates.
If she fills each box, how many boxes
will she fill, and how many plates will
be left over?
23.
Jen has 47 stickers. She wants to give
an equal number of stickers to each of
her 5 cousins. How many stickers will
she give each cousin, and how many
stickers will be left over?
A
11 R3
C
11 R5
A
6 R5
C
7 R5
B
12 R3
D
12 R5
B
8 R7
D
9 R2
________________
Writing Math Jim solved 6)39 and got the quotient 5 R9.
Explain why Jim’s answer is incorrect.
Practice
6–45
Use with text pages 130–132.
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73744_CH6L5_PRAC.indd 6–45
11/30/07 4:06:10 AM
Name
Chapter 6, Lesson 5
Enrichment
Date
No Remainders Allowed!
CA Standard
NS 3.2
Guido’s Pizzeria sells only whole pies. Customers tell Guido how many slices
they want. Guido figures out how many pies have exactly that many slices.
Guido makes pizzas with 6, 7, or 8 slices.
6
7
8
The number of slices customers asked for are shown below. How many
pies of each size did Guido make—with no remainder?
1.
41 slices
2.
75 slices
3.
59 slices
4.
53 slices
5.
107 slices
6.
599 slices
BONUS: Guido goofed! For order 5, his slices totaled 106. What is a
possible pie combination he made?
Writing Math How can you use multiplication to check your
answer to a division problem?
Enrichment
6–46
Use with text pages 130–132.
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73744_C6L5_ENR.indd 6–46
11/30/07 4:06:38 AM
Chapter 6, Lesson 5
Name
Leveled Problem Solving
Date
Division with Remainders
CA Standard
NS 3.2
Solve each problem.
1.
Callie had 38 stickers. She put
6 stickers on each of 6 pages. How
many stickers were left over?
2.
Aki has 99 buttons. She wants to put
them on 11 sweaters equally, with no
buttons left over. How many buttons
will be on each sweater?
3.
Kareem put 5 carrot sticks on each of
8 plates. He had 4 carrot sticks left
over. How many carrot sticks does
he have?
4.
Lisa has 62 more pages to read in
Beezus and Ramona. She plans to
read 9 pages every night beginning
on Monday. How many pages will she
read on Sunday?
5.
Josh has 2 dozen eggs. He uses 5 eggs
for each extra-large loaf of his special
pumpkin bread. How many loaves of
bread can he bake? How many eggs
will be left over?
6.
Brendan has 75 stamps in his
collection. He puts 8 stamps on each
page in his album. How many more
stamps does he need to fill 10 pages
with no stamps left over?
Leveled Problem Solving
6–47
Use with text pages 130–132.
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73744_C6L5_PS.indd 6–47
11/30/07 4:07:09 AM
Name
Chapter 6, Lesson 5
Homework
Date
Division with Remainders
CA Standard
NS 3.2
Divide.
21 ÷ 4
5冄2
苶苶
9
2.
3冄2
苶苶
2
3.
7冄3
苶苶
1
4.
6冄1
苶苶
9
↓ ↓
5 R1
苶苶
1
4冄苶2
-20
Multiply. 4 × 5
ᎏ
1
Subtract. 21 - 20
This is the remainder.
1.
Solution: 21 ÷ 4 = 5 R1
5.
15 ÷ 2 =
6.
41 ÷ 7 =
7.
52 ÷ 9 =
8.
35 ÷ 8 =
9.
43 ÷ 5 =
10.
28 ÷ 6 =
4QJSBM3FWJFX
(Chapter 1, Lessons 2–3) KEY NS 1.1
11.
Write the value of the underlined digit in 349,186.
12.
Write the number in standard form.
six hundred thirty-four thousand, one hundred twelve
13.
There were 238,754 visitors to the San Diego Zoo in one year.
Write the number in word form.
Homework
6–48
Use with text pages 130–132.
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73744_CH6L5_HMWK.indd 6–48
11/30/07 4:07:38 AM
Name
Chapter 6, Lesson 6
Daily Routines
Date
Problem Solving: Field Trip
Problem of the Day
KEY NS 3.4
Ryan has 44 stickers he wants to give away to 7 friends. If he divides
the stickers up equally between his friends, how many stickers will he
have left over?
Number Sense Review
KEY NS 1.1
What is the value of the digit 6 in each number?
1.
456,703,249
2.
321,762,057
3.
698,343,109
Word of the Day
MR 2.3
inequality
What are the different symbols you have learned that show an
inequality? What is the difference between these symbols?
Facts Practice
KEY AF 2.1
Copy and complete.
1.
3.
36 + 29 = 65
= 65
(94 - 58) + 47 = 36 + 47
+ 47 = 36 +
Daily Routines
2.
4.
6–49
15 + (64 + 8) = 15 + 72
15 +
=
+ 72
(50 + 13) + 82 = 63 + 82
+
=
Use with Chapter 6, Lesson 6
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73744_C6L6_DR.indd 6–49
11/30/07 4:08:25 AM
Name
Chapter 6 Test
Date
Chapter 6 Test
Circle the letter of the correct answer.
1
What multiplication expression is
represented by the blocks below?
What expression shows the
relationship between
multiplication and division
compared to 3 × 5 = 15?
A
2
3
15 ÷ 1 = 1
B
15 ÷ 5 = 5
C
15 ÷ 5 = 3
D
15 ÷ 3 = 3
What multiplication expression is
represented by the array below?
4
A
2 × 14
B
3 × 11
C
3×6
D
3×7
What expression shows the
relationship between multiplication
and division compared to
8 × 3 = 24?
A
24 ÷ 8 = 8
A
2 × 14
B
24 ÷ 3 = 8
B
3 × 11
C
24 ÷ 3 = 3
C
3×6
D
24 × 3 = 8
D
5×6
5
Using the commutative property,
rewrite the following expression:
9 × 4 = 36
Assessment Resources 4
A
4 × 9 = 36
C
4 × 36 = 9
B
9 × 36 = 4
D
4 × 9 = 38
6–51
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Name
6
7
What is any number multiplied by 1?
9
What is 3 ÷ 3?
A
0
A
1
B
1
B
3
C
10
C
6
D
the original number
D
9
Three friends decide to buy
crayons. Caroline buys 3 groups
of crayons, Tania buys 7 groups of
crayons, and Tao buys no groups of
crayons. If each group of crayons
has 4 crayons, how many crayons
does Tao have?
10
Fernando has 12 plants. He decides
to place them all near each other in
groups of 3. How many plants are in
each group that he creates?
A
1
B
4
A
0
C
6
B
1
D
12
C
4
D
12
11
8
Chapter 6 Test
Date
Using the associative property,
rewrite the following expression:
2 × (4 × 5)
A
2 × (3 × 5)
B
2 × (5 + 4)
C
(2 × 4) × 5
D
6×5
Assessment Resources 4
12
What is 0 ÷ 7?
A
0
B
1
C
7
D
14
What is 9 ÷ 0?
A
0
B
1
C
9
D
cannot divide by 0
6–52
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11/30/07 4:09:45 AM
Name
13
Susan took all of her marbles and
laid them out. She has 3 rows of
marbles arranged in 7 columns.
How many marbles does she have?
16
A
4
3
B
5
B
7
C
3
C
14
D
8
D
21
Artie has 36 tin cans organized in
12 columns. How many rows of
cans does he have?
A
B
C
D
15
5 × 4 is to 4 × 5 as 8 × 3 is
to 3 ×
A
17
14
Chapter 6 Test
Date
1
3
12
Rhoda has 29 pretzel logs to divide
evenly between the members of her
team. If the team has 9 members,
how many pretzels will be left over?
A
0
B
1
C
2
D
3
36
Frank counted how many chickens
there are in the coop using tally
marks. How many chickens are
there?
A
11
C
50
B
13
D
53
Assessment Resources 4
6–53
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Name
18
19
Chapter 6 Test
Date
Bonita is dividing her box of 12
muffins into 5 parts for 5 friends.
How many muffins do they each
receive?
20
If 9 × 8 is 72, then what is 72 ÷ 9?
A
8
B
9
A
5 with 2 left over
C
10
B
4 with 3 left over
D
11
C
2 with 2 left over
D
3 with 4 left over
If 5 × 8 is 40, then what is 40 ÷ 5?
A
5
B
6
C
7
D
8
Assessment Resources 4
6–54
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11/30/07 4:10:14 AM
Name
Date
Chapter 6 Test
Individual Student Record Form
Use the chapter test to identify your students’ mastery of
the skills in the chapter. The item analysis below will help
you recognize strengths and weaknesses.
Correct
Answer
Student
Response
Record the student’s response in the column to the right
of the correct answer.
California State Standards
1. C
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and division
of whole numbers and understand the relationships among the operations.
2. D
4NS3.0
3. D
4NS3.0
4. B
4NS3.0
5. A
4NS3.0
6. D
4NS3.0
7. A
4NS3.0
8. C
4NS3.0
9. A
4NS3.0
10. B
4NS3.0
11. A
4NS3.0
12. D
4NS3.0
13. D
4NS3.0
14. B
4NS3.0
15. D
4NS3.0
16. D
4AF1.0
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
17. C
4NS3.2
Demonstrate an understanding of, and the ability to use, standard algorithms for
multiplying a multidigit number by a two-digit number and for dividing a multidigit
number by a one-digit number; use relationships between them to simplify
computations and to check results.
18. C
4NS3.0
19. D
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and division
of whole numbers and understand the relationships among the operations.
20. A
4NS3.0
out of 20
Assessment Resources 4
6–55
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11/30/07 4:10:51 AM
Teacher Name
Date
Chapter 6 Test
Class Record Form
Chapter Test 6
Use the chapter test to identify your students’ mastery
of the California Mathematics Contents Standards in the
chapter.
