Chapter Resources
Grade 4, Chapter 7
Contents
Resources for Chapter 7: More Expressions and
Equations
• Lesson Quizzes Lessons 7.1–7.5
Daily Routines
Reteach
Practice
Enrichment
Leveled Problem Solving
Homework
• Chapter 7 Test
Individual and Class Record Sheets
• Unit 3 Test
Individual and Class Record Sheets
B
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Booklet 7 of 29
TTL_73744_U3_C07.indd 7–1
7–1
2/1/08 3:05:54 PM
Name
Date
Chapter 7, Lesson 1
Lesson Quiz
Lesson 1 Quiz
What do you do first when evaluating each expression?
1.
5-8÷2
2.
6×3+4
3.
7 × (5 + 3) ÷ 2
4.
4 + 8 × 3 - 10
Lesson Quiz
Use with Chapter 7, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 7, Lesson 2
Lesson Quiz
Lesson 2 Quiz
Simplify.
1.
12 ÷ 6 + 3 × 7
2.
5 × (10 - 2) - 5
Solve.
3.
4.
Use parentheses to change the value of 3 × 4 + 2.
Use the numbers 1, 2, and 3 and the operations of subtraction
and division to write an expression. Find its value.
Lesson Quiz
7–2
Use with Chapter 7, Lesson 2
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CAPEG4_C07_LessonQuiz.indd 7–2
2/6/08 8:29:38 PM
Name
Date
Chapter 7, Lesson 3
Lesson Quiz
Lesson 3 Quiz
Complete. Use >, <, or =.
1.
2+6×5
2.
(4 + 7) + 5
3 × (10 - 1)
10 + 18 ÷ 3
Lesson Quiz
Use with Chapter 7, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 7, Lesson 4
Lesson Quiz
Lesson 4 Quiz
Find the missing number that makes each equation true.
1.
(4 + 6) × 7 =
2.
8×(
×7
- 2) = 5 × 8
Lesson Quiz
7–3
Use with Chapter 7, Lesson 4
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CAPEG4_C07_LessonQuiz.indd 7–3
2/6/08 8:29:53 PM
Name
Date
Chapter 7, Lesson 5
Lesson Quiz
Lesson 5 Quiz
Tickets to the play are $8 for adults and $5 for children. Write an
expression for each situation.
1.
4 adult tickets and 2 children’s tickets
2.
How much change do you get from $30 if you buy 3 adult
tickets?
3.
If you have $38 and buy 1 adult ticket, how many children’s
tickets can you get?
4.
Evaluate the expressions you wrote for Exercises 1–3.
Lesson Quiz
Use with Chapter 7, Lesson 5
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Lesson Quiz
7–4
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CAPEG4_C07_LessonQuiz.indd 7–4
2/6/08 8:30:09 PM
Name
Chapter 7, Lesson 1
Daily Routines
Date
Hands On: Expressions with All
Four Operations
Problem of the Day
KEY NS 3.0
Tran earns $7 an hour working at the pet store. How much money
would Tran make if he works 4 hours?
Number Sense
KEY NS 3.0
On your whiteboard, write two multiplication and division fact
families which include the number 6.
Word of the Day
AF 1.0
properties
How are the properties for addition and multiplication similar?
How are they different?
Facts Practice
KEY AF 1.3
Add parentheses to make the value of each expression equal to 8.
1.
12 - 7 + 3
2.
20 - 4 + 8
4.
18 - 13 + 3
5.
11 - 1 + 2
Daily Routines
7–5
3.
10 - 1 + 1
Use with Chapter 7, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–5
11/30/07 4:24:03 AM
Name
Chapter 7, Lesson 1
Reteach
Date
Hands On: Expressions with
All Four Operations
CA Standards
AF 1.2,
AF 1.3
What is the value of 6 + 4 ÷ (2 - 1)?
Step 1 Do the operation inside the parentheses first.
(2 - 1) = 1
Step 2 Then divide in order from left to right.
4÷1=4
Step 3 Last do the addition from left to right.
6 + 4 = 10
Solution: The value of 6 + 4 ÷ (2 - 1) is 10.
Use the numbers and operation symbols below to make an
expression with the value of 7. Remember to follow the order of
operations.
1.
3, 2, 1, +, ×
2.
1, 2, 16, ÷, -
Using each set of parentheses, solve each expression to
get three different values.
3.
(4 + 8) ÷ 2 × 3 - 1 =
5.
4 + 8 ÷ 2 × (3 - 1) =
4.
4 + (8 ÷ 2) × 3 - 1 =
Writing Math Why do you think parentheses were not
placed around the 2 and 3 in problems 3, 4, and 5? Explain.
Reteach
7–6
Use with text pages 142–143.
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73744_C07L1_RET.indd 7–6
11/30/07 4:26:01 AM
Name
Date
Hands On: Expressions with All
Four Operations
Chapter 7, Lesson 1
Practice
CA Standards
AF 1.3
AF 1.2,
Use the numbers and operation symbols below to make an
expression with the value of 4. Remember to follow the order
of operations.
1.
6
2
1
×
-
2.
8
2
0
÷
+
3.
1
2
4
2
×
-
Write the expression shown below three times. Add one set of
parentheses to each expression to get three different values.
6+4÷2×6-3
4.
5.
6.
Writing Math Which expression from problems 4–6 has the
same value as the expression without parentheses? Tell the order of
the operations you did to get the same answer.
Practice
7–7
Use with text pages 142–143.
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73744_C07L1_PRAC.indd 7–7
11/30/07 4:26:30 AM
Name
Chapter 7, Lesson 1
Enrichment
Date
Solving Expressions
CA Standards
AF 1.2,
AF 1.3
Find the value of each equation. Then use the values you found to
answer the riddle below by filling in the blanks with the appropriate
letters.
Riddle: Why was the zero so sad?
1.
(4 + 8) ÷ 2 × 4 - 3 =
2.
4 + (8 ÷ 2) × 4 - 3 =
3.
4 + 8 ÷ (2 × 4) - 3 =
4.
4 + 8 ÷ 2 × (4 - 3) =
5.
(10 - 3) × 2 + 1 =
6.
10 - (3 × 2) + 1 =
7.
10 - 3 × (2 + 1) =
8.
(12 - 5) + 4 =
9.
12 - (5 + 4) =
5=H
15 = 0
1=V
21 = N
17 = D
2=U
8=L
11 = E
3=A
10.
ANSWER: __ ___ __ __ ___ ___ ___ __ __ __ __ ___
5 11 5 3 17 21 15 1 3 8 2 11
Writing Math Sam worked out the expression 10 - 2 × 5
and got an answer of 40. Is he correct? Explain.
Enrichment
7–8
Use with text pages 142–143.
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73744_C07L1_ENR.indd 7–8
11/30/07 4:27:35 AM
Chapter 7, Lesson 1
Name
Leveled Problem Solving
Date
Hands On: Expressions with All
Four Operations
CA Standard
AF 1.2,
AF 1.3
Solve each problem. Write an equation to get your answer.
Remember that information from one problem will help you
solve the next one.
1.
John’s family had an open house party
on New Year’s Day. 4 guests came at
noon. Ten minutes later, 2 more guests
arrived. At 12:30, one guest left. How
many guests remained at the party?
2.
At 12:40, 6 more guests arrived at
John’s house. Then 2 couples left.
How many guests are there now
at the party?
3.
Over the next hour, the number of
guests at the party tripled. Then,
Mr. and Mrs. Ortiz and their three
children left to go to another party.
How many guests were left?
4.
By 2:30, half of the remaining guests
had left. Then John’s friends Gail, Bob,
and Bob’s cousin arrived and gave the
party a needed lift. What was the guest
count now?
5.
Bob and his cousin left at 4:15 and five
minutes later John’s Uncle Art, Aunt
Louise, and their 4 children arrived,
apologizing for being so late. Shortly
after, 3 more couples left. How many
guests are still at the party?
6.
After the other guests had gone,
John’s father invited Uncle Art and
his family to stay for the night.
They gratefully accepted. If John has
two sisters besides his parents, how
many people slept that night at his
house?
Leveled Problem Solving
7–9
Use with text pages 142–143.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L1_PS.indd 7–9
11/30/07 4:28:10 AM
Name
Date
Hands On: Expressions with All
Four Operations
Chapter 7, Lesson 1
Homework
CA Standards
AF 1.2,
AF 1.3
What is the value of 16 - 10 ÷ 2 × 3?
Step 1 Follow the order of operations. Evaluate 10 ÷ 2 using number tiles.
1
-
6
×
5
3
Step 2 Now do the multiplication in the expression. Use the tiles to replace 5 × 3.
1
-
6
1
5
Step 3 Finish by doing the subtraction in the expression.
16 - 15 = 1
Solution: The value of 16 - 10 ÷ 2 × 3 is 1.
Use the numbers and operation symbols below to make an expression
with the value of 6. Remember to follow the order of operations.
1.
1
2
3
2.
1
4
1
3.
2
2
×
2
6
2
÷
2
+
4QJSBM3FWJFX
-
-
×
(Chapter 5, Lesson 3) KEY AF 1.2, AF 1.0
Use the numbers and symbols below to make each equation true .
4, 3, =, >
4.
8-
5.
10 -
6.
×2
÷2
2
3
Molly has the equation 2 × 3 + 6 - 5 = 13. Where should she put
parentheses to make this equation correct?
Homework
7–10
Use with text pages 142–143.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L1_HMWK.indd 7–10
11/30/07 4:28:44 AM
Name
Chapter 7, Lesson 2
Daily Routines
Date
Hands On: Expressions with
All Four Operations
Problem of the Day
KEY AF 1.2
Explain each step in solving the problem shown below.
(7 + 8) ÷ 3 × 4 – 2
Number Sense
KEY NS 3.1
Write and solve a subtraction problem in which the thousands
need to be regrouped as hundreds and the tens need to be
regrouped as ones.
Number of the Day
KEY NS 3.0
12
Write all the ways 12 can be the answer to a multiplication problem.
Facts Practice
KEY NS 1.1
Write each number in word form.
1.
54,291
4.
10,800,450
Daily Routines
2.
5
320,670
3.
759,781
553,781,000
7–11
Use with Chapter 7, Lesson 2
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–11
11/30/07 4:24:25 AM
Name
Chapter 7, Lesson 2
Reteach
Date
Expressions with All Four
Operations
CA Standards
AF 1.2,
AF 1.3
Find 48 ÷ (3 × 4) + 2.
Step 1 Do the
operations in parentheses
first.
48 ÷ (3 × 4) + 2
Step 2 Multiply and
divide from left to right.
Step 3 Add and subtract
from left to right.
48 ÷ 12 + 2
4+2=6
Think: (3 × 4) = 12
Think: 48 ÷ 12 = 4
48 ÷ 12 + 2
4+2
Solution: 48 ÷ (3 × 4) + 2 = 6
Simplify each expression. Follow the order of operations.
1.
(3 + 6) × 8
2.
24 ÷ (2 × 2)
3.
(3 × 9) - 8
4.
12 × 3 + (8 - 4)
5.
(4 + 8) ÷ 3
6.
15 ÷ (5 × 3)
7.
4 × 3 + 12
8.
3×9+2×6
9.
5 × (49 ÷ 7)
Write an expression for each situation.
10.
The sum of 8 and the
product of 5 and 3
11.
8 times the difference
of 15 and 6
12.
9 more than 36
divided by 6
Writing Math Lila and Frank evaluated the expression
7 × 4 ÷ 2 + 5. Lila got 4 and Frank got 19. Explain what they each
did to get their answer.
Reteach
7–12
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_RET.indd 7–12
11/30/07 4:29:13 AM
Name
Chapter 7, Lesson 2
Practice
Date
Expressions with All Four
Operations
CA Standards
AF 1.2,
AF 1.3
Simplify each expression. Follow the order of operations.
1.
(6 + 3) × 4
2.
(7 - 5) × 6
3.
(15 + 3) ÷ 6
4.
8 + (5 × 3)
5.
9 - (21 ÷ 7)
6.
3 × (12 - 8)
7.
7 + (6 × 3) - 10
8.
30 - (3 × 3) + 4
9.
(18 - 3) ÷ 5
11.
18 + 9 × 7 - 13
12.
10.
6+5×4-7
5 × (6 + 3) × 2
Write an expression for each situation.
13.
the sum of 21 and the product of 8 and 7
14.
73 more than 6 times 9
15.
3 fewer than 42 divided by 7
Test Practice
Circle the letter of the correct answer.
16.
17.
18.
Karen owns 3 guitars that have 6 strings each and 2 mandolins that have 8 strings
each. How many strings do her instruments have in all?
A
34
C
19
B
36
D
5
There are 30 students in the classroom. If three groups of 4 students leave the room,
how many students are left?
A
26
C
12
B
18
D
20
David owns 4 guitars with 6 strings each and a guitar with 4 main strings and 22 special
resonating strings. How would you find how may strings his instruments have in all?
Practice
7–13
Use with text pages 144–146.
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73744_C07L2_PRAC.indd 7–13
11/30/07 4:29:36 AM
Name
Chapter 7, Lesson 2
Enrichment
Date
Finding the Lowest Point
CA Standards
AF 1.2,
AF 1.3
Below is a table showing the lowest point on six continents. Use
the information to help you solve each problem.
The World’s Lowest Points
Continent
Asia
Africa
North America
South America
Europe
Australia
Lowest Point
Location
Dead Sea
Lake Assal
Death Valley
Valdes Peninsula
Caspian Sea
Lake Eyre
Feet Below Sea Level
Israel–Jordan
Djibouti
California
Argentina
Russia–Kazakhstan
South Australia
1,348
512
282
131
92
52
Simplify each expression and write the lowest point it represents.
1.
2 × 200 + 5 × 20 + 24 ÷ 2
2.
300 - 200 + 5 × 6 + 1
3.
