Chapter Resources
Grade 4, Chapter 18
Contents
Resources for Chapter 18: Compare and Order Fractions
• Lesson Quizzes Lessons 18.1–18.4
Daily Routines
Reteach
Practice
Enrichment
Leveled Problem Solving
Homework
• Chapter 18 Test
Individual and Class Record Sheets
• Unit 8 Test
Individual and Class Record Sheets
B
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Booklet 18 of 29
TTL_73744_U8_C18.indd 18–1
18–1
2/1/08 3:17:59 PM
Name
Date
Chapter 18, Lesson 1
Lesson Quiz
Lesson 1 Quiz
Compare. Write >, <, or = for each
number lines to help you.
1.
2.
3.
4.
5.
. Use fraction tiles or
_1 _1
5
3
_4 _5
6
6
_1 _6
2
8
3
_ _1
12
4
7
_
_2
12 4
Lesson Quiz
Use with Chapter 18, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 18, Lesson 2
Lesson Quiz
Lesson 2 Quiz
Compare. Write >, <, or = for each
1.
2.
3.
.
_3 _4
5
6
4
_
_2
10 5
6
_5 _
8
10
Order the fractions from least to greatest.
4.
5.
_1 _5 _3
3 6 5
_3 _5 _1
4 8 2
Lesson Quiz
18–3
Use with Chapter 18, Lesson 2
Copyright © Houghton Mifflin Company. All rights reserved.
CAPEG4_C18_LessonQuiz.indd 18–3
12/3/07 2:20:41 PM
Name
Chapter 18, Lesson 3
Lesson Quiz
Date
Lesson 3 Quiz
Write each improper fraction as a mixed number. Write each mixed
number as an improper fraction.
1.
2.
3.
4.
5.
12
_
10
3
2_
4
14
_
3
2
3_
5
_9
2
Lesson Quiz
Use with Chapter 18, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Chapter 18, Lesson 4
Lesson Quiz
Date
Lesson 4 Quiz
Order the numbers from least to greatest. Use number lines to help
you.
1.
2.
3.
1 2 7
2_ 2_ 1_
5 4 8
9
5 2
1_ 1_ 1_
10 6 3
3 11 1
1 _ _ 1_
5 12 8
Lesson Quiz
18–4
Use with Chapter 18, Lesson 4
Copyright © Houghton Mifflin Company. All rights reserved.
CAPEG4_C18_LessonQuiz.indd 18–4
12/3/07 2:20:49 PM
Name
Chapter 18, Lesson 1
Daily Routines
Date
Hands On: Compare Fractions
Problem of the Day
KEY NS 3.2
How many grams are 6 kilograms?
Number Sense Review
KEY NS 1.8
Use Workmat 4 to plot these numbers on the number line.
–3, 4, 10, –9, 0
Word of the Day
MR 2.3
compare
Think of everyday occurrences when you might compare things.
Facts Practice
KEY NS 1.8
Compare using >, <, or =.
1.
–17 ____ –3
2.
15 ____ –20
3.
0 ____ –6
4.
–2 ____ –5
5.
–20 ____ 41
6.
31 ____ –10
Daily Routines
18–5
Use with Chapter 18, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–5
1/31/08 11:45:45 AM
Name
Chapter 18, Lesson 1
Reteach
Date
Hands On: Compare Fractions
CA Standard
NS 1.9
3
2
Compare _
and _
.
5
3
3
Show _ using
5
2
Step 2 Show _
using
3
fraction strips.
Step 1
fraction strips.
1
5
1
5
1
5
1
5
1
3
1
5
1
3
Step 3 Compare the
two sets of fraction strips.
Which is longer?
1
3
3
2
<_
Solution: _
5
3
Compare. Write >, <, or = for each .
1.
_3 _1
2.
_1 _2
3.
5
_
_3
4.
_3 _1
5.
6
_3 _
6.
11
_5 _
7.
_3 _4
8.
_2 _3
9.
_1 _1
11.
_1 _2
12.
4
8
8
16
5
6
10.
3
7
9
14
_4 _5
8
8
10
5
3
5
5
6
8
7
8
6
5
_
_2
25
5
Writing Math In problem 12, Ronnie changed __25 to __15 and
changed the answer to >. Is he correct? Explain.
Reteach
18–6
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_RET.indd 18–6
12/1/07 12:20:17 PM
Name
Chapter 18, Lesson 1
Practice
Date
Hands On: Compare Fractions
Compare. Write >, <, or = for each . Use fraction tiles or
number lines to help you.
1.
6
5
_
_
10
1
10
1
10
2.
10
1
10
1
10
1
10
1
10
1
10
1
10
1 1
10 10
1
10
_3 _6
4
3.
8
1
4
1
8
1
4
1
8
1
8
1
8
1
8
5.
3
_1 _
6.
8.
_8 _7
9.
6
_2 _
10.
9
8
6
12
4
12
1
9
1
8
6
_
_3
6
3
1
4
4.
12
_1 _4
4
_
_3
12
6
_3 _4
4
5
9
1
3
1
9
1
9
7.
11.
1
9
3
_1 _
5
15
_8 _6
9
9
Test Practice
Circle the letter of the correct answer.
12.
7
11
Andy drew a line that was _
of an inch long. Ally drew a line that was _
of an inch
8
36
3
long. Akim drew a line that was _ of an inch long. Which person’s line, if any, was
longest?
13.
4
A
Andy’s line
C
Ally’s line
B
Akim’s line
D
They were all equal.
Fred split a square into 4 equal smaller squares and shaded 2 of the squares. Frank
split a square into 8 equal rectangles and shaded 6 of the rectangles. Francine split a
square into 6 equal rectangles and shaded 3 of the rectangles. Which person, if any,
shaded in a larger fraction of his or her square?
A
Fred
C
Francine
B
Frank
D
They were all equal.
Writing Math Maggie changed all the denominators in problem 12 to 36, but left
the numerators the same. She said that Ally’s line was now the longest. Is she right? Explain.
Practice
18–7
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_PRAC.indd 18–7
12/12/07 2:54:54 AM
Name
Chapter 18, Lesson 1
Enrichment
Date
Hands On: Compare Fractions
CA Standard
NS 1.9
Compare. Write >, <, or = for each . Use fraction tiles or number
lines to help you. Then match the number and sign to the letter and
fill in the blanks to complete the answer to the riddle.
Riddle: What did the large fraction say to the small fraction?
<
- N
>
- O
=
- T
4
1. __
3
__
8
1
2. __
6
4. __
4
__
7
5
5. ___
9
7. ___
2
__
6
8
7
12
3
__
4
2
Answer: “I C [
]U[
1
][
2
] M[
3
3
6. __
2
__
3
6
]RE [
4
2
__
6
6
1
__
2
10
2
3. __
]HA[
5
] Y[
6
] U.”
7
Writing Math Patrick says that __26 was greater than __13 . Is he
right? Why or why not?
Enrichment
18–8
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_ENR.indd 18–8
12/1/07 12:22:02 PM
Chapter 18, Lesson 1
Name
Leveled Problem Solving
Date
Hands On: Compare Fractions
CA Standard
NS 1.9
Solve each problem. Use fraction tiles or number lines to
help you if needed.
1.
3.
5.
4
One snail moved ___
of a foot before
12
6
stopping. A second snail moved ___
of
12
a foot before it took a rest. Which snail
moved the farthest?
1
Jerry swam __
of a mile across the lake
3
and rested on a raft. Then he swam
2
another __
of a mile to the opposite
6
shore. Did he swim more, less, or the
same distance before he rested than
after he rested?
1
Three friends shared a pizza. Paul ate __
8
2
of the pizza. Abe ate __
and
Carrie
ate
4
3
__
.
Who
ate
the
most?
Who ate the
8
least?
Leveled Problem Solving
2.
4.
3
The male mountain goat climbed __
of a
4
mile up the rocky cliff side. The female
1
goat climbed __
of a mile. Who climbed
4
the highest?
1
Tomas ran __
of a mile around the track.
2
3
Wendy ran __
of a mile around the
4
track. Who ran the farthest?
6.
18–9
Three friends drove to a national park
to go hiking. They decided to share
3
of the way.
the driving. Moritz drove __
5
3
___
Pablo drove 10 of the way and Reggie
2
of the way. Who drove the
drove ___
20
greatest distance? Who drove the
least distance?
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_PS.indd 18–9
12/1/07 1:56:04 PM
Name
Chapter 18, Lesson 1
Homework
Date
Hands On: Compare Fractions
_6_
8
CA Standard
NS 1.9
_24_
You can use a model.
1
8
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
4
Solution: _68_ > _24_
Compare. Write >, <, or = for each
lines to help you.
5
1. ___
10
4
5. __
5
2
__
4
2
__
5
4QJSBM3FWJFX
. Use fraction tiles or number
2
2. __
7
__
9
1
3. __
3
__
4
3
4. __
6
___
16
3
6. __
4
__
8
3
7. __
3
___
10
3
8. __
5
__
7
3
6
4
9
8
7
(Chapter 13, Lessons 2, 4) KEY NS 3.0, KEY NS 3.4
Divide. Use multiplication to check.
9.
11.
420 ÷ 4
10.
622 ÷ 2
A restaurant served 410 people on Saturday and Sunday. If the
same number of people ate there each day, how many were
served on Saturday?
Homework
18–10
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_HMWK.indd 18–10
12/12/07 2:56:00 AM
Name
Chapter 18, Lesson 2
Daily Routines
Date
Compare and Order Fractions
Problem of the Day
KEY NS 1.9
Sophie has eaten _12 of her pizza. Model this fraction on a number line.
0
1
4
1
2
3
4
1
Number Sense Review
KEY NS 3.0
Find the other multiplication fact and two division facts that make
up the fact family.
1.
6 × 7 = 42
2.
3 × 4 = 12
3.
7 × 8 = 56
Word of the Day
KEY NS 4.2
prime
Give five examples of prime numbers.
Facts Practice
KEY NS 3.2
Multiply or divide.
1.
121 ÷ 11
2.
11 × 11
3.
10 × 10
4.
100 ÷ 10
5.
16 ÷ 4
6.
4×4
Daily Routines
18–11
Use with Chapter 18, Lesson 2
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–11
12/1/07 12:16:36 PM
Name
Chapter 18, Lesson 2
Reteach
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
3 _
Compare _
, 2 , and _1_. Order the fractions from greatest to least.
2
5 3
Step 1 Find equivalent fractions with
a common denominator.
×6
3
5
=
×6
Step 2 Compare the numerators.
20 > 18 > 15
× 15
18
30
2
3
× 10
=
1
2
20
30
20
18
15
__
> __
> __
30
30
30
15
30
=
_2_ > _3_ > _1_
5
3
2
× 15
Solution: The order of the fractions from
2 _
, 3 , _12_.
greatest to least is _
× 10
3 5
Compare. Write >, <, or = for each
3
1. __
4
__18
1
2. __
3
.
__29
5
3. ___
10
__35
3
4. __
8
__26
Order each group of fractions from greatest to least. Draw number
lines to help if you wish.
3
5. __
5
1 __
, __
, 1
5 6
4
9. ___
10
1 ___
, __
, 3
5 10
4
6. __,
8
5
10. __
6
1 __
__
, 5
4 8
1
7. __
2 ___
, __
, 11
6 12
12
11. ___
3
3 __
, __
, 1
6 6
25
5
2
, ___
, __
25 5
3
8. ___
21
5
12. __
9
2
2
, ___
, __
21 7
6 ___
, __
, 1
9 18
Writing Math Is the problem in the example harder or easier
to solve than problems 5 to 12? Explain.
Reteach
18–12
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_RET.indd 18–12
12/1/07 2:02:18 PM
Name
Chapter 18, Lesson 2
Practice
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
Compare. Write >, <, or = for each .
1.
6
3
_
_
4.
6
_
_2
5.
_1 _3
8.
_8 _5
9.
6
_3 _
10
12
4
9
6
_3 _6
2.
10
6
4
6.
9
6
3.
8
10.
12
_1 _6
3
9
1
_
_3
12
7.
6
_4 _5
11.
6
4
3
_1 _
5
15
_8 _9
9
9
Order the fractions from least to greatest. Use number lines to help you.
12.
_1 _3 _2
4
4
4
13.
_2 _6 _4
7
7
14.
7
_7 _3 _5
9
9
15.
9
_5 _3 _1
8
8
4
Test Practice
Circle the letter of the correct answer.
16.
Which set of fractions is ordered from
greatest to least?
A
_2 , _1 , _3
C
_2 , _3 , _4
B
_3 , _3 , _3
D
_1 , _1 , _1
3 2 5
4 5 6
17.
2
Ted drew a line that was _
of an inch
6
11
long. Toni drew a line that was _
of
36
an inch long. Tara drew a line that
5 5 5
1
was _
of an inch long. Which person’s
6
line, if any, was longer?