Item
The record below will allow you to group students for
differentiated instruction.
California Mathematics Contents Standards
1.
4NS3.0
2.
4NS3.0
3.
4NS3.0
4.
4NS3.0
5.
4NS3.0
6.
4NS3.0
7.
4NS3.0
8.
4NS3.0
9.
4NS3.0
10.
4NS3.0
11.
4NS3.0
12.
4NS3.0
13.
4NS3.0
14.
4NS3.0
15.
4NS3.0
16.
4AF1.0
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
17.
4NS3.2
Demonstrate an understanding of, and the ability
to use, standard algorithms for multiplying a
multi digit number by a two-digit number and
for dividing a multi digit number by a one-digit
number; use relationships between them to
simplify computations and to check results.
18.
4NS3.0
19.
4NS3.0
20.
4NS3.0
Students solve problems involving addition,
subtraction, multiplication, and division of whole
numbers and understand the relationships
among the operations.
Groups for differentiated instruction
Students solve problems involving addition,
subtraction, multiplication, and division of whole
numbers and understand the relationships
among the operations.
6–56
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12/2/07 9:23:45 AM
Chapter Resources
Grade 4, Chapter 6
Contents
Unit 3: Multiplication and Division
• Unit 3 Prerequisite Skills Test
• Unit 3 Pretest
• Family Letter/Carta a la familia
Individual and Class Record Sheets
Resources for Chapter 6: Relate Multiplication and Division
• Lesson Quizzes Lessons 6.1–6.5
Daily Routines
Reteach
Practice
Enrichment
Leveled Problem Solving
Homework
• Chapter 6 Test
Individual and Class Record Sheets
B
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Booklet 6 of 29
TTL_73744_U3_C06.indd 6–1
6–1
2/1/08 3:12:57 PM
Name
Unit 3 Prerequisite
Skills Test
Date
Unit 3 Prerequisite Skills Test
Show the expressions using addition.
1
3 NS 2.2
2×4
2
5+5+5
or 3 + 3 + 3 + 3 + 3
2 + 2 + 2 + 2 or 4 + 4
Solve.
3
3 NS 2.2
3×5
3 NS 2.2
How can 7 × 4 be solved using addition?
7+7+7+7
or 4 + 4 + 4 + 4 + 4 + 4 + 4
3 NS 2.2
4
What division does 12 – 3 – 3 – 3 – 3 = 0 show?
12 ÷ 3
3 NS 2.2
5
Mary wants to show 20 ÷ 5 using subtraction. How can she show this?
-
-
-
-
20 – 5 – 5 – 5 – 5
3 NS 2.2
6
What is the product of 7 × 8?
3 NS 2.2
7
18
56
Assessment Resources 4
What is the product of 6 and 3?
6–3
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73744_U3_US.indd 6–3
11/30/07 2:51:58 AM
Name
8
Unit 3 Prerequisite
Skills Test
Date
3 NS 2.2
What is 0 × 5?
9
What is 6 ÷ 2?
0
10
3
3 NS 2.2
What is 5 ÷ 5?
11
1
12
3 NS 2.2
What is 9 ÷ 3?
3 NS 2.2
3
3 AF 1.1
Kenesha has 9 boxes of crayons with 8 crayons in each box. What multiplication
sentence shows how many crayons she has?
9 × 8 = 72
or 8 × 9 = 72
3 NS 2.2
13
Each of Erik’s 4 friends gave him 9 marbles. How many marbles did Erik receive?
36
14
Lian decides to plant a vegetable garden. Her garden looks like this: 3
AF 1.1
What multiplication sentence shows how many plants Lian has in her garden?
3 × 5 = 15 or 5 × 3 = 15
Assessment Resources 4
6–4
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73744_U3_US.indd 6–4
11/30/07 2:52:43 AM
Name
Unit 3 Prerequisite
Skills Test
Date
Find the missing number in each number sentence.
15
6×
= 24
3 AF 1.2
16
4
17
42 ÷
=7
3 AF 1.2
6
3 NS 2.2
Lee had a bag of buttons. She divided the buttons into 7 groups. If each group had
7 buttons in it, how many buttons did Lee have?
49
Solve.
18
3 AF 1.5
Find the missing number. What property does this number sentence show?
×8=8×5
commutative property
3 AF 1.5
19
Michelle needs to find the missing number in a number sentence. What property
does she need to use? 2 × (5 × 7) = (2 × 5) ×
associative property
3 AF 1.5
20
Find the missing number. What property does this number sentence show?
4×1×8=8×
×1
commutative property
Assessment Resources 4
6–5
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73744_U3_US.indd 6–5
11/30/07 2:53:02 AM
Name
Date
Unit 3 Prerequisite
Skills Test
Individual Student Record Form
Unit 3 Prerequisite Skills Test
Use the Prerequisite Skills Test to identify your students’
mastery of the skills prerequisite to the unit. The item
analysis below will help you recognize strengths and
weaknesses.
Item
Number
Correct
Response?
Indicate whether the student’s response was correct in the
column to the right of the item number.
California State Standards
1.
3NS2.2
Memorize to automaticity the multiplication table for numbers between 1 and 10.
2.
3NS2.2
3.
3NS2.2
4.
3NS2.2
5.
3NS2.2
6.
3NS2.2
7.
3NS2.2
8.
3NS2.2
9.
3NS2.2
10.
3NS2.2
11.
3NS2.2
12.
3AF1.1
Students select appropriate symbols, operations, and properties to represent,
describe, simplify, and solve simple number relationships.
13.
3NS2.2
Memorize to automaticity the multiplication table for numbers between 1 and 10.
14.
3AF1.1
Students select appropriate symbols, operations, and properties to represent,
describe, simplify, and solve simple number relationships.
15.
3AF1.2
Solve problems involving numeric equations or inequalities.
16.
3AF1.2
17.
3NS2.2
Memorize to automaticity the multiplication table for numbers between 1 and 10.
18.
3AF1.5
19.
3AF1.5
Recognize and use the commutative and associative properties of multiplication
(e.g., if 5 × 7 = 35, then what is 7 × 5? and if 5 × 7 x 3 = 105, then what is
7 × 3 × 5?).
20.
3AF1.5
out of 20
Assessment Resources 4
6–6
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73784_IRF_US_U3.indd 6–6
1/31/08 10:32:35 AM
Name
Date
Unit 3 Prerequisite
Skills Test
Class Record Form
Unit 3 Prerequisite Skills Test
Use the Prerequisite Skills Test to identify your students’
mastery of the skills prerequisite to the unit.
Item
Number
The record below will allow you to group students for
differentiated instruction.
Groups for Differentiated Instruction
California State Standards
1.
3NS2.2
Memorize to automaticity the multiplication table
for numbers between 1 and 10.
2.
3NS2.2
3.
3NS2.2
4.
3NS2.2
5.
3NS2.2
6.
3NS2.2
7.
3NS2.2
8.
3NS2.2
9.
3NS2.2
10.
3NS2.2
11.
3NS2.2
12.
3AF1.1
Students select appropriate symbols,
operations, and properties to represent,
describe, simplify, and solve simple number
relationships.
13.
3NS2.2
Memorize to automaticity the multiplication table
for numbers between 1 and 10.
14.
3AF1.1
Students select appropriate symbols,
operations, and properties to represent,
describe, simplify, and solve simple number
relationships.
15.
3AF1.2
16.
3AF1.2
Solve problems involving numeric equations or
inequalities.
17.
3NS2.2
Memorize to automaticity the multiplication table
for numbers between 1 and 10.
18.
3AF1.5
19.
3AF1.5
20.
3AF1.5
Recognize and use the commutative and
associative properties of multiplication (e.g., if
5 × 7 = 35, then what is 7 × 5? and if 5 × 7 ×
3 = 105, then what is 7 × 3 × 5?).
6–7
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73784_CRF_US_U3.indd 6–7
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Name
Unit 3 Pretest
Date
Unit 3 Pretest
Solve.
1
4 NS 3.0
Write a division fact that is in the same family as 6 × 7 = 42.
42 ÷ 6 = 7 or 42 ÷ 7 = 6
4 NS 3.0
2
What multiplication fact is represented by the array below?
7 × 4 or 4 × 7
4 NS 3.0
3
What is any number multiplied by 1?
The original number
4 AF 1.2
4
Rewrite 6 × (3 × 7) using the associative property.
(6 × 3) × 7
4 NS 4.0
5
4 NS 4.0
What are the factors of 12?
6
What are two multiples of 12?
1, 2, 3, 4, 6, and 12
Possible Answer :
24 and 36
4 NS 3.4
7
What is the remainder when 39 is divided by 5?
4
4 NS 3.4
8
What is 48 ÷ 6?
8
4 NS 3.0
9
What is the remainder of 9 ÷ 2?
1
6–9
Assessment Resources 4
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73744_U3_UP.indd 6–9
2/21/08 9:30:16 AM
10483
Nets Gr4 CA Math ‘08 Reprint 73744_U3_UP ljc 05-02-07 edit ds 05-08-07
1pp
Name
Unit 3 Pretest
Date
Solve using the order of operations.
10
5 × (3 + 1) - 8
4 AF 1.2
11
28 ÷ 4 × 6 - 3
12
12
( (7 × 4) - 15 ) ÷ 13
39
4 AF 1.2
13
(9 + 1) × 7 - 3 × (6 + 2)
1
14
4 AF 1.2
4 AF 1.2
46
Adita played violin for 80 minutes. Hana played for less than half this time. Write
an expression that could be used to find the number of minutes Hana played.