300 + 2 × 500 + 9 × 4 + 12
Solve each problem using a number sentence.
4.
Irina lives at half the elevation of the Caspian Sea. Her house is
20 feet high. If she stands on her roof, how far below sea level is she?
5.
Allen drove halfway out of Death Valley, then he stopped after another
50 feet to take a drink from his water bottle. How far below sea level is he?
6.
Corey visited Lake Eyre and then walked up a hill 82 feet above sea level.
How many feet in elevation has he traveled?
Writing Math Connie did problem 4 above and got an
answer of 66 feet. What did she do wrong? Explain.
Enrichment
7–14
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_ENR.indd 7–14
11/30/07 4:31:06 AM
Chapter 7, Lesson 2
Name
Date
Leveled Problem Solving
Expressions with All Four
Operations
CA Standards
AF 1.2,
AF 1.3
Write and evaluate an expression to solve each problem.
1.
Hillary likes to take photographs with
her camera. She took 40 pictures one
week. She took twice as many the
following week. How many pictures
did she take in the two weeks?
2.
Vic puts his photos in albums. He has
1 album of 25 pages. There are 4
photos on each page. He also has a
20-page album with 3 photos on each
page. How many photos does he have
in the two albums?
3.
José took 3 rolls of film with him on
the class field trip. Each rolls contains
36 pictures. He used up 2 rolls. There
were 10 pictures left on the third roll
when he got home. How many pictures
of the class trip did José take?
4.
Brad took the photos at his aunt’s
wedding. He took 22 pictures
before the wedding, half as many
during the wedding, and twice as
many pictures after the wedding.
How many wedding pictures did
Brad take in all?
5.
Lien went to the store to buy a new
camera. The camera cost $86. She
also bought 2 rolls of film that cost
$5 each. She paid for her purchases
with a $100 bill. What change did she
receive back?
6.
Maria takes pictures in both black and
white and color. She took 47 black and
white pictures one day and 6 more than
that in color. The same day, Teresa took
34 pictures in black and white and half
as many in color. How many pictures did
they both take that day?
Leveled Problem Solving
7–15
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_PS.indd 7–15
1/27/08 10:29:44 AM
Name
Chapter 7, Lesson 2
Homework
Date
Expressions with All Four
Operations
CA Standards
AF 1.2,
AF 1.3
Evaluate 7 + (12 ÷ 3 ) × 5
Step 1
7 + (12 ÷ 3 ) × 5 Simplify inside parentheses.
Step 2
7 + 4 × 5 Multiply and divide from left to right.
Step 3
7 + 20 Add and subtract from left to right.
Solution: The value of 7 + (12 ÷ 3 ) × 5 is 27.
Simplify each expression. Follow the order of operations.
1.
(7 + 8) × 2
2.
(12 - 7) × 8
3.
(9 + 7) ÷ 8
4.
25 + (4 × 5) - 15
5.
70 - (8 × 5) ÷ 10
6.
(28 - 4) ÷ 3
Write an expression for each situation.
7.
38 fewer than 8 times 6
8.
22 more than 25 divided by 5
9.
159 fewer than 4 times the sum of 20 and 46
4QJSBM3FWJFX
10.
(Chapter 4, Lesson 3) KEY NS 3.1, KEY NS 3.0
Subtract. Use addition to check your answer.
5,291 - 3,682 =
11.
Use inverse operations to find the missing number.
206 +
12.
= 389
Ted had 500 bottle caps in his collection. Jan had 174 bottle caps in her
collection. How many more bottle caps does Ted have than Jan?
Homework
7–16
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_HMWK.indd 7–16
11/30/07 4:32:05 AM
Name
Chapter 7, Lesson 3
Daily Routines
Date
Equations and Inequalities with All
Four Operations
Problem of the Day
KEY AF 1.3
Write an expression to represent the phrase given below.
Then solve the expression.
Seven less than three times the sum of 5 and 4.
Number Sense
KEY NS 1.31
On your whiteboard write 3 different numbers which round
to 91,000.
Number of the Day
KEY NS 1.11
45
What are some ways to show 45?
Facts Practice
KEY NS 3.11
Find each sum.
1.
648 + 827
2.
859 + 61 + 571
3.
1,958 + 487
4.
4,782 + 8,391
5.
40,549 + 281,391
6.
200,391 + 589,891
Daily Routines
7–17
Use with Chapter 7, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–17
11/30/07 4:24:46 AM
Name
Chapter 7, Lesson 3
Reteach
Date
Equations and Inequalities
with All Four Operations
CA Standard
AF 1.0
Phil bought 6 used books at the library sale. Willa bought twice as many books as
Phil. Write a number sentence that compares the number of books each bought.
Step 1 Write an expression for the books bought by each person.
Phil’s books
Willa’s books
6
6×2
Step 2 Compare the two expressions, using =, <, or >.
6<6×2
Solution: 6 < 12
Copy and complete. Use >, <, or =.
1.
2 × 11 + 6 × 1
3.
50 ÷ 5 - 2
5.
92 + (16 ÷ 4)
46 + 37
80 ÷ 10
99 - (2 × 4)
Write +, -, ×, or ÷ in each
6
9.
8 ÷ 2 + 12 = 4 × 3
11.
90
42 - 8 + 16
(2 × 5) × 5
4.
31 + (2 × 7)
74 - 22
16
6. ___
2
- (2 + 1)
20 ÷ 5
to make each number sentence true.
2+8=2×8+4
7.
2.
4
2 + 10 = 15 + 8 × 5
14
8. ___
2
10.
12.
× 3 = 23
56 ÷ 8
8
36 - __
=8
2
2
30 = 6 × 6 + 1
(2 + 2)
Writing Math Hank looked at problem 12 and knew before
he added each side of the equation that the missing operation had to
be a × or ÷. How did he know? Explain.
Reteach
7–18
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_RET.indd 7–18
11/30/07 4:32:29 AM
Name
Date
Equations and Inequalities with
All Four Operations
Chapter 7, Lesson 3
Practice
CA Standard
AF 1.0
Copy and complete. Use >, <, or =.
1.
2×3×5
90 ÷ 3
2.
10 + 6 × 8
63 - 5
3.
81 ÷ 9 + 4
6×2+5
4.
60
_
-1
5.
86
6.
40 ÷ 5 × 2
30 - 18
7.
7×8÷2
4×8+6
8.
4×6+7
62 ÷ 2
3+2×1
12
13 × 4 + 28
Write +, -, ×, or ÷ in each
sentence true.
9.
3 × 4 = 20
5=
8
18
_
+4
10.
5
11.
6 + 1 - 2 = 30
12.
7
to make each number
3
5-1
3 = 30 - 9
Writing Math Roger changed one operation sign on each
side of the equation in problem 1, in order to go from = to <. Was his
math correct? What did he change the sign to?
Practice
7–19
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_PRAC.indd 7–19
11/30/07 4:32:56 AM
Name
Chapter 7, Lesson 3
Enrichment
Date
Comparing Populations
CA Standard
AF 1.0
Many Native Americans live in Western states. The table below
shows the five states with the largest populations of Native
Americans. Use the information to solve the problems.
Native American Population
State
Population
California
410,510
Arizona
286,680
Oklahoma
278,124
New Mexico
183,972
Texas
145,954
1.
Write an inequality that compares the number of Native Americans in California to
those in Texas and Oklahoma combined.
2.
How many more Native Americans would Oklahoma need to equal the number of
Native Americans in Arizona? Write an equation for this comparison.
3.
Texas has 45,460 more Native Americans than the state of Alaska. How many Native
Americans live in Alaska? Show your answer in an inequality.
4.
Arizona and New Mexico are neighboring states. Arizona has more Native Americans
than New Mexico. How many more Native Americans live in Arizona than live in
New Mexico? Write an inequality to show your answer.
Writing Math Lynn wanted to find out which state’s Native
American population was closest to half of the Native American
population of California. How would she go about finding the answer?
Explain.
Enrichment
7–20
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_ENR.indd 7–20
11/30/07 4:33:43 AM
Chapter 7, Lesson 3
Name
Date
Leveled Problem Solving
Equations and Inequalities with
All Four Operations
CA Standard
AF 1.0
Write equations or inequalities to solve the problems.
1.
Bill went on 4 rides at the amusement
park. Juanita went on twice as many
rides as Bill did. Henry went on 4 more
rides than Bill did. Compare how many
rides Juanita went on to how many
rides Henry went on.
2.
Each ride at the amusement park
requires tickets. The merrygo-round costs 2 tickets. The Ferris
wheel costs 2 times as many tickets.
The roller coaster costs 4 more tickets
than the merry-go-round. Compare
how many tickets needed to ride the
Ferris wheel to the number needed to
ride the roller coaster.
3.
The shooting gallery on the midway
awarded 40 stuffed animals as prizes
one week. The ring toss awarded
30 more stuffed animals than the
shooting gallery. The softball throw
presented patrons with twice as many
stuffed animals than the shooting
gallery. Compare the number of stuffed
animals given by the ring toss to the
number given by the softball throw.
4.
The concession booth sold 75 cotton
candies one night at the amusement
park. It also sold 3 times as many
cups of lemonade. People bought
70 more bags of popcorn as they did
cotton candies. Compare the number
of cups of lemonade sold that
evening to the number of bags of
popcorn sold.
5.
One night 350 people visited the
park’s haunted house. Half as many
attended the magic show. 100 fewer
people attended the fun house as the
haunted house. Compare the number
who attended the magic show to the
number who went into the fun house.
6.
A total of 650 people came to the
amusement park on Thursday night.
456 more admissions were recorded
on Friday night. Three times as
many patrons went to the park
on Saturday night as on Thursday
night. Compare the number of paid
admissions on Friday night to those on
Saturday night.
Leveled Problem Solving
7–21
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_PS.indd 7–21
11/30/07 4:34:19 AM
Name
Chapter 7, Lesson 3
Homework
Date
Equations and Inequalities
with All Four Operations
CA Standard
AF 1.0
Ed read 9 books last summer. Angie read twice as many books as Ed. Hernando
read 9 more books than Ed. In a number sentence, compare how many books
Angie and Hernando read.
Step 1
Write an expression for the number of books each person read.
Books read by Angie
Books read by Hernando
9×2
9+9
Step 2
Evaluate each.
9×2
9+9
18
18
Step 3 Compare the 2 evaluations.
9×2
=
9+9
18
=
18
Solution: 9 × 2 = 9 + 9
Copy and complete. Use >, <, or =.
1.
(100 - 40) × 2
3.
8+7
5.
15 - (6 × 2)
100 + 20
1 × 15
4QJSBM3FWJFX
(16 ÷ 4) + 1
2.
20 + (2 × 3)
30 ÷ 2
4.
(6 × 8) + 10
40
___
× (5 × 10)
10
6.
(70 ÷ 2) + 5
(2 × 15) + 10
(Chapter 5, Lesson 4) KEY AF 1.2, KEY AF 2.0
Copy and complete.
7.
34 - 16 = 18
8.
= 18
(86 + 12) - 31= 34 + 33
- 31 =
=
9.
What do you know about the value of the
× 6 = × 6
Homework
7–22
and in this equation?
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_HMWK.indd 7–22
11/30/07 4:34:50 AM
Name
Chapter 7, Lesson 4
Daily Routines
Date
Multiply Equals by Equals
Problem of the Day
KEY AF 1.3
James wrote a 4 page story. Latisha wrote 1 more than 3 times as
many pages as James. Jorge wrote 7 more pages than James. Write
a number sentence to compare the number of pages Latisha wrote to
the number Jorge wrote.
Number Sense
KEY NS 3.0
Write 5 basic multiplication facts which involve the number 8.
Word of the Day
MR 3.3
remainder
Give some examples of when you might have a remainder in real life.
Facts Practice
AF 1.0
Use multiplication properties and division rules to find each
missing number.
1.
45 × 3 = 3 × ____
2.
(8 × 5) × 9 = 8 × (___ × 9)
3.
____ × 99 = 0
4.
113 × ____ = 113
5.
49 ÷ 49 = ____
6.
0 ÷ 5 = ____
Daily Routines
7–23
Use with Chapter 7, Lesson 4
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–23
11/30/07 4:25:06 AM
Name
Chapter 7, Lesson 4
Reteach
Date
Multiply Equals by Equals
CA Standards
AF 2.0
AF 2.2,
To keep equations true, you must do the same thing on both sides of the equation.
Is 2 + (3 × 6) = 2 + 18 still equal if each side is multiplied by 4?
Step 1 Simplify the original equation.
Step 2 Multiply each side by 4.
2 + (3 × 6) = 2 + 18
20 × 4 = 20 × 4
2 + 18 = 20
80 = 80
20 = 20
Solution: Both sides of the equation are still equal.
Copy and complete.
1.
2 × (9 + 2) = 2 ×
2.
(6 - 4) ×
=2×8
3.
+ (4 × 7) = 12 + 28
4.
3 × (50 ÷ 5) = 3 ×
5.
× (6 × 8) = 3 × 48
6.
9×(
8.
2×9=2×(
7.
6 × 36 = 6 × (6 ×
)
÷ 3) = 9 × 5
- 5)
Writing Math Nick said the equation 10 × 2 = (5 × 2) + (1 + 1)
is correct. Is he correct? Explain.
Reteach
7–24
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_RET.indd 7–24
11/30/07 4:35:16 AM
Name
Date
Multiply Equals by Equals
Chapter 7, Lesson 4
Practice
CA Standards
AF 2.0
AF 2.2,
Copy and complete.
1.
(4 + 6) ×
= 10 × 5
2.
30 - (3 × 9) = 30 ÷ 8 + 11 = 4 + 11
3.
4.
12 × (
- 3) = 12 × 3
5.
7 × (24 ÷ 3) = 7 ×
× (6 × 7) = 4 × 42
6.
7.
3 + 63 ÷ 9 = 3 +
8.