3 5 4
A
B
Tara’s line
Ted’s line
C
D
Toni’s line
They were all equal.
Writing Math In problem 16 above, which was the
easiest set of fractions to order? Which was the hardest? Explain.
Practice
18–13
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_PRAC.indd 18–13
12/12/07 3:34:00 AM
Name
Chapter 18, Lesson 2
Enrichment
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
The table below shows four major minority groups in the state of
California and what fraction they make up of the total population.
Use the data to solve each problem.
Minorities of California
Minority
Fraction of Population
Latin Americans
Native Americans
African Americans
Asian Americans
9
__
25
1
___
100
3
__
50
6
__
50
1.
Are there more Native Americans or
African Americans in California?
2.
Are there more Latin Americans than
Asian Americans?
3.
What minority group is double the
number of African Americans?
4.
One fourth of the total state population
is Mexican American. Which minority
group is larger, Mexican Americans or
Latin Americans?
5.
If all the minorities in the table were added together, what
part or fraction of the total population would they be?
Writing Math For problem 5, Holly tried to make 50 the
common denominator before adding the fractions. Was this a good
decision? Why or why not?
Enrichment
18–14
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_ENR.indd 18–14
12/12/07 3:36:31 AM
Chapter 18, Lesson 2
Name
Leveled Problem Solving
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
Solve each problem.
1.
Edie, George, and Art dug holes to
2
plant seedlings. Edie dug __
feet.
4
3
__
George’s hole was 4 feet deep and
1
Art’s was __
feet deep. Order the
4
fractions from least to greatest.
2.
3.
The weather was very hot and the
students watered their seedlings daily.
1
Art poured __
gallon of water on his
2
3
seedling. Edie poured ___
of a gallon
10
on hers. George watered his seedling
6
with ___
of a gallon. Order the fractions
10
from greatest to least.
4.
5.
Estella has divided her garden into
three sections. The section where she
2
grows tomatoes takes up __
of the
6
1
__
garden. She plants 4 of the garden with
5
beans. Corn is in the remaining ___
.
12
Order the vegetables by the space they
use from greatest to least.
6.
Leveled Problem Solving
18–15
3
Edie’s seedling was __
feet in
5
2
length. Art’s was __
feet long and
5
4
__
George’s was 5 feet tall. Who planted
the tallest seedling? The shortest
seedling?
3
Hank’s vegetable garden covers __
6
1
of
an
of an acre. Polly’s garden is __
3
5
of
an
acre.
acre and Estella’s is __
6
Whose garden is the largest?
Whose is the smallest?
2
Hank’s biggest tomato weighs __
of
5
a pound. Estella’s largest tomato
7
weighs ___
of a pound, while Polly’s
20
3
largest weighs in at ___
pound. Order
10
the tomatoes by owner from least to
greatest weight.
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_PS.indd 18–15
12/1/07 2:04:33 PM
Name
Chapter 18, Lesson 2
Homework
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
Compare _6_ and _2_.
8
_6_
8
4
_24_.
Way 1 You can use a model.
1
8
1
8
1
4
1
8
1
8
1
8
Way 2 You can use equivalent fractions.
(2 × 2)
_2_ = _____
= _48_
4
(4 × 2)
_6_ is greater than
8
Solution: _68_ > _24_
1
8
1
4
_6_ > _2_
8
4
Compare. Write >, <, or = for each
5
1. ___
2
__
4
10
5
5. __
5
4
__
5
_4_, so
8
.
2
2. __
7
__
9
1
3. __
4
__
8
3
4. __
6
___
16
3
6. __
4
__
8
3
7. __
3
___
10
7
8. __
4
__
4
3
6
4
9
8
7
Order the fractions from least to greatest. Use number lines to help you.
1 4 3
9. __, __, __
5 5 5
4QJSBM3FWJFX
3 5 4
10. __, __, __
6 6 6
5 2 7
11. __, __, __
9 3 9
4 7 9
12. __, ___, ___
8 16 16
(Chapter 13, Lessons 2, 3, 4) KEY NS 3.0, KEY NS 3.2, KEY NS 3.4
Divide. Use multiplication to check.
13.
15.
486 ÷ 3
14.
864 ÷ 2
Five trucks carried 250 tons of coal. If the trucks each carried the
same load, how many tons of coal did each have?
Homework
18–16
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_HMWK.indd 18–16
12/12/07 3:39:36 AM
Name
Chapter 18, Lesson 3
Daily Routines
Date
Write Mixed Numbers and Improper Fractions
Problem of the Day
KEY NS 1.9
5
Tenecia ate _38 of a box of raisins and her cousin Beau ate __
of a box
16
of raisins. Who ate more raisins?
Number Sense Review
KEY NS 1.8
Use Workmat 4 to order the numbers –2, 1, –6, –3, and 5 and list
them from least to greatest.
Number of the Day
KEY NS 4.2
6
The number 6 is called a perfect number because the sum of its
factors (other than itself) is the number. Can you find another perfect
number under 30?
Facts Practice
KEY AF 2.0
Solve each equation.
1.
4r = 16
2.
56 = 8p
b
3. _
3
= 12
4.
w
9 = __
6
5.
11t = 55
s
6. _
4
= 15
Daily Routines
18–17
Use with Chapter 18, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–17
1/31/08 11:46:22 AM
Name
Chapter 18, Lesson 3
Reteach
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
13
Write __
as a mixed number.
4
Way 1
You can draw a picture.
Way 2 You can divide the numerator by
the denominator.
Remember: The fraction bar stands for
13
means 13 divided by 4.
“divide by,” so __
4
4
4
+
4
4
+
4
4
+
1
4
3
= 3 14
-12
1
13
The picture shows that __
= 3 _14_.
4
number of wholes
13
4
number of parts
13
So, __
= 3 _14_.
4
Solution: 3 _14_.
Write an improper fraction for the shaded parts. Then write each as
a mixed number or a whole number.
1.
2.
3.
4.
5.
6.
Writing Math Suppose one less part in problem 5 was
shaded. Would the answer be a whole number or a mixed number?
Explain.
Reteach
18–18
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_RET.indd 18–18
12/12/07 3:40:39 AM
Name
Chapter 18, Lesson 3
Practice
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
Write an improper fraction and a mixed number or whole
number to describe the shaded parts.
1.
2.
3.
Write a mixed number and an improper fraction for each letter.
A
B
1
4.
E
5.
C
2
D E
3
B
6.
F
4
D
7.
A
8.
C
9.
F
Test Practice
Circle the letter of the correct answer.
10.
Which improper fraction is equivalent
11.
3
to 3 _ ?
8
A
27
_
B
27
_
3
8
C
28
_
D
33
_
8
8
Julie brought 3 pies to Thanksgiving
dinner. Each pie was cut into 8 pieces.
Each person ate 2 pieces, and there
were no pieces left over. How many
people were at the dinner?
A
10 people
C
12 people
B
14 people
D
16 people
Writing Math If one more section in problem 1 was shaded,
would the answer be a mixed number or a whole number? Explain.
Practice
18–19
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_PRAC.indd 18–19
12/12/07 3:42:10 AM
Name
Chapter 18, Lesson 3
Enrichment
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
To change an improper fraction to a mixed number, you divide. To
change a mixed number to an improper fraction, you multiply. Each
table below shows the division and the resulting improper fraction
and mixed number. Complete each table.
Division
Improper
Fraction
1.
16 ÷ 3
16
__
3
2.
19 ÷ 2
Mixed
Number
9 _12_
1_78_
4.
Division
Improper
Fraction
6 _23_
12
__
5
11.
7.
10 ÷ 2
8.
15 ÷ 6
15
__
6
Division
Improper
Fraction
5 _16_
13.
14.
Mixed
Number
23
__
6
12.
10.
Mixed
Number
4 _45_
6.
Mixed
Number
18 ÷ 5
9.
Improper
Fraction
28
__
7
5.
11
__
9
3.
Division
15 ÷ 3
Writing Math If you were to add a fourth column to problem
1 with the heading Multiplication, what would you put in that column?
Enrichment
18–20
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_ENR.indd 18–20
12/1/07 2:06:19 PM
Chapter 18, Lesson 3
Name
Leveled Problem Solving
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
Solve each problem.
1.
Jerry bought 2 pies. He cut each pie
into 6 slices. Over a week, he ate all
of one pie and 2 slices of the second.
How much of the total number of slices
did he eat? Write your answer as an
improper fraction.
2.
Ms. Rodriguez had 2 boxes of chalk at
the start of the school year. Each box
contained 10 pieces of chalk. By the
end of the school year, she had used
all of the chalk in one box and half
of the other. How much of the chalk
did she use? Write your answer as a
mixed number.
3.
Allie had 11 guests at her birthday
party. She served 2 birthday cakes.
If she and her guests each ate 2 slices
of cake, how many slices did she need
to cut each cake into?
4.
Howie colored pictures of pinwheels.
Each pinwheel had 5 sections. If Howie
colored 13 sections, what was the least
number of pinwheels in the coloring
book? Write the sections colored as an
improper fraction.
5.
Kayla bought a bag of grapefruit.
Each morning for 5 days she and her
father each ate one half of a grapefruit.
Her mother ate 3 halves total in that
time. How much grapefruit did they
eat altogether? Write your answer as
an improper fraction and as a mixed
number.
6.
In the school walkathon, Bev walked
1
2
2__
miles, Dennis walked 3___
miles, and
5
10
Leveled Problem Solving
18–21
3
Natalie walked 2__
miles. What was the
5
total distance they walked? Write your
answer as a whole number and as an
improper fraction.
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_PS.indd 18–21
12/1/07 2:06:39 PM
Name
Chapter 18, Lesson 3
Homework
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
Write an improper fraction and a mixed number to describe the shaded part.
Step 1 There are 3 whole squares and _25_
of the fourth square is shaded.
17
Step 2 _55_ + _55_ + _55_ + _25_ = __
5
Step 3 1 + 1 + 1 + _25_ = 3 _25_
17
Solution: 3 _25_ and __
5
Write an improper fraction and a mixed number or whole number
to describe the shaded parts.
1.
2.
4QJSBM3FWJFX
3.
(Chapter 15, Lesson 4) KEY NS 3.2
Find the missing number.
4.
200 mm =
cm
5.
3,000 m =
km
6.
A building is 6 meters high. What is its height in centimeters?
Homework
18–22
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_HMWK.indd 18–22
12/1/07 2:06:57 PM
Name
Chapter 18, Lesson 4
Daily Routines
Date
Compare and Order Fractions and
Mixed Numbers
Problem of the Day
KEY NS 1.2
Natasha, Elena and Madison are running a race. After 20 minutes,
Madison has run 0.9 miles, Natasha has run 2.1 miles, and Elena has
run 1.8 miles. Order the runners from fastest to slowest.
Number Sense Review
KEY NS 3.2
Tell how many meters.
1.
3 kilometers
2.
400 decimeters
3.
200 centimeters
Number of the Day
NS 1.5
1
_
4
How many fourths make up one whole?
Facts Practice
KEY NS 3.0
Estimate to find the products or quotients.
1.
83 × 4
2.
690 × 21
3.
520 × 33
4.
82 ÷ 9
5.
50 ÷ 7
6.
145 ÷ 12
Daily Routines
18–23
Use with Chapter 18, Lesson 4
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–23
12/1/07 12:19:31 PM
Name
Chapter 18, Lesson 4
Reteach
Date
Compare and Order Fractions
and Mixed Numbers
CA Standards
NS 1.9, NS 1.5
Compare and order 1_13_, 1_36_, _76_.
Way 1 Use number lines and compare.
11
3
0
1
2
13
6
0
1
2
11
6
0
1
_7_ is farthest to the left.
6
1_36_ is farthest to the right.
1_13_ is in the middle.
So, _76_ < 1_13_ < 1_36_.
Way 2 Use equivalent fractions.
Change the mixed numbers to improper
fractions. Then write the fractions using
the same denominator.
1_13_ = _43_ = _86_
1_36_ = _96_
_7_
6
Compare the improper fractions.
2
_7_ < _8_ < _9_
6
6
6
Solution: _76_ < 1_13_ < 1_36_
Order the numbers from greatest to least. Use number lines to help
you if needed.
1.
3 ___
5
2__
, 18 , 2__
7 7
7
2.
5
2 ___
4__
, 39 , 4__
3 9
9
3.
10 ___
4
7___
, 7___
, 65
10 20 10
4.
9
1 ___
1__
, 12 , __
6 12 6
5.
3 ___
46
9 __
, 9 8 , ___
5 10 5
43
50
50
Lynn was comparing ___
to ___
and decided ___
was greater
6
12
12
because 50 is greater than 43. Is her reasoning correct? Explain.
