Puzzles, Twisters & Teasers 3-1
Name LESSON
Date
Class
Puzzles, Twisters & Teasers
3-1 Baseball for Breakfast For each equation, write the letter of the property that it illustrates. 1. 9(3 4) 9 3 9 4
B Commutative Property of Addition
2. 3.5 x x 3.5
H Commutative Property of Multiplication
3. (5 n) 2 5 (n 2)
A Associative Property of Multiplication
1
1
4. 6 3 8 6 3 8
N Associative Property of Addition
5. 4.5m m 4.5
E Distributive Property
For each expression, write the letter of the expression that has the same value. 6. 3 50 6
O (3 50) 6
7. 3(50 6)
L (3 50) 6
8. 3 (50 6)
R 3 (5 6)
9. 3(44)
Y 3 50 3 6
10. 3 5 6
T 3 50 3 6
Use the above answers to find out what baseball and pancakes have in common.
2
8
2
8
3
4
9
9
9
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5
5
9
10
1
6
7
1
1
10
12
Holt Mathematics
Problem Solving 3-1 Properties of Rational Numbers
Challenge 3-1 Find a Path
LESSON
LESSON
To solve these puzzles, begin at START and move to a square containing a property or operation. Then move to a square in which this property or operation is used to write an equivalent expression. Continue in this way to find a path through all of the squares. You may only use horizontal or vertical moves. An example is shown at right.
Write the correct answer. 37 9 13 START
Add
Commutative Property of 9 (37 13) Addition Associative Property of Addition
9 37 13
1.
1. Terrell buys books that cost $18, $17, and $12. Write an expression for the total cost of the books before tax. Then show how Terrell can use mental math and properties of rational numbers to simplify the expression.
9 50
Add
59
2. 8 21
Commutative Property of Multiplication
2 7
Associative Property of Multiplication
86
2 8 21 7
2 7
21 8 START
14
Add
Multiply
59
48
Multiply
3.
Add
Multiply
Add
26
1 4 6 2
START
Commutative Property of Addition
1
21 14 1
4 2 4 6
Associative Property of Addition
7(3 2) 1 START
(21 14) 1
Add
Distributive Property
rewrite it as
as (18 12) 17 30 17 47
6 5 25 6 5 30
5(60 4) 5 60 5 4 320
1
4. Lisa said the equation (4 x ) y (x 4) y is an example of the Associative Property of Addition. Do you agree or disagree? Why?
(3.7 1.3) 9
Choose the letter for the best answer.
Disagree; she used the Comm. Prop. of Add. to change the order of 4 and x.
6. Carlos wants to simplify using the Distributive Property. Which expression should he use? F 9(20 1) H 9(20 1) G 9(20 1) J 9 (20 1)
5. Ms. Chen teaches 5 classes. Each class has 32 students. Which expression could not be used to find her total number of students? 1 A 5(30 2) C 5 (2 64) B 5(40 8) D 5 (2 32)
73 721
8. Which property states that (1.7 2) 6 1.7 (2 6)? F Associative Property of Multiplication G Commutative Property of Addition H Commutative Property of Multiplication J Distributive Property
7. Which of the following illustrates the Distributive Property? Distributive Property
1
1
A 4 2 2 4 1 1 B 4(7 2) 4 7 4 2 1
1 4 2 6
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Multiply
Use the Assoc. Prop. of Mult. to
Assoc. Props. of Add. to write it
Associative Property of Addition
4. 2 24
18 17 12; use the Comm. and
3. Brad has 5 boxes of baseball cards. Each box contains 64 cards. Show how Brad can use the Distributive Property to find the total number of cards in the boxes.
Commutative Property of 3.7 1.3 9 Addition
3.7 9 1.3 START
2. Sondra wants to rewrite the expression (6 15) 25 so that she can simplify it using mental math. Which property should she use and how should she rewrite the expression? What result will she get after simplifying?
9
1
C 4 (7 2) (4 7) 2
35 1
D 4(7
Holt Mathematics
1 ) (4 2
7)
1 2
10
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Mathematics
Puzzles, Twisters & Teasers 3-1 Baseball for Breakfast
Reading Strategies 3-1 Follow a Procedure
LESSON
LESSON
Use these steps to help you simplify expressions like 53 19 7.