2h < 80 or h < __ or h < 40
80
4 AF 1.0
2
15
Ramon can fold 30 shirts in 1 hour. Carla can fold 15 more shirts in 1 hour than
Ramon. What expression shows how many shirts Carla can fold in 1 hour?
4 AF 1.0
30 + 15
Use the figure below for questions 16 and 17.
=
16
How many squares would equal
3 stars?
4 AF
17
1.1
What sign belongs in the oval
below?
4
AF 1.1
6
=
18
Eno bought 4 movie tickets for
$4 each. What shows the cost of
all the tickets?
4 NS
19
3.0
4 × 4 or 4 + 4 + 4 + 4
20
Luz has 7 more hair clips than Maria.
Together, they have 19 clips. How
many clips does Luz have? 4 AF 1.1
13
Pedro’s truck can hold 20 crates of berries. Each crate contains 12 baskets of berries.
How many baskets of berries can Pedro’s truck hold?
4 MR 2.2
240
Assessment Resources 4
6–10
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73744_U3_UP.indd 6–10
12/1/07 9:31:53 PM
Name
Date
Unit 3 Pretest
Individual Student Record Form
Unit 3 Pretest
Use the Unit Pretest to identify your students’ knowledge
of the skills in the upcoming unit. The item analysis below
will help you recognize strengths and weaknesses.
Item
Number
Correct
Response?
Indicate whether the student’s response was correct in the
column to the right of the item number.
California State Standards
1.
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and
division of whole numbers and understand the relationships among the
operations.
2.
4NS3.0
3.
4NS3.0
4.
4AF1.2
Interpret and evaluate mathematical expressions that now use parentheses.
5.
4NS4.0
Students know how to factor small whole numbers.
6.
4NS4.0
7.
4NS3.4
8.
4NS3.4
9.
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and
division of whole numbers and understand the relationships among the
operations.
10.
4AF1.2
Interpret and evaluate mathematical expressions that now use parentheses.
11.
4AF1.2
12.
4AF1.2
13.
4AF1.2
14.
4AF1.0
15.
4AF1.0
16.
4AF1.1
17.
4AF1.1
18.
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and
division of whole numbers and understand the relationships among the
operations.
19.
4AF1.1
Use letters, boxes, or other symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an understanding and the use of the
concept of a variable).
20.
4MR2.2
Apply strategies and results from simpler problems to more complex problems.
Solve problems involving division of multidigit numbers by one-digit numbers.
Students use and interpret variables, mathematical symbols, and properties to
write and simplify expressions and sentences.
Use letters, boxes, or other symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an understanding and the use of the
concept of a variable).
out of 20
Assessment Resources 4
6–11
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73784_IRF_UP3.indd 6–11
11/30/07 3:27:29 AM
Name
Date
Unit 3 Pretest
Class Record Form
Unit 3 Pretest
Use the Unit Pretest to identify your students’ knowledge
of the California Mathematics Contents Standards in the
upcoming chapter.
Item
Number
The record below will allow you to group students for
differentiated instruction.
California Mathematics Contents Standards
1.
4NS3.0
2.
4NS3.0
3.
4NS3.0
4.
4AF1.2
Interpret and evaluate mathematical expressions that now use
parentheses.
5.
4NS4.0
Students know how to factor small whole numbers..
6.
4NS4.0
7.
4NS3.4
8.
4NS3.4
9.
4NS3.0
Students solve problems involving addition, subtraction,
multiplication, and division of whole numbers and understand the
relationships among the operations.
10.
4AF1.2
11.
4AF1.2
Interpret and evaluate mathematical expressions that now use
parentheses.
12.
4AF1.2
13.
4AF1.2
14.
4AF1.0
15.
4AF1.0
16.
4AF1.1
17.
4AF1.1
18.
4NS3.0
Students solve problems involving addition, subtraction,
multiplication, and division of whole numbers and understand the
relationships among the operations.
19.
4AF1.1
Use letters, boxes, or other symbols to stand for any number in
simple expressions or equations (e.g., demonstrate an understanding
and the use of the concept of a variable).
20.
4MR2.2
Apply strategies and results from simpler problems to more complex
problems.
Groups for differentiated
instruction
Students solve problems involving addition, subtraction,
multiplication, and division of whole numbers and understand the
relationships among the operations.
Solve problems involving division of multidigit numbers by one-digit
numbers.
Students use and interpret variables, mathematical symbols, and
properties to write and simplify expressions and sentences.
Use letters, boxes, or other symbols to stand for any number in
simple expressions or equations (e.g., demonstrate an understanding
and the use of the concept of a variable).
Assessment Resources 4
6–12
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73784_CRF_UP3.indd 6–12
11/30/07 3:31:02 AM
Family Letter for Unit 3
Dear Family,
Vocabulary
During the next few weeks our math class will
be learning how to multiply and divide whole
numbers. We will also continue to work with
expressions, equations, and inequalities.
You can expect to see work that provides
practice in multiplying and dividing basic facts
as well as in evaluating expressions, solving
equations, and comparing inequalities.
As we learn how to evaluate expressions with
all four operations, you may wish to use the
following sample as a guide.
Evaluating Expressions with all Four Operations
Follow these steps to evaluate 30 - (3 + 2) x 4.
• First, do the operations inside the parentheses.
• Then do any multiplication and division
in order from left to right.
• Finally, do any addition and subtraction in
order from left to right.
Knowing how to evaluate expressions and solve
equations using all four operations will allow
students to solve real-world problems.
dividend The number that is divided
in a division problem.
In 10 ÷ 2 = 5, the dividend is 10.
divisor The number by which a
number is divided. In 10 ÷ 2 = 5, the
divisor is 2.
factor One of two or more numbers
that are multiplied to give a product.
product The answer in a
multiplication problem.
quotient The answer in a division
problem. In 10 ÷ 2 = 5, the quotient
is 5.
30 - (3 + 2) × 4
30 - 5 × 4
30 - 20
10
Education Place
Visit www.eduplace.com/camaf/
for eGlossary, eGames, test-prep
practice, and more.
Sincerely,
Your Child’s Teacher
Chapter Resources 4
6–13
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73744_U03.EFL.indd 6–13
11/30/07 3:31:56 AM
Carta a la familia: Unidad 3
Estimada familia:
Vocabulario
Durante las próximas semanas, aprenderemos
a multiplicar y dividir números enteros en la
clase de matemáticas. También continuaremos
trabajando con expresiones, ecuaciones y
desigualdades.
Verán que trabajaremos con ejercicios para
practicar la multiplicación y la división
de operaciones básicas y para practicar la
evaluación de expresiones, la resolución de
ecuaciones y la comparación de desigualdades.
Mientras aprendemos a evaluar expresiones
con las cuatro operaciones, pueden utilizar la
siguiente muestra como guía.
dividendo Número que se divide en
un problema de división.
En 10 ÷ 2 = 5, el dividendo es 10.
divisor Número entre el cual se
divide un número. En 10 ÷ 2 = 5, el
divisor es 2.
factor Uno de dos o más números
que se multiplican para obtener un
producto.
producto Resultado de un problema
de multiplicación.
cociente Resultado de un problema
de división. En 10 ÷ 2 = 5, el
cociente es 5.
Hallar el valor de expresiones con las cuatro operaciones 30 - (3 + 2) × 4
Sigan estos pasos para hallar 30 - (3 + 2) x 4.
• Primero, resuelvan las operaciones que
están dentro del paréntesis.
• Luego resuelvan todas las multiplicaciones y
divisiones de izquierda a derecha.
• Por último, resuelvan todas las sumas y
restas de izquierda a derecha.
30 - 5 × 4
30 - 20
10
Al saber cómo hallar el valor de expresiones y
resolver ecuaciones con las cuatro operaciones,
los estudiantes podrán resolver problemas de la
vida real.
Atentamente,
Visiten Education Place en
www.eduplace.com/camaf/,
donde encontrarán el glosario
electrónico, eGames, práctica
para preparación para exámenes
y más.
El maestro de su hijo
Recursos del capítulo 4
6–14
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73744_U03_SP.indd 6–14
11/30/07 3:32:32 AM
Name
Date
Chapter 6, Lesson 1
Lesson Quiz
Lesson 1 Quiz
Greg used 12 counters to make 2 rows of 6.
1.
What multiplication equations can he write for his array?
2.
What division equations can he write?
3.
If he puts 4 counters in each row with the same counters, what
array will he make?
4.
What new equations can he write?
Lesson Quiz
Use with Chapter 6, Lesson 1
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Name
Date
Chapter 6, Lesson 2
Lesson Quiz
Lesson 2 Quiz
Write a fact family for each set of numbers.
1.
6, 2, 12
2.
10, 8, 80
Lesson Quiz
6–15
Use with Chapter 6, Lesson 2
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CAPEG4_C06_LessonQuiz.indd 6–15
11/30/07 3:33:20 AM
Name
Date
Chapter 6, Lesson 3
Lesson Quiz
Lesson 3 Quiz
Name the property or rule shown by each equation.
1.
5 × (2 × 6) = (5 × 2) × 6
2.
15 × 1 = 15
3.
14 ÷ 14 = 1
4.
8 ÷ 0 has no solution.
Lesson Quiz
Use with Chapter 6, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 6, Lesson 4
Lesson Quiz
Lesson 4 Quiz
Use a multiplication table.
1.
Where are the multiples of 5?
2.
What pattern in the multiplication table is shown by the even
numbers?
Alternate squares that are multiples of 2.
Lesson Quiz
6–16
Use with Chapter 6, Lesson 4
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CAPEG4_C06_LessonQuiz.indd 6–16
11/30/07 3:33:41 AM
Name
Date
Chapter 6, Lesson 5
Lesson Quiz
Lesson 5 Quiz
Find the quotient and remainder.