Reteach
18–24
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_RET.indd 18–24
12/12/07 3:44:01 AM
Name
Chapter 18, Lesson 4
Practice
Date
Compare and Order Fractions and
Mixed Numbers
CA Standards
NS 1.9, NS 1.5
Compare. Write >, <, or = for each .
1.
2_
5
4
2_
10
2.
2
1_
_43
3.
1_
1 _78
4.
3_
13
_
3
3
3
4
6
3
9
Order the numbers from least to greatest. Use number lines to help you.
5.
4
2
2_ 1_
2_
6.
1
6_
61
_
7.
7
_
1_ 1_
1
5
10
10
8.
32
_
2
1
5_
5_
5
8
8
8
4
3
3
6
9
3
6_
6
9
6
Test Practice
Circle the letter of the correct answer.
9.
Which number is the greatest?
1_
3
15
11
_
B
5
A
C
10.
4
1_
5
Which number is the least?
2_
3
4
10
_
B
4
A
_1
D 1
3
C
4
2_
16
_4
D 2
8
Writing Math Jon was ordering fractions in which the
denominators were 2, 3, and 4. He said he couldn’t do it because
there was no common denominator for these three numbers.
Is he correct? Explain.
Practice
18–25
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_PRAC.indd 18–25
12/1/07 2:07:49 PM
Name
Date
Compare and Order Fractions
and Mixed Numbers
Chapter 18, Lesson 4
Enrichment
CA Standards
NS 1.9, NS 1.5
The liter is a basic measurement of volume in the metric system. Many liquid
products now come in liter bottles in the United States. The table below shows U.S.
measurements that are about equal to a liter. Use the data to answer questions 1–3.
Volume Measurements
Metric
U.S.
1 liter
1
2 __
pints
10
1 liter
6
1 ___
quarts
100
1 liter
26
___
gallons
100
1.
The athlete drank 3 liters of water on a hot day. How many pints
would that be as a mixed number and fraction?
2.
About how many liters would make 1 gallon of liquid?
3.
What would 4 liters be in quarts? Write as a mixed number and a fraction.
4.
If 5 milliliters make 1 teaspoon, what fraction expresses how
much of a teaspoon 1 milliliter is?
5.
If a tablespoon is 3 times the volume of a teaspoon, how many
milliliters will fill a tablespoon?
Writing Math What operations did you use to find the
answers to problems 4 and 5?
Enrichment
18–26
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_ENR.indd 18–26
12/12/07 3:44:46 AM
Chapter 18, Lesson 4
Name
Leveled Problem Solving
Date
Compare and Order Fractions
and Mixed Numbers
CA Standards
NS 1.9, NS 1.5
Solve each problem.
1.
1
Jamie slept for 7__
hours one night.
4
2.
3
Maria slept for 7__
hours the same
8
night. Who slept longer?
3.
5.
Mr. Kosinski watched TV before he
3
went to bed. He watched TV for 1__
5
hours before dozing off. He woke up
4
1___
hours later and watched TV for
10
4
another 1___
hours. Order these three
20
periods of time from shortest
to longest.
1
Steve jogged 2__
miles on Monday,
2
4.
2
Stan did his homework in 2__
hours.
3
1
It took Heidi 2__
hours to do the same
4
assignment. Felicia finished the same
5
homework in 2___
hours. Who finished
12
their homework in the shortest time?
Who took the longest?
6.
6
4
2__
miles on Wednesday, and 2___
miles
5
10
on Friday. Order his runs from shortest
to longest using improper fractions.
Leveled Problem Solving
1
Ralph slept for 3__
hours one night and
3
then woke after a dream. He went back
3
hours.
to sleep and slept another 3___
12
Did he sleep longer before or after his
dream?
18–27
2
Nancy lives 4__
miles from her
3
19
school. Dave lives ___
miles from school.
4
2
Raoul’s house is 4__
miles from school.
4
Order the three distances from closest
to farthest from school.
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_PS.indd 18–27
12/1/07 2:09:50 PM
Name
Chapter 18, Lesson 4
Homework
Date
Compare and Order Fractions
and Mixed Numbers
CA Standards
NS 1.9, NS 1.5
1_3_ 1_45_
4
Way 1 Put each number on a number line.
0
1
1 34
2
0
1
4
5
2
Way 2 Change to equivalent fractions.
35
1_34_ = _74_ = __
20
36
1_45_ = _95_ = __
20
36
35
__
is less than __
.
20
20
Solution: 1_34_ < 1_45_
Compare. Write >, <, or = for each
1.
2
4
3 __
3 ___
5 10
2.
3
1
2 __
2 __
7 5
3.
3
5
__
1__
84
1
4. __
3
.
1__69
4QJSBM3FWJFX
(Chapter 17, Lesson 2) NS 1.5
Find the fractional part of each number.
1
5. __
of 9
1
6. __
of 10
3
2
7.
Colin has 36 bananas. One third of them are ripe. How many of
the bananas are ripe?
Homework
18–28
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_HMWK.indd 18–28
12/1/07 2:10:12 PM
Name
Chapter 18, Lesson 5
Daily Routines
Date
Problem Solving: Field Trip
Problem of the Day
KEY NS 1.9
On Monday, Patrick ran 3_34 miles. On Wednesday he ran 2_78 miles, and
15
miles. On which day did Patrick run the farthest?
on Friday he ran 3__
16
Number Sense Review
KEY NS 3.0
Write an example of the Commutative Property of Multiplication.
Word of the Day
MR 2.3
function rule
Can you find a function rule if you only know one input and one
output value?
Facts Practice
KEY NS 3.2
Find the missing number.
1.
500 cm = ____ m
2.
____ mm = 7 m
3.
30 dm = ____ cm
4.
4 km = ____ m
5.
____ cm = 9,000 mm
6.
____ km = 100,000 cm
Daily Routines
18–29
Use with Chapter 18, Lesson 5
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–29
1/31/08 11:47:00 AM
Name
Chapter 18 Test
Date
Chapter 18 Test
Circle the letter of the correct answer.
1
3
Pedro finished _ of his homework
6
2
before dinner and _ of his
6
homework after dinner. Which
statement below is true?
4
A
B
C
D
1
8
Pedro finished equal amounts of his
homework before and after dinner.
1
A __
Pedro finished most of his
homework before dinner.
B
C
Pedro finished most of his
homework after dinner.
D
Which statement below is true?
5
A __
4
B
C
D
2
1
__
6
1
__
3
1
__
4
Pedro finished exactly half of his
homework before dinner.
3
Which fraction is larger than _?
A
1
8
Which fraction is smaller than the
fraction in the model above?
4
2
Look at the fraction strip below.
9
___
12
1
__
3
9
___
24
7
__
8
Assessment Resources 4
B
C
D
2
= __
6 3
1
1 __
__
<
2 3
3 __
4
__
>
4 6
2
2 __
__
<
3 4
18–31
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C18_U8_CT.indd 18–31
12/1/07 2:11:34 PM
Name
5
Chapter 18 Test
Date
Use the number line below.
1
4
0
2
4
3
4
7
Use the number line below.
0
1
1
8
2
8
3
8
4
8
5
8
6
8
7
8
1
Which fraction is greater than _?
2
2
1
__
__
A
C
8
8
6
3
B __
D __
8
8
1
0
1
6
2
6
3
6
4
6
5
6
1
Which fraction is smaller than _?
6
1
A __
4
3
B __
4
2
C __
4
3
D __
6
2
6
8
Use the number lines below to
compare the fractions.
1
3
0
0
1
6
2
6
2
3
3
6
4
6
5
6
1
9
3
> __
3 6
5 __
2
__
<
6 3
3 __
2
__
>
6 3
1
1 __
__
<
6 3
1
A __
C
D
Assessment Resources 4
3
A
quarters
C
dimes
B
nickels
D
pennies
1
Which statement is true?
B
Joyce has a bag of coins. __ of the
12
5
coins are dimes, __ are quarters,
12 __
1
__3 are pennies, and
are nickels.
12
12
What type of coin does the bag
have the most of?
Carlota ordered 4 whole subs for
a party. At the party, 10 quarter
pieces of the subs were eaten. How
many subs were left over?
A
B
C
D
1
1
1__
2
3
1__
4
1
2__
2
18–32
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C18_U8_CT.indd 18–32
12/1/07 2:11:51 PM
Name
10
At the end of the day, a restaurant
1
still has 3_ pies that weren’t
4
sold. How can this mixed
number be expressed as an
improper fraction?
13
C
D
4
13
___
4
14
___
4
15
___
4
B
C
D
14
11
One Saturday, Kim watched 3 whole
movies and one-fifth of another
movie. How would she express the
number of movies she watched as a
mixed number?
C
D
5
1
3__
4
16
___
5
1
3__
5
B
C
D
15
3
1
1__ > 1__
4
2
5
1
1__ > 1__
4
8
1
1
1__ < 1__
2
4
1
2
1__ > 1__
8
4
Which mixed number is less
11
than __?
3
A
12
1
8__ miles
2
3
8__ miles
4
4
8__ miles
6
4
8___ miles
12
Which is a true statement?
A
1
A 4__
B
The distance of four bike
3
1
trails are 8_ miles, 8_ miles,
2
4
4
4
miles, and 8_ miles. Which is the
8__
12
6
longest trail?
A
12
A ___
B
Chapter 18 Test
Date
Carlos has painted __ walls in his
2
home white. Which choice shows
this fraction expressed as a mixed
number?
1
A 6__
C 7
2
3
1
B 6__
D 7__
4
2
15
Assessment Resources 4
B
C
D
3
3__
4
1
3__
4
5
3__
6
1
4__
3
18–33
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C18_U8_CT.indd 18–33
12/1/07 2:12:02 PM
Name
16
Van has four pencils that
3
1
measure 4 _ inches, 4 _ inches,
2
4
1
7
4 _ inches, and 4 __ inches long.
3
12
Which is the shortest length?
A
B
C
D
Chapter 18 Test
Date
19
1
4 __ inches
2
7
4 ___ inches
12
1
4 __ inches
3
3
4 __ inches
4
Manuel was on a rafting trip with
his friends. The first day they
2
rafted for 3_ hours, and the second
8
5
day they rafted for 4 _ hours.
8
How many hours did they raft
over the two days?
A
B
C
D
17
Mrs. Sanchez took her family
hiking for 4 days. They hiked
29
1
3_ miles on Wednesday, __ miles
3
8
3
on Thursday, 2__ miles on Friday,
12
5
and 3__ miles on Saturday.
12
On which day did they hike the
longest distance?
A
B
Wednesday
Thursday
C
D
20
Friday
Karl was taking a bike ride
along the river. He biked for
8
2__ miles before lunch. Then
12
9
he biked for another 1__ miles
12
after lunch. How many miles did
he bike in all?
A
Saturday
B
C
18
Natasha went on a camping trip.
5
She walked for 4 _ hours in the
8
woods to get to the campground.
Her friend Emily said it took her less
time. Which could be the amount
of time it took Emily to walk to the
campground?
11
1
A 4 ___ hours
C 4 __ hours
12
4
6
4
B 4 __ hours
D 4 __ hours
5
8
Assessment Resources 4
7
6__
8
2
7__
8
5
7__
8
7
7__
8
D
1
4 ___
12
2
4 ___
12
3
4 ___
12
5
4 ___
12
18–34
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C18_U8_CT.indd 18–34
12/1/07 2:12:13 PM
Name
Date
Chapter Test 18
Individual Student Record Form
Chapter Test 18
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. B
4NS1.9
2. D
4NS1.9
3. B
4NS1.9
4. C
4NS1.9
5. A
4NS1.5
6. D
4NS1.5
7. B
4NS1.5
8. A
4NS1.5
9. B
4NS1.9
10. B
4NS1.9
11. D
4NS1.9
12. D
4NS1.9
13. B
4NS1.9
14. A
4NS1.9
15. B
4NS1.9
16. C
4NS1.9
17. B
4NS1.9
18. C
4MR1.1
19. D
4MR1.1
20. D
4MR1.1
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
Explain different interpretations of fractions, for example, parts of a whole, parts
of a set, and division of whole numbers by whole numbers; explain equivalence of
fractions.
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
Analyze problems by identifying relationships, distinguishing relevant from irrelevant
information, sequencing and prioritizing information, and observing patterns.
out of 20
18–35
Copyright © Houghton Mifflin Company. All rights reserved.
73784_IRF_C18_CT.indd 18–35
12/1/07 2:13:02 PM
Teacher Name
Date
Chapter 18 Test
Class Record Form
Chapter 18 Test
Use the chapter test to identify your students’ mastery
of the California Mathematics Contents Standards in the
Item
chapter. The record below will allow you to group students
for differentiated instruction.
California Mathematics Contents Standards
1.
4NS1.9
2.
4NS1.9
3.
4NS1.9
4.
4NS1.9
5.
4NS1.5
6.