For each equation, write the letter of the property that it illustrates.
Step 1: Choose two numbers that are easy to add. 53 19 7 Step 2: Rewrite the expression so the two numbers are next to each other.
1. 9(3 4) 9 3 9 4
E
B Commutative Property of Addition
2. 3.5 x x 3.5
B
H Commutative Property of Multiplication
3. (5 n) 2 5 (n 2)
N
A Associative Property of Multiplication
4. 6 3 8 6 3 8
A
N Associative Property of Addition
5. 4.5m m 4.5
H
E Distributive Property
1
Use the Commutative Property of Addition: 53 19 7 53 7 19 Step 3: Rewrite the expression so the two numbers are grouped together. Use the Associative Property of Addition: 53 7 19 (53 7) 19
1
For each expression, write the letter of the expression that has the same value.
L
6. 3 50 6
Step 4: Simplify. Add: (53 7) 19 60 19 79 Use expression 1.5 18 3.5 for Exercises 1–4.
7. 3(50 6)
Y
L (3 50) 6
8. 3 (50 6)
O
R 3 (5 6)
9. 3(44)
T
Y 3 50 3 6
R
T 3 50 3 6
1. Which two numbers are easy to add?
1.5 and 3.5
10. 3 5 6
2. Rewrite the expression so that the two numbers that are easy to add are next to each other. Which property lets you do this?
O (3 50) 6
Use the above answers to find out what baseball and pancakes have in common.
1.5 3.5 18; Commutative Property of Addition 3. Rewrite the expression so that the two numbers that are easy to add are grouped together. Which property lets you do this?
(1.5 3.5) 18; Associative Property of Addition 4. Simplify the expression.
(1.5 3.5) 18 5 18 23
Copyright © by Holt, Rinehart and Winston. All rights reserved.
11
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Mathematics
B
O
T
H
R
E
L
Y
2
8
9
5
10
1
6
7
O
N
T
H
E
8
3
9
5
1
B
A
T
T
E
R
2
4
9
9
1
10
Copyright © by Holt, Rinehart and Winston. All rights reserved.
88
12
Holt Mathematics
Holt Mathematics
Date
Class
Puzzles, Twisters & Teasers
3-1 Baseball for Breakfast For each equation, write the letter of the property that it illustrates. 1. 9(3 4) 9 3 9 4
B Commutative Property of Addition
2. 3.5 x x 3.5
H Commutative Property of Multiplication
3. (5 n) 2 5 (n 2)
A Associative Property of Multiplication
1
1
4. 6 3 8 6 3 8
N Associative Property of Addition
5. 4.5m m 4.5
E Distributive Property
For each expression, write the letter of the expression that has the same value. 6. 3 50 6
O (3 50) 6
7. 3(50 6)
L (3 50) 6
8. 3 (50 6)
R 3 (5 6)
9. 3(44)
Y 3 50 3 6
10. 3 5 6
T 3 50 3 6
Use the above answers to find out what baseball and pancakes have in common.
2
8
2
8
3
4
9
9
9
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5
5
9
10
1
6
7
1
1
10
12
Holt Mathematics
Problem Solving 3-1 Properties of Rational Numbers
Challenge 3-1 Find a Path
LESSON
LESSON
To solve these puzzles, begin at START and move to a square containing a property or operation. Then move to a square in which this property or operation is used to write an equivalent expression. Continue in this way to find a path through all of the squares. You may only use horizontal or vertical moves. An example is shown at right.
Write the correct answer. 37 9 13 START
Add
Commutative Property of 9 (37 13) Addition Associative Property of Addition
9 37 13
1.
1. Terrell buys books that cost $18, $17, and $12. Write an expression for the total cost of the books before tax. Then show how Terrell can use mental math and properties of rational numbers to simplify the expression.
9 50
Add
59
2. 8 21
Commutative Property of Multiplication
2 7
Associative Property of Multiplication
86
2 8 21 7
2 7
21 8 START
14
Add
Multiply
59
48
Multiply
3.