1.
_____________
5)27
2.
31 ÷ 4
3.
50 ÷ 6
Show how to check each answer.
4.
18 ÷ 5 = 3 R3
5.
44 ÷ 8 = 5 R4
Lesson Quiz
Use with Chapter 6, Lesson 5
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Lesson Quiz
6–17
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CAPEG4_C06_LessonQuiz.indd 6–17
11/30/07 3:33:56 AM
Name
Chapter 6, Lesson 1
Daily Routines
Date
Hands On: Relate Multiplication and Division
Problem of the Day
KEY AF 1.3
Kaleigh saw 11 robins and 8 finches in her backyard yesterday
morning. This morning she saw 7 robins and 5 finches.
How many more birds did she see yesterday?
Number Sense Review
KEY NS 3.1
In what place would you need to start regrouping if subtracting
a number from 340,000?
Number of the Day
KEY NS 1.0
9
Nine is the number of place values in one hundred million.
What are the names of those place values?
Facts Practice
KEY NS 3.1
Add.
1.
94,204 + 25,489
2.
6,673 + 729
3.
14,056 + 8,422
4.
5,241 + 5,967
5.
31,489 + 42,330
6.
121,854 + 48,326
Daily Routines
6–19
Use with Chapter 6, Lesson 1
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73744_C6L1_DR.indd 6–19
12/9/07 11:17:50 PM
Name
Chapter 6, Lesson 1
Reteach
Date
Hands On: Relate Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
An array shows objects arranged in equal rows and columns.
You can use an array to multiply and divide.
2 rows × 3 columns = 6
3 rows × 2 columns = 6
6÷2=3
6÷3=2
Write all the multiplication and division equations for each array.
1.
2.
3.
6 × 3 = 18
4 × 3 = 12
5 × 5 = 25
3 × 6 = 18
18 ÷ 3 = 6
18 ÷ 6 = 3
3 × 4 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
25 ÷ 5 = 5
Writing Math How are the arrays for 5 × 3 and 3 × 5 alike?
They both use 15 objects in rows and
columns.
Reteach
6–20
Use with text pages 120–121.
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73744_C6L1_RET.indd 6–20
11/30/07 3:36:19 AM
Name
Chapter 6, Lesson 1
Practice
Date
Hands On: Relate Multiplication
to Division
CA Standards
NS 3.0, MR 2.3
Write all the multiplication and division equations for each array.
1.
2.
3 × 6 = 18
6 × 3 = 18
18 ÷ 3 = 6
18 ÷ 6 = 3
3.
4.
2 × 6 = 12 5 × 5 = 25
6 × 2 = 12 25 ÷ 5 = 5
12 ÷ 6 = 2
12 ÷ 2 = 6
5 × 4 = 20
4 × 5 = 20
20 ÷ 4 = 5
20 ÷ 5 = 4
Test Practice
Circle the letter of the correct answer.
5.
Which equation does not go with the
array?
6.
There are 3 rows of 3 counters each.
Which equation goes with this array?
A
3+3=6
B
3×3=9
A
4 × 3 = 12
C
4 + 3 = 12
C
3÷3=1
B
3 × 4 = 12
D
12 ÷ 3 = 4
D
9-3=6
Writing Math Can you make an array with 23 counters?
Explain your answer.
Yes; you can make an array with one row and
23 columns, or 23 rows and one column.
Practice
6–21
Use with text pages 120–121.
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73744_CH6L1_PRAC.indd 6–21
11/30/07 3:36:52 AM
Name
Date
The Stars and Stripes
Chapter 6, Lesson 1
Enrichment
CA Standards
NS 3.0, MR 2.3
The first official United States flag was flown in 1777. It had 13 stars and 13 stripes, one
star and stripe for each colony. It looked like this:
From 1787 to 1790, the colonies became states. As new states entered the Union,
beginning in 1791 with Vermont and ending in 1959 with Hawaii, stars were added to the
flag. (The number of stripes remains 13, for the original colonies.) The numbers of stars in
the different flags are shown in the table below:
Official Flag of the United States
13 Stars 15 Stars 20 Stars 21 Stars 23 Stars
24 Stars 25 Stars 26 Stars 27 Stars 28 Stars
29 Stars 30 Stars 31 Stars 32 Stars 33 Stars
34 Stars 35 Stars 36 Stars 37 Stars 38 Stars
43 Stars 44 Stars 45 Stars 46 Stars 48 Stars
49 Stars
50 Stars
Look at the table. Which numbers of stars can be arranged in two or more unique
arrays? On separate paper, draw all the possible unique arrays for those flags. Write two
multiplication equations for each set of arrays.
See students’ work.
Finally, go to www.usflag.org on the Internet to see pictures of all the U.S. flags. Compare
your arrays to the way the stars were really arranged.
Writing Math Tell how you would arrange 51 stars on the
U.S. flag if another state joined the Union.
Answers will vary.
Enrichment
6–22
Use with text pages 120–121.
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73744_C6L1_ENR.indd 6–22
11/30/07 3:39:45 AM
Chapter 6, Lesson 1
Name
Leveled Problem Solving
Date
Hands On: Relate Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
Solve each problem.
1.
Tranh has 18 dinosaur statues. He
wants to arrange them in an array.
Write a multiplication equation that
describes one possible array.
2.
6 × 3, 3 × 6, 2 × 9, 9 × 2,
18 × 1, or 1 × 18 = 18
3.
Mac has 36 rocks in his collection.
What are all the arrays he can make?
3 × 8, 8 × 3, 4 × 6, or
6 × 4 = 24
4.
Mr. Hansen has 48 pictures of his
grandchildren. Write division equations
to describe all the different arrays he
can make with the pictures if he wants
at least 3 pictures in each row.
6.
48 ÷ 3 = 16, 48 ÷ 4 = 12,
48 ÷ 6 = 8, 48 ÷ 8 = 6,
48 ÷ 12 = 4, 48 ÷ 16 = 3
Leveled Problem Solving
María had her seashells in a 5 × 8
array. Then one shell broke. Write
multiplication equations for all the
arrays she can make using the new
number of shells.
Level
II
39 × 1 = 39, 13 × 3 =
39, 3 × 13 = 39,
1 × 39 = 39
1 × 36, 36 × 1, 2 × 18,
18 × 2, 3 × 12, 12 × 3,
4 × 9, 9 × 4, 6 × 6 = 36
5.
Debra is planting 24 tulip bulbs in
an array. She wants at least 3 bulbs
in each row and column. Write a
multiplication equation to describe one
possible array.
Level I
6–23
Sue has 50 stickers. She wants to
arrange them in three different square
arrays. Write multiplication equations to
describe the arrays.
Level III
3 × 3 = 9, 4 × 4 = 16,
5 × 5 = 25 (9 + 16 +
25 = 50)
Use with text pages 120–121.
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73744_C6L1_PS.indd 6–23
11/30/07 3:40:14 AM
Name
Chapter 6, Lesson 1
Homework
Date
Hands On: Relate Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
An array can show multiplication and division.
3 × 4 = 12
4 × 3 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
Write the multiplication and division equations for each array.
1.
2.
6 × 4 = 24
4 × 6 = 24
24 ÷ 6 = 4
24 ÷ 4 = 6
4QJSBM3FWJFX
4.
3.
3×2=6
2×3=6
6÷2=3
6÷3=2
4 × 4 = 16
16 ÷ 4 = 4
(Chapter 4, Lesson 3; Chapter 5, Lesson 2) KEY NS 3.0, KEY NS 3.1
Simplify the
expression.
Subtract.
3,614
- 1,509
________
5.
(25 + 13) + (46 - 10)
2,105
74
6.
Ursula gives Julio 23 of her Solar Adventures trading cards and 14 to Suri.
If she started with 85 trading cards, how many does she have left?
48 trading cards
Homework
6–24
Use with text pages 120–121.
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73744_CH6L1_HMWK.indd 6–24
11/30/07 3:40:42 AM
Name
Chapter 6, Lesson 2
Daily Routines
Date
Relate Multiplication and Division
Problem of the Day
KEY NS 1.1
Write 4,378,619 in expanded notation.
Number Sense
KEY NS 1.1
Use Workmat 2 to write seventy-three million, eight hundred
sixteen thousand, four hundred forty-five in standard form.
Word of the Day
AF 1.1
equation
Do equations always have an equals sign?
Facts Practice
Gr3 NS 2.2
Multiply.
1.
3×7
2.
5×6
3.
8×8
4.
7×9
5.
2×9
6.
4×9
Daily Routines
6–25
Use with Chapter 6, Lesson 2
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73744_C6L2_DR.indd 6–25
1/31/08 10:34:40 AM
Name
Chapter 6, Lesson 2
Reteach
Date
Relate Multiplication and Division
CA Standard
NS 3.0
Arrays can be used to represent fact families.
Find 18 ÷ 6.
Step 1 Think: How many groups of 6 are in 18?
× 6 = 18
3 × 6 = 18
Step 2 There are 3 groups of 6 in 18.
Solution: So, 18 ÷ 6 = 3.
The multiplication and division equations that can be written using the numbers
3, 6, and 18 form a fact family.
6 × 3 = 18
18 ÷ 6 = 3
3 × 6 = 18
18 ÷ 3 = 6
Write the fact family for each array or set of numbers.
1.
2.
5 × 4 = 20
4 × 5 = 20
20 ÷ 4 = 5
20 ÷ 5 = 4
3.
2 × 7 = 14
7 × 2 = 14
14 ÷ 2 = 7
14 ÷ 7 = 2
5, 7, 35
5 × 7 = 35
7 × 5 = 35
35 ÷ 7 = 5
35 ÷ 5 = 7
Writing Math Do the numbers 1, 2, and 3 make a fact family
using multiplication and division? Explain your answer.