5 × (8 - 3) = 5 ×
Test Practice
Circle the letter of the correct answer.
9.
10.
Fran multiplied one side of an equation by 12. How much must she
multiply the other side by to keep the equation true?
A
6
C
10
B
12
D
24
Carl multiplied one side of an equation by 5. To make it an inequality,
what must he multiply the other side by?
A
5
C
a number
B
(2 + 3)
D
any number but 5
Writing Math Kelly multiplied one side of an equation
by 6 and the other side by (36 ÷ 6). Does she still have an equation?
Explain.
Practice
7–25
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_PRAC.indd 7–25
11/30/07 4:35:51 AM
Name
Date
Solving Equations
Chapter 7, Lesson 4
Enrichment
CA Standards
AF 2.0
AF 2.2,
Complete each equation. Then use the values you found to find
the answer to the riddle below by filling in the blanks with the
appropriate letters.
Riddle: Why were the two sides of the inequality fighting?
1.
3 × (2 × 4) = 3 ×
2.
(6 - 2) ×
3.
7×3-4=
4.
3 + (8 × 4) = 5 × 6 +
=6+6
×3-1
× (2 + 1) = 15 - 3
5.
3=E
6=V
5=N
4=T
8=G
6.
ANSWER: They wanted to __ __ __
8 3 4
__ __ __ __
3 6 3 5
Writing Math If the parentheses were removed from
problem 4 above would the answer remain the same? Explain.
Enrichment
7–26
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_ENR.indd 7–26
11/30/07 4:36:18 AM
Chapter 7, Lesson 4
Name
Date
Leveled Problem Solving
Multiply Equals by Equals
CA Standards
AF 2.0
AF 2.2,
Solve each problem. After the answer write an equation that
helped you to get the answer.
1.
Alex picked 8 apples and 2 pears from
the orchard. Janet picked 4 apples. How
many pears does she have to pick to
have the same amount of fruit as Alex?
2.
Jorge filled 2 bags with 4 peaches in
each bag. Rod has only one bag. How
many peaches must he put in his bag
to equal Jorge’s number of peaches?
3.
A farmer had six baskets of pears. Each
basket held 15 pears. He lost one of
the baskets when it fell off his tractor.
How many pears does he now have?
4.
Hector has 3 apple trees in his yard.
Each tree has 50 apples. Jill has
5 apple trees in her yard. How many
apples must each tree in Jill’s yard
have to match the number of apples
Hector has?
5.
Ling bought 8 oranges and ate 2 of
them. Carl bought twice as many
oranges as Ling. How many oranges
must he eat to have the same number
of oranges as Ling?
6.
Ben picked 6 baskets of avocados. Each
basket held 30 avocados. 40 avocados
were bad and had to be thrown away.
Thad picked 5 baskets and 10 were bad.
He had the same number of avocados as
Ben. How many avocados did he have in
each basket?
Leveled Problem Solving
7–27
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_PS.indd 7–27
11/30/07 4:36:47 AM
Name
Chapter 7, Lesson 4
Homework
Date
Multipy Equals by Equals
CA Standards
AF 2.0
AF 2.2,
Will the equation 3 × 6 = 2 × 9 still be true if both sides are multiplied by 5?
Step 1
Simplify both sides of the equation.
3×6 = 2×9
18
= 18
Step 2
Rewrite the equation multiplying each side by 5.
18 × 5 = 18 × 5
90
=
Step 3
90
Note that both sides are equal as they were before.
Solution: The equation 3 × 6 = 2 × 9 remains true if both sides are multiplied by 5.
Copy and complete.
1.
5 × (2 + 1) = 5 ×
2.
(6 - 2) ×
3.
4 + (9 - 2) = 4 +
4.
12 × 2 + 5 = 12 + 12 +
5.
(8 ÷
)×3=4×3
6.
7.
4×(
+ 2) = 4 × 8
8.
4QJSBM3FWJFX
9.
=4×9
+ (6 × 7) = 8 + 42
7 × (20 ÷ 5) = 7 ×
(Chapter 6, Lesson 4) KEY NS 3.0, MR 2.3
Divide. Then check your answer.
18 ÷ 6 =
10.
Find the missing number.
21 ÷
11.
=3
Jake has 15 apples. He gave one third of the apples to Judy.
How many apples did he give her?
Homework
7–28
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_HMWK.indd 7–28
11/30/07 4:37:11 AM
Name
Date
Chapter 7, Lesson 5
Daily Routines
Problem Solving: Write an Expression
Problem of the Day
AF 2.0
Write all the pairs of numbers that can be written in the blanks
below to make the equation true.
6 × (14 + 7) = 21 × (___ + ___)
Number Sense
KEY NS 1.2
What place value would you need to change to make 539,138 greater
than 540,502?
Word of the Day
MR 2.3
operation
Which numerical operation do you use most often during a day? Give
some examples of how you use it.
Facts Practice
KEY NS 1.1
Write each number in standard form.
1.
40,000 + 5,000 + 90 + 8
2.
100,000 + 7,000 + 500 + 80 + 2
3.
10,000 + 6,000 + 20
4.
2,000,000 + 300,000 + 8,000 + 800 + 30 + 1
5.
5,000,000 + 300,000 + 90,000 + 4
6.
3,000,000 + 7,000 + 600 + 40 + 3
Daily Routines
7–29
Use with Chapter 7, Lesson 5
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–29
11/30/07 4:25:29 AM
Name
Chapter 7, Lesson 5
Reteach
Date
Problem Solving:
Write an Expression
CA Standard
AF 1.3
MR 2.4,
Rusty has 6 pottery students. She gets paid $60 by the school to teach the class .
The amount includes the student fees plus the cost to buy two packages of clay.
If each student pays $8 to take the class, how much did the clay cost?
Read It Look for the information you need to solve the problem.
Organize It Write an expression.
$60
amount
Rusty
received
-
(6 × $8)
=
fees paid
by students
$12
amount
spent for
clay
Solve It First, do the operations inside the parentheses. Then, do the addition and
subtraction in order from left to right.
The clay cost
$12
.
Write an expression and solve each problem.
1.
Gorge uses 2 pounds of clay to make a
platter. He can make 8 platters a day.
How much clay will he use if he makes
platters for 7 days?
2.
Samantha wants to buy a clay vase.
She earns $3 an hour baby-sitting.
She baby-sits 2 hours a week. A vase
costs $18. How many weeks will
Samantha have to save her earnings to
have enough money to buy the vase?
Writing Math What is the first operation you should do in
this expression: $12 - (3 × $2)?
Reteach
7–30
Use with text pages 154–155.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L5_RET.indd 7–30
11/30/07 4:37:39 AM
Name
Chapter 7, Lesson 5
Practice
Date
Problem Solving:
Write an Expression
CA Standards
AF 1.3
MR 2.4,
Use the table for Problems 1–4. Write an equation to solve
each problem.
Ben’s Points
Game
Points
1
2
3
4
Total
8
12
6
18
44
1.
In Game 4, Ben scored half of his team’s total points. How many points did his team
score in Game 4?
2.
Ben’s friend Jason scored 3 fewer points than Ben did in Game 1, and 2 fewer points
than Ben in Game 2. How many total points did Jason score in Games 1 and 2?
3.
Ben scored an equal amount of points in Games 5 and 6. Ben’s points in Game 5
equaled the total amount of points he scored in Games 3 and 4. How many total
points did Ben score in Games 5 and 6?
4.
Ben’s team, including Ben, scored a total of 141 points in the first four games. How
many points did Ben’s teammates score in the first 4 games?
Test Practice
Circle the letter of the correct answer.
5.
Martin is on Ben’s team. In Games 1 and 2 he scored half the points Ben did. In
Game 3 he scored one more point than Ben, and in Game 4 he scored 0 points. Which
expression will Martin use to find out how many points he scored in all four games?
A
(8 + 12) ÷ 2 + (6 + 1)
B
12 + 8 ÷ 2 - 6
C
(18 - 12) × 2 + (6 + 1)
D
12 - 8 ÷ 2 + (6 + 1)
Practice
7–31
Use with text pages 154–155.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L5_PRAC.indd 7–31
11/30/07 4:38:09 AM
Name
Chapter 7, Lesson 5
Enrichment
Date
Problem Solving:
Write an Expression
CA Standards
MR 2.4,
AF 1.3
Work with a partner. Cut out the cards below. Arrange the cards to
write expressions. Arrange every card to the left of the equal sign.
Fill in the answer to the expression to the right of the equal sign.
How many expressions can you write that have different answers?
Make a list of the completed expressions.
(
(
16
)
2
4
8
16 +
÷
×
=
)
+
2
÷
4
×
8
=
Example: (16 ÷ 4) + 8 × 2 = 20
Writing Math Akira wrote this expression: (2 × 16 + 4) ÷ 8 =. He says the
answer is 2 R6. What did he do wrong? What is the correct answer?
Enrichment
7–32
Use with text pages 154–155.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L5_ENR.indd 7–32
11/30/07 4:38:34 AM
Chapter 7, Lesson 5
Name
Date
Leveled Problem Solving
Problem Solving:
Write an Expression
CA Standards
AF 1.3
MR 2.4,
Write an equation to solve each problem.
1.
Mandy has 9 coins. The coins are
quarters, dimes, and nickels. She has
2 quarters and 5 nickels. How many
dimes does Mandy have?
2.
Annie has 16 coins. The value of the
coins totals 50 cents. She has 10 pennies
and 2 dimes. The rest of the coins are
nickels. How many nickels does she
have?
3.
Mandy has $37. She has 2 one-dollar
bills and 1 ten-dollar bill. The rest are
five-dollar bills. How many five-dollar
bills does she have?
4.
Annie had $38. She bought 3 CDs and
a book. She had $4 left over. If the CDs
cost $9 each, what did the book cost?
5.
Teri bought 3 T-shirts and 2 pairs of
socks. She paid a total of $30. If the
socks were $3 a pair, how much was
each T-shirt?
6.
Meredith bought 4 notebooks that cost
$2 a piece. She also bought 3 packs of
pencils for $6 total. She had a $3 off
coupon for purchases of $10 or more.
How much did she spend on school
supplies?
Leveled Problem Solving
7–33
Use with text pages 154–155.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L5_PS.indd 7–33
11/30/07 4:39:01 AM
Name
Chapter 7, Lesson 5
Homework
Date
Problem Solving:
Write an Expression
CA Standards
AF 1.3
MR 2.4,
Write an expression to solve each problem.
Read It Look for information.
Mr. Henderson bought 5 cups and 5 saucers. His total purchase cost $50.
If each saucer cost $2, how much did he pay for each cup?
Organize It Write an expression to solve the problem.
($50 total
purchase
5 × $2)
cost of
saucers
÷
5
=
number
of cups
cost of each cup
Solve It First, do the operations inside the parentheses. Do the multiplication and
division in order from left to right. Then, do the addition and subtraction in order from left
to right. Finally, do the operations outside the parentheses in the same order.
Each cup cost
1.
Mrs. Henderson bought 18 pieces of pottery. She bought 11 mugs, 4 bowls, and
some plates. How many plates did she buy?
2.
She also bought 3 hand mirrors, 2 spoon rests, and 5 toothbrush holders to give as
gifts to her friends. The hand mirrors cost $5 each. The spoon rests cost $2 each.
Altogether, she spent $34 on the gifts. How much did the 5 toothbrush holders cost?
4QJSBM3FWJFX
(Chapter 6, Lesson 5) KEY NS 3.2
Divide. Then check your answer.
3.
5.
17 ÷ 3 =
4.
126 ÷ 10 =
Margie wants to ship 40 mugs. Each shipping carton holds 12 mugs. How many full
cartons will she have? How many mugs will be left over?
Homework
7–34
Use with text pages 154–155.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L5_HMWK.indd 7–34
11/30/07 4:39:25 AM
Name
Chapter 7 Test
Date
Chapter 7 Test
Circle the letter of the correct answer.
1
3
Use the order of operations to
solve the following expression:
Ricardo, Lee, and Jessica collect
baseball cards. Ricardo has 8 cards.
Lee and Jessica have 5 cards each.
2 × (5 + 3) - 6
2
A
1
B
4
C
7
D
10
How many cards do they have
altogether?
Which equation below is true?
A
12 - 6 ÷ 2 + 4 = 7
B
(12 - 6) ÷ 2 + 4 = 7
C
12 - 6 ÷ (2 + 4) = 7
D
(12 - 6) ÷ (2 + 4) = 7
Assessment Resources 4
4
A
8
B
13
C
18
D
23
Ricardo decides to give Lee and
Jessica some of his 8 baseball
cards. If he gives both Lee and
Jessica 2 cards each, how many
will he have left?
A
4
B
5
C
6
D
7
7–35
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C7_U3_CT.indd 7–35
11/30/07 4:40:20 AM
Name
5
Chapter 7 Test
Date
Use the order of operations to solve
the following expression:
8
Which value of
equation true?
12 + 24 ÷ (6 - 2)
6
16 ÷ (
A
4
A
=0
B
9
B
=1
C
14
C
=2
D
18
D
=3
Luz and Tyler drink milk with their
lunch. This week, Luz drank 3 more
cartons of milk than Tyler. If Tyler
number of cartons, how
drank
many did Luz drink?
A
9
3
-3
B
A
2
B
2×
C
2+
÷2
D
+3
10
7
Evaluate the expression for
(
+ 1) × 6
Evaluate the expression for
= 4:
2 × (3 +
A
36
A
5
B
30
B
6
C
24
C
11
D
10
D
16
Assessment Resources 4
- 1) = 16
Hiro has twice as many sisters
number of
as Leon. Leon has
sisters. How many sisters does
Hiro have?
C
D
makes the
= 5:
)
7–36
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73784_C7_U3_CT.indd 7–36
11/30/07 4:40:36 AM
Name
11
Solve the equation.