4NS1.5
7.
4NS1.5
8.
4NS1.5
9.
4NS1.9
10.
4NS1.9
11.
4NS1.9
12.
4NS1.9
13.
4NS1.9
14.
4NS1.9
15.
4NS1.9
16.
4NS1.9
17.
4NS1.9
18.
4MR1.1 Analyze problems by identifying relationships,
distinguishing relevant from irrelevant
4MR1.1 information, sequencing and prioritizing
4MR1.1 information, and observing patterns.
19.
20.
Groups for differentiated instruction
dentify on a number line the relative position of
positive fractions, positive mixed numbers, and
positive decimals to two decimal places.
Explain different interpretations of fractions, for
example, parts of a whole, parts of a set, and
division of whole numbers by whole numbers;
explain equivalence of fractions.
Identify on a number line the relative position of
positive fractions, positive mixed numbers, and
positive decimals to two decimal places.
18–36
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73784_U8_C18_CRF_CT.indd 18–36
12/1/07 2:13:22 PM
Name
Unit 8 Test
Date
Unit 8 Test
Circle the letter of the correct answer.
1
3
8
4
__
- __
=
9
9
2
A __
9
4
B __
9
9
C __
4
4
D __
4
Look at the figure below.
What fraction of the figure is shaded?
1
A __
3
3
B __
8
5
C __
8
3
D ___
10
Subtract.
4
Jason has to read 24 pages in his
history book by the end of the
3
week. If he has completed __
of the
4
2
assignment, how many pages has
he read?
In a science lab, Lindsay has a
3
container of liquid that is ___
full.
10
7
Marita’s container is ___
full. What
10
A
12
fraction of a container of liquid will
they have if Lindsay adds her liquid
to Marita’s?
B
15
C
16
10
A ___
D
18
20
4
B ___
10
9
C ___
10
10
D ___
10
Assessment Resources 4
5
A book of postage stamps has 20
2
of a book to
stamps. If Juan used __
5
send out invitations to a party, how
many people did he invite?
A
5
B
6
C
8
D
10
18–37
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73784_UT_U8.indd 18–37
1/27/08 10:46:15 AM
Name
6
Look at the fraction strips below.
1
4
1
8
1
4
1
8
1
8
1
4
1
8
1
8
8
1
8
12
9
B ___
16
6
C ___
12
12
D ___
18
1
8
2
A __
8
3
B __
8
4
C __
8
7
D __
8
9
2
A __
5
4
B __
5
4
C ___
10
4
D ___
20
1
3
1
1
3
3
1 1 1 1 1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12 12 12 12 12
2
Which fraction is equivalent to __
?
3
B
C
D
8
How can the fraction ___
be
20
expressed in its simplest form?
Look at the fraction strips below.
A
2
Which fraction is equivalent to __
?
3
4
A ___
1
4
1
Which fraction is equivalent to __
?
4
7
Unit 8 Test
Date
10
4
___
12
6
___
12
8
___
12
9
___
12
Assessment Resources 4
Luisa had $20 to buy school
supplies. She spent $7 for
notebooks, $4 for a calculator,
and $4 for pens and pencils. What
fraction of her $20 did she have
left?
1
A __
2
1
B __
3
1
C __
4
1
D __
5
18–38
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73784_UT_U8.indd 18–38
1/30/08 3:46:34 PM
Name
Use this illustration to answer questions
11 and 12.
1
3
1
3
1
4
1
6
1
8
1
4
1
5
1
6
1
8
1
5
1
6
1
8
1
8
Use these number lines to answer
questions 13 and 14.
1
3
1
4
1
5
11
Unit 8 Test
Date
1
8
1
4
3
8
1
2
5
8
3
4
0
1
6
1
3
1
2
2
3
5
6
1
7
8
1
1
4
1
5
1
6
1
8
0
1
5
1
6
1
8
1
6
1
8
13
1
8
1
A __
Which of these fractions has a
3
3
B __
8
3
C __
6
2
D __
4
1
value greater than __
?
3
1
A __
4
2
B __
9
3
C __
6
2
D __
8
Which of these fractions has the
smallest value?
14
Which statement is true?
3
A __
12
3
> __
8
6
5
2
B __ < __
8
3
3
2
C __ > __
6
8
5
2
D __ < __
3
8
Which of these fractions is the
smallest?
2
A __
3
2
B __
5
3
__
C
6
3
__
D
8
Assessment Resources 4
18–39
Copyright © Houghton Mifflin Company. All rights reserved.
73784_UT_U8.indd 18–39
1/27/08 10:46:49 AM
Name
15
16
Unit 8 Test
Date
Which of these mixed numbers is
16
?
another way to write ___
3
17
Which of these numbers is greater
2
?
than 3 __
3
A
1
4 __
3
A
7
3 ___
10
B
1
5 __
3
B
4
3 __
6
C
2
5 __
3
C
9
3 ___
16
D
2
6 __
3
D
1
3 __
2
3
Zenaida ran __
mile each day for one
4
18
21
week, running a total of ___
miles.
4
What is another way that she could
record her total running distance?
A
B
C
D
3
4 __
4
1
5 __
4
3
5 __
4
1
6 __
4
Which of these number statements
is true?
A
3
1
4 __
> 4 __
8
4
B
3
7
7 __
> 7 ___
5
10
C
5
2
3 __
< 3 __
6
3
D
3
4
5 __
= 5 __
7
8
miles
miles
miles
miles
Assessment Resources 4
18–40
Copyright © Houghton Mifflin Company. All rights reserved.
73784_UT_U8.indd 18–40
2/21/08 7:36:06 AM
Name
19
Unit 8 Test
Date
The table below shows how many
students in Mr. Blanco’s class
ordered lunch from the cafeteria.
Day
20
3
calls for __
cup of sugar. How much
4
sugar will he need to make 3 pies?
Number of students
Monday
Jonah is using a pie recipe that
A
3
1 __
cups
4
B
1
2 __
cups
4
18
Tuesday
21
Wednesday
16
C
1
2 __
cups
2
Thursday
20
D
Friday
19
3
2 __
cups
4
There are 24 students in the class.
2
On which day did exactly __
of the
3
class order lunch?
A
Monday
B
Tuesday
C
Wednesday
D
Thursday
Assessment Resources 4
18–41
Copyright © Houghton Mifflin Company. All rights reserved.
73784_UT_U8.indd 18–41
2/24/08 12:27:55 PM
Name
Date
Unit 8 Test
Individual Student Record Form
Unit 8 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
Record the student’s response in the column to the right
of the correct answer.
California State Standards
1. B
4NS1.5
Explain different interpretations of fractions, for example, parts of a whole, parts
of a set, and division of whole numbers by whole numbers; explain equivalence
of fractions.
2. D
4NS2.0
3. B
4NS2.0
Students extend their use and understanding of whole numbers to the addition and
subtraction of simple decimals.
4. D
4NS1.5
5. C
4NS1.5
6. A
4NS1.5
7. C
4NS1.5
8. D
4NS1.9
9. A
4NS1.9
10. C
4MR2.0
Students use strategies, skills, and concepts in finding solutions.
11. C
4NS1.9
12. D
4NS1.9
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
13. A
4NS1.5
14. B
4NS1.5
15. B
4NS1.9
16. B
4NS1.9
17. A
4NS1.9
18. A
4NS1.9
19. C
4MR1.1
20. B
4MR1.1
Explain different interpretations of fractions, for example, parts of a whole,
parts of a set, and division of whole numbers by whole numbers; explain equivalence
of fractions.
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
Explain different interpretations of fractions, for example, parts of a whole, parts
of a set, and division of whole numbers by whole numbers; explain equivalence of
fractions.
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
Analyze problems by identifying relationships, distinguishing relevant from irrelevant
information, sequencing and prioritizing information, and observing patterns.
out of 20
18–43
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73784_IRF_UT_U8.indd 18–43
12/12/07 3:46:02 AM
Teacher Name
Date
Unit 8 Test
Class Record Form
Unit 8 Test
Use the unit test to identify your students’ mastery of the
California Mathematics Contents Standards in the unit.
Item
The record below will allow you to group students for
differentiated instruction.
California Mathematics Contents Standards
1.
4NS1.5
Explain different interpretations of fractions, for example,
parts of a whole, parts of a set, and division of whole
numbers by whole numbers; explain equivalence of
fractions.
2.
4NS2.0
3.
4NS2.0
Students extend their use and understanding of whole
numbers to the addition and subtraction of simple
decimals.
4.
4NS1.5
5.
4NS1.5
6.
4NS1.5
7.
4NS1.5
8.
4NS1.9
9.
4NS1.9
Explain different interpretations of fractions, for example,
parts of a whole, parts of a set, and division of whole
numbers by whole numbers; explain equivalence of
fractions.
Identify on a number line the relative position of positive
fractions, positive mixed numbers, and positive decimals
to two decimal places.
10.
4MR2.0 Students use strategies, skills, and concepts in finding
solutions.
11.
4NS1.9
12.
4NS1.9
13.
4NS1.5
14.
4NS1.5
15.
4NS1.9
16.
4NS1.9
17.
4NS1.9
18.
4NS1.9
19.
4MR1.1 Analyze problems by identifying relationships,
distinguishing relevant from irrelevant information,
4MR1.1 sequencing and prioritizing information, and observing
patterns.
20.
Groups for differentiated instruction
Identify on a number line the relative position of positive
fractions, positive mixed numbers, and positive decimals
to two decimal places.
Explain different interpretations of fractions, for example,
parts of a whole, parts of a set, and division of whole
numbers by whole numbers; explain equivalence of
fractions.
Identify on a number line the relative position of positive
fractions, positive mixed numbers, and positive decimals
to two decimal places.
18–44
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73784_U8_CRF_UT.indd 18–44
12/12/07 3:47:16 AM
Chapter Resources
Grade 4, Chapter 18
Contents
Resources for Chapter 18: Compare and Order Fractions
• Lesson Quizzes Lessons 18.1–18.4
Daily Routines
Reteach
Practice
Enrichment
Leveled Problem Solving
Homework
• Chapter 18 Test
Individual and Class Record Sheets
• Unit 8 Test
Individual and Class Record Sheets
B
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Booklet 18 of 29
TTL_73744_U8_C18.indd 18–1
18–1
2/1/08 3:17:59 PM
Name
Date
Chapter 18, Lesson 1
Lesson Quiz
Lesson 1 Quiz
Compare. Write >, <, or = for each
number lines to help you.
1.
2.
3.
4.
5.
. Use fraction tiles or
_1 _1
5
3
_4 _5
6
6
_1 _6
2
8
3
_ _1
12
4
7
_
_2
12 4
Lesson Quiz
Use with Chapter 18, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Date
Chapter 18, Lesson 2
Lesson Quiz
Lesson 2 Quiz
Compare. Write >, <, or = for each
1.
2.
3.
.
_3 _4
5
6
4
_
_2
10 5
6
_5 _
8
10
Order the fractions from least to greatest.
4.
5.
_1 _5 _3
3 6 5
_3 _5 _1
4 8 2
Lesson Quiz
18–3
Use with Chapter 18, Lesson 2
Copyright © Houghton Mifflin Company. All rights reserved.
CAPEG4_C18_LessonQuiz.indd 18–3
12/3/07 2:20:41 PM
Name
Chapter 18, Lesson 3
Lesson Quiz
Date
Lesson 3 Quiz
Write each improper fraction as a mixed number. Write each mixed
number as an improper fraction.
1.
2.
3.
4.
5.
12
_
10
3
2_
4
14
_
3
2
3_
5
_9
2
Lesson Quiz
Use with Chapter 18, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
Name
Chapter 18, Lesson 4
Lesson Quiz
Date
Lesson 4 Quiz
Order the numbers from least to greatest. Use number lines to help
you.
1.
2.
3.
1 2 7
2_ 2_ 1_
5 4 8
9
5 2
1_ 1_ 1_
10 6 3
3 11 1
1 _ _ 1_
5 12 8
Lesson Quiz
18–4
Use with Chapter 18, Lesson 4
Copyright © Houghton Mifflin Company. All rights reserved.
CAPEG4_C18_LessonQuiz.indd 18–4
12/3/07 2:20:49 PM
Name
Chapter 18, Lesson 1
Daily Routines
Date
Hands On: Compare Fractions
Problem of the Day
KEY NS 3.2
How many grams are 6 kilograms?
Number Sense Review
KEY NS 1.8
Use Workmat 4 to plot these numbers on the number line.
–3, 4, 10, –9, 0
Word of the Day
MR 2.3
compare
Think of everyday occurrences when you might compare things.
Facts Practice
KEY NS 1.8
Compare using >, <, or =.
1.
–17 ____ –3
2.
15 ____ –20
3.
0 ____ –6
4.
–2 ____ –5
5.
–20 ____ 41
6.