No; 1 × 2 ≠ 3, 2 × 1 ≠ 3, 3 ÷ 2 ≠ 1, and
3 ÷ 1 ≠ 2.
Reteach
6–26
Use with text pages 122–123.
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73744_C6L2_RET.indd 6–26
11/30/07 3:42:36 AM
Name
Chapter 6, Lesson 2
Practice
Date
Relate Multiplication and Division
CA Standard
NS 3.0
Write the fact family for each array or set of numbers.
1.
2.
3.
2 × 7 = 14
7 × 2 = 14
14 ÷ 2 = 7
14 ÷ 7 = 2
3 × 7 = 21
7 × 3 = 21
21 ÷ 3 = 7
21 ÷ 7 = 3
5 × 4 = 20
4 × 5 = 20
20 ÷ 5 = 4
20 ÷ 4 = 5
2, 7, 14
Complete the fact family.
4.
3×9=
9 × = 27
27
3
÷3 =9
27 ÷ = 3
27
9
5.
5×7 =
7 × = 35
35
5
÷5 =7
35 ÷ = 5
35
7
Test Practice
Circle the letter of the correct answer.
6.
Find the missing number:
7.
× 7 = 63
Find the missing number:
48 ÷
=6
A
6
C
7
A
6
C
7
B
8
D
9
B
8
D
9
Writing Math Give an example of a fact family that contains
only two “members.” Explain why there are two and not four members.
Possible answer: 5 × 5 = 25 and 25 ÷ 5 = 5;
There is only one way to multiply the factors
5 × 5. There is only one way to divide 25 ÷ 5 = 5.
Practice
6–27
Use with text pages 122–123.
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73744_CH6L2_PRAC.indd 6–27
11/30/07 3:43:09 AM
Name
Date
Fact Family Dominoes
Chapter 6, Lesson 2
Enrichment
CA Standard
NS 3.0
Dominoes are tiles that use dots (called pips) for numbers. There are
two sets of pips on each domino, separated by a line. For example,
the 2 | 6 domino is shown below.
You and three friends will play dominoes and practice fact families at
the same time.
What You Need:
• 41 index cards
• markers
• 1 number cube
• 4 books or pieces of cardboard
Get Ready:
1.
Make the dominoes. Divide each card in half. Draw the pips. Make two dominoes for
each combination: 2 | 2, 2 | 3, 2 | 4, 2 | 5, 2 | 6, 2 | 7, 3 | 3, 3 | 4, 3 | 5, 3 | 6, 3 | 7, 4 | 4, 4 | 5,
4 | 6, 4 | 7, 5 | 5, 5 | 6, 5 | 7, 6 | 6, 6 | 7, 7 | 7.
2.
Mix up the dominoes and put them in a pile facedown.
3.
Everyone takes seven dominoes. Leave the rest in the pile. Use a book or a folded
piece of cardboard to hide your dominoes from each other.
How to Play:
The object is to get rid of all your dominoes.
4.
The first person puts a domino in the middle of the table and says all of the members
of the fact family for the two numbers.
5.
The next person puts down a domino that “matches” and says the fact family. For
example, if the first domino is 3 | 6, it can be matched with a domino that has a 3 or
6 on it. If you can’t make a match, take another domino from the pile. If you still can’t
make a match, it’s the next person’s turn.
6.
Continue going around the circle until one player has used all of his or her dominoes.
That player is the winner.
Writing Math Why do you think a set of numbers such as
3, 7, and 21 is called a fact family ?
Students may suggest that the numbers are
related like family members are.
Enrichment
6–28
Use with text pages 122–123.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L2_ENR.indd 6–28
11/30/07 3:43:39 AM
Chapter 6, Lesson 2
Name
Leveled Problem Solving
Date
Relate Multiplication and Division
CA Standard
NS 3.0
Use the numbers in each problem to write a fact family.
1.
3.
5.
There are 36 buttons in 9 rows, with
4 buttons in each row.
2.
Rusty planted 35 trees in 5 rows, with
7 trees in each row.
Level
9 × 4 = 36
5 × 7 = 35
4 × 9 = 36
7 × 5 = 35
36 ÷ 9 = 4
35 ÷ 5 = 7
36 ÷ 4 = 9
35 ÷ 7 = 5
There are 4 rows, with 7 T-shirts in
each row.
4.
At Frank’s Football Factory, there are
6 rows of footballs, with 8 balls in
each row.
Level
4 × 7 = 28
6 × 8 = 48
7 × 4 = 28
8 × 6 = 48
28 ÷ 4 = 7
48 ÷ 6 = 8
28 ÷ 7 = 4
48 ÷ 8 = 6
There are 63 stickers in 7 rows.
6.
There are 56 candles in 8 rows on
Mr. Booth’s birthday cake. Level
8 × 7 = 56
9 × 7 = 63
7 × 9 = 63
7 × 8 = 56
63 ÷ 7 = 9
56 ÷ 8 = 7
63 ÷ 9 = 7
56 ÷ 7 = 8
Leveled Problem Solving
6–29
I
II
III
Use with text pages 122–123.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L2_PS.indd 6–29
11/30/07 3:44:04 AM
Name
Chapter 6, Lesson 2
Homework
Date
Relate Multiplication and Division
CA Standard
NS 3.0
Write the fact family for each array or set of numbers.
1.
Some numbers can make
a fact family. You can
write multiplication and
division equations using
those numbers.
2.
2 × 8 = 16
8 × 2 = 16
16 ÷ 8 = 2
16 ÷ 2 = 8
3 × 7 = 21
7 × 3 = 21
9 × 4 = 36
4 × 9 = 36
36 ÷ 9 = 4
36 ÷ 4 = 9
21 ÷ 7 = 3
21 ÷ 3 = 7
The numbers 3, 7, and
21 are a fact family.
3.
3, 5, 15
4.
3 × 5 = 15
5 × 3 = 15
15 ÷ 5 = 3
15 ÷ 3 = 5
4QJSBM3FWJFX
4, 8, 32
5.
4 × 8 = 32
8 × 4 = 32
32 ÷ 8 = 4
32 ÷ 4 = 8
4, 7, 28
4 × 7 = 28
7 × 4 = 28
28 ÷ 4 = 7
28 ÷ 7 = 4
(Chapter 3, Lesson 4) KEY NS 3.1
Add. Use estimation to verify your answer.
6.
3,478
+ 655
______
_______
7.
4,133
8.
17,961
+ 4,813
________
22,774
Mrs. Fox traveled 338 miles from Chula Vista to Fresno and 295 miles
from Fresno to Crescent City. How far did she travel in all?
633 miles
Homework
6–30
Use with text pages 122–123.
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73744_CH6L2_HMWK.indd 6–30
11/30/07 3:44:34 AM
Name
Chapter 6, Lesson 3
Daily Routines
Date
Multiplication Properties and Division Rules
Problem of the Day
KEY NS 3.0
If 7 × 9 = 63, what is 63 ÷ 9?
Algebra and Functions Review
KEY AF 1.3
Use Workmat 1 to write down the expression 7 – 2 + 3 – 1.
Add parentheses so the value of the expression is equal to 1.
Word of the Day
MR 1.1
inverse operations
What is the inverse operation of each of the following expressions?
1.
45 + 16
2.
56 ÷ 7
3.
82 – 39
4.
15 × 3
Facts Practice
KEY NS 3.1
Subtract.
1.
7,452 - 2,626
2.
9,386 - 129
3.
16,924 - 3,945
4.
48,391 - 39,733
5.
8,193 - 7,642
6.
56,247 - 485
Daily Routines
6–31
Use with Chapter 6, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L3_DR.indd 6–31
11/30/07 3:46:57 AM
Name
Chapter 6, Lesson 3
Reteach
Date
Multiplication Properties and
Division Rules
Commutative
Property
When you change
the order of the
factors, the product
stays the same
CA Standards
NS 3.0, AF 1.0
Identity Property
Zero Property
When you multilply
any number by 1,
the product is equal
to that number.
When you multiply
any number by 0,
the product is 0.
Associative
Property
When you group
factors in different
ways, the product
stays the same.
3×2=6
4 × 3 = 12
3 × 4 = 12
1×9=9
2×3=6
6 × 3 = 18 3 × 6 = 18
6×0=0
Use properties and rules to solve. If there is no solution, explain why.
1.
1 × 43 =
2.
43
× 12 = 0
4.
5×3=3×
5
× 4) × 3
4÷4=
3.
5
5.
0
7.
5 × (4 × 3) = (
1
÷5=0
9×
6.
0
8.
28 ÷
=9
1
= 28
1
4÷0=
9.
cannot be
divided by 0
Writing Math What is the product of 937,568 × 0 × 622,001?
How do you know?
0; Any number multiplied by 0 = 0.
Reteach
6–32
Use with text pages 124–126.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L3_RET.indd 6–32
11/30/07 3:47:38 AM
Name
Chapter 6, Lesson 3
Practice
Date
Multiplication Properties and
Division Rules
CA Standards
NS 3.0, AF 1.0
Use properties and rules to solve.
1.
1 × 436 =
2.
436
3.
(10 × 85) × 12 = 10 × (
122
× 12)
4.
85
÷ 1 = 999
5.
848 ÷ 0 =
0 ÷ 125,699 =
0
6.
999
7.
122 × 17 = 17 ×
5,133 × 0 =
0
8.
÷ 423 = 1
423
cannot divide by 0
Test Practice
Circle the letter of the correct answer.
9.
10.
Which is an example of the Identity Property of Multiplication?
A
14 × 0 = 0
C
83 × 0 = 83
B
(6 × 2) × 8 = 6 × (2 × 8)
D
1 × 555 = 555
Which is true about division sentences that include 0?