3×
12
A
=3
B
=6
C
= 10
D
= 27
14
= 11 - 2
Three fourth-grade classes donate
the same number of cans to a food
pantry.
Altogether, the three classes gave
the food pantry 33 cans. How many
cans did each class give?
Which symbol belongs in the oval?
24 - 6
2+9
A
11
A
=
B
22
B
<
C
33
C
>
D
99
D
≤
15
13
Chapter 7 Test
Date
Otis practiced the piano for
10 minutes. Elizabeth practiced
more than twice as many
minutes as Otis. Which equation
or inequality shows how many
minutes Elizabeth practiced?
Ayita and Manuel worked at a car
wash. Ayita washed 1 more car than
Manuel. Manuel washed 4 cars.
How many cars did Ayita wash?
A
1
B
3
A
10 × 2 <
C
4
B
10 × 2 =
D
5
C
10 ÷ 2 >
D
10 ÷ 2 =
Assessment Resources 4
7–37
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C7_U3_CT.indd 7–37
11/30/07 4:41:03 AM
Name
16
Solve the equation.
A
=1
Sarah has 2 more pets than Camilla.
Altogether, Sarah and Camilla have
6 pets. How many pets does Camilla
have?
B
=3
A
2
C
= 14
B
4
D
= 28
C
5
D
6
7×
17
19
= 3 + 18
Solve the equation.
÷4=2×4
18
Chapter 7 Test
Date
A
= 32
B
= 12
C
=4
D
=2
20
Jae Ho bought 5 tickets to
the movies.
Hector is taking 4 bags with him
to his aunt’s house. He can fit 5
shirts in each bag. How many shirts
can he take with him to his aunt’s
house?
A
9
B
16
C
20
D
25
They were 7 dollars each. Which
expression below shows how much
it cost for all 5 tickets?
A
7-5
B
7+5
C
7×5
D
7÷5
Assessment Resources 4
7–38
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C7_U3_CT.indd 7–38
11/30/07 4:41:19 AM
Name
Date
Chapter Test 7
Individual Student Record Form
Chapter Test 7
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. Record
Correct
Answer
Student
Response
the student’s response in the column to the right of the
correct answer.
California State Standards
1. D
4AF1.2
Interpret and evaluate mathematical expressions that now use parentheses.
2. B
4AF1.2
3. C
4AF1.0
4. A
4AF1.0
5. D
4AF1.2
Interpret and evaluate mathematical expressions that now use parentheses.
6. D
4AF1.0
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
7. B
4AF1.1
8. C
4AF1.1
Use letters, boxes, or other symbols to stand for any number in simple expressions
or equations.
9. B
4AF1.0
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
10. D
4AF1.1
11. A
4AF1.1
Use letters, boxes, or other symbols to stand for any number in simple expressions
or equations.
12. C
4AF1.0
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
13. A
4AF2.0
Students know how to manipulate equations.
14. A
4AF2.0
15. D
4AF2.0
16. B
4AF2.0
17. A
4AF2.0
18. C
4MR2.2
19. A
4MR2.2
20. C
4MR2.2
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
Apply strategies and results from simpler problems to more complex problems.
out of 20
7–39
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73784_IRF_C7_CT.indd 7–39
11/30/07 4:41:55 AM
Teacher Name
Date
Chapter 7 Test
Class Record Form
Chapter Test 7
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.
4AF1.2
2.
4AF1.2
3.
4AF1.0
4.
4AF1.0
5.
4AF1.2
Interpret and evaluate mathematical
expressions that now use parentheses.
6.
4AF1.0
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
7.
4AF1.1
8.
4AF1.1
Use letters, boxes, or other symbols to stand
for any number in simple expressions or
equations.
9.
4AF1.0
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
10.
4AF1.1
11.
4AF1.1
Use letters, boxes, or other symbols to stand
for any number in simple expressions or
equations.
12.
4AF1.0
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
13.
4AF2.0
Students know how to manipulate equations.
14.
4AF2.0
15.
4AF2.0
16.
4AF2.0
17.
4AF2.0
18.
19.
4MR2.2 Apply strategies and results from simpler
problems to more complex problems.
4MR2.2
20.
4MR2.2
Groups for differentiated instruction
Interpret and evaluate mathematical
expressions that now use parentheses.
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
7–40
Copyright © Houghton Mifflin Company. All rights reserved.
73784_U3_C7_CRF_CT.indd 7–40
11/30/07 4:42:21 AM
Name
Unit 3 Test
Date
Unit 3 Test
Circle the letter of the correct answer.
1
2
3
Susan invited 12 of her friends
to her birthday party. Each friend
gave her one birthday gift. If Susan
decided to share her gifts equally
among her 12 friends, how many
gifts does each friend receive?
Which of the following equations
is related to the equation below?
7 × 9 = 63
A
63 ÷ 1 = 63
B
63 ÷ 9 = 7
A
1
C
63 ÷ 9 = 9
B
3
D
63 ÷ 7 = 7
C
4
D
6
4
If 3 × 5 = 15, what is 15 ÷ 3?
A
B
C
D
3
Between Monday and Friday,
Fernando picks 3 flowers from his
garden each day. He has 3 friends
and divides his flowers equally
among them. How many flowers
does each friend receive?
A
3
B
4
C
5
D
6
5
4
15
Assessment Resources 4
7–41
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73784_UT_U3.indd 7–41
12/9/07 11:19:55 PM
Name
5
Unit 3 Test
Date
Which of the following equations is
related to
7
Using the associative property,
rewrite the following expression.
3 × (6 × 7)
4 × 6 = 24?
6
A
24 ÷ 1 = 24
A
3 × (6 × 6)
B
24 ÷ 6 = 4
B
6 × (3 + 7)
C
24 ÷ 6 = 6
C
(3 × 6) × 7
D
24 ÷ 4 = 4
D
6×7
What is any number multiplied by 0?
8
What is 6 ÷ 0?
A
0
A
0
B
1
B
1
C
10
C
9
D
The original number
D
not possible
Assessment Resources 4
7–42
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73784_UT_U3.indd 7–42
11/30/07 4:47:51 AM
Name
9
10
Unit 3 Test
Date
Aretha has 48 balls that she puts
into 8 equal rows, 6 balls in a row. If
Aretha wants to divide the 48 balls
into 6 equal rows, how many balls
would be in each row?
A
6
B
8
C
10
D
12
Chen sorted his toy cars into groups
of 5. He recorded the groups using
tally marks.
11
12
What is the total number of toy cars?
Gloria is using tally marks to help her
multiply 5 × 9. What was her answer?
A
9
B
5
C
45
D
50
Marco divides his box of 25 pears
among 4 friends. How many pears
does each friend get?
A
4
B
6
A
6
C
6
B
5
D
7
C
20
D
25
Assessment Resources 4
7–43
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73784_UT_U3.indd 7–43
11/30/07 4:48:08 AM
Name
13
What is 26 divided by 5?
A
5
B
5 remainder 1
C
D
14
16
Juan gives Anil and Percy some of
his 12 football cards. He gives 3
cards to Anil and 2 to Percy. How
many cards does Juan have left?
A
5
B
6
C
7
D
8
5 remainder 2
6
Use the order of operations to solve
the following expression.
4 × (6 + 3) - 4
A
23
B
28
C
30
D
15
Unit 3 Test
Date
17
Tara and her sister want to see how
far they can run in 20 minutes. Tara
runs 3 miles and her sister runs
less than half that distance. Which
inequality or equation below shows
this relationship?
A
×2<3
B
×2=3
C
+ 3 = 20
D
+ 3 > 20
32
(7 + 5 + 4) × (3 + 2) = ?
A
21
B
80
C
94
D
100
Assessment Resources 4
7–44
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73784_UT_U3.indd 7–44
11/30/07 4:48:22 AM
Name
18
Ling Na studies more than two hours
a day, Monday through Friday. Which
equation or inequality below shows
her total study time for the week?
20
Solve the equation.
12 ×
= 36
B
=3
C
= 48
D
=8
=2×5
B
=5+2
C
>5+2
D
= 40 − 4
A
>2×5
A
19
Unit 3 Test
Date
Solve the equation.
8×
= 32
A
=8
B
=4
C
=1
D
= 256
Assessment Resources 4
7–45
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73784_UT_U3.indd 7–45
11/30/07 4:48:37 AM
Name
Date
Unit 3 Test
Individual Student Record Form
Unit 3 Test
Use the unit test to identify your students’ mastery of the
skills in the unit. The item analysis below will help you
recognize strengths and weaknesses.
Correct
Answer
Student
Response
1. A
Record the student’s response in the column to the right
of the correct answer.
California State Standards
2. B
4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of
whole numbers and understand the relationships among the operations.
4NS3.0
3. B
4NS3.0
4. C
4NS3.0
5. B
4NS3.0
6. A
4NS3.0
7. C
4NS3.0
8. D
4NS3.0
9. B
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
4NS3.2 number by a one-digit number; use relationships between them to simplify
4NS3.2 computations and to check results.
10. D
11. C
12. C
13. B
4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of
whole numbers and understand the relationships among the operations.
4NS3.0
14. D
4AF1.2
15. B
4AF1.2
16. C
4AF1.0
17. A
4AF1.0
18. A
4AF1.0
19. B
4AF2.0
20. B
4AF2.0
Interpret and evaluate mathematical expressions that now use parentheses.
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
Students know how to manipulate equations.
out of 20
Assessment Resources 4
7–47
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73784_IRF_UT_U3.indd 7–47
11/30/07 4:56:15 AM
Teacher Name
Date
Unit 3 Test
Class Record Form
Unit 3 Test
Use the unit test to identify your students’ mastery of the
California Mathematics Contents Standards in the unit.
Item
1.
The record below will allow you to group students for
differentiated instruction.
California Mathematics Contents Standards
3.
4NS3.0 Students solve problems involving addition,
subtraction, multiplication, and division of whole
4NS3.0 numbers and understand the relationships
4NS3.0 among the operations.
4.
4NS3.0
5.
4NS3.0
6.
4NS3.0
7.
4NS3.0
8.
4NS3.0
9.
4NS3.2 Demonstrate an understanding of, and the ability
to use, standard algorithms for multiplying a
4NS3.2 multidigit number by a two-digit number and
4NS3.2 for dividing a multidigit number by a one-digit
number; use relationships between them to
simplify computations and to check results.
2.
10.
11.
12.
13.
4NS3.0 Students solve problems involving addition,
subtraction, multiplication, and division of whole
4NS3.0 numbers and understand the relationships
among the operations.
14.
4AF1.2
15.
4AF1.2
16.
4AF1.0
17.
4AF1.0
18.
4AF1.0
19.
4AF2.0
20.
4AF2.0
Groups for differentiated instruction
Interpret and evaluate mathematical expressions
that now use parentheses.
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
Students know how to manipulate equations.
Assessment Resources 4
7–48
Copyright © Houghton Mifflin Company. All rights reserved.
73784_U3_CRF_UT.indd 7–48
11/30/07 4:56:51 AM
Chapter Resources
Grade 4, Chapter 7
Contents
Resources for Chapter 7: More Expressions and
Equations
• Lesson Quizzes Lessons 7.1–7.5
Daily Routines
Reteach
Practice
Enrichment
Leveled Problem Solving
Homework
• Chapter 7 Test
Individual and Class Record Sheets
• Unit 3 Test
Individual and Class Record Sheets
B
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Booklet 7 of 29
TTL_73744_U3_C07.indd 7–1
7–1
2/1/08 3:05:54 PM
Name
Date
Chapter 7, Lesson 1
Lesson Quiz
Lesson 1 Quiz
What do you do first when evaluating each expression?
1.
5-8÷2
2.
6×3+4
3.
7 × (5 + 3) ÷ 2
4.
4 + 8 × 3 - 10
Lesson Quiz
Use with Chapter 7, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 7, Lesson 2
Lesson Quiz
Lesson 2 Quiz
Simplify.
1.
12 ÷ 6 + 3 × 7
2.
5 × (10 - 2) - 5
Solve.
3.
4.
Use parentheses to change the value of 3 × 4 + 2.
Use the numbers 1, 2, and 3 and the operations of subtraction
and division to write an expression. Find its value.
Lesson Quiz
7–2
Use with Chapter 7, Lesson 2
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CAPEG4_C07_LessonQuiz.indd 7–2
2/6/08 8:29:38 PM
Name
Date
Chapter 7, Lesson 3
Lesson Quiz
Lesson 3 Quiz
Complete. Use >, <, or =.
1.
2+6×5
2.
(4 + 7) + 5
3 × (10 - 1)
10 + 18 ÷ 3
Lesson Quiz
Use with Chapter 7, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 7, Lesson 4
Lesson Quiz
Lesson 4 Quiz
Find the missing number that makes each equation true.
1.
(4 + 6) × 7 =
2.
8×(
×7
- 2) = 5 × 8
Lesson Quiz
7–3
Use with Chapter 7, Lesson 4
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CAPEG4_C07_LessonQuiz.indd 7–3
2/6/08 8:29:53 PM
Name
Date
Chapter 7, Lesson 5
Lesson Quiz
Lesson 5 Quiz
Tickets to the play are $8 for adults and $5 for children. Write an
expression for each situation.
1.
4 adult tickets and 2 children’s tickets
2.
How much change do you get from $30 if you buy 3 adult
tickets?
3.
If you have $38 and buy 1 adult ticket, how many children’s
tickets can you get?
4.
Evaluate the expressions you wrote for Exercises 1–3.
Lesson Quiz
Use with Chapter 7, Lesson 5
Copyright © Houghton Mifflin Company. All rights reserved.
Lesson Quiz
7–4
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CAPEG4_C07_LessonQuiz.indd 7–4
2/6/08 8:30:09 PM
Name
Chapter 7, Lesson 1
Daily Routines
Date
Hands On: Expressions with All
Four Operations
Problem of the Day
KEY NS 3.0
Tran earns $7 an hour working at the pet store. How much money
would Tran make if he works 4 hours?