31 ____ –10
Daily Routines
18–5
Use with Chapter 18, Lesson 1
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–5
1/31/08 11:45:45 AM
Name
Chapter 18, Lesson 1
Reteach
Date
Hands On: Compare Fractions
CA Standard
NS 1.9
3
2
Compare _
and _
.
5
3
3
Show _ using
5
2
Step 2 Show _
using
3
fraction strips.
Step 1
fraction strips.
1
5
1
5
1
5
1
5
1
3
1
5
1
3
Step 3 Compare the
two sets of fraction strips.
Which is longer?
1
3
3
2
<_
Solution: _
5
3
Compare. Write >, <, or = for each .
1.
_3 _1
2.
_1 _2
3.
5
_
_3
4.
_3 _1
5.
6
_3 _
6.
11
_5 _
7.
_3 _4
8.
_2 _3
11.
_1 _2
12.
9.
4
8
>
=
8
16
_1 _1
5
>
6
10.
3
7
>
<
9
14
_4 _5
8
<
8
10
<
5
3
<
=
5
5
6
8
>
7
<
8
6
5
_
_2
25
<
5
Writing Math In problem 12, Ronnie changed __25 to __15 and
changed the answer to >. Is he correct? Explain.
5
1 are equal.
No, he is wrong because __
and _
5
25
Reteach
18–6
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_RET.indd 18–6
12/1/07 12:20:17 PM
Name
Chapter 18, Lesson 1
Practice
Date
Hands On: Compare Fractions
Compare. Write >, <, or = for each . Use fraction tiles or
number lines to help you.
1.
6
5
_
_
10
1
10
1
10
4.
8.
2.
10
1
10
1
10
1
10
1
10
1
10
1
10
>
1 1
10 10
1
10
_8 _7
9.
9
=
>8
1
4
1
8
3
_1 _
6
<
1
8
=
1
8
1
8
10.
12
3
1
9
1
8
6.
12
_1 _4
1
4
=
6
_2 _
4
3.
8
1
8
5.
6
4
1
4
6
_
_3
12
_3 _6
4
_
_3
12
<
6
_3 _4
4
<5
9
1
3
1
9
1
9
1
9
<
7.
11.
3
_1 _
5
=
15
_8 _6
9
>9
Test Practice
Circle the letter of the correct answer.
12.
7
11
Andy drew a line that was _
of an inch long. Ally drew a line that was _
of an inch
8
36
3
long. Akim drew a line that was _ of an inch long. Which person’s line, if any, was
4
longest?
13.
A
Andy’s line
C
Ally’s line
B
Akim’s line
D
They were all equal.
Fred split a square into 4 equal smaller squares and shaded 2 of the squares. Frank
split a square into 8 equal rectangles and shaded 6 of the rectangles. Francine split a
square into 6 equal rectangles and shaded 3 of the rectangles. Which person, if any,
shaded in a larger fraction of his or her square?
A
Fred
C
Francine
B
Frank
D
They were all equal.
Writing Math Maggie changed all the denominators in problem 12 to 36, but left
the numerators the same. She said that Ally’s line was now the longest. Is she right? Explain.
3
11
7
Yes, because _
of an inch is longer than either _
or _
36
36
36
of an inch.
Practice
18–7
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_PRAC.indd 18–7
12/12/07 2:54:54 AM
Name
Chapter 18, Lesson 1
Enrichment
Date
Hands On: Compare Fractions
CA Standard
NS 1.9
Compare. Write >, <, or = for each . Use fraction tiles or number
lines to help you. Then match the number and sign to the letter and
fill in the blanks to complete the answer to the riddle.
Riddle: What did the large fraction say to the small fraction?
<
- N
>
- O
=
- T
4
1. __
>
3
__
8
1
2. __
6
4. __
>
4
__
7
5
5. ___
9
7. ___
>
2
__
6
8
7
12
Answer: “I C [
2
10
O] U [ N ] [ T ]
1
2
3
M[
<
3
__
4
=
1
__
2
2
3. __
6
=
2
__
6
3
6. __
<
2
__
3
6
O] R E [ T ] H A [ N ]
4
5
O ] U.”
Y[
6
7
Writing Math Patrick says that __26 was greater than __13 . Is he
right? Why or why not?
Possible answer: He is wrong; if you show both
fractions on a number line, they are at the same
point and therefore equal in value.
Enrichment
18–8
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_ENR.indd 18–8
12/1/07 12:22:02 PM
Chapter 18, Lesson 1
Name
Leveled Problem Solving
Date
Hands On: Compare Fractions
CA Standard
NS 1.9
Solve each problem. Use fraction tiles or number lines to
help you if needed.
1.
4
One snail moved ___
of a foot before
12
6
stopping. A second snail moved ___
of
12
a foot before it took a rest. Which snail
moved the farthest?
2.
the male goat
the second snail
3.
1
Jerry swam __
of a mile across the lake
3
and rested on a raft. Then he swam
2
another __
of a mile to the opposite
6
shore. Did he swim more, less, or the
same distance before he rested than
after he rested?
4.
1
Three friends shared a pizza. Paul ate __
8
2
of the pizza. Abe ate __
and
Carrie
ate
4
3
__
.
Who
ate
the
most?
Who ate the
8
least?
II
Wendy
6.
Three friends drove to a national park
to go hiking. They decided to share
3
of the way.
the driving. Moritz drove __
5
3
___
Pablo drove 10 of the way and Reggie
2
of the way. Who drove the
drove ___
20
greatest distance? Who drove the
least distance?
Level III
Moritz; Reggie
Abe; Paul
Leveled Problem Solving
1
Tomas ran __
of a mile around the track.
2
3
of a mile around the
Wendy ran __
4
track. Who ran the farthest?Level
He swam the same
distance before and
after.
5.
3
The male mountain goat climbed __
of a
4
mile up the rocky cliff side. The female
1
goat climbed __
of a mile. Who climbed
4
the highest?
Level I
18–9
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_PS.indd 18–9
12/1/07 1:56:04 PM
Name
Chapter 18, Lesson 1
Homework
Date
Hands On: Compare Fractions
_6_
8
CA Standard
NS 1.9
_24_
You can use a model.
1
8
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
4
Solution: _68_ > _24_
Compare. Write >, <, or = for each
lines to help you.
5
1. ___
10
=
4
5. __
5
2
__
4
2
2. __
3
2
__
5
3
6. __
6
>
. Use fraction tiles or number
7
__
9
1
3. __
4
__
8
3
7. __
4
<
9
=
4QJSBM3FWJFX
3
__
4
3
4. __
3
___
10
3
8. __
8
<
7
>
6
___
16
=
<
5
__
7
(Chapter 13, Lessons 2, 4) KEY NS 3.0, KEY NS 3.4
Divide. Use multiplication to check.
9.
11.
420 ÷ 4
105
10.
622 ÷ 2
311
A restaurant served 410 people on Saturday and Sunday. If the
same number of people ate there each day, how many were
served on Saturday? 205
Homework
18–10
Use with text pages 392–393.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L1_HMWK.indd 18–10
12/12/07 2:56:00 AM
Name
Chapter 18, Lesson 2
Daily Routines
Date
Compare and Order Fractions
Problem of the Day
KEY NS 1.9
Sophie has eaten _12 of her pizza. Model this fraction on a number line.
0
1
4
1
2
3
4
1
Number Sense Review
KEY NS 3.0
Find the other multiplication fact and two division facts that make
up the fact family.
1.
6 × 7 = 42
2.
3 × 4 = 12
3.
7 × 8 = 56
Word of the Day
KEY NS 4.2
prime
Give five examples of prime numbers.
Facts Practice
KEY NS 3.2
Multiply or divide.
1.
121 ÷ 11
2.
11 × 11
3.
10 × 10
4.
100 ÷ 10
5.
16 ÷ 4
6.
4×4
Daily Routines
18–11
Use with Chapter 18, Lesson 2
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–11
12/1/07 12:16:36 PM
Name
Chapter 18, Lesson 2
Reteach
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
3 _
Compare _
, 2 , and _1_. Order the fractions from greatest to least.
2
5 3
Step 1 Find equivalent fractions with
a common denominator.
×6
3
5
=
Step 2 Compare the numerators.
20 > 18 > 15
× 15
18
30
×6
2
3
× 10
=
1
2
20
30
20
18
15
__
> __
> __
30
30
30
15
30
=
_2_ > _3_ > _1_
5
3
2
× 15
Solution: The order of the fractions from
2 _
, 3 , _12_.
greatest to least is _
× 10
3 5
Compare. Write >, <, or = for each
3
1. __
4
> __18
1
2. __
3
.
> __29
5
3. ___
10
< __35
3
4. __
8
> __26
Order each group of fractions from greatest to least. Draw number
lines to help if you wish.
3
5. __
5
1 __
, __
, 1
5 6
3 _
1, _
1
_
,
5 5 6
4
9. ___
10
1 ___
, __
, 3
5 10
3 _
4 , __
__
,1
10 10 5
4
6. __,
8
1 __
__
, 5
4 8
1
7. __
3
5 _
1
_
, 4, _
8 8 4
5
10. __
6
2 ___
, __
, 11
6 12
3 __
, __
, 1
6 6
3
8. ___
21
3 _
1
_
, 1, _
6 3 6
12
11. ___
25
5
2
, ___
, __
25 5
3 __
2 , __
2
_
,
7 21 21
5
12. __
5
2 , __
12 , _
__
25 5 25
5, _
2
11 , _
__
12 6 6
2
2
, ___
, __
21 7
9
6 ___
, __
, 1
9 18
1
6 _
_
, 5 , __
9 9 18
Writing Math Is the problem in the example harder or easier
to solve than problems 5 to 12? Explain.
Possible answer: It is harder because the 3
denominators are different and finding a common
denominator involves 3 numbers instead of 2.
Reteach
18–12
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_RET.indd 18–12
12/1/07 2:02:18 PM
Name
Chapter 18, Lesson 2
Practice
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
Compare. Write >, <, or = for each .
1.
4.
8.
6
3
_
_
10
>
6
_
_2
5.
_8 _5
9.
12
9
=
>
4
6
_3 _6
2.
10
4
=
_1 _3
6
<
6.
9
6
_3 _
6
=
3.
8
10.
12
_1 _6
3
9
<
1
_
_3
12
<
7.
6
_4 _5
4
>
11.
6
3
_1 _
5
=
15
_8 _9
9
<
9
Order the fractions from least to greatest. Use number lines to help you.
12.
_1 _3 _2
4
4
4
13.
_1 ; _2 ; _3
4 4 4
_2 _6 _4
7
7
14.
7
_2 ; _4 ; _6
7 7 7
_7 _3 _5
9
9
15.
9
_3 ; _5 ; _7
9 9 9
_5 _3 _1
8
8
4
_1 ; _3 ; _5
4 8 8
Test Practice
Circle the letter of the correct answer.
16.
Which set of fractions is ordered from
greatest to least?
A
_2 , _1 , _3
C
_2 , _3 , _4
B
_3 , _3 , _3
D
_1 , _1 , _1
3 2 5
4 5 6
17.
2
Ted drew a line that was _
of an inch
6
11
long. Toni drew a line that was _
of
36
an inch long. Tara drew a line that
5 5 5
1
was _
of an inch long. Which person’s
6
line, if any, was longer?
3 5 4
A
B
Tara’s line
Ted’s line
C
D
Toni’s line
They were all equal.
Writing Math In problem 16 above, which was the
easiest set of fractions to order? Which was the hardest? Explain.
C was easiest because the denominators
were the same; B was hardest because all
denominators were different—the fractions had
to be renamed using the common denominator.
Practice
18–13
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_PRAC.indd 18–13
12/12/07 3:34:00 AM
Name
Chapter 18, Lesson 2
Enrichment
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
The table below shows four major minority groups in the state of
California and what fraction they make up of the total population.
Use the data to solve each problem.
Minorities of California
Minority
Fraction of Population
9
__
25
1
___
100
3
__
50
6
__
50
Latin Americans
Native Americans
African Americans
Asian Americans
1.
Are there more Native Americans or
African Americans in California?
2.
What minority group is double the
number of African Americans?
4.
African Americans
3.
Are there more Latin Americans than
Asian Americans?
yes
Asian Americans
One fourth of the total state population
is Mexican American. Which minority
group is larger, Mexican Americans or
Latin Americans?
Latin Americans
5.
If all the minorities in the table were added together, what
part or fraction of the total population would they be?
55
___
or just over half
100
Writing Math For problem 5, Holly tried to make 50 the
common denominator before adding the fractions. Was this a good
decision? Why or why not?
1
No, because ___
100 , the smallest fraction, cannot
be easily renamed as 50ths. She should have
renamed the fractions as 100ths instead.
Enrichment
18–14
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_ENR.indd 18–14
12/12/07 3:36:31 AM
Chapter 18, Lesson 2
Name
Leveled Problem Solving
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
Solve each problem.