A
0÷8=8
C
0÷8=0
B
8÷0=0
D
8÷0=8
Writing Math Compare the products of 4 × 0 and
444,444 × 0. Explain.
The products are the same. The product of any
number multiplied by 0 is 0.
Practice
6–33
Use with text pages 124–126.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_CH6L3_PRAC.indd 6–33
11/30/07 3:48:14 AM
Name
Chapter 6, Lesson 3
Enrichment
Date
Elementary Math
CA Standards
NS 3.0, AF 1.0
Scientists have discovered 110 elements. You have heard of some of them, such as
oxygen, nitrogen, and hydrogen. Did you know that iron and silver are elements too?
Each element has a number. Here are some of them:
hydrogen
1
sulfur
16
gold
79
helium
2
chromium
24
lead
82
beryllium
4
copper
29
californium
98
carbon
6
krypton
36
oxygen
8
iodine
53
Use the elements and their numbers to solve each problem.
For Problems 1–6, write your answer as a number.
36
0
1.
1 × krypton =
3.
lead × 0 =
5.
iodine ÷ iodine =
0
79
4. gold ÷ 1 =
6. californium ÷ 0 = cannot
divide by 0
2.
1
0 ÷ copper =
For Problems 7 and 8, write your answer using the element names.
7.
2×8=8×2=
sulfur
8.
(6 × 4) × 1 = 6 × (4 × 1) =
chromium
Writing Math The word commutative means “change” or
“trade.” Why is Commutative Property a good name to describe
4 × 3 = 12 and 3 × 4 = 12?
Students might say that the factors 4 and 3
change or trade places.
Enrichment
6–34
Use with text pages 124–126.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L3_ENR.indd 6–34
11/30/07 3:48:52 AM
Chapter 6, Lesson 3
Name
Leveled Problem Solving
Date
Multiplication Properties
and Division Rules
CA Standards
NS 3.0, AF 1.0
Solve each problem.
1.
One billion is 1 followed by 9 zeros.
What is 1 billion × 1?
2.
One quadrillion is 1 followed by
15 zeros. What is 1 quadrillion ÷ 1?
4.
One septillion is 1 followed by
24 zeros. What is 0 ÷ 1 septillion?
6.
One centillion is 1 followed by
303 zeros! What is 1 centillion
divided by 0?
Level
III
cannot divide by 0
0
Leveled Problem Solving
One quintillion is 1 followed by
18 zeros. What is 1 quintillion divided
by 1 quintillion?
Level II
1
1 quadrillion
5.
I
0
1 billion
3.
One trillion is 1 followed by 12 zeros.
What is 1 trillion × 0?
Level
6–35
Use with text pages 124–126.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L3_PS.indd 6–35
11/30/07 3:49:21 AM
Name
Chapter 6, Lesson 3
Homework
Date
Multiplication Properties and
Division Rules
CA Standards
NS 3.0, AF 1.0
Use properties and rules to solve.
1×7=
The Identity Property of Multiplication states that when you multiply
any number by one, the product is equal to that number.
Solution: 1 × 7 = 7
1.
6×5=5×
2.
6
3.
0
(3 × 7) × 2 = 3 × (
× 2)
4.
7
5.
0 ÷ 71 =
29 ÷
1 × 45 =
45
6.
0
7.
0 × 61 =
÷ 23 = 1
23
= 29
1
4QJSBM3FWJFX
8.
(Chapter 5, Lessons 2–3) KEY AF 1.2, AF 1.0
Simplify the expression.
(38 - 4) + 12
9.
46
10.
Complete the equation.
20 + 7 = (16 - ) + 14
3
Perry Porcupine has the sum of 73 and 15 quills. His sister Pamela
has 7 fewer quills than Perry. Write an expression for the number of quills Pamela
has.
(73 + 15) - 7
Homework
6–36
Use with text pages 124–126.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_CH6L3_HMWK.indd 6–36
11/30/07 3:49:46 AM
Name
Chapter 6, Lesson 4
Daily Routines
Date
Hands On: Patterns in Multiplication
and Division
Problem of the Day
KEY NS 3.0
An array has 5 rows and 4 counters in each row.
Use the array to write multiplication and division equations.
Number Sense
KEY NS 3.1
A hiker climbs 704 feet and then 235 feet before descending 150
feet. How high is she?
Number of the Day
KEY NS 1.1
10
Give an example of when you might need to multiply by 10.
Facts Practice
KEY NS 3.1
Add or subtract.
1.
156 + 72
2.
297 + 13 - 100
3.
837 - 490
4.
(1,023 - 211) + 15
Daily Routines
6–37
Use with Chapter 6, Lesson 4
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L4_DR.indd 6–37
11/30/07 3:56:34 AM
Name
Chapter 6, Lesson 4
Reteach
Date
Hands on: Patterns in Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
You can use a multiplication table to help you divide.
To find 42 ÷ 6, you can use a multiplication table.
Step 1 Look down the column for 6 until you find 42.
Step 2 Follow the row to the left to find the quotient.
ⴛ 0 1 2 3 4 5 6 7 8 9
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
2
0
2
4
6
8
10 12 14 16 18
3
0
3
6
9
12 15 18 21 24 27
4
0
4
8
12 16 20 24 28 32 36
5
0
5
10 15 20 25 30 35 40 45
6
0
6
12 18 24 30 36 42 48 54
7
0
7
14 21 28 35 42 49 56 63
8
0
8
16 24 32 40 48 56 64 72
9
0
9
18 27 36 45 54 63 72 81
Solution: 42 ÷ 6 = 7
Use the multiplication table to answer each question.
1.
24 ÷ 6 =
4
2.
81 ÷ 9 =
9
3.
32 ÷ 8 =
4
4.
20 ÷ 4 =
5
5.
49 ÷ 7 =
7
6.
56 ÷ 7 =
8
7.
12 ÷ 3 =
4
8.
63 ÷ 9 =
7
9.
72 ÷ 8 =
9
Writing Math You know that 42 ÷ 6 = 7. How does that
help you solve 42 ÷ 7?
42 ÷ 6 = 7 is one member of a fact family.
Another member is 42 ÷ 7 = 6.
Reteach
6–38
Use with text pages 128–129.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L4_RET.indd 6–38
11/30/07 3:57:17 AM
Name
Chapter 6, Lesson 4
Practice
Date
Hands On: Patterns in
Multiplication and Division
CA Standard
NS 3.0, MR 2.3
Use a multiplication table to answer each question.
1.
List different multiples of 8 that are shown in the table.
0, 8, 16, 24, 32, 40, 48, 56, 64, 72
2.
Is 42 a square number? Why or why not?
No. No number multiplied by itself equals 42.
3.
Use the table to find the quotient of 56 ÷ 7. Describe how you found it.
8; I found 7 at the top. I looked down the column to 56,
then I looked all the way left to find the quotient.
4.
Find 12 in four different places in the table. Write a division sentence for
each 12 you find.
12 ÷ 4 = 3; 12 ÷ 3 = 4; 12 ÷ 2 = 6; 12 ÷ 6 = 2;
5.
Use the table to find the product of 4 × 7. Describe how you found it.
28; I looked across the row for 4 and down the column
for 7. They meet at 28.
Test Practice
Circle the letter of the correct answer.
6.
Which number is a square number?
A
15
C
25
B
35
D
48
7.
15 is the product of which factors?
A
B
8 × 7,
7×8
5 × 2,
2×5
C
D
15 × 0,
0 × 15
5 × 3,
3×5
Writing Math What pattern do square numbers form
on the multiplication table?
The diagonal numbers from the top left to the bottom
right are all square numbers.
Practice
6–39
Use with text pages 128–129.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_CH6L4_PRAC.indd 6–39
11/30/07 3:57:59 AM
Name
Chapter 6, Lesson 4
Enrichment
Date
Extend the Pattern
CA Standards
NS 3.0, MR 2.3
Look at the products of the square numbers in the multiplication table.
Do you see the pattern?
ⴛ
0
1
2
3
4
5
6
7
8
9
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
2
0
2
4
6
8
10 12 14 16 18
3
0
3
6
9
12 15 18 21 24 27
4
0
4
8
12 16 20 24 28 32 36
5
0
5
10 15 20 25 30 35 40 45
6
0
6
12 18 24 30 36 42 48 54
7
0
7
14 21 28 35 42 49 56 63
8
0
8
16 24 32 40 48 56 64 72
9
0
9
18 27 36 45 54 63 72 81
1
4
3
9 16 25 36 49 64 81
5
7
9 11 13 15 17
The difference of the products is an odd number. The difference
increases by 2 each time.
Extend the pattern to solve these multiplication problems.
100: 81 + 19
144: 121 + 23
3. 12 × 12
196: 169 + 27
5. 14 × 14
1.
10 × 10
121: 100 + 21
169: 144 + 25
4. 13 × 13
225: 196 + 29
6. 15 × 15
2.
11 × 11
Writing Math It is easy to multiply using a calculator. Why
do you need to memorize products?
Possible answer: You don’t always have a
calculator.
Enrichment
6–40
Use with text pages 128–129.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L4_ENR.indd 6–40
11/30/07 3:58:31 AM
Chapter 6, Lesson 4
Name
Leveled Problem Solving
Date
Hands On: Patterns in Multiplication
and Division
CA Standards
NS 3.0, MR 2.3
Use a multiplication table to solve.
1.
Find the number 4 three times in
the table. Write multiplication
sentences and division sentences for
each 4.
2.
1 × 4 = 4, 4 × 1 = 4,
4 ÷ 1 = 4, 4 ÷ 4 = 1,
2 × 2 = 4, 4 ÷ 2 = 2
3.
