Lesson 12�7 941
The End-of-Year Assessment in the Assessment Handbook is a written assessment that you may use to assess students’ proficiency with Grade-Level Goals.
Input student data from Progress Check 12 and the End-of-Year Assessment into the Assessment Management Spreadsheets.
Materials � Study Link 12�6
� Assessment Handbook, pp. 142 –149, 211–215, 227, and 290–293
� End-of-Year Assessment (Assessment Handbook, pp. 150, 151, 234–241, and 244–245)
� slate; calculator
Find whole-number factors of numbers. [Number and Numeration Goal 3]
12�1,12�3–12�5
1 4, 5
Compare and order fractions. [Number and Numeration Goal 6]
12�1, 12�5 2 11
Compare and order integers. [Number and Numeration Goal 6]
12�1, 12�3 6, 7
Add and subtract signed numbers. [Operations and Computation Goal 2]
12�2,12�4–12�6
3, 4 1
Add and subtract decimals. [Operations and Computation Goal 2]
12�2, 12�4�
Solve problems involving division. [Operations and Computation Goal 4]
12�2–12�6�
Use scaling to model rate situations. [Operations and Computation Goal 7]
12�2–12�6 5 3, 4 1–3 13, 14�
Analyze and interpret data. [Data and Chance Goal 2]
12�3–12�6 12
Find the volumes of rectangular prisms. [Measurement and Reference Frames Goal 2]
12�1, 12�3,12�5
9
Convert among units of capacity. [Measurement and Reference Frames Goal 3]
12�2,12�4–12�6
6 2 8
Solve open sentences. [Patterns, Functions, and Algebra Goal 2]
12�2, 12�4,12�6
7 10
ASSESSMENT ITEMSSELF ORAL/SLA OPEN
RESPONSETE WRITTEN
CONTENT ASSESSED LESSON(S)
PART BPART A
Math Boxes 12�7
Study Link 12�7: End-of-Year Family Letter
Materials � Math Journal 2, p. 328
� Math Masters, pp. 354–357
Looking Back: Cumulative AssessmentL
Looking Ahead: Preparing for Grade 5L
Objective To assess students’ progress on mathematical
content through the end of Unit 12.
Progress Check 12�
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942 Unit 12 Progress Check 12
LESSON
12�7
Name Date Time
Self Assessment Progress Check 12
Think about each skill listed below. Assess your own progress by checking
the most appropriate box.
Skills I can do this on I can do this on I can do this if my own and explain my own. I get help or look how to do it. at an example.
1. Find factors and
factor pairs.
2. Compare and order
positive and negative
fractions.
3. Add positive and
negative numbers.
4. Subtract positive and
negative numbers.
5. Solve rate problems.
6. Convert among units
of capacity.
7. Solve open
sentences.
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Assessment Handbook, p. 211
Assessment Master
1 Looking Back: Cumulative Assessment
� Math Message Follow-Up INDEPENDENTACTIVITY
(Self Assessment, Assessment Handbook, p. 211)
The Self Assessment offers students the opportunity to reflect upon their progress.
� Oral and Slate Assessments WHOLE-CLASS ACTIVITY
Problems 2, 3, and 4 provide summative information and can be used for grading purposes. Problem 1 provides formative information.
Oral Assessment 1. Pose addition and subtraction problems involving positive
and negative integers. Have students explain their solution strategies. Suggestions:
● 6 + (–8) = –2
● 15 – (–12) = 27
● 20 + (–15) = 5
● –10 – (12) = –22
● –7 – (–9) = 2
● –12 + (–18) = –30
● –20 – (14) = –34
● –16 + 15 = –1
2. Have students show “thumbs-up” if the two quantities are equivalent and “thumbs-down” if they are not. Suggestions:
● 4 quarts and 1 gallon up
● 1 pint and 3 cups down
● 1 liter and 1,000 mL up
● 3 pints and 1 1 _ 2 quarts up
● 3 liters and 300 mL down
● 2 1 _ 2 gallons and 10 quarts up
Getting Started
Study Link 12�6 Follow-Up Briefly review students’ answers.
Math Message • Self AssessmentComplete the Self Assessment (Assessment Handbook, page 211).