1.
Edie, George, and Art dug holes to
2
plant seedlings. Edie dug __
feet.
4
3
__
George’s hole was 4 feet deep and
1
Art’s was __
feet deep. Order the
4
fractions from least to greatest.
2.
3
1, _
2, _
_
4 4 4
3.
The weather was very hot and the
students watered their seedlings daily.
1
Art poured __
gallon of water on his
2
3
seedling. Edie poured ___
of a gallon
10
on hers. George watered his seedling
6
with ___
of a gallon. Order the fractions
10
from greatest to least.
4.
3
Hank’s vegetable garden covers __
6
1
of
an
of an acre. Polly’s garden is __
3
5
of
an
acre.
acre and Estella’s is __
6
Whose garden is the largest?
Whose is the smallest?
Level
II
Estella’s; Polly’s
Estella has divided her garden into
three sections. The section where she
2
grows tomatoes takes up __
of the
6
1
__
garden. She plants 4 of the garden with
5
beans. Corn is in the remaining ___
.
12
Order the vegetables by the space they
use from greatest to least.
6.
2
Hank’s biggest tomato weighs __
of
5
a pound. Estella’s largest tomato
7
weighs ___
of a pound, while Polly’s
20
3
largest weighs in at ___
pound. Order
10
the tomatoes by owner from least to
greatest weight.
Level III
Polly, Estella, Hank
corn, tomatoes,
beans
Leveled Problem Solving
I
George; Art
6 _
3
__
, 1 , __
10 2 10
5.
3
Edie’s seedling was __
feet in
5
2
length. Art’s was __
feet long and
5
4
__
George’s was 5 feet tall. Who planted
the tallest seedling? The shortest
seedling?
Level
18–15
Use with text pages 394–397.
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73744_C18L2_PS.indd 18–15
12/1/07 2:04:33 PM
Name
Chapter 18, Lesson 2
Homework
Date
Compare and Order Fractions
CA Standards
NS 1.9, NS 1.5
Compare _6_ and _2_.
8
_6_
8
4
_24_.
Way 1 You can use a model.
1
8
1
8
1
8
1
4
1
8
1
8
Way 2 You can use equivalent fractions.
(2 × 2)
_2_ = _____
= _48_
4
(4 × 2)
_6_ is greater than
8
Solution: _68_ > _24_
1
8
1
4
_6_ > _2_
8
4
Compare. Write >, <, or = for each
5
1. ___
2
__
4
10
2
2. __
=
5
5. __
5
7
__
9
3
.
1
3. __
3
6. __
>
8
9
=
=
3
___
10
3
7. __
6
___
16
3
4. __
<
4
__
8
6
4
__
8
4
<
4
__
5
_4_, so
8
7
8. __
4
__
4
7
>
=
Order the fractions from least to greatest. Use number lines to help you.
1 4 3
9. __, __, __
3 5 4
10. __, __, __
5 5 5
3 _
1, _
4
_
,
5 5 5
4QJSBM3FWJFX
6 6 6
5 2 7
11. __, __, __
4 7 9
12. __, ___, ___
9 3 9
3 _
5
_
, 4, _
6 6 6
5 _
7
_
, 2, _
9 3 9
8 16 16
9
4 , __
7,_
__
16 8 16
(Chapter 13, Lessons 2, 3, 4) KEY NS 3.0, KEY NS 3.2, KEY NS 3.4
Divide. Use multiplication to check.
13.
15.
486 ÷ 3
162
14.
864 ÷ 2
432
Five trucks carried 250 tons of coal. If the trucks each carried the
same load, how many tons of coal did each have? 50
Homework
18–16
Use with text pages 394–397.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L2_HMWK.indd 18–16
12/12/07 3:39:36 AM
Name
Chapter 18, Lesson 3
Daily Routines
Date
Write Mixed Numbers and Improper Fractions
Problem of the Day
KEY NS 1.9
5
Tenecia ate _38 of a box of raisins and her cousin Beau ate __
of a box
16
of raisins. Who ate more raisins?
Number Sense Review
KEY NS 1.8
Use Workmat 4 to order the numbers –2, 1, –6, –3, and 5 and list
them from least to greatest.
Number of the Day
KEY NS 4.2
6
The number 6 is called a perfect number because the sum of its
factors (other than itself) is the number. Can you find another perfect
number under 30?
Facts Practice
KEY AF 2.0
Solve each equation.
1.
4r = 16
2.
56 = 8p
b
3. _
3
= 12
4.
w
9 = __
6
5.
11t = 55
s
6. _
4
= 15
Daily Routines
18–17
Use with Chapter 18, Lesson 3
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–17
1/31/08 11:46:22 AM
Name
Chapter 18, Lesson 3
Reteach
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
13
Write __
as a mixed number.
4
Way 1
You can draw a picture.
Way 2 You can divide the numerator by
the denominator.
Remember: The fraction bar stands for
13
means 13 divided by 4.
“divide by,” so __
4
4
4
+
4
4
4
4
+
+
1
4
3
= 3 14
-12
1
13
The picture shows that __
= 3 _14_.
4
number of wholes
13
4
number of parts
13
So, __
= 3 _14_.
4
Solution: 3 _14_.
Write an improper fraction for the shaded parts. Then write each as
a mixed number or a whole number.
1.
2.
10 _
__
; 31
3
3
4.
3.
29 _
__
; 45
6
6
5.
3
11
__; 2_
4
4
2
17 ; 3_
__
5
5
6.
16
__
;4
4
14 ; 4_
2
__
3
3
Writing Math Suppose one less part in problem 5 was
shaded. Would the answer be a whole number or a mixed number?
Explain.
A mixed number because it would now
15
3
or 3 _
.
be __
4
4
Reteach
18–18
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_RET.indd 18–18
12/12/07 3:40:39 AM
Name
Chapter 18, Lesson 3
Practice
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
Write an improper fraction and a mixed number or whole
number to describe the shaded parts.
1.
2.
8
2
_
; 2_
3
3.
9
4
_
; 1_
5
3
6
14
_
; 1_
5
8
8
Write a mixed number and an improper fraction for each letter.
A
B
1
4.
E
5.
2 _
3_
; 11
3
3
C
2
D E
3
B
6.
6
2; _
F
4
D
7.
A
8.
1 _
1 _
3_
; 10 1 _
;4
3
3
3
3
3
C
9.
2 _
2_
;8
3
3
F
12
4; _
3
Test Practice
Circle the letter of the correct answer.
10.
Which improper fraction is equivalent
11.
3
to 3 _ ?
8
A
27
_
B
27
_
3
8
C
28
_
D
33
_
8
8
Julie brought 3 pies to Thanksgiving
dinner. Each pie was cut into 8 pieces.
Each person ate 2 pieces, and there
were no pieces left over. How many
people were at the dinner?
A
10 people
C
12 people
B
14 people
D
16 people
Writing Math If one more section in problem 1 was shaded,
would the answer be a mixed number or a whole number? Explain.
9
A whole number, because _
is the same as 3.
3
Practice
18–19
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_PRAC.indd 18–19
12/12/07 3:42:10 AM
Name
Chapter 18, Lesson 3
Enrichment
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
To change an improper fraction to a mixed number, you divide. To
change a mixed number to an improper fraction, you multiply. Each
table below shows the division and the resulting improper fraction
and mixed number. Complete each table.
Division
Improper
Fraction
Mixed
Number
Division
Improper
Fraction
Mixed
Number
16 ÷ 3
16
__
3
1
5_
5.
28 ÷ 7
28
__
7
4
2.
19 ÷ 2
19
__
2
9 _12_
6.
24
24 ÷ 5 __
5
4 _45_
3.
11 ÷ 9
11
__
9
2
1_
7.
10 ÷ 2
10
__
2
5
15 ÷ 8
15
__
8
1_78_
8.
15 ÷ 6
15
__
6
3
2_
Division
Improper
Fraction
Mixed
Number
Division
Improper
Fraction
Mixed
Number
18
__
5
20
__
3
3
3_
5
12.
23 ÷ 6
23
__
6
5
3_
6 _23_
13.
31 ÷ 6
2
2_
5
14.
15 ÷ 3
1.
4.
18 ÷ 5
9.
10.
20 ÷ 3
11.
12 ÷ 5
12
__
5
3
9
31
__
6
15
__
3
6
6
5 _16_
5
Writing Math If you were to add a fourth column to problem
1 with the heading Multiplication, what would you put in that column?
(5 × 3) + 1
Enrichment
18–20
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_ENR.indd 18–20
12/1/07 2:06:19 PM
Chapter 18, Lesson 3
Name
Leveled Problem Solving
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
Solve each problem.
1.
Jerry bought 2 pies. He cut each pie
into 6 slices. Over a week, he ate all
of one pie and 2 slices of the second.
How much of the total number of slices
did he eat? Write your answer as an
improper fraction.
2.
5
1 boxes
or 1_
1__
8
_
slices
6
3.
10
Allie had 11 guests at her birthday
party. She served 2 birthday cakes.
If she and her guests each ate 2 slices
of cake, how many slices did she need
to cut each cake into?
4.
Kayla bought a bag of grapefruit.
Each morning for 5 days she and her
father each ate one half of a grapefruit.
Her mother ate 3 halves total in that
time. How much grapefruit did they
eat altogether? Write your answer as
an improper fraction and as a mixed
number.
6.
13 _
__
; 6 1 grapefruit
2
2
Leveled Problem Solving
2
Howie colored pictures of pinwheels.
Each pinwheel had 5 sections. If Howie
colored 13 sections, what was the least
number of pinwheels in the coloring
book? Write the sections colored as an
improper fraction.
Level II
13
3 pinwheels; __
5
12 slices
5.
Ms. Rodriguez had 2 boxes of chalk at
the start of the school year. Each box
contained 10 pieces of chalk. By the
end of the school year, she had used
all of the chalk in one box and half
of the other. How much of the chalk
did she use? Write your answer as a
mixed number.
Level I
In the school walkathon, Bev walked
1
2
2__
miles, Dennis walked 3___
miles, and
5
10
3
miles. What was the
Natalie walked 2__
5
total distance they walked? Write your
answer as a whole number and as an
improper fraction.
Level III
80
8 miles, __
of a mile
10
18–21
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_PS.indd 18–21
12/1/07 2:06:39 PM
Name
Chapter 18, Lesson 3
Homework
Date
Write Mixed Numbers and
Improper Fractions
CA Standards
NS 1.9, NS 1.7
Write an improper fraction and a mixed number to describe the shaded part.
Step 1 There are 3 whole squares and _25_
of the fourth square is shaded.
17
Step 2 _55_ + _55_ + _55_ + _25_ = __
5
Step 3 1 + 1 + 1 + _25_ = 3 _25_
17
Solution: 3 _25_ and __
5
Write an improper fraction and a mixed number or whole number
to describe the shaded parts.
1.
2.
9 _
1
_
;
4
2 2
10 _
__
; 3 13
3
4QJSBM3FWJFX
3.
6 _
1
_
;
1
5 5
(Chapter 15, Lesson 4) KEY NS 3.2
Find the missing number.
20
3
4.
200 mm =
5.
3,000 m =
6.
A building is 6 meters high. What is its height in centimeters?
cm
km
Homework
18–22
600 cm
Use with text pages 398–399.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L3_HMWK.indd 18–22
12/1/07 2:06:57 PM
Name
Chapter 18, Lesson 4
Daily Routines
Date
Compare and Order Fractions and
Mixed Numbers
Problem of the Day
KEY NS 1.2
Natasha, Elena and Madison are running a race. After 20 minutes,
Madison has run 0.9 miles, Natasha has run 2.1 miles, and Elena has
run 1.8 miles. Order the runners from fastest to slowest.
Number Sense Review
KEY NS 3.2
Tell how many meters.
1.
3 kilometers
2.
400 decimeters
3.
200 centimeters
Number of the Day
NS 1.5
1
_
4
How many fourths make up one whole?
Facts Practice
KEY NS 3.0
Estimate to find the products or quotients.
1.
83 × 4
2.
690 × 21
3.
520 × 33
4.
82 ÷ 9
5.
50 ÷ 7
6.
145 ÷ 12
Daily Routines
18–23
Use with Chapter 18, Lesson 4
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–23
12/1/07 12:19:31 PM
Name
Chapter 18, Lesson 4
Reteach
Date
Compare and Order Fractions
and Mixed Numbers
CA Standards
NS 1.9, NS 1.5
Compare and order 1_13_, 1_36_, _76_.
Way 1 Use number lines and compare.
Change the mixed numbers to improper
fractions. Then write the fractions using
the same denominator.
11
3
0
1
2
13
6
0
1
1_13_ = _43_ = _86_
2
11
6
0
1
Way 2 Use equivalent fractions.