Find the number 16 three times in the
table. Write multiplication sentences
and division sentences for each 16.
4.
Find the number 36 in the table. Write
multiplication sentences and division
sentences for each 36.
Level II
4 × 9 = 36, 9 × 4 =
36, 36 ÷ 4 = 9,
36 ÷ 9 = 4, 6 × 6 =
36, 36 ÷ 6 = 6
Name five numbers that are found only
once in the table.
6.
Possible answer:
1, 25, 49, 64, 81
Leveled Problem Solving
I
9 × 1 = 9, 1 × 9 = 9,
9 ÷ 1 = 9, 9 ÷ 9 = 1,
3 × 3 = 9, 9 ÷ 3 = 3
8 × 2 = 16, 2 × 8 =
16, 16 ÷ 8 = 2,
16 ÷ 2 = 8, 4 × 4 =
16, 16 ÷ 4 = 4
5.
Find the number 9 three times in
the table. Write multiplication
sentences and division sentences
for each 9.
Level
What type of numbers is found an odd
number of times in the table? Level
III
Possible answers:
square numbers,
odd numbes
6–41
Use with text pages 128–129.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L4_PS.indd 6–41
11/30/07 3:59:04 AM
Name
Chapter 6, Lesson 4
Homework
Date
Hands On: Patterns in
Multiplication and Division
CA Standards
NS 3.0, MR 2.3
columns
Multiplication
ⴛ 0 1 2 3 4 5 6 7 8 9
The product of two numbers is shown in
the table in the square where the row and
column of the two factors meet.
Division
To divide, find the column of the number
you are dividing by. Look down the column
to find the number you are dividing. Follow
that row to the left to find the quotient.
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
2
0
2
4
6
8
10 12 14 16 18
3
0
3
6
9
12 15 18 21 24 27
4
0
4
8
12 16 20 24 28 32 36
5
0
5
10 15 20 25 30 35 40 45
6
0
6
12 18 24 30 36 42 48 54
7
0
7
14 21 28 35 42 49 56 63
8
0
8
16 24 32 40 48 56 64 72
9
0
9
18 27 36 45 54 63 72 81
rows
Use the multiplication table to answer each question.
1.
Find the product of 3 and 7 in
two places in the table. Write two
multiplication sentences using
3 and 7 as factors.
2.
Find the product of 5 and 9 in
two places in the table. Write two
multiplication sentences using
5 and 9 as factors.
3 × 7 = 21, 7 × 3 = 21 5 × 9 = 45, 9 × 5 = 45
3.
Find 42 in two places in the table. Write
a division sentence for each 42.
4.
Find 36 in three places in the table.
Write a division sentence for each 36.
42 ÷ 7 = 6, 42 ÷ 6 = 7. 36 ÷ 6 = 6, 36 ÷ 4 = 9,
36 ÷ 9 = 4
4QJSBM3FWJFX
(Chapter 2, Lessons 3–4) KEY NS 1.3
Round each number to the place of the underlined digit.
5.
35,671
6.
35,700
7.
842,105,367
842,000,000
The Transamerica Pyramid in San Francisco is 10,236 inches high.
How many inches is that rounded to the nearest thousand?
10,000 inches
Homework
6–42
Use with text pages 128–129.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_CH6L4_HMWK.indd 6–42
11/30/07 4:04:17 AM
Name
Chapter 6, Lesson 5
Daily Routines
Date
Division with Remainders
Problem of the Day
KEY NS 3.0
Write a fact family using the numbers 4, 9, and 36.
Algebra and Functions Review
KEY AF 2.1
If 54 + 638 = 54 + (329 + 309), can you find the value of the
expression in the parentheses without adding?
Number of the Day
AF 1.0
1
What is the difference between adding by 1 and multiplying by 1?
Facts Practice
KEY AF 1.3
Simplify each expression.
1.
(22 - 5) + 12
2.
(30 - 14) + 41
3.
(93 - 60) + (36 + 8)
4.
(77 - 52) + (16 - 9)
5.
100 - (33 + 7) + 4
6.
84 - (45 + 27) + 8
Daily Routines
6–43
Use with Chapter 6, Lesson 5
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L5_DR.indd 6–43
11/30/07 4:05:20 AM
Name
Chapter 6, Lesson 5
Reteach
Date
Division with Remainders
CA Standard
NS 3.2
You will divide numbers with remainders.
Find 13 ÷ 4.
Step 1 Think of
multiplication facts that
have products close to 13.
Quotient
Divisor
ⴛ 1 2
3
4
5
1
1
2
3
4
5
2
2
4
6
8
10
3
3
6
9
12 15
4
4
8
12 16 20
5
5
10 15 20 25
Step 2 Find the quotient.
Step 3 Show the
remainder.
_ _ _ _ _ _ _ _3_ _ _ _ _
4 )13
- 12 ← Multiply. 3 × 4
_ _ _ _ _ _ _ _3_ _ _ _ _ R1
4 )13
- 12
1 ← Subtract. 13 - 12
1 ← remainder
There is 1 left over.
16 is too many.
Try 3 as the quotient.
Solution: 13 ÷ 4 = 3 R1.
Divide.
7 R1
1.
_____________
3 )22
5.
_____________
8 )30
9.
_____________
8 )59
5 R1
2.
_____________
4 )21
6.
_____________
2 )15
10.
_____________
5 )47
3 R6
4 R2
3.
_____________
7 )30
7.
_____________
9 )37
7 R1
7 R3
9 R1
4.
_____________
2 )19
8.
_____________
3 )17
4 R1
9 R2
11.
5 R2
7 R3 12. 25 ÷ 3 = 8 R1
38 ÷ 5 =
Writing Math What is a remainder?
It is the number left over after you divide.
Reteach
6–44
Use with text pages 130–132.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L5_RET.indd 6–44
11/30/07 4:05:45 AM
Name
Chapter 6, Lesson 5
Practice
Date
Division with Remainders
CA Standard
NS 3.2
Divide.
1.
____________
4)14
2.
3 R2
6.
_____________
8)34
7.
40 ÷ 6 =
6 R4
3.
3 R1
4 R2
11.
_________
2) 7
4.
6 R2
_____________
7) 40
8.
5 R5
12.
_____________
3)20
13.
5 R2
5.
4 R2
_____________
9)17
9.
1 R8
37 ÷ 7 =
_____________
6)26
7 R1
___________
6)32
10.
5 R2
80 ÷ 7 =
14.
11 R3
_____________
5)36
_____________
3)28
9 R1
55 ÷ 9 =
15.
6 R1
41 ÷ 7 =
5 R6
Find each missing number.
16.
4÷
= 1 R1
÷ 7 = 6 R2
19.
3
44
17.
10 ÷ 3 = 3 R
÷ 4 = 7 R3
20.
1
31
18.
33 ÷ 9 = 3 R
21.
110 ÷
6
= 12 R2 9
Test Practice
Circle the letter of the correct answer.
22.
Mary is packing plates in boxes. She
has 93 plates. Each box holds 8 plates.
If she fills each box, how many boxes
will she fill, and how many plates will
be left over?
23.
Jen has 47 stickers. She wants to give
an equal number of stickers to each of
her 5 cousins. How many stickers will
she give each cousin, and how many
stickers will be left over?
A
11 R3
C
11 R5
A
6 R5
C
7 R5
B
12 R3
D
12 R5
B
8 R7
D
9 R2
________________
Writing Math Jim solved 6)39 and got the quotient 5 R9.
Explain why Jim’s answer is incorrect.
6 goes into 39 one more time. The quotient
should be 6 R3. The remainder cannot be
larger than the divisor.
Practice
6–45
Use with text pages 130–132.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_CH6L5_PRAC.indd 6–45
11/30/07 4:06:10 AM
Name
Chapter 6, Lesson 5
Enrichment
Date
No Remainders Allowed!
CA Standard
NS 3.2
Guido’s Pizzeria sells only whole pies. Customers tell Guido how many slices
they want. Guido figures out how many pies have exactly that many slices.
Guido makes pizzas with 6, 7, or 8 slices.
6
7
8
The number of slices customers asked for are shown below. How many
pies of each size did Guido make—with no remainder?
Sample answers given.
5 @ 7 slices, 1 @ 6 slices
9 @ 7 slices, 2 @ 6 slices
2. 75 slices
5 @ 8 slices, 1 @ 7 slices, 2 @ 6 slices
3. 59 slices
4. 53 slices 5 @ 8 slices, 1 @ 7 slices, 1 @ 6 slices
10 @ 8 slices, 3 @ 7 slices, 1 @ 6 slices
5. 107 slices
6. 599 slices 74 @ 8 slices, 1 @ 7 slices
1.
41 slices
BONUS: Guido goofed! For order 5, his slices totaled 106. What is a
possible pie combination he made?
10 @ 8 slices, 2 @ 7 slices, 2 @ 6 slices
Writing Math How can you use multiplication to check your
answer to a division problem?
Multiply the quotient by the divisor, then add
the remainder. If that equals the dividend, the
answer is correct.
Enrichment
6–46
Use with text pages 130–132.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L5_ENR.indd 6–46
11/30/07 4:06:38 AM
Chapter 6, Lesson 5
Name
Leveled Problem Solving
Date
Division with Remainders
CA Standard
NS 3.2
Solve each problem.
1.
Callie had 38 stickers. She put
6 stickers on each of 6 pages. How
many stickers were left over?
2.
2 stickers
3.
Kareem put 5 carrot sticks on each of
8 plates. He had 4 carrot sticks left
over. How many carrot sticks does
he have?
4.
Lisa has 62 more pages to read in
Beezus and Ramona. She plans to
read 9 pages every night beginning
on Monday. How many pages will she
read on Sunday?