Number Sense
KEY NS 3.0
On your whiteboard, write two multiplication and division fact
families which include the number 6.
Word of the Day
AF 1.0
properties
How are the properties for addition and multiplication similar?
How are they different?
Facts Practice
KEY AF 1.3
Add parentheses to make the value of each expression equal to 8.
1.
12 - 7 + 3
2.
20 - 4 + 8
4.
18 - 13 + 3
5.
11 - 1 + 2
Daily Routines
7–5
3.
10 - 1 + 1
Use with Chapter 7, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–5
11/30/07 4:24:03 AM
Name
Chapter 7, Lesson 1
Reteach
Date
Hands On: Expressions with
All Four Operations
CA Standards
AF 1.2,
AF 1.3
What is the value of 6 + 4 ÷ (2 - 1)?
Step 1 Do the operation inside the parentheses first.
(2 - 1) = 1
Step 2 Then divide in order from left to right.
4÷1=4
Step 3 Last do the addition from left to right.
6 + 4 = 10
Solution: The value of 6 + 4 ÷ (2 - 1) is 10.
Use the numbers and operation symbols below to make an
expression with the value of 7. Remember to follow the order of
operations.
1.
3, 2, 1, +, ×
2×3+1
2.
1, 2, 16, ÷, -
16 ÷ 2 - 1
Using each set of parentheses, solve each expression to
get three different values.
3.
(4 + 8) ÷ 2 × 3 - 1 =
5.
4 + 8 ÷ 2 × (3 - 1) =
17
12
4.
4 + (8 ÷ 2) × 3 - 1 =
15
Writing Math Why do you think parentheses were not
placed around the 2 and 3 in problems 3, 4, and 5? Explain.
Possible answer: The number 6 cannot be
divided into 8 and have an answer that is a
whole number.
Reteach
7–6
Use with text pages 142–143.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L1_RET.indd 7–6
11/30/07 4:26:01 AM
Name
Date
Hands On: Expressions with All
Four Operations
Chapter 7, Lesson 1
Practice
CA Standards
AF 1.3
AF 1.2,
Use the numbers and operation symbols below to make an
expression with the value of 4. Remember to follow the order
of operations.
1.
6
2
×
1
-
6-1×2
2.
8
2
÷
0
+
8÷2+0
3.
1
2
4
2
×
-
12 - 4 × 2
Write the expression shown below three times. Add one set of
parentheses to each expression to get three different values.
6+4÷2×6-3
(6 + 4) ÷ 2 × 6 - 3 = 27
6 + (4 ÷ 2) × 6 - 3 = 15
5.
6. 6 + 4 ÷ 2 × (6 - 3) = 12
4.
Writing Math Which expression from problems 4–6 has the
same value as the expression without parentheses? Tell the order of
the operations you did to get the same answer.
Problem 5 has the same value, 15. I did the
division first, then the multiplication and then,
working from the left to right, the addition and
subtraction.
Practice
7–7
Use with text pages 142–143.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L1_PRAC.indd 7–7
11/30/07 4:26:30 AM
Name
Chapter 7, Lesson 1
Enrichment
Date
Solving Expressions
CA Standards
AF 1.2,
AF 1.3
Find the value of each equation. Then use the values you found to
answer the riddle below by filling in the blanks with the appropriate
letters.
Riddle: Why was the zero so sad?
21
2
3. 4 + 8 ÷ (2 × 4) - 3 =
15
5. (10 - 3) × 2 + 1 =
1
7. 10 - 3 × (2 + 1) =
3
9. 12 - (5 + 4) =
17
8
4. 4 + 8 ÷ 2 × (4 - 3) =
5
6. 10 - (3 × 2) + 1 =
8. (12 - 5) + 4 = 11
(4 + 8) ÷ 2 × 4 - 3 =
1.
2.
4 + (8 ÷ 2) × 4 - 3 =
5=H
15 = 0
1=V
21 = N
17 = D
2=U
8=L
11 = E
3=A
10.
HE HAD NO VALUE
ANSWER: __ ___ __ __ ___ ___ ___ __ __ __ __ ___
5 11 5 3 17 21 15 1 3 8 2 11
Writing Math Sam worked out the expression 10 - 2 × 5
and got an answer of 40. Is he correct? Explain.
Possible answer: No, he should have done the
multiplication first and then the subtraction.
Enrichment
7–8
Use with text pages 142–143.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L1_ENR.indd 7–8
11/30/07 4:27:35 AM
Chapter 7, Lesson 1
Name
Leveled Problem Solving
Date
Hands On: Expressions with All
Four Operations
CA Standard
AF 1.2,
AF 1.3
Solve each problem. Write an equation to get your answer.
Remember that information from one problem will help you
solve the next one.
1.
John’s family had an open house party
on New Year’s Day. 4 guests came at
noon. Ten minutes later, 2 more guests
arrived. At 12:30, one guest left. How
many guests remained at the party?
2.
4+2-1=5
3.
I
5+6-4=7
Over the next hour, the number of
guests at the party tripled. Then,
Mr. and Mrs. Ortiz and their three
children left to go to another party.
How many guests were left?
4.
By 2:30, half of the remaining guests
had left. Then John’s friends Gail, Bob,
and Bob’s cousin arrived and gave the
party a needed lift. What was the guest
count now?
Level II
16 ÷ 2 + 3 = 11
7 × 3 - 5 = 16
5.
At 12:40, 6 more guests arrived at
John’s house. Then 2 couples left.
How many guests are there now
at the party?
Level
Bob and his cousin left at 4:15 and five
minutes later John’s Uncle Art, Aunt
Louise, and their 4 children arrived,
apologizing for being so late. Shortly
after, 3 more couples left. How many
guests are still at the party?
11 - 2 + 6 - 6 = 9
6.
After the other guests had gone,
John’s father invited Uncle Art and
his family to stay for the night.
They gratefully accepted. If John has
two sisters besides his parents, how
many people slept that night at his
house?
Level III
6 + 5 = 11
Leveled Problem Solving
7–9
Use with text pages 142–143.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L1_PS.indd 7–9
11/30/07 4:28:10 AM
Name
Date
Hands On: Expressions with All
Four Operations
Chapter 7, Lesson 1
Homework
CA Standards
AF 1.2,
AF 1.3
What is the value of 16 - 10 ÷ 2 × 3?
Step 1 Follow the order of operations. Evaluate 10 ÷ 2 using number tiles.
1
-
6
×
5
3
Step 2 Now do the multiplication in the expression. Use the tiles to replace 5 × 3.
1
-
6
1
5
Step 3 Finish by doing the subtraction in the expression.
16 - 15 = 1
Solution: The value of 16 - 10 ÷ 2 × 3 is 1.
Use the numbers and operation symbols below to make an expression
with the value of 6. Remember to follow the order of operations.
1.
1
2
3
×
2
-
12 - 2 × 3
2.
1
4
1
6
÷
2
-
14 - 16 ÷ 2
3.
2
2
2
+
×
2+2×2
4QJSBM3FWJFX
(Chapter 5, Lesson 3) KEY AF 1.2, AF 1.0
Use the numbers and symbols below to make each equation true .
4, 3, =, >
4.
8-
5.
10 -
6.
×2
÷2
2
3
6-3×1
5-4+2
Molly has the equation 2 × 3 + 6 - 5 = 13. Where should she put
parentheses to make this equation correct?
She should put them around 3 + 6.
Homework
7–10
Use with text pages 142–143.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L1_HMWK.indd 7–10
11/30/07 4:28:44 AM
Name
Chapter 7, Lesson 2
Daily Routines
Date
Hands On: Expressions with
All Four Operations
Problem of the Day
KEY AF 1.2
Explain each step in solving the problem shown below.
(7 + 8) ÷ 3 × 4 – 2
Number Sense
KEY NS 3.1
Write and solve a subtraction problem in which the thousands
need to be regrouped as hundreds and the tens need to be
regrouped as ones.
Number of the Day
KEY NS 3.0
12
Write all the ways 12 can be the answer to a multiplication problem.
Facts Practice
KEY NS 1.1
Write each number in word form.
1.
54,291
4.
10,800,450
Daily Routines
2.
5
320,670
3.
759,781
553,781,000
7–11
Use with Chapter 7, Lesson 2
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–11
11/30/07 4:24:25 AM
Name
Chapter 7, Lesson 2
Reteach
Date
Expressions with All Four
Operations
CA Standards
AF 1.2,
AF 1.3
Find 48 ÷ (3 × 4) + 2.
Step 1 Do the
operations in parentheses
first.
48 ÷ (3 × 4) + 2
Step 2 Multiply and
divide from left to right.
Step 3 Add and subtract
from left to right.
48 ÷ 12 + 2
4+2=6
Think: (3 × 4) = 12
Think: 48 ÷ 12 = 4
48 ÷ 12 + 2
4+2
Solution: 48 ÷ (3 × 4) + 2 = 6
Simplify each expression. Follow the order of operations.
1.
(3 + 6) × 8
2.
24 ÷ (2 × 2)
3.
(4 + 8) ÷ 3
6.
6
72
4.
12 × 3 + (8 - 4)
5.
40
7.
4 × 3 + 12
(3 × 9) - 8
19
15 ÷ (5 × 3)
4
8.
24
3×9+2×6
1
9.
5 × (49 ÷ 7)
35
39
Write an expression for each situation.
10.
The sum of 8 and the
product of 5 and 3
(5 × 3) + 8
11.
8 times the difference
of 15 and 6
12.
8 × (15 - 6)
9 more than 36
divided by 6
(36 ÷ 6) + 9
Writing Math Lila and Frank evaluated the expression
7 × 4 ÷ 2 + 5. Lila got 4 and Frank got 19. Explain what they each
did to get their answer.
Lila put parentheses around the first set of
numbers and another around the second set.
Frank put parentheses around the middle
numbers.
Reteach
7–12
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_RET.indd 7–12
11/30/07 4:29:13 AM
Name
Chapter 7, Lesson 2
Practice
Date
Expressions with All Four
Operations
CA Standards
AF 1.2,
AF 1.3
Simplify each expression. Follow the order of operations.
1.
(6 + 3) × 4
2.
8 + (5 × 3)
5.
7 + (6 × 3) - 10
8.
23
7.
9 - (21 ÷ 7)
6.
30 - (3 × 3) + 4
9.
11.
18 + 9 × 7 - 13
12.
19
68
3 × (12 - 8)
12
25
6+5×4-7
(15 + 3) ÷ 6
3
6
15
10.
3.
12
36
4.
(7 - 5) × 6
(18 - 3) ÷ 5
3
5 × (6 + 3) × 2
90
Write an expression for each situation.
21 + (8 × 7)
(6 × 9) + 73
14. 73 more than 6 times 9
15. 3 fewer than 42 divided by 7 (42 ÷ 7) - 3
13.
the sum of 21 and the product of 8 and 7
Test Practice
Circle the letter of the correct answer.
16.
17.
18.
Karen owns 3 guitars that have 6 strings each and 2 mandolins that have 8 strings
each. How many strings do her instruments have in all?
A
34
C
19
B
36
D
5
There are 30 students in the classroom. If three groups of 4 students leave the room,
how many students are left?
A
26
C
12
B
18
D
20
David owns 4 guitars with 6 strings each and a guitar with 4 main strings and 22 special
resonating strings. How would you find how may strings his instruments have in all?
First, I’d multiply 4 × 6 and add it to the
addition problem 4 + 22.
Practice
7–13
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_PRAC.indd 7–13
11/30/07 4:29:36 AM
Name
Chapter 7, Lesson 2
Enrichment
Date
Finding the Lowest Point
CA Standards
AF 1.2,
AF 1.3
Below is a table showing the lowest point on six continents. Use
the information to help you solve each problem.
The World’s Lowest Points
Continent
Asia
Africa
North America
South America
Europe
Australia
Lowest Point
Location
Dead Sea
Lake Assal
Death Valley
Valdes Peninsula
Caspian Sea
Lake Eyre
Feet Below Sea Level
Israel–Jordan
Djibouti
California
Argentina
Russia–Kazakhstan
South Australia
1,348
512
282
131
92
52
Simplify each expression and write the lowest point it represents.
512; Lake Assal
131; Valdes Peninsula
2. 300 - 200 + 5 × 6 + 1
1,348; Dead Sea
3. 300 + 2 × 500 + 9 × 4 + 12
1.
2 × 200 + 5 × 20 + 24 ÷ 2
Solve each problem using a number sentence.
4.
Irina lives at half the elevation of the Caspian Sea. Her house is
20 feet high. If she stands on her roof, how far below sea level is she?
92 ÷ 2 - 20 = 26 feet
5.
Allen drove halfway out of Death Valley, then he stopped after another
50 feet to take a drink from his water bottle. How far below sea level is he?
282 ÷ 2 - 50 = 91 feet
6.
Corey visited Lake Eyre and then walked up a hill 82 feet above sea level.
How many feet in elevation has he traveled?
52 + 82 = 134 feet
Writing Math Connie did problem 4 above and got an
answer of 66 feet. What did she do wrong? Explain.
Possible answer: Connie added 20 feet instead
of subtracting it from the elevation of the house.
Enrichment
7–14
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_ENR.indd 7–14
11/30/07 4:31:06 AM
Chapter 7, Lesson 2
Name
Date
Leveled Problem Solving
Expressions with All Four
Operations
CA Standards
AF 1.2,
AF 1.3
Write and evaluate an expression to solve each problem.
1.
Hillary likes to take photographs with
her camera. She took 40 pictures one
week. She took twice as many the
following week. How many pictures
did she take in the two weeks?
2.
(25 × 4) + (20 × 3);
160 photos
40 + (2 × 40); 120
pictures
3.