1_36_ = _96_
_7_
6
Compare the improper fractions.
_7_ < _8_ < _9_
6
6
6
2
_7_ is farthest to the left.
6
1_36_ is farthest to the right.
1_13_ is in the middle.
So, _76_ < 1_13_ < 1_36_.
Solution: _76_ < 1_13_ < 1_36_
Order the numbers from greatest to least. Use number lines to help
you if needed.
1.
3 ___
5
2__
, 18 , 2__
7 7
7
5 __
18 _
3
2_
,
,
2
7 7
7
3.
10 ___
4
7___
, 7___
, 65
10 20 10
5.
3 ___
46
9 __
, 9 8 , ___
5 10 5
2.
10 __
65
7__
, 7 4 , __
20 10 10
8
3 __
46
9 __
, 9_
,
10 5 5
4.
5
2 ___
4__
, 39 , 4__
3 9
9
9
1 ___
1__
, 12 , __
6 12 6
39
2 _
4_
, 4 5 , __
3
9 9
9 _
12
_
, 1 1 , __
6 6 12
43
50
50
Lynn was comparing ___
to ___
and decided ___
was greater
6
12
12
because 50 is greater than 43. Is her reasoning correct? Explain.
No, she is incorrect. Since the denominators
are different, you cannot just compare the
43
50
1 , while __
1.
= 7_
is only 4_
numerators. __
6
Reteach
6
12
18–24
6
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_RET.indd 18–24
12/12/07 3:44:01 AM
Name
Chapter 18, Lesson 4
Practice
Date
Compare and Order Fractions and
Mixed Numbers
CA Standards
NS 1.9, NS 1.5
Compare. Write >, <, or = for each .
1.
2_
5
4
2_
10
3.
1_
1 _78
3
3
4
>
<
=
2.
2
1_
_43
4.
3_
13
_
3
6
3
9
<
Order the numbers from least to greatest. Use number lines to help you.
5.
5
2_
7.
7
_
1_ 1_
1
5
10
10
8
4
1_
8
8
3
2
2_
4
5
4
2
1_
, 2_
, 2_
6.
1
6_
61
_
6_
6 _
1
, 6_
, 61
6_
3
8
7
1_
, 1_
, 1_
8.
32
_
2
1
5_
5_
1 _
2
, 32 , 5 _
5_
8
4
5
8
10
10
3
6
9
3
6
9
6
3
9
6
6
9
3
Test Practice
Circle the letter of the correct answer.
9.
Which number is the greatest?
1_
3
15
11
_
B
5
A
C
10.
4
1_
5
Which number is the least?
2_
3
4
10
_
B
4
A
_1
D 1
3
C
4
2_
16
_4
D 2
8
Writing Math Jon was ordering fractions in which the
denominators were 2, 3, and 4. He said he couldn’t do it because
there was no common denominator for these three numbers.
Is he correct? Explain.
He is incorrect. A common denominator for 2,
3, and 4 is 12.
Practice
18–25
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_PRAC.indd 18–25
12/1/07 2:07:49 PM
Name
Date
Compare and Order Fractions
and Mixed Numbers
Chapter 18, Lesson 4
Enrichment
CA Standards
NS 1.9, NS 1.5
The liter is a basic measurement of volume in the metric system. Many liquid
products now come in liter bottles in the United States. The table below shows U.S.
measurements that are about equal to a liter. Use the data to answer questions 1–3.
Volume Measurements
Metric
1.
U.S.
1 liter
1
2 __
pints
10
1 liter
6
1 ___
quarts
100
1 liter
26
___
gallons
100
The athlete drank 3 liters of water on a hot day. How many pints
would that be as a mixed number and fraction?
3 __
6 __
; 63
10 10
2.
About how many liters would make 1 gallon of liquid?
about 4 liters
3.
What would 4 liters be in quarts? Write as a mixed number and a fraction.
24 ___
; 424
4 ___
100 100
4.
If 5 milliliters make 1 teaspoon, what fraction expresses how
much of a teaspoon 1 milliliter is?
1
_
5
5.
If a tablespoon is 3 times the volume of a teaspoon, how many
milliliters will fill a tablespoon?
15 milliliters
Writing Math What operations did you use to find the
answers to problems 4 and 5?
Possible answer: In problem 4, I used division
1
; in problem 5, I used
to get the fraction _
5
multiplication to get the whole number 15.
Enrichment
18–26
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_ENR.indd 18–26
12/12/07 3:44:46 AM
Chapter 18, Lesson 4
Name
Leveled Problem Solving
Date
Compare and Order Fractions
and Mixed Numbers
CA Standards
NS 1.9, NS 1.5
Solve each problem.
1.
1
Jamie slept for 7__
hours one night.
4
2.
3
Maria slept for 7__
hours the same
8
night. Who slept longer?
Maria
3.
before
Mr. Kosinski watched TV before he
3
went to bed. He watched TV for 1__
5
hours before dozing off. He woke up
4
1___
hours later and watched TV for
10
4
another 1___
hours. Order these three
20
periods of time from shortest
to longest.
4.
5.
Heidi; Stan
10
1
Steve jogged 2__
miles on Monday,
2
6.
6
4
miles on Wednesday, and 2___
miles
2__
5
10
on Friday. Order his runs from shortest
to longest using improper fractions.
5 __
14
_
, 26 , __
2 10 5
Leveled Problem Solving
2
Stan did his homework in 2__
hours.
3
1
hours to do the same
It took Heidi 2__
4
assignment. Felicia finished the same
5
homework in 2___
hours. Who finished
12
their homework in the shortest time?
Who took the longest?
Level II
3
4 , 1__
4 , 1_
1__
5
20
1
Ralph slept for 3__
hours one night and
3
then woke after a dream. He went back
3
to sleep and slept another 3___
hours.
12
Did he sleep longer before or after his
dream?
Level I
2
Nancy lives 4__
miles from her
3
19
school. Dave lives ___
miles from school.
4
2
Raoul’s house is 4__
miles from school.
4
Order the three distances from closest
to farthest from school.
19
2 , 4_
2 , __
4_
4 3 4
18–27
Level III
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_PS.indd 18–27
12/1/07 2:09:50 PM
Name
Chapter 18, Lesson 4
Homework
Date
Compare and Order Fractions
and Mixed Numbers
CA Standards
NS 1.9, NS 1.5
1_3_ 1_45_
4
Way 1 Put each number on a number line.
0
1
1 34
2
0
1
4
5
2
Way 2 Change to equivalent fractions.
35
1_34_ = _74_ = __
20
36
1_45_ = _95_ = __
20
36
35
__
is less than __
.
20
20
Solution: 1_34_ < 1_45_
Compare. Write >, <, or = for each
1.
2
4
3 __
3 ___
5 10
2.
3
1
2 __
2 __
7 5
3.
3
5
__
1__
84
=
>
.
>
<
6
1__
3 9
1
4. __
4QJSBM3FWJFX
(Chapter 17, Lesson 2) NS 1.5
Find the fractional part of each number.
1
5. __
of 9
1
6. __
of 10
3
2
7.
3
5
Colin has 36 bananas. One third of them are ripe. How many of
the bananas are ripe?
Homework
12
18–28
Use with text pages 400–402.
Copyright © Houghton Mifflin Company. All rights reserved.
73744_C18L4_HMWK.indd 18–28
12/1/07 2:10:12 PM
Name
Chapter 18, Lesson 5
Daily Routines
Date
Problem Solving: Field Trip
Problem of the Day
KEY NS 1.9
On Monday, Patrick ran 3_34 miles. On Wednesday he ran 2_78 miles, and
15
miles. On which day did Patrick run the farthest?
on Friday he ran 3__
16
Number Sense Review
KEY NS 3.0
Write an example of the Commutative Property of Multiplication.
Word of the Day
MR 2.3
function rule
Can you find a function rule if you only know one input and one
output value?
Facts Practice
KEY NS 3.2
Find the missing number.
1.
500 cm = ____ m
2.
____ mm = 7 m
3.
30 dm = ____ cm
4.
4 km = ____ m
5.
____ cm = 9,000 mm
6.
____ km = 100,000 cm
Daily Routines
18–29
Use with Chapter 18, Lesson 5
Copyright © Houghton Mifflin Company. All rights reserved.
C18_G4CAMath_Daily Rout_T.indd 18–29
1/31/08 11:47:00 AM
Name
Chapter 18 Test
Date
Chapter 18 Test
4NS1.9
Circle the letter of the correct answer.
1
3
4NS1.9
4
_
Pedro finished of his homework
6
2
before dinner and _ of his
1
8
6
homework after dinner. Which
statement below is true?
A
B
C
D
Pedro finished equal amounts of his
homework before and after dinner.
1
A __
Pedro finished most of his
homework before dinner.
B
C
Pedro finished most of his
homework after dinner.
D
4NS1.9
3
Which fraction is larger than _?
Which statement below is true?
5
A __
4
B
C
D
2
1
__
6
1
__
3
1
__
4
Pedro finished exactly half of his
homework before dinner.
4NS1.9
A
1
8
Which fraction is smaller than the
fraction in the model above?
4
2
Look at the fraction strip below.
9
___
12
1
__
3
9
___
24
7
__
8
Assessment Resources 4
B
C
D
2
= __
6 3
1
1 __
__
<
2 3
3 __
4
__
>
4 6
2
2 __
__
<
3 4
18–31
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73784_C18_U8_CT.indd 18–31
12/1/07 2:11:34 PM
Name
Chapter 18 Test
Date
4NS1.5
5
Use the number line below.
1
4
0
2
4
3
4
4NS1.5
7
Use the number line below.
0
1
1
8
2
8
3
8
4
8
5
8
6
8
7
8
1
Which fraction is greater than _?
2
2
1
__
__
A
C
8
8
6
3
B __
D __
8
8
1
0
1
6
2
6
3
6
4
6
5
6
1
Which fraction is smaller than _?
6
1
A __
4
3
B __
4
2
C __
4
3
D __
6
2
4NS1.5
8
4NS1.5
6
Use the number lines below to
compare the fractions.
1
3
0
0
1
6
2
6
2
3
3
6
4
6
D
5
6
1
9
3
> __
3 6
5 __
2
__
<
6 3
3 __
2
__
>
6 3
1
1 __
__
<
6 3
Assessment Resources 4
A
quarters
C
dimes
B
nickels
D
pennies
4NS1.9
1
A __
C
3
1
Which statement is true?
B
Joyce has a bag of coins. __ of the
12
5
coins are dimes, __ are quarters,
12 __
1
__3 are pennies, and
are nickels.
12
12
What type of coin does the bag
have the most of?
Carlota ordered 4 whole subs for
a party. At the party, 10 quarter
pieces of the subs were eaten. How
many subs were left over?
A
B
C
D
1
1
1__
2
3
1__
4
1
2__
2
18–32
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73784_C18_U8_CT.indd 18–32
12/1/07 2:11:51 PM
Name
Chapter 18 Test
Date
4NS1.9
10
At the end of the day, a restaurant
1
still has 3_ pies that weren’t
4
sold. How can this mixed
number be expressed as an
improper fraction?
4NS1.9
13
A
12
A ___
B
C
D
4
13
___
4
14
___
4
15
___
4
B
C
D
4NS1.9
11
14
C
D
Which is a true statement?
A
B
C
1
A 4__
5
1
3__
4
16
___
5
1
3__
5
D
3
1
1__ > 1__
4
2
5
1
1__ > 1__
4
8
1
1
1__ < 1__
2
4
1
2
1__ > 1__
8
4
4NS1.9
15
Which mixed number is less
11
than __?
3
A
4NS1.9
12
1
8__ miles
2
3
8__ miles
4
4
8__ miles
6
4
8___ miles
12
4NS1.9
One Saturday, Kim watched 3 whole
movies and one-fifth of another
movie. How would she express the
number of movies she watched as a
mixed number?
B
The distance of four bike
3
1
trails are 8_ miles, 8_ miles,
2
4
4
4
miles, and 8_ miles. Which is the
8__
12
6
longest trail?
15
Carlos has painted __ walls in his
B
2
home white. Which choice shows
this fraction expressed as a mixed
number?
1
A 6__
C 7
2
3
1
B 6__
D 7__
4
2
Assessment Resources 4
C
D
3
3__
4
1
3__
4
5
3__
6
1
4__
3
18–33
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C18_U8_CT.indd 18–33
12/1/07 2:12:02 PM
Name
4MR1.1
4NS1.9
16
Van has four pencils that
3
1
measure 4 _ inches, 4 _ inches,
2
4
1
7
4 _ inches, and 4 __ inches long.
3
12
Which is the shortest length?
A
B
C
D
Chapter 18 Test
Date
19
1
4 __ inches
2
7
4 ___ inches
12
1
4 __ inches
3
3
4 __ inches
4
Manuel was on a rafting trip with
his friends. The first day they
2
rafted for 3_ hours, and the second
8
5
day they rafted for 4 _ hours.