Add
Multiply
Add
26
1 4 6 2
START
Commutative Property of Addition
1
21 14 1
4 2 4 6
Associative Property of Addition
7(3 2) 1 START
(21 14) 1
Add
Distributive Property
rewrite it as
as (18 12) 17 30 17 47
6 5 25 6 5 30
5(60 4) 5 60 5 4 320
1
4. Lisa said the equation (4 x ) y (x 4) y is an example of the Associative Property of Addition. Do you agree or disagree? Why?
(3.7 1.3) 9
Choose the letter for the best answer.
Disagree; she used the Comm. Prop. of Add. to change the order of 4 and x.
6. Carlos wants to simplify using the Distributive Property. Which expression should he use? F 9(20 1) H 9(20 1) G 9(20 1) J 9 (20 1)
5. Ms. Chen teaches 5 classes. Each class has 32 students. Which expression could not be used to find her total number of students? 1 A 5(30 2) C 5 (2 64) B 5(40 8) D 5 (2 32)
73 721
8. Which property states that (1.7 2) 6 1.7 (2 6)? F Associative Property of Multiplication G Commutative Property of Addition H Commutative Property of Multiplication J Distributive Property
7. Which of the following illustrates the Distributive Property? Distributive Property
1
1
A 4 2 2 4 1 1 B 4(7 2) 4 7 4 2 1
1 4 2 6
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Multiply
Use the Assoc. Prop. of Mult. to
Assoc. Props. of Add. to write it
Associative Property of Addition
4. 2 24
18 17 12; use the Comm. and
3. Brad has 5 boxes of baseball cards. Each box contains 64 cards. Show how Brad can use the Distributive Property to find the total number of cards in the boxes.
Commutative Property of 3.7 1.3 9 Addition
3.7 9 1.3 START
2. Sondra wants to rewrite the expression (6 15) 25 so that she can simplify it using mental math. Which property should she use and how should she rewrite the expression? What result will she get after simplifying?
9
1
C 4 (7 2) (4 7) 2
35 1
D 4(7
Holt Mathematics
1 ) (4 2
7)
1 2
10
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Mathematics
Puzzles, Twisters & Teasers 3-1 Baseball for Breakfast
Reading Strategies 3-1 Follow a Procedure
LESSON
LESSON
Use these steps to help you simplify expressions like 53 19 7.
For each equation, write the letter of the property that it illustrates.
Step 1: Choose two numbers that are easy to add. 53 19 7 Step 2: Rewrite the expression so the two numbers are next to each other.
1. 9(3 4) 9 3 9 4
E
B Commutative Property of Addition
2. 3.5 x x 3.5
B
H Commutative Property of Multiplication
3. (5 n) 2 5 (n 2)
N
A Associative Property of Multiplication
4. 6 3 8 6 3 8
A
N Associative Property of Addition
5. 4.5m m 4.5
H
E Distributive Property
1
Use the Commutative Property of Addition: 53 19 7 53 7 19 Step 3: Rewrite the expression so the two numbers are grouped together. Use the Associative Property of Addition: 53 7 19 (53 7) 19
1
For each expression, write the letter of the expression that has the same value.
L
6. 3 50 6
Step 4: Simplify. Add: (53 7) 19 60 19 79 Use expression 1.5 18 3.5 for Exercises 1–4.
7. 3(50 6)
Y
L (3 50) 6
8. 3 (50 6)
O
R 3 (5 6)
9. 3(44)
T
Y 3 50 3 6
R
T 3 50 3 6
1. Which two numbers are easy to add?
1.5 and 3.5
10. 3 5 6
2. Rewrite the expression so that the two numbers that are easy to add are next to each other. Which property lets you do this?
O (3 50) 6
Use the above answers to find out what baseball and pancakes have in common.
1.5 3.5 18; Commutative Property of Addition 3. Rewrite the expression so that the two numbers that are easy to add are grouped together. Which property lets you do this?
(1.5 3.5) 18; Associative Property of Addition 4. Simplify the expression.
(1.5 3.5) 18 5 18 23
Copyright © by Holt, Rinehart and Winston. All rights reserved.
11
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Mathematics
B
O
T
H
R
E
L
Y
2
8
9
5
10
1
6
7
O
N
T
H
E
8
3
9
5
1
B
A
T
T
E
R
2
4
9
9
1
10
Copyright © by Holt, Rinehart and Winston. All rights reserved.
88
12
Holt Mathematics
Holt Mathematics