José took 3 rolls of film with him on
the class field trip. Each rolls contains
36 pictures. He used up 2 rolls. There
were 10 pictures left on the third roll
when he got home. How many pictures
of the class trip did José take?
4.
Brad took the photos at his aunt’s
wedding. He took 22 pictures
before the wedding, half as many
during the wedding, and twice as
many pictures after the wedding.
How many wedding pictures did
Brad take in all?
Level
22 +
22 + __
2
(36 × 2) + (36 - 10)
or (36 × 3) - 10; 98
pictures
5.
Vic puts his photos in albums. He has
1 album of 25 pages. There are 4
photos on each page. He also has a
20-page album with 3 photos on each
page. How many photos does he have
in the two albums?
Level
I
II
(22 × 2); 77 pictures
Lien went to the store to buy a new
camera. The camera cost $86. She
also bought 2 rolls of film that cost
$5 each. She paid for her purchases
with a $100 bill. What change did she
receive back?
6.
100 - 86 - (2 × 5); $4
Maria takes pictures in both black and
white and color. She took 47 black and
white pictures one day and 6 more than
that in color. The same day, Teresa took
34 pictures in black and white and half
as many in color. How many pictures did
they both take that day?
Level III
47 + (47 + 6) + 34 +
34
__
; 151 pictures
2
Leveled Problem Solving
7–15
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_PS.indd 7–15
1/27/08 10:29:44 AM
Name
Chapter 7, Lesson 2
Homework
Date
Expressions with All Four
Operations
CA Standards
AF 1.2,
AF 1.3
Evaluate 7 + (12 ÷ 3 ) × 5
Step 1
7 + (12 ÷ 3 ) × 5 Simplify inside parentheses.
Step 2
7 + 4 × 5 Multiply and divide from left to right.
Step 3
7 + 20 Add and subtract from left to right.
Solution: The value of 7 + (12 ÷ 3 ) × 5 is 27.
Simplify each expression. Follow the order of operations.
1.
(7 + 8) × 2
2.
25 + (4 × 5) - 15
5.
30
4.
(12 - 7) × 8
3.
70 - (8 × 5) ÷ 10
6.
40
30
66
(9 + 7) ÷ 8
2
(28 - 4) ÷ 3
8
Write an expression for each situation.
8 × 6 - 38
25 ÷ 5 + 22
8. 22 more than 25 divided by 5
4 × (20 + 46) - 159
9. 159 fewer than 4 times the sum of 20 and 46
7.
38 fewer than 8 times 6
4QJSBM3FWJFX
10.
(Chapter 4, Lesson 3) KEY NS 3.1, KEY NS 3.0
Subtract. Use addition to check your answer.
1,609
5,291 - 3,682 =
11.
Use inverse operations to find the missing number.
206 +
12.
183 = 389
Ted had 500 bottle caps in his collection. Jan had 174 bottle caps in her
collection. How many more bottle caps does Ted have than Jan?
326 more bottle caps
Homework
7–16
Use with text pages 144–146.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L2_HMWK.indd 7–16
11/30/07 4:32:05 AM
Name
Chapter 7, Lesson 3
Daily Routines
Date
Equations and Inequalities with All
Four Operations
Problem of the Day
KEY AF 1.3
Write an expression to represent the phrase given below.
Then solve the expression.
Seven less than three times the sum of 5 and 4.
Number Sense
KEY NS 1.31
On your whiteboard write 3 different numbers which round
to 91,000.
Number of the Day
KEY NS 1.11
45
What are some ways to show 45?
Facts Practice
KEY NS 3.11
Find each sum.
1.
648 + 827
2.
859 + 61 + 571
3.
1,958 + 487
4.
4,782 + 8,391
5.
40,549 + 281,391
6.
200,391 + 589,891
Daily Routines
7–17
Use with Chapter 7, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–17
11/30/07 4:24:46 AM
Name
Chapter 7, Lesson 3
Reteach
Date
Equations and Inequalities
with All Four Operations
CA Standard
AF 1.0
Phil bought 6 used books at the library sale. Willa bought twice as many books as
Phil. Write a number sentence that compares the number of books each bought.
Step 1 Write an expression for the books bought by each person.
Phil’s books
Willa’s books
6
6×2
Step 2 Compare the two expressions, using =, <, or >.
6<6×2
Solution: 6 < 12
Copy and complete. Use >, <, or =.
1.
2 × 11 + 6 × 1
3.
50 ÷ 5 - 2
5.
92 + (16 ÷ 4)
=
<
46 + 37
80 ÷ 10
>
99 - (2 × 4)
Write +, -, ×, or ÷ in each
×
6
9.
8 ÷ 2 + 12 = 4 × 3
11.
90
÷
+
42 - 8 + 16
=
(2 × 5) × 5
4.
31 + (2 × 7)
<
74 - 22
>
20 ÷ 5
16
6. ___
2
- (2 + 1)
to make each number sentence true.
2+8=2×8+4
7.
2.
4
2 + 10 = 15 + 8 × 5
14
8. ___
2
10.
12.
× 3 = 23
56 ÷ 8
+
8
36 - __
=8
2
-
2
30 = 6 × 6 + 1
×
(2 + 2)
Writing Math Hank looked at problem 12 and knew before
he added each side of the equation that the missing operation had to
be a × or ÷. How did he know? Explain.
Possible answer: The parentheses around 2 + 2 means
that they have to performed before any other operation.
If the earlier operation was addition or subtraction there
would be no need for the parentheses.
Reteach
7–18
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_RET.indd 7–18
11/30/07 4:32:29 AM
Name
Date
Equations and Inequalities with
All Four Operations
Chapter 7, Lesson 3
Practice
CA Standard
AF 1.0
Copy and complete. Use >, <, or =.
= 90 ÷ 3
2. 10 + 6 × 8 = 63 - 5
3. 81 ÷ 9 + 4 < 6 × 2 + 5
60
_
4.
-1 < 3+2×1
12
5. 86 > 13 × 4 + 28
6. 40 ÷ 5 × 2 > 30 - 18
7. 7 × 8 ÷ 2 < 4 × 8 + 6
8. 4 × 6 + 7 = 62 ÷ 2
1.
2×3×5
Write +, -, ×, or ÷ in each
sentence true.
9.
3 × 4 = 20
to make each number
-8
18
+ 5=_
+4
3
11. 6 + 1 - 2 = 30 ÷ 5 - 1
12. 7 × 3 = 30 - 9
10.
5
Writing Math Roger changed one operation sign on each
side of the equation in problem 1, in order to go from = to <. Was his
math correct? What did he change the sign to?
Accept all answers student can justify.
Practice
7–19
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_PRAC.indd 7–19
11/30/07 4:32:56 AM
Name
Chapter 7, Lesson 3
Enrichment
Date
Comparing Populations
CA Standard
AF 1.0
Many Native Americans live in Western states. The table below
shows the five states with the largest populations of Native
Americans. Use the information to solve the problems.
Native American Population
1.
State
Population
California
410,510
Arizona
286,680
Oklahoma
278,124
New Mexico
183,972
Texas
145,954
Write an inequality that compares the number of Native Americans in California to
those in Texas and Oklahoma combined.
410,510 < 145,954 + 278,124
2.
How many more Native Americans would Oklahoma need to equal the number of
Native Americans in Arizona? Write an equation for this comparison.
8,556; 286,680 = 278,124 + 8,556
3.
Texas has 45,460 more Native Americans than the state of Alaska. How many Native
Americans live in Alaska? Show your answer in an inequality.
100,494; 145,954 > 100,494
4.
Arizona and New Mexico are neighboring states. Arizona has more Native Americans
than New Mexico. How many more Native Americans live in Arizona than live in
New Mexico? Write an inequality to show your answer.
102,708; 183,972 < 183,972 + 102,708
Writing Math Lynn wanted to find out which state’s Native
American population was closest to half of the Native American
population of California. How would she go about finding the answer?
Explain.
Possible answer: She would divide the California
population in half and then find the state whose
number of Native Americans is closest to that number.
Enrichment
7–20
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_ENR.indd 7–20
11/30/07 4:33:43 AM
Chapter 7, Lesson 3
Name
Date
Leveled Problem Solving
Equations and Inequalities with
All Four Operations
CA Standard
AF 1.0
Write equations or inequalities to solve the problems.
1.
Bill went on 4 rides at the amusement
park. Juanita went on twice as many
rides as Bill did. Henry went on 4 more
rides than Bill did. Compare how many
rides Juanita went on to how many
rides Henry went on.
2.
4×2=4+4
3.
2×2<2+4
The shooting gallery on the midway
awarded 40 stuffed animals as prizes
one week. The ring toss awarded
30 more stuffed animals than the
shooting gallery. The softball throw
presented patrons with twice as many
stuffed animals than the shooting
gallery. Compare the number of stuffed
animals given by the ring toss to the
number given by the softball throw.
4.
40 + 30 < 40 × 2
5.
The concession booth sold 75 cotton
candies one night at the amusement
park. It also sold 3 times as many
cups of lemonade. People bought
70 more bags of popcorn as they did
cotton candies. Compare the number
of cups of lemonade sold that
evening to the number of bags of
popcorn sold.
Level
II
75 × 3 > 75 + 70
One night 350 people visited the
park’s haunted house. Half as many
attended the magic show. 100 fewer
people attended the fun house as the
haunted house. Compare the number
who attended the magic show to the
number who went into the fun house.
6.
350 ÷ 2 < 350 - 100
Leveled Problem Solving
Each ride at the amusement park
requires tickets. The merrygo-round costs 2 tickets. The Ferris
wheel costs 2 times as many tickets.
The roller coaster costs 4 more tickets
than the merry-go-round. Compare
how many tickets needed to ride the
Ferris wheel to the number needed to
ride the roller coaster.
Level I
7–21
A total of 650 people came to the
amusement park on Thursday night.
456 more admissions were recorded
on Friday night. Three times as
many patrons went to the park
on Saturday night as on Thursday
night. Compare the number of paid
admissions on Friday night to those on
Saturday night.
Level III
650 + 456 < 650 × 3
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_PS.indd 7–21
11/30/07 4:34:19 AM
Name
Chapter 7, Lesson 3
Homework
Date
Equations and Inequalities
with All Four Operations
CA Standard
AF 1.0
Ed read 9 books last summer. Angie read twice as many books as Ed. Hernando
read 9 more books than Ed. In a number sentence, compare how many books
Angie and Hernando read.
Step 1
Write an expression for the number of books each person read.
Books read by Angie
Books read by Hernando
9×2
9+9
Step 2
Evaluate each.
9×2
9+9
18
18
Step 3 Compare the 2 evaluations.
9×2
=
9+9
18
=
18
Solution: 9 × 2 = 9 + 9
Copy and complete. Use >, <, or =.
1.
(100 - 40) × 2
3.
8+7
5.
15 - (6 × 2)
=
=
100 + 20
1 × 15
<
4QJSBM3FWJFX
(16 ÷ 4) + 1
2.
20 + (2 × 3)
4.
(6 × 8) + 10
6.
(70 ÷ 2) + 5
>
<
=
30 ÷ 2
40
___
× (5 × 10)
10
(2 × 15) + 10
(Chapter 5, Lesson 4) KEY AF 1.2, KEY AF 2.0
Copy and complete.
7.
34 - 16 = 18
18
9.
8.
= 18
What do you know about the value of the
× 6 = × 6
(86 + 12) - 31= 34 + 33
98
- 31 =
67
=
67
67
and in this equation?
They are equal.
Homework
7–22
Use with text pages 148–150.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L3_HMWK.indd 7–22
11/30/07 4:34:50 AM
Name
Chapter 7, Lesson 4
Daily Routines
Date
Multiply Equals by Equals
Problem of the Day
KEY AF 1.3
James wrote a 4 page story. Latisha wrote 1 more than 3 times as
many pages as James. Jorge wrote 7 more pages than James. Write
a number sentence to compare the number of pages Latisha wrote to
the number Jorge wrote.
Number Sense
KEY NS 3.0
Write 5 basic multiplication facts which involve the number 8.
Word of the Day
MR 3.3
remainder
Give some examples of when you might have a remainder in real life.
Facts Practice
AF 1.0
Use multiplication properties and division rules to find each
missing number.
1.
45 × 3 = 3 × ____
2.
(8 × 5) × 9 = 8 × (___ × 9)
3.
____ × 99 = 0
4.
113 × ____ = 113
5.
49 ÷ 49 = ____
6.
0 ÷ 5 = ____
Daily Routines
7–23
Use with Chapter 7, Lesson 4
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–23
11/30/07 4:25:06 AM
Name
Chapter 7, Lesson 4
Reteach
Date
Multiply Equals by Equals
CA Standards
AF 2.0
AF 2.2,
To keep equations true, you must do the same thing on both sides of the equation.
Is 2 + (3 × 6) = 2 + 18 still equal if each side is multiplied by 4?
Step 1 Simplify the original equation.
Step 2 Multiply each side by 4.
2 + (3 × 6) = 2 + 18
20 × 4 = 20 × 4
2 + 18 = 20
80 = 80
20 = 20
Solution: Both sides of the equation are still equal.
Copy and complete.
1.
2 × (9 + 2) = 2 ×
12
3
3.
5.
7.
11
8
2.
(6 - 4) ×
+ (4 × 7) = 12 + 28
4.
3 × (50 ÷ 5) = 3 ×
× (6 × 8) = 3 × 48
6.
9×(
8.
2×9=2×(
6 × 36 = 6 × (6 ×
6
)
15
=2×8
10
÷ 3) = 9 × 5
14
- 5)
Writing Math Nick said the equation 10 × 2 = (5 × 2) + (1 + 1)
is correct. Is he correct? Explain.
Possible answer: He is incorrect, because
while the numbers have the same value, on
the left they are multiplied together and on the
right they are added.