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Slate Assessment 3. Pose rate problems. Encourage students to use rate tables if
necessary. Suggestions:
● If 1 pound of apples costs 40 cents, what is the cost of 5 pounds? $2.00
● Roberto earns $3 per hour babysitting. How much does he earn in 4 hours? $12 In 2 1 _ 2 hours? $7.50
● The Hole-in-One shop sells used golf balls for $2.40 per dozen. What is the cost of 1 golf ball? $0.20 Of 4 golf balls? $0.80 Of 1 _ 2 -dozen golf balls? $1.20
● Mitchell walks at the rate of about 3 miles per hour. At that rate, what distance will he walk in 20 minutes? About 1 mile In 1 _ 2 hour? About 1 1 _ 2 miles In 10 minutes? About 1 _ 2 mile In 3 hours? About 9 miles In 1 1 _ 3 hours? About 4 miles
● Caroline reads about 25 pages per hour. About how many pages could she read in 3 hours? 75 pages In 5 hours? 125 pages In 1 1 _ 2 hours? 37 1 _ 2 pages
● Carlos eats about 3 servings of fruit per day. About how many servings is that in 4 days? 12 servings In 1 week? 21 servings In 4 weeks? 84 servings
● Hamburgers cost 70 cents each. What is the cost of 2 hamburgers? $1.40 Of 4 hamburgers? $2.80 Of 1 dozen hamburgers? $8.40
4. Pose problems involving unit prices. Encourage students to use rate tables if necessary. Have them round their answers to the nearest tenth of a cent. Suggestions:
● A 6-pack of cola costs $2.40. What is the price per can? 40 cents
● A box of 8 pieces of chalk costs 64 cents. What is the cost of 1 piece of chalk? 8 cents
● A 46-ounce can of pineapple juice costs $1.75. What is the price per ounce? 3.8 cents
● A 6-ounce can of tomato paste costs 34 cents. What is the price per ounce? 5.7 cents
● An 8-pack of yogurt costs $4.00. What is the cost per container? $0.50
● Twelve bars of soap cost $3.60. What is the price per bar? $0.30
● A 15-ounce can of green beans costs 90 cents. What is the price per ounce? 6 cents
Lesson 12�7 943
1. The Davis family drove 280 miles to visit relatives.
It took 5 hours. At that rate, about how many miles
did the Davises drive in 3 hours? About miles
Fill in the rate table, if needed.
2. Jan earned $19.50 last week for mowing 3 lawns.
At that rate, what would Jan earn for mowing 5 lawns?
Fill in the rate table, if needed.
3. Tina works 7 hours per day, 5 days per week. She earns $56.00 per day.
a. How much does she earn per hour?
b. How much does she earn per week?
4. List the factor pairs of 40.
and and
and and
5. Name all the factors of 64.
LESSON
12�7 Written Assessment
Name Date Time
Progress Check 12
Part A
$32.50
$8
$280
1 4 10
2 5 8
40
20
168
Miles 56 112 168 224 280
Hours 1 2 3 4 5
Dollars 6.50 13 19.50 26 32.50
Lawns 1 2 3 4 5
1, 2, 4, 8, 16, 32, 64
Assessment Handbook, p. 212
Assessment Master
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944 Unit 12 Progress Check 12
Name Date Time
Written Assessment continuedLESSON
12�7
6. Insert �, �, or � to make a true number sentence.
a. �25 22 b. 0 �2
c. �10 �100 d. �82 �64
7. Order the numbers from smallest to largest.
�30, 4, 15, �2, 17, �8
smallest largest
8. Use the diagram to help you solve the problems.
a. c � 2 gal
b. 10 qt � gal qt
c. 22 c � qt pt
d. 13 pt � qt pt
e. 15 qt � c
9. Calculate the volume.
a. b.
Number model: Number model:
Volume � cm3 Volume � cm3
10. Solve the open sentences.
a. 0.930 � 3.59 � y y � b. 51.9 � b � 69.07 b �
c. 1.89 � 0.206 � q q � d. 1.46 � k � 0.028 k �
�
��
�
�30 �8 �2 4 15 17
32
2
(4 � 2) � 5 � 40 (7 � 3) � 2 � 42
2
1
1
5
6
60
40
4.52
1.684 1.488
17.17
42
5 c
m
4 cm 2 cm
2 c
m
7 cm 3 cm
Assessment Handbook, p. 213
Assessment Master
� Written Assessment INDEPENDENTACTIVITY
(Assessment Handbook, pp. 212–214)
Part A Recognizing Student AchievementProblems 1–10 provide summative information and may be used for grading purposes.