Level II
8 pages
Josh has 2 dozen eggs. He uses 5 eggs
for each extra-large loaf of his special
pumpkin bread. How many loaves of
bread can he bake? How many eggs
will be left over?
6.
4 loaves; 4 eggs left
over
Leveled Problem Solving
I
9 buttons
44
5.
Aki has 99 buttons. She wants to put
them on 11 sweaters equally, with no
buttons left over. How many buttons
will be on each sweater?
Level
6–47
Brendan has 75 stamps in his
collection. He puts 8 stamps on each
page in his album. How many more
stamps does he need to fill 10 pages
with no stamps left over? Level III
5 stamps
Use with text pages 130–132.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C6L5_PS.indd 6–47
11/30/07 4:07:09 AM
Name
Chapter 6, Lesson 5
Homework
Date
Division with Remainders
CA Standard
NS 3.2
Divide.
5 R4
21 ÷ 4
1.
5冄2
苶苶
9
↓ ↓
5 R1
苶苶
1
4冄苶2
-20
Multiply. 4 × 5
ᎏ
1
Subtract. 21 - 20
This is the remainder.
15 ÷ 2 =
3.
6.
7 R1
8.
9.
4 R3
11.
7冄3
苶苶
1
41 ÷ 7 =
43 ÷ 5 =
8 R3
3冄2
苶苶
2
3 R1
4.
7.
5 R6
35 ÷ 8 =
4QJSBM3FWJFX
2.
4 R3
Solution: 21 ÷ 4 = 5 R1
5.
7 R1
6冄1
苶苶
9
52 ÷ 9 =
5 R7
10.
28 ÷ 6 =
4 R4
(Chapter 1, Lessons 2–3) KEY NS 1.1
Write the value of the underlined digit in 349,186.
40,000
12.
Write the number in standard form.
six hundred thirty-four thousand, one hundred twelve
634,112
13.
There were 238,754 visitors to the San Diego Zoo in one year.
Write the number in word form.
two hundred thirty-eight thousand, seven
hundred fifty-four
Homework
6–48
Use with text pages 130–132.
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Name
Chapter 6, Lesson 6
Daily Routines
Date
Problem Solving: Field Trip
Problem of the Day
KEY NS 3.4
Ryan has 44 stickers he wants to give away to 7 friends. If he divides
the stickers up equally between his friends, how many stickers will he
have left over?
Number Sense Review
KEY NS 1.1
What is the value of the digit 6 in each number?
1.
456,703,249
2.
321,762,057
3.
698,343,109
Word of the Day
MR 2.3
inequality
What are the different symbols you have learned that show an
inequality? What is the difference between these symbols?
Facts Practice
KEY AF 2.1
Copy and complete.
1.
3.
36 + 29 = 65
= 65
(94 - 58) + 47 = 36 + 47
+ 47 = 36 +
Daily Routines
2.
4.
6–49
15 + (64 + 8) = 15 + 72
15 +
=
+ 72
(50 + 13) + 82 = 63 + 82
+
=
Use with Chapter 6, Lesson 6
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73744_C6L6_DR.indd 6–49
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Name
Chapter 6 Test
Date
Chapter 6 Test
4NS3.0
3
Circle the letter of the correct answer.
4NS3.0
1
What multiplication expression is
represented by the blocks below?
What expression shows the
relationship between
multiplication and division
compared to 3 × 5 = 15?
A
15 ÷ 1 = 1
B
15 ÷ 5 = 5
C
15 ÷ 5 = 3
D
15 ÷ 3 = 3
A
2 × 14
B
3 × 11
C
3×6
D
3×7
4NS3.0
2
What multiplication expression is
represented by the array below?
4NS3.0
4
What expression shows the
relationship between multiplication
and division compared to
8 × 3 = 24?
A
24 ÷ 8 = 8
A
2 × 14
B
24 ÷ 3 = 8
B
3 × 11
C
24 ÷ 3 = 3
C
3×6
D
24 × 3 = 8
D
5×6
4NS3.0
5
Using the commutative property,
rewrite the following expression:
9 × 4 = 36
Assessment Resources 4
A
4 × 9 = 36
C
4 × 36 = 9
B
9 × 36 = 4
D
4 × 9 = 38
6–51
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73744_C6_U3_CT.indd 6–51
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Name
6
Chapter 6 Test
Date
What is any number multiplied by 1?
A
0
B
9
4NS3.0
What is 3 ÷ 3?
A
1
1
B
3
C
10
C
6
D
the original number
D
9
4NS3.0
4NS3.0
7
Three friends decide to buy
crayons. Caroline buys 3 groups
of crayons, Tania buys 7 groups of
crayons, and Tao buys no groups of
crayons. If each group of crayons
has 4 crayons, how many crayons
does Tao have?
10
Fernando has 12 plants. He decides
to place them all near each other in
groups of 3. How many plants are in
each group that he creates?
A
1
B
4
A
0
C
6
B
1
D
12
C
4
D
12
11
4NS3.0
8
Using the associative property,
rewrite the following expression:
2 × (4 × 5)
A
2 × (3 × 5)
B
2 × (5 + 4)
C
(2 × 4) × 5
D
6×5
Assessment Resources 4
4NS3.0
12
What is 0 ÷ 7?
A
0
B
1
C
7
D
14
What is 9 ÷ 0?
A
0
B
1
C
9
D
cannot divide by 0
4NS3.0
4NS3.0
6–52
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73744_C6_U3_CT.indd 6–52
11/30/07 4:09:45 AM
Name
13
Chapter 6 Test
Date
Susan took all of her marbles and
laid them out. She has 3 rows of
marbles arranged in 7 columns.
How many marbles does she have?
16
5 × 4 is to 4 × 5 as 8 × 3 is
to 3 ×
4AF1.0
4NS3.0
A
4
B
5
A
3
B
7
C
3
C
14
D
8
D
21
4NS3.2
17
4NS3.0
14
Artie has 36 tin cans organized in
12 columns. How many rows of
cans does he have?
A
B
C
D
1
3
12
Rhoda has 29 pretzel logs to divide
evenly between the members of her
team. If the team has 9 members,
how many pretzels will be left over?
A
0
B
1
C
2
D
3
36
4NS3.0
15
Frank counted how many chickens
there are in the coop using tally
marks. How many chickens are
there?
A
11
C
50
B
13
D
53
Assessment Resources 4
6–53
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73744_C6_U3_CT.indd 6–53
11/30/07 4:10:01 AM
Name
18
Chapter 6 Test
Date
Bonita is dividing her box of 12
muffins into 5 parts for 5 friends.
How many muffins do they each
receive?
20
4NS3.0
If 9 × 8 is 72, then what is 72 ÷ 9?
A
8
B
9
A
5 with 2 left over
C
10
B
4 with 3 left over
D
11
C
2 with 2 left over
D
3 with 4 left over
4NS3.0
4NS3.0
19
If 5 × 8 is 40, then what is 40 ÷ 5?
A
5
B
6
C
7
D
8
Assessment Resources 4
6–54
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73744_C6_U3_CT.indd 6–54
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Name
Date
Chapter 6 Test
Individual Student Record Form
Use the chapter test to identify your students’ mastery of
the skills in the chapter. The item analysis below will help
you recognize strengths and weaknesses.
Correct
Answer
Student
Response
Record the student’s response in the column to the right
of the correct answer.
California State Standards
1. C
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and division
of whole numbers and understand the relationships among the operations.
2. D
4NS3.0
3. D
4NS3.0
4. B
4NS3.0
5. A
4NS3.0
6. D
4NS3.0
7. A
4NS3.0
8. C
4NS3.0
9. A
4NS3.0
10. B
4NS3.0
11. A
4NS3.0
12. D
4NS3.0
13. D
4NS3.0
14. B
4NS3.0
15. D
4NS3.0
16. D
4AF1.0
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
17. C
4NS3.2
Demonstrate an understanding of, and the ability to use, standard algorithms for
multiplying a multidigit number by a two-digit number and for dividing a multidigit
number by a one-digit number; use relationships between them to simplify
computations and to check results.
18. C
4NS3.0
19. D
4NS3.0
Students solve problems involving addition, subtraction, multiplication, and division
of whole numbers and understand the relationships among the operations.
20. A
4NS3.0
out of 20
Assessment Resources 4
6–55
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73784_IRF_C6_CT.indd 6–55
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Teacher Name
Date
Chapter 6 Test
Class Record Form
Chapter Test 6
Use the chapter test to identify your students’ mastery
of the California Mathematics Contents Standards in the
chapter.
Item
The record below will allow you to group students for
differentiated instruction.
California Mathematics Contents Standards
1.
4NS3.0
2.
4NS3.0
3.
4NS3.0
4.
4NS3.0
5.
4NS3.0
6.
4NS3.0
7.
4NS3.0
8.
4NS3.0
9.
4NS3.0
10.
4NS3.0
11.
4NS3.0
12.
4NS3.0
13.
4NS3.0
14.
4NS3.0
15.
4NS3.0
16.
4AF1.0
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
17.
4NS3.2
Demonstrate an understanding of, and the ability
to use, standard algorithms for multiplying a
multi digit number by a two-digit number and
for dividing a multi digit number by a one-digit
number; use relationships between them to
simplify computations and to check results.
18.
4NS3.0
19.
4NS3.0
20.
4NS3.0
Students solve problems involving addition,
subtraction, multiplication, and division of whole
numbers and understand the relationships
among the operations.
Groups for differentiated instruction
Students solve problems involving addition,
subtraction, multiplication, and division of whole
numbers and understand the relationships
among the operations.
6–56
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73784_U3_C6_CRF_CT.indd 6–56
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