8
How many hours did they raft
over the two days?
A
B
C
D
4NS1.9
17
Mrs. Sanchez took her family
hiking for 4 days. They hiked
29
1
3_ miles on Wednesday, __ miles
3
8
3
on Thursday, 2__ miles on Friday,
12
5
and 3__ miles on Saturday.
12
On which day did they hike the
longest distance?
A
B
Wednesday
Thursday
C
D
4MR1.1
20
Friday
Karl was taking a bike ride
along the river. He biked for
8
2__ miles before lunch. Then
12
9
he biked for another 1__ miles
12
after lunch. How many miles did
he bike in all?
A
Saturday
B
4MR1.1
18
Natasha went on a camping trip.
5
She walked for 4 _ hours in the
8
woods to get to the campground.
Her friend Emily said it took her less
time. Which could be the amount
of time it took Emily to walk to the
campground?
11
1
A 4 ___ hours
C 4 __ hours
12
4
6
4
B 4 __ hours
D 4 __ hours
5
8
Assessment Resources 4
7
6__
8
2
7__
8
5
7__
8
7
7__
8
C
D
1
4 ___
12
2
4 ___
12
3
4 ___
12
5
4 ___
12
18–34
Copyright © Houghton Mifflin Company. All rights reserved.
73784_C18_U8_CT.indd 18–34
12/1/07 2:12:13 PM
Name
Date
Chapter Test 18
Individual Student Record Form
Chapter Test 18
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. B
4NS1.9
2. D
4NS1.9
3. B
4NS1.9
4. C
4NS1.9
5. A
4NS1.5
6. D
4NS1.5
7. B
4NS1.5
8. A
4NS1.5
9. B
4NS1.9
10. B
4NS1.9
11. D
4NS1.9
12. D
4NS1.9
13. B
4NS1.9
14. A
4NS1.9
15. B
4NS1.9
16. C
4NS1.9
17. B
4NS1.9
18. C
4MR1.1
19. D
4MR1.1
20. D
4MR1.1
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
Explain different interpretations of fractions, for example, parts of a whole, parts
of a set, and division of whole numbers by whole numbers; explain equivalence of
fractions.
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
Analyze problems by identifying relationships, distinguishing relevant from irrelevant
information, sequencing and prioritizing information, and observing patterns.
out of 20
18–35
Copyright © Houghton Mifflin Company. All rights reserved.
73784_IRF_C18_CT.indd 18–35
12/1/07 2:13:02 PM
Teacher Name
Date
Chapter 18 Test
Class Record Form
Chapter 18 Test
Use the chapter test to identify your students’ mastery
of the California Mathematics Contents Standards in the
Item
chapter. The record below will allow you to group students
for differentiated instruction.
California Mathematics Contents Standards
1.
4NS1.9
2.
4NS1.9
3.
4NS1.9
4.
4NS1.9
5.
4NS1.5
6.
4NS1.5
7.
4NS1.5
8.
4NS1.5
9.
4NS1.9
10.
4NS1.9
11.
4NS1.9
12.
4NS1.9
13.
4NS1.9
14.
4NS1.9
15.
4NS1.9
16.
4NS1.9
17.
4NS1.9
18.
4MR1.1 Analyze problems by identifying relationships,
distinguishing relevant from irrelevant
4MR1.1 information, sequencing and prioritizing
4MR1.1 information, and observing patterns.
19.
20.
Groups for differentiated instruction
dentify on a number line the relative position of
positive fractions, positive mixed numbers, and
positive decimals to two decimal places.
Explain different interpretations of fractions, for
example, parts of a whole, parts of a set, and
division of whole numbers by whole numbers;
explain equivalence of fractions.
Identify on a number line the relative position of
positive fractions, positive mixed numbers, and
positive decimals to two decimal places.
18–36
Copyright © Houghton Mifflin Company. All rights reserved.
73784_U8_C18_CRF_CT.indd 18–36
12/1/07 2:13:22 PM
Name
Unit 8 Test
Date
Unit 8 Test
Circle the letter of the correct answer.
1
Look at the figure below.
3
4NS1.5
8
4
__
- __
=
9
9
2
A __
9
4
B __
9
9
C __
4
4
D __
4
What fraction of the figure is shaded?
1
A __
3
3
B __
8
5
C __
8
3
D ___
10
Jason has to read 24 pages in his
history book by the end of the
3
week. If he has completed __
of the
4
assignment, how many pages has
he read?
In a science lab, Lindsay has a
3
container of liquid that is ___
full.
10
7
Marita’s container is ___
full. What
10
A
12
fraction of a container of liquid will
they have if Lindsay adds her liquid
to Marita’s?
B
15
C
16
10
A ___
D
18
20
4
B ___
10
9
C ___
10
10
D ___
10
Assessment Resources 4
4NS2.0
4NS1.5
4
4NS2.0
2
Subtract.
4NS1.5
5
A book of postage stamps has 20
2
of a book to
stamps. If Juan used __
5
send out invitations to a party, how
many people did he invite?
A
5
B
6
C
8
D
10
18–37
Copyright © Houghton Mifflin Company. All rights reserved.
73784_UT_U8.indd 18–37
1/27/08 10:46:15 AM
Name
4NS1.5
6
Look at the fraction strips below.
1
4
1
8
1
4
1
8
1
8
1
4
1
8
1
8
8
1
8
2
Which fraction is equivalent to __
?
3
4
A ___
1
4
12
9
B ___
16
6
C ___
12
12
D ___
18
1
8
1
Which fraction is equivalent to __
?
4
2
A __
8
3
B __
8
4
C __
8
7
D __
8
9
4NS1.9
8
How can the fraction ___
be
20
expressed in its simplest form?
2
A __
5
4
B __
5
4
C ___
10
4
D ___
20
4NS1.5
7
Unit 8 Test
Date
Look at the fraction strips below.
1
3
1
1
3
3
1 1 1 1 1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12 12 12 12 12
2
?
Which fraction is equivalent to __
3
4MR2.0
10
4
A ___
12
6
B ___
12
8
C ___
12
9
D ___
12
Assessment Resources 4
Luisa had $20 to buy school
supplies. She spent $7 for
notebooks, $4 for a calculator,
and $4 for pens and pencils. What
fraction of her $20 did she have
left?
1
A __
2
1
B __
3
1
C __
4
1
D __
5
18–38
Copyright © Houghton Mifflin Company. All rights reserved.
73784_UT_U8.indd 18–38
1/30/08 3:46:34 PM
Name
Unit 8 Test
Date
Use this illustration to answer questions
Use these number lines to answer
11 and 12.
4NS1.9 questions 13 and 14.
4NS1.5
1
3
1
3
1
4
1
4
1
5
11
1
4
1
5
1
6
1
8
1
3
1
6
1
8
1
5
1
6
1
8
1
8
1
6
1
5
1
6
1
8
1
6
1
8
13
1
8
1
4
3
8
1
2
5
8
3
4
0
1
6
1
3
1
2
2
3
5
6
1
7
8
1
3
3
B __
8
3
C __
6
2
D __
4
1
A __
4
2
B __
9
3
C __
6
2
D __
8
4NS1.5
14
4NS1.9
Which of these fractions is the
smallest?
2
A __
3
2
B __
5
3
__
C
6
3
__
D
8
Assessment Resources 4
Which of these fractions has the
smallest value?
1
A __
Which of these fractions has a
1
value greater than __
?
3
12
1
8
1
4
1
5
1
8
0
Which statement is true?
3
A __
3
> __
8
6
5
2
B __ < __
8
3
3
2
C __ > __
6
8
5
2
D __ < __
3
8
18–39
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73784_UT_U8.indd 18–39
1/27/08 10:46:49 AM
Name
15
Unit 8 Test
Date
Which of these mixed numbers is
16
another way to write ___
? 4NS1.9
3
17
Which of these numbers is greater
2
than 3 __
?
4NS1.9
3
A
1
4 __
3
A
7
3 ___
10
B
1
5 __
3
B
4
3 __
6
C
2
5 __
3
C
9
3 ___
16
D
2
6 __
3
D
1
3 __
2
4NS1.9
3
16 Zenaida ran __ mile each day for one
4
21
miles.
week, running a total of ___
4
18
What is another way that she could
record her total running distance?
A
B
C
D
3
4 __
4
1
5 __
4
3
5 __
4
1
6 __
4
Which of these number statements
is true?
4NS1.9
A
3
1
4 __
> 4 __
8
4
B
3
7
7 __
> 7 ___
5
10
C
5
2
3 __
< 3 __
6
3
D
3
4
5 __
= 5 __
7
8
miles
miles
miles
miles
Assessment Resources 4
18–40
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Name
19
Unit 8 Test
Date
4MR2.0
The table below shows how many
students in Mr. Blanco’s class
ordered lunch from the cafeteria.
Day
20
3
cup of sugar. How much
calls for __
4
sugar will he need to make 3 pies?
Number of students
Monday
Jonah is using a pie recipe that
A
3
1 __
cups
4
B
1
2 __
cups
4
18
Tuesday
21
Wednesday
16
C
1
2 __
cups
2
Thursday
20
D
Friday
19
3
2 __
cups
4
There are 24 students in the class.
2
of the
On which day did exactly __
3
class order lunch?
A
Monday
B
Tuesday
C
Wednesday
D
Thursday
Assessment Resources 4
4MR1.1
18–41
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2/24/08 12:27:55 PM
Name
Date
Unit 8 Test
Individual Student Record Form
Unit 8 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
Record the student’s response in the column to the right
of the correct answer.
California State Standards
1. B
4NS1.5
Explain different interpretations of fractions, for example, parts of a whole, parts
of a set, and division of whole numbers by whole numbers; explain equivalence
of fractions.
2. D
4NS2.0
3. B
4NS2.0
Students extend their use and understanding of whole numbers to the addition and
subtraction of simple decimals.
4. D
4NS1.5
5. C
4NS1.5
6. A
4NS1.5
7. C
4NS1.5
8. D
4NS1.9
9. A
4NS1.9
10. C
4MR2.0
Students use strategies, skills, and concepts in finding solutions.
11. C
4NS1.9
12. D
4NS1.9
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
13. A
4NS1.5
14. B
4NS1.5
15. B
4NS1.9
16. B
4NS1.9
17. A
4NS1.9
18. A
4NS1.9
19. C
4MR1.1
20. B
4MR1.1
Explain different interpretations of fractions, for example, parts of a whole,
parts of a set, and division of whole numbers by whole numbers; explain equivalence
of fractions.
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
Explain different interpretations of fractions, for example, parts of a whole, parts
of a set, and division of whole numbers by whole numbers; explain equivalence of
fractions.
Identify on a number line the relative position of positive fractions, positive mixed
numbers, and positive decimals to two decimal places.
Analyze problems by identifying relationships, distinguishing relevant from irrelevant
information, sequencing and prioritizing information, and observing patterns.
out of 20
18–43
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Teacher Name
Date
Unit 8 Test
Class Record Form
Unit 8 Test
Use the unit test to identify your students’ mastery of the
California Mathematics Contents Standards in the unit.
Item
The record below will allow you to group students for
differentiated instruction.
California Mathematics Contents Standards
1.
4NS1.5
Explain different interpretations of fractions, for example,
parts of a whole, parts of a set, and division of whole
numbers by whole numbers; explain equivalence of
fractions.
2.
4NS2.0
3.
4NS2.0
Students extend their use and understanding of whole
numbers to the addition and subtraction of simple
decimals.
4.
4NS1.5
5.
4NS1.5
6.
4NS1.5
7.
4NS1.5
8.
4NS1.9
9.
4NS1.9
Explain different interpretations of fractions, for example,
parts of a whole, parts of a set, and division of whole
numbers by whole numbers; explain equivalence of
fractions.
Identify on a number line the relative position of positive
fractions, positive mixed numbers, and positive decimals
to two decimal places.
10.
4MR2.0 Students use strategies, skills, and concepts in finding
solutions.
11.
4NS1.9
12.
4NS1.9
13.
4NS1.5
14.
4NS1.5
15.
4NS1.9
16.
4NS1.9
17.
4NS1.9
18.
4NS1.9
19.
4MR1.1 Analyze problems by identifying relationships,
distinguishing relevant from irrelevant information,
4MR1.1 sequencing and prioritizing information, and observing
patterns.
20.
Groups for differentiated instruction
Identify on a number line the relative position of positive
fractions, positive mixed numbers, and positive decimals
to two decimal places.
Explain different interpretations of fractions, for example,
parts of a whole, parts of a set, and division of whole
numbers by whole numbers; explain equivalence of
fractions.
Identify on a number line the relative position of positive
fractions, positive mixed numbers, and positive decimals
to two decimal places.
18–44
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