Problem(s) Description
1–3 Solve rate problems.
4, 5 Find factors and factor pairs.
6 Compare integers.
7 Order integers.
8 Find equivalent capacities.
9 Calculate volume.
10 Solve open sentences.
Part B Informing InstructionProblems 11–14 provide formative information.
Problem Description
11 Compare and order fractions.
12 Determine the reasonableness of a statistic.
13 Determine which box of cereal is the better buy.
14 Make informed consumer decisions.
Name Date Time
Written Assessment continuedLESSON
12�7
Part B
smallest
smallest
largest
largest
11. Order the fractions from smallest to largest.
a. ��1
7
0�, �
1
7�, ��
7
7�, �
4
7�, ��
5
7�
b. �1
6
2�, ��
1
3�, �
2
9�, �
1
2
5
0�, �
4
4�
12. It was reported that on New Year’s Day in 1907, Theodore Roosevelt shook
hands with 8,513 people. Does this seem reasonable? Explain your answer.
13. A store charges $1.58 for a 20-ounce box of Puff Flakes cereal and
$1.72 for a 24-ounce box of the same cereal. Which is the better buy?
Explain why.
��170� ��
77
� ��57
� �17
� �47
�
��13
� �29
� �162� �
1250� �
44
�
14. Joey goes to Doreen’s Delicious
Doughnuts to buy doughnuts for
the class party. What is the least
amount of money he will have to
pay for 30 doughnuts?
Explain.
$12.10
Sample answer:
Sample answer: Yes. If he shook hands for 18 hours that
day, it would be about 8 hands per minute. That’s a lot of
hands, but it seems like a president might do that.
At Doreen’s the bigger the package, the cheaper the
doughnut. Joey should buy two dozens for $4.80 per
dozen and one half-dozen for $2.50, for a total of
$4.80 � $4.80 � $2.50 � $12.10.
Sample answer: The cereal in the 20-oz box costs 7.9
cents per ounce, while the same cereal in the 24-oz box
costs 7.17 cents per ounce.
the 24-oz box
Assessment Handbook, p. 214
Assessment MasterName Date Time
LESSON
12�7 Open Response Progress Check 12
Buying Cookies
Raheem and India volunteered to buy cookies for the class party. They wanted at least
4 different kinds of cookies, and they wanted to spend as little money as possible. They
decided that 3 pounds of cookies would be enough. When they went to the store, they
saw these prices for packages of cookies:
mint creams . . . . . . . . . . . . . . . .$2.79/lb chocolate chip . . . . . . . . . .$2.39/12 oz
fudge marshmallow . . . . . . . . . . $1.69/12 oz oatmeal . . . . . . . . . . . . . . $2.03/17 oz
sugar wafers . . . . . . . . . . . . . . . $2.99/8 oz windmill . . . . . . . . . . . . . . $2.59/lb
vanilla wafers . . . . . . . . . . . . . . $1.39/11 oz ginger snaps . . . . . . . . . . $0.60/8 oz
1. What 4 packages of cookies would you recommend they buy so that they have a total
of about 3 pounds and they spend as little money as possible? Show all of your work,
and explain how you found your answer. Hint: 1 pound = 16 ounces
2. If they follow your recommendations, how much money will they spend on cookies?
Show your work.
3. About what is the cost per pound of the 3 pounds of cookies you selected?
Show your work.
See the Assessment Handbook for rubricsand students’ work samples.
Assessment Handbook, p. 215
Assessment Master
Use the checklists on pages 291 and
293 of the Assessment Handbook to
record results. Then input the data
into the Assessment Management
Spreadsheets to keep an ongoing
record of students’ progress toward
Grade-Level Goals.
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� Open Response INDEPENDENTACTIVITY
(Assessment Handbook, p. 215)
Buying CookiesThe open-response item requires students to apply concepts and skills from Unit 12 to solve a multistep problem. See Assessment Handbook, pages 145–149 for rubrics and students’ work samples for this problem.