Reteach
7–24
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_RET.indd 7–24
11/30/07 4:35:16 AM
Name
Date
Multiply Equals by Equals
Chapter 7, Lesson 4
Practice
CA Standards
AF 2.0
AF 2.2,
Copy and complete.
5
1.
(4 + 6) ×
= 10 × 5
2.
30 - (3 × 9) = 30 -
3.
32
4.
12 × (
5.
7 × (24 ÷ 3) = 7 ×
4
6.
27
÷ 8 + 11 = 4 + 11
6
- 3) = 12 × 3
8
× (6 × 7) = 4 × 42
7.
3 + 63 ÷ 9 = 3 +
8.
5 × (8 - 3) = 5 ×
7
5
Test Practice
Circle the letter of the correct answer.
9.
10.
Fran multiplied one side of an equation by 12. How much must she
multiply the other side by to keep the equation true?
A
6
C
10
B
12
D
24
Carl multiplied one side of an equation by 5. To make it an inequality,
what must he multiply the other side by?
A
5
C
a number
B
(2 + 3)
D
any number but 5
Writing Math Kelly multiplied one side of an equation
by 6 and the other side by (36 ÷ 6). Does she still have an equation?
Explain.
Yes, because 6 and (36 ÷ 6) are equal.
Practice
7–25
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_PRAC.indd 7–25
11/30/07 4:35:51 AM
Name
Date
Solving Equations
Chapter 7, Lesson 4
Enrichment
CA Standards
AF 2.0
AF 2.2,
Complete each equation. Then use the values you found to find
the answer to the riddle below by filling in the blanks with the
appropriate letters.
Riddle: Why were the two sides of the inequality fighting?
8
1.
3 × (2 × 4) = 3 ×
2.
(6 - 2) ×
3.
7×3-4=
4.
3 + (8 × 4) = 5 × 6 +
4
5.
3
=6+6
6
×3-1
5
× (2 + 1) = 15 - 3
3=E
6=V
5=N
4=T
8=G
6.
GET __EVEN
__ __ __
ANSWER: They wanted to __ __ __
8 3 4
3 6 3 5
Writing Math If the parentheses were removed from
problem 4 above would the answer remain the same? Explain.
Yes, it would remain the same because you
would multiply 8 × 4 first and then go back to
the left and add 3.
Enrichment
7–26
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_ENR.indd 7–26
11/30/07 4:36:18 AM
Chapter 7, Lesson 4
Name
Date
Leveled Problem Solving
Multiply Equals by Equals
CA Standards
AF 2.0
AF 2.2,
Solve each problem. After the answer write an equation that
helped you to get the answer.
1.
Alex picked 8 apples and 2 pears from
the orchard. Janet picked 4 apples. How
many pears does she have to pick to
have the same amount of fruit as Alex?
2.
Level I
6; 8 + 2 = 4 + 6
3.
8; 2 × 4 = 8 × 1
A farmer had six baskets of pears. Each
basket held 15 pears. He lost one of
the baskets when it fell off his tractor.
How many pears does he now have?
4.
Ling bought 8 oranges and ate 2 of
them. Carl bought twice as many
oranges as Ling. How many oranges
must he eat to have the same number
of oranges as Ling?
6.
10; 8 - 2 = (8 × 2) - 10
Leveled Problem Solving
Hector has 3 apple trees in his yard.
Each tree has 50 apples. Jill has
5 apple trees in her yard. How many
apples must each tree in Jill’s yard
have to match the number of apples
Hector has?
Level
30; 50 × 3 = 30 × 5
75; Possible answer:
(6 × 15) - 15 = 5 × 15
5.
Jorge filled 2 bags with 4 peaches in
each bag. Rod has only one bag. How
many peaches must he put in his bag
to equal Jorge’s number of peaches?
7–27
II
Ben picked 6 baskets of avocados. Each
basket held 30 avocados. 40 avocados
were bad and had to be thrown away.
Thad picked 5 baskets and 10 were bad.
He had the same number of avocados as
Ben. How many avocados did he have in
each basket?
Level III
30; 6 × 30 - 40 = 5
× 30 - 10
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_PS.indd 7–27
11/30/07 4:36:47 AM
Name
Chapter 7, Lesson 4
Homework
Date
Multipy Equals by Equals
CA Standards
AF 2.0
AF 2.2,
Will the equation 3 × 6 = 2 × 9 still be true if both sides are multiplied by 5?
Step 1
Simplify both sides of the equation.
3×6 = 2×9
18
= 18
Step 2
Rewrite the equation multiplying each side by 5.
18 × 5 = 18 × 5
90
=
Step 3
90
Note that both sides are equal as they were before.
Solution: The equation 3 × 6 = 2 × 9 remains true if both sides are multiplied by 5.
Copy and complete.
1.
5 × (2 + 1) = 5 ×
3
2.
(6 - 2) ×
3.
4 + (9 - 2) = 4 +
7
4.
12 × 2 + 5 = 12 + 12 +
5.
(8 ÷
2
)×3=4×3
6.
7.
4×(
6
+ 2) = 4 × 8
8.
4QJSBM3FWJFX
9.
5
+ (6 × 7) = 8 + 42
7 × (20 ÷ 5) = 7 ×
4
(Chapter 6, Lesson 4) KEY NS 3.0, MR 2.3
3
Find the missing number.
21 ÷
11.
=4×9
Divide. Then check your answer.
18 ÷ 6 =
10.
8
9
7
=3
Jake has 15 apples. He gave one third of the apples to Judy.
How many apples did he give her?
5 apples
Homework
7–28
Use with text pages 152–153.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C07L4_HMWK.indd 7–28
11/30/07 4:37:11 AM
Name
Date
Chapter 7, Lesson 5
Daily Routines
Problem Solving: Write an Expression
Problem of the Day
AF 2.0
Write all the pairs of numbers that can be written in the blanks
below to make the equation true.
6 × (14 + 7) = 21 × (___ + ___)
Number Sense
KEY NS 1.2
What place value would you need to change to make 539,138 greater
than 540,502?
Word of the Day
MR 2.3
operation
Which numerical operation do you use most often during a day? Give
some examples of how you use it.
Facts Practice
KEY NS 1.1
Write each number in standard form.
1.
40,000 + 5,000 + 90 + 8
2.
100,000 + 7,000 + 500 + 80 + 2
3.
10,000 + 6,000 + 20
4.
2,000,000 + 300,000 + 8,000 + 800 + 30 + 1
5.
5,000,000 + 300,000 + 90,000 + 4
6.
3,000,000 + 7,000 + 600 + 40 + 3
Daily Routines
7–29
Use with Chapter 7, Lesson 5
Copyright © Houghton Mifflin Company. All rights reserved.
C07_G4_CAMath_Daily Rout_T.indd 7–29
11/30/07 4:25:29 AM
Name
Chapter 7, Lesson 5
Reteach
Date
Problem Solving:
Write an Expression
CA Standard
AF 1.3
MR 2.4,
Rusty has 6 pottery students. She gets paid $60 by the school to teach the class .
The amount includes the student fees plus the cost to buy two packages of clay.
If each student pays $8 to take the class, how much did the clay cost?
Read It Look for the information you need to solve the problem.
Organize It Write an expression.
$60
amount
Rusty
received
-
(6 × $8)
=
fees paid
by students
$12
amount
spent for
clay
Solve It First, do the operations inside the parentheses. Then, do the addition and
subtraction in order from left to right.
The clay cost
$12
.
Write an expression and solve each problem.
1.
Gorge uses 2 pounds of clay to make a
platter. He can make 8 platters a day.
How much clay will he use if he makes
platters for 7 days?
2.
(2 × 8) × 7 = 112
pounds
Samantha wants to buy a clay vase.
She earns $3 an hour baby-sitting.
She baby-sits 2 hours a week. A vase
costs $18. How many weeks will
Samantha have to save her earnings to
have enough money to buy the vase?
$18 ÷ (3 × 2) =
3 weeks
Writing Math What is the first operation you should do in
this expression: $12 - (3 × $2)?
3 × $2; You always do the operation in
parentheses first.
Reteach
7–30
Use with text pages 154–155.
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73744_C07L5_RET.indd 7–30
11/30/07 4:37:39 AM
Name
Chapter 7, Lesson 5
Practice
Date
Problem Solving:
Write an Expression
CA Standards
AF 1.3
MR 2.4,
Use the table for Problems 1–4. Write an equation to solve
each problem.
Ben’s Points
1.
Game
Points
1
2
3
4
Total
8
12
6
18
44
In Game 4, Ben scored half of his team’s total points. How many points did his team
score in Game 4?
18 × 2 = 36 points
2.
Ben’s friend Jason scored 3 fewer points than Ben did in Game 1, and 2 fewer points
than Ben in Game 2. How many total points did Jason score in Games 1 and 2?
(8 - 3) + (12 - 2) = 15 points
3.
Ben scored an equal amount of points in Games 5 and 6. Ben’s points in Game 5
equaled the total amount of points he scored in Games 3 and 4. How many total
points did Ben score in Games 5 and 6?
(6 + 18) × 2 = 48 points
4.
Ben’s team, including Ben, scored a total of 141 points in the first four games. How
many points did Ben’s teammates score in the first 4 games?
141 - (8 + 12 + 6 + 18) = 97 points
Test Practice
Circle the letter of the correct answer.
5.
Martin is on Ben’s team. In Games 1 and 2 he scored half the points Ben did. In
Game 3 he scored one more point than Ben, and in Game 4 he scored 0 points. Which
expression will Martin use to find out how many points he scored in all four games?
A
(8 + 12) ÷ 2 + (6 + 1)
B
12 + 8 ÷ 2 - 6
C
(18 - 12) × 2 + (6 + 1)
D
12 - 8 ÷ 2 + (6 + 1)
Practice
7–31
Use with text pages 154–155.
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73744_C07L5_PRAC.indd 7–31
11/30/07 4:38:09 AM
Name
Chapter 7, Lesson 5
Enrichment
Date
Problem Solving:
Write an Expression
CA Standards
MR 2.4,
AF 1.3
Work with a partner. Cut out the cards below. Arrange the cards to
write expressions. Arrange every card to the left of the equal sign.
Fill in the answer to the expression to the right of the equal sign.
How many expressions can you write that have different answers?
Make a list of the completed expressions.
(
(
16
)
2
4
8
16 +
÷
×
=
)
+
2
÷
4
×
8
=
Example: (16 ÷ 4) + 8 × 2 = 20
Some possible combinations: (16 ÷ 8) + 4 ×
2 = 10; (16 ÷ 2) + 4 × 8 = 40; (8 ÷ 2) + 16 × 4 =
68; (8 ÷ 4) + 16 × 2 = 34; (4 ÷ 2) + 16 × 8 = 130;
16 ÷ (4 × 2) + 8 = 10; 16 ÷ (8 × 2) + 4 = 5;
8 ÷ (4 × 2) + 16 = 17
Writing Math Akira wrote this expression: (2 × 16 + 4) ÷ 8 =. He says the
answer is 2 R6. What did he do wrong? What is the correct answer?
He added 2 and 16 instead of multiplying 2 by
16; 4 R4
Enrichment
7–32
Use with text pages 154–155.
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73744_C07L5_ENR.indd 7–32
11/30/07 4:38:34 AM
Chapter 7, Lesson 5
Name
Date
Leveled Problem Solving
Problem Solving:
Write an Expression
CA Standards
AF 1.3
MR 2.4,
Write an equation to solve each problem.
1.
Mandy has 9 coins. The coins are
quarters, dimes, and nickels. She has
2 quarters and 5 nickels. How many
dimes does Mandy have?
2.
(50¢ - 10 × 1¢ - 2 ×
10¢) ÷ 5 = 4 nickels
9 - (2 + 5) = 2 dimes
3.
Mandy has $37. She has 2 one-dollar
bills and 1 ten-dollar bill. The rest are
five-dollar bills. How many five-dollar
bills does she have?
4.
Teri bought 3 T-shirts and 2 pairs of
socks. She paid a total of $30. If the
socks were $3 a pair, how much was
each T-shirt?
$38 - ($9 × 3) - $4 = $7
6.
Meredith bought 4 notebooks that cost
$2 a piece. She also bought 3 packs of
pencils for $6 total. She had a $3 off
coupon for purchases of $10 or more.
How much did she spend on school
supplies?
Level III
(4 × $2) + $6 -
($30 - 2 × $3) ÷
3 = $8
Leveled Problem Solving
Annie had $38. She bought 3 CDs and
a book. She had $4 left over. If the CDs
cost $9 each, what did the book cost?
Level II
($37 - 2 × $1 - 1 ×
$10) ÷ $5 =
5 five-dollar bills
5.
Annie has 16 coins. The value of the
coins totals 50 cents. She has 10 pennies
and 2 dimes. The rest of the coins are
nickels. How many nickels does she
have?
Level I
$3 = $11
7–33
Use with text pages 154–155.
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73744_C07L5_PS.indd 7–33
11/30/07 4:39:01 AM
Name
Chapter 7, Lesson 5
Homework
Date
Problem Solving:
Write an Expression
CA Standards
AF 1.3
MR 2.4,
Write an expression to solve each problem.
Read It Look for information.
Mr. Henderson bought 5 cups and 5 saucers. His total purchase cost $50.
If each saucer cost $2, how much did he pay for each cup?
Organize It Write an expression to solve the problem.
($50 total
purchase
5 × $2)
cost of
saucers
÷
5
=
number
of cups
cost of each cup
Solve It First, do the operations inside the parentheses. Do the multiplication and
division in order from left to right. Then, do the addition and subtraction in order from left
to right. Finally, do the operations outside the parentheses in the same order.
Each cup cost
1.
$8.00
Mrs. Henderson bought 18 pieces of pottery. She bought 11 mugs, 4 bowls, and
some plates. How many plates did she buy?
18 - (11 + 4) = 3 plates
2.
She also bought 3 hand mirrors, 2 spoon rests, and 5 toothbrush holders to give as
gifts to her friends. The hand mirrors cost $5 each. The spoon rests cost $2 each.