� End-of-Year Assessment INDEPENDENTACTIVITY
(Assessment Handbook, pp. 150, 151, and 234–241)
The End-of-Year Assessment (Assessment Handbook, pages 234–241) provides an additional assessment opportunity that you may use as part of your balanced assessment plan. This assessment covers many of the important concepts and skills presented in Fourth Grade Everyday Mathematics. It should be used along with ongoing and periodic assessments. Please see pages 150 and 151 in the Assessment Handbook for further information.
2 Looking Ahead: Preparing for Grade 5
� Math Boxes 12�7 INDEPENDENTACTIVITY
(Math Journal 2, p. 328)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 12-5.
� Study Link 12�7: INDEPENDENTACTIVITY
End-of-Year Family Letter(Math Masters, pp. 354–357)
Home Connection The End-of-Year Family Letter thanks family members for their participation in Fourth Grade Everyday Mathematics, suggests activities that can be
done at home during the vacation, and provides a preview of Fifth Grade Everyday Mathematics.
STUDY LINK
12�7 Family Letter
py
gg
p
Name Date Time
Congratulations!By completing Fourth Grade Everyday Mathematics, your child has accomplished a great deal. Thank you for all of your support.
This Family Letter is a resource to use throughout your child’s vacation. It includes an extended list of Do-Anytime Activities, directions for games that can be played at home, a list of mathematics-related books to check out over vacation, and a sneak preview of what your child will be learning in Fifth Grade Everyday Mathematics. Enjoy the vacation!
Do-Anytime ActivitiesMathematics means more when it is rooted in real-life situations. To help your child review many of the concepts he or she has learned in fourth grade, we suggest the following activities for you and your child to do together over vacation. These activities will help your child build on the skills he or she has learned this year and help prepare him or her for Fifth Grade Everyday Mathematics.
1. Have your child practice any multiplication and division facts that he or she has not yet mastered. Include some quick drills.
2. Provide items for your child to measure. Have your child use personal references, as well as U.S. customary and metric measuring tools.
3. Use newspapers and magazines as sources of numbers, graphs, and tables that your child may read and discuss.
4. Have your child practice multidigit multiplication and divisionusing the algorithms that he or she is most comfortable with.
5. Ask your child to look at advertisements and find the sale prices of items using the original prices and rates of discount or find rates of discount using original prices and sale prices. Have your child use a calculator and calculate unit prices to determine best or better buys.
6. Continue the World Tour by reading about other countries.
Ever
yd
ay Mathematics
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Math Masters, pp. 354–357
Study Link Masters
Lesson 12�7 945
Math Boxes LESSON
12�7
Date Time
4. Subtract.
a. -$75 - (+$25) =
b. -$45 - (-$30) =
c. -$60 - (+$60) =
d. $55 - (-$25) =
e. $300 - (-$100) =
1. Multiply. Show your work.
79 ∗ 405 =
2. a. Complete the table.
3. It is estimated that in an average
lifetime of 75 years, a person takes
about 50,000 trips in a car.
a. At that rate, about how many times a
day would a person ride in a car?
times
b. Does this number make sense to you?
31,995
b. How many inches are in 11 feet?
inches132
2
yes
-$100-$15-$120
$80
$400
5. Calculate the volume.
Number model:
Volume =
cm3
6. A 10-ounce can of peas costs $0.55.
A 16-ounce can of peas costs $1.19.
a. What is the price per ounce for each
can? (Round to the nearest cent.)
10-oz can:
16-oz can:
b. Which can of peas is the better buy?
5.5 cm
12 cm
3 cm
198
$0.06
$0.07
10-oz can
18 19
47 60
138 47
47
(12 ∗ 5.5) ∗ 3 = 198
10812 24
16 27
Number of Inches 144 192 324
Number of Feet
1 2 9 12
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Math Journal 2, p. 328
Student Page
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Copyright
© W
right
Gro
up/M
cG
raw
-Hill
Assessment Masters 211
LESSON
12�7
Name Date Time
Self Assessment Progress Check 12
Think about each skill listed below. Assess your own progress by checking
the most appropriate box.
Skills I can do this on I can do this on I can do this if my own and explain my own. I get help or look how to do it. at an example.
1. Find factors and
factor pairs.
2. Compare and order
positive and negative
fractions.
3. Add positive and
negative numbers.
4. Subtract positive and
negative numbers.
5. Solve rate problems.
6. Convert among units
of capacity.
7. Solve open
sentences.
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