Altogether, she spent $34 on the gifts. How much did the 5 toothbrush holders cost?
$34 - (3 × $5) - (2 × $2) = $15
4QJSBM3FWJFX
(Chapter 6, Lesson 5) KEY NS 3.2
Divide. Then check your answer.
3.
5.
17 ÷ 3 =
5 R2
4.
126 ÷ 10 =
12 R6
Margie wants to ship 40 mugs. Each shipping carton holds 12 mugs. How many full
cartons will she have? How many mugs will be left over?
3 R4
Homework
7–34
Use with text pages 154–155.
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73744_C07L5_HMWK.indd 7–34
11/30/07 4:39:25 AM
Name
Chapter 7 Test
Date
Chapter 7 Test
4AF1.0
Circle the letter of the correct answer.
3
4AF1.2
1
Use the order of operations to
solve the following expression:
Ricardo, Lee, and Jessica collect
baseball cards. Ricardo has 8 cards.
Lee and Jessica have 5 cards each.
2 × (5 + 3) - 6
A
1
B
4
C
7
D
10
How many cards do they have
altogether?
4AF1.2
2
Which equation below is true?
A
12 - 6 ÷ 2 + 4 = 7
B
(12 - 6) ÷ 2 + 4 = 7
C
12 - 6 ÷ (2 + 4) = 7
D
(12 - 6) ÷ (2 + 4) = 7
Assessment Resources 4
A
8
B
13
C
18
D
23
4AF1.0
4
Ricardo decides to give Lee and
Jessica some of his 8 baseball
cards. If he gives both Lee and
Jessica 2 cards each, how many
will he have left?
A
4
B
5
C
6
D
7
7–35
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73784_C7_U3_CT.indd 7–35
11/30/07 4:40:20 AM
Name
5
Chapter 7 Test
Date
Use the order of operations to solve
the following expression:
8
Which value of
equation true?
12 + 24 ÷ (6 - 2)
16 ÷ (
A
=0
9
B
=1
C
14
C
=2
D
18
D
=3
A
4
B
4AF1.2
makes the
- 1) = 16
4AF1.0
4AF1.0
6
Luz and Tyler drink milk with their
lunch. This week, Luz drank 3 more
cartons of milk than Tyler. If Tyler
number of cartons, how
drank
many did Luz drink?
A
4AF1.0
9
3
-3
B
Hiro has twice as many sisters
number of
as Leon. Leon has
sisters. How many sisters does
Hiro have?
A
2
B
2×
C
2+
C
÷2
D
+3
D
4AF1.1
4AF1.1
7
Evaluate the expression for
(
+ 1) × 6
10
Evaluate the expression for
= 4:
2 × (3 +
A
36
A
5
B
30
B
6
C
24
C
11
D
10
D
16
Assessment Resources 4
= 5:
)
7–36
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11/30/07 4:40:36 AM
Name
11
4AF1.1
Solve the equation.
3×
A
=3
B
=6
C
= 10
D
= 27
14
= 11 - 2
Which symbol belongs in the oval?
24 - 6
Three fourth-grade classes donate
the same number of cans to a food
pantry.
4AF2.0
Altogether, the three classes gave
the food pantry 33 cans. How many
cans did each class give?
4AF1.0
12
Chapter 7 Test
Date
2+9
A
11
A
=
B
22
B
<
C
33
C
>
D
99
D
≤
4AF2.0
4AF2.0
13
15
Otis practiced the piano for
10 minutes. Elizabeth practiced
more than twice as many
minutes as Otis. Which equation
or inequality shows how many
minutes Elizabeth practiced?
Ayita and Manuel worked at a car
wash. Ayita washed 1 more car than
Manuel. Manuel washed 4 cars.
How many cars did Ayita wash?
A
1
B
3
A
10 × 2 <
C
4
B
10 × 2 =
D
5
C
10 ÷ 2 >
D
10 ÷ 2 =
Assessment Resources 4
7–37
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11/30/07 4:41:03 AM
Name
16
4AF2.0
Solve the equation.
A
=1
Sarah has 2 more pets than Camilla.
Altogether, Sarah and Camilla have
6 pets. How many pets does Camilla
have?
B
=3
A
2
C
= 14
B
4
D
= 28
C
5
D
6
7×
17
4MR2.2
4AF2.0
Solve the equation.
A
= 32
B
= 12
C
=4
D
=2
19
= 3 + 18
÷4=2×4
4MR2.2
20
4MR2.2
18
Chapter 7 Test
Date
Jae Ho bought 5 tickets to
the movies.
Hector is taking 4 bags with him
to his aunt’s house. He can fit 5
shirts in each bag. How many shirts
can he take with him to his aunt’s
house?
A
9
B
16
C
20
D
25
They were 7 dollars each. Which
expression below shows how much
it cost for all 5 tickets?
A
7-5
B
7+5
C
7×5
D
7÷5
Assessment Resources 4
7–38
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11/30/07 4:41:19 AM
Name
Date
Chapter Test 7
Individual Student Record Form
Chapter Test 7
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. Record
Correct
Answer
Student
Response
the student’s response in the column to the right of the
correct answer.
California State Standards
1. D
4AF1.2
Interpret and evaluate mathematical expressions that now use parentheses.
2. B
4AF1.2
3. C
4AF1.0
4. A
4AF1.0
5. D
4AF1.2
Interpret and evaluate mathematical expressions that now use parentheses.
6. D
4AF1.0
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
7. B
4AF1.1
8. C
4AF1.1
Use letters, boxes, or other symbols to stand for any number in simple expressions
or equations.
9. B
4AF1.0
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
10. D
4AF1.1
11. A
4AF1.1
Use letters, boxes, or other symbols to stand for any number in simple expressions
or equations.
12. C
4AF1.0
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
13. A
4AF2.0
Students know how to manipulate equations.
14. A
4AF2.0
15. D
4AF2.0
16. B
4AF2.0
17. A
4AF2.0
18. C
4MR2.2
19. A
4MR2.2
20. C
4MR2.2
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
Apply strategies and results from simpler problems to more complex problems.
out of 20
7–39
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Teacher Name
Date
Chapter 7 Test
Class Record Form
Chapter Test 7
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.
4AF1.2
2.
4AF1.2
3.
4AF1.0
4.
4AF1.0
5.
4AF1.2
Interpret and evaluate mathematical
expressions that now use parentheses.
6.
4AF1.0
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
7.
4AF1.1
8.
4AF1.1
Use letters, boxes, or other symbols to stand
for any number in simple expressions or
equations.
9.
4AF1.0
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
10.
4AF1.1
11.
4AF1.1
Use letters, boxes, or other symbols to stand
for any number in simple expressions or
equations.
12.
4AF1.0
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
13.
4AF2.0
Students know how to manipulate equations.
14.
4AF2.0
15.
4AF2.0
16.
4AF2.0
17.
4AF2.0
18.
19.
4MR2.2 Apply strategies and results from simpler
problems to more complex problems.
4MR2.2
20.
4MR2.2
Groups for differentiated instruction
Interpret and evaluate mathematical
expressions that now use parentheses.
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
7–40
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11/30/07 4:42:21 AM
Name
Unit 3 Test
Date
Unit 3 Test
4NS3.0
Circle the letter of the correct answer.
4NS3.0
1
3
Susan invited 12 of her friends
to her birthday party. Each friend
gave her one birthday gift. If Susan
decided to share her gifts equally
among her 12 friends, how many
gifts does each friend receive?
7 × 9 = 63
A
63 ÷ 1 = 63
B
63 ÷ 9 = 7
A
1
C
63 ÷ 9 = 9
B
3
D
63 ÷ 7 = 7
C
4
D
4NS3.0
6
4
4NS3.0
2
Which of the following equations
is related to the equation below?
If 3 × 5 = 15, what is 15 ÷ 3?
A
B
C
D
3
Between Monday and Friday,
Fernando picks 3 flowers from his
garden each day. He has 3 friends
and divides his flowers equally
among them. How many flowers
does each friend receive?
A
3
B
4
C
5
D
6
5
4
15
Assessment Resources 4
7–41
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73784_UT_U3.indd 7–41
12/9/07 11:19:55 PM
Name
Unit 3 Test
Date
4NS3.0
5
Which of the following equations is
related to
4NS3.0
7
Using the associative property,
rewrite the following expression.
3 × (6 × 7)
4 × 6 = 24?
A
24 ÷ 1 = 24
A
3 × (6 × 6)
B
24 ÷ 6 = 4
B
6 × (3 + 7)
C
24 ÷ 6 = 6
C
(3 × 6) × 7
D
24 ÷ 4 = 4
D
6×7
4NS3.0
6
What is any number multiplied by 0?
8
What is 6 ÷ 0?
A
0
A
0
B
1
B
1
C
10
C
9
D
The original number
D
not possible
Assessment Resources 4
4NS3.0
7–42
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Name
Unit 3 Test
Date
4NS3.2
9
Aretha has 48 balls that she puts
into 8 equal rows, 6 balls in a row. If
Aretha wants to divide the 48 balls
into 6 equal rows, how many balls
would be in each row?
11
4NS3.2
A
6
B
8
C
10
D
12
4NS3.2
10
Chen sorted his toy cars into groups
of 5. He recorded the groups using
tally marks.
Gloria is using tally marks to help her
multiply 5 × 9. What was her answer?
A
9
B
5
C
45
D
50
4NS3.0
12
What is the total number of toy cars?
Marco divides his box of 25 pears
among 4 friends. How many pears
does each friend get?
A
4
B
6
A
6
C
6
B
5
D
7
C
20
D
25
Assessment Resources 4
7–43
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Name
Unit 3 Test
Date
4NS3.0
13
What is 26 divided by 5?
A
5
B
5 remainder 1
C
D
16
5
B
6
C
7
D
8
4AF1.0
6
Use the order of operations to solve
the following expression.
4 × (6 + 3) - 4
A
23
B
28
C
30
D
15
A
5 remainder 2
4AF1.2
14
Juan gives Anil and Percy some of
his 12 football cards. He gives 3
cards to Anil and 2 to Percy. How
many cards does Juan have left?
4AF1.0
17
Tara and her sister want to see how
far they can run in 20 minutes. Tara
runs 3 miles and her sister runs
less than half that distance. Which
inequality or equation below shows
this relationship?
A
×2<3
B
×2=3
C
+ 3 = 20
D
+ 3 > 20
32
(7 + 5 + 4) × (3 + 2) = ?
A
21
B
80
C
94
D
100
Assessment Resources 4
4AF1.2
7–44
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Name
Unit 3 Test
Date
4AF1.0
18
Ling Na studies more than two hours
a day, Monday through Friday. Which
equation or inequality below shows
her total study time for the week?
4AF2.0
20
Solve the equation.
A
= 36
B
=3
C
= 48
D
=8
>2×5
A
=2×5
B
=5+2
C
>5+2
D
= 40 − 4
12 ×
4AF2.0
19
Solve the equation.
= 32
8×
A
=8
B
=4
C
=1
D
= 256
Assessment Resources 4
7–45
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73784_UT_U3.indd 7–45
11/30/07 4:48:37 AM
Name
Date
Unit 3 Test
Individual Student Record Form
Unit 3 Test
Use the unit test to identify your students’ mastery of the
skills in the unit. The item analysis below will help you
recognize strengths and weaknesses.
Correct
Answer
Student
Response
1. A
Record the student’s response in the column to the right
of the correct answer.
California State Standards
2. B
4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of
whole numbers and understand the relationships among the operations.
4NS3.0
3. B
4NS3.0
4. C
4NS3.0
5. B
4NS3.0
6. A
4NS3.0
7. C
4NS3.0
8. D
4NS3.0
9. B
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
4NS3.2 number by a one-digit number; use relationships between them to simplify
4NS3.2 computations and to check results.
10. D
11. C
12. C
13. B
4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of
whole numbers and understand the relationships among the operations.
4NS3.0
14. D
4AF1.2
15. B
4AF1.2
16. C
4AF1.0
17. A
4AF1.0
18. A
4AF1.0
19. B
4AF2.0
20. B
4AF2.0
Interpret and evaluate mathematical expressions that now use parentheses.
Students use and interpret variables, mathematical symbols, and properties to write
and simplify expressions and sentences.
Students know how to manipulate equations.
out of 20
Assessment Resources 4
7–47
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11/30/07 4:56:15 AM
Teacher Name
Date
Unit 3 Test
Class Record Form
Unit 3 Test
Use the unit test to identify your students’ mastery of the
California Mathematics Contents Standards in the unit.
Item
1.
The record below will allow you to group students for
differentiated instruction.
California Mathematics Contents Standards
3.
4NS3.0 Students solve problems involving addition,
subtraction, multiplication, and division of whole
4NS3.0 numbers and understand the relationships
4NS3.0 among the operations.
4.
4NS3.0
5.
4NS3.0
6.
4NS3.0
7.
4NS3.0
8.
4NS3.0
9.
4NS3.2 Demonstrate an understanding of, and the ability
to use, standard algorithms for multiplying a
4NS3.2 multidigit number by a two-digit number and
4NS3.2 for dividing a multidigit number by a one-digit
number; use relationships between them to
simplify computations and to check results.
2.
10.
11.
12.
13.
4NS3.0 Students solve problems involving addition,
subtraction, multiplication, and division of whole
4NS3.0 numbers and understand the relationships
among the operations.
14.
4AF1.2
15.
4AF1.2
16.
4AF1.0
17.
4AF1.0
18.
4AF1.0
19.
4AF2.0
20.
4AF2.0
Groups for differentiated instruction
Interpret and evaluate mathematical expressions
that now use parentheses.
Students use and interpret variables,
mathematical symbols, and properties to write
and simplify expressions and sentences.
Students know how to manipulate equations.
Assessment Resources 4
7–48
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