Post on 15-Mar-2018
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Lesson 5�6 343
Advance PreparationFor Part 1, place copies of Math Masters, page 403 or 431 near the Math Message. For the optional Readiness
activity in Part 3, make transparencies of Math Masters, pages 432 and 433, and tape them together.
Teacher’s Reference Manual, Grades 4–6 pp. 39, 40, 126–132, 260, 261
Key Concepts and Skills• Write numbers in expanded notation.
[Number and Numeration Goal 4]
• Use the partial-products algorithm to
solve multiplication problems with 2-digit
multipliers.
[Operations and Computation Goal 4]
• Estimate whether a product is in the tens,
hundreds, thousands, or more.
[Operations and Computation Goal 6]
• Apply the Distributive Property
of Multiplication over Addition.
[Patterns, Functions, and Algebra Goal 4]
Key ActivitiesStudents learn how to extend the partial-
products algorithm to 2-digit multipliers.
They make rough estimates and then use
the partial-products method.
Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Operations and Computation Goal 6]
Ongoing Assessment: Informing Instruction See page 345.
MaterialsMath Journal 1, pp. 122 and 123
Study Link 5�5
Math Masters, p. 403 or 431; p. 388 or 389
(optional)
slate
Playing Name That NumberStudent Reference Book, p. 254
Math Masters, p. 489 (optional)
per partnership: deck of number
cards (the Everything Math Deck,
if available)
Students practice representing
numbers in different ways.
Math Boxes 5�6Math Journal 1, p. 121
Students practice and maintain skills
through Math Box problems.
Study Link 5�6Math Masters, p. 154
Students practice and maintain skills
through Study Link activities.
READINESS
Modeling Multiplication with Base-10 Blockstransparencies of Math Masters, pp. 432
and 433 � base-10 blocks � erasable
marker � transparent tape
Students explore the partial-products
algorithm using a concrete model.
ENRICHMENTScoring a Dart GameMath Masters, p. 155
Students solve a multistep number story
involving a dart game.
ENRICHMENTSolving Venn Diagram PuzzlesMath Masters, p. 156
Students apply their understanding of
extended multiplication and division facts.
ENRICHMENTWriting Multiplication Number StoriesStudents write and solve multiplication
number stories.
Teaching the Lesson Ongoing Learning & Practice
132
4
Differentiation Options
Partial-ProductsMultiplication (Part 2)
Objectives To introduce and provide practice with the
partial-products algorithm for 2-digit multipliers.
Op
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eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
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344 Unit 5 Big Numbers, Estimation, and Computation
122
Multiplication Number StoriesLESSON
5 � 6
Date Time
Follow these steps for each problem.
a. Decide which two numbers need to be multiplied to give the exact answer.
Write the two numbers.
b. Estimate whether the answer will be in the tens, hundreds, thousands, or more.
Write a number model for the estimate. Circle the box to show your estimate.
c. On the grid below, find the exact answer by multiplying the two numbers.
Write the answer.
1. The average person in the United States drinks about 61 cups of soda per month.
About how many cups of soda is that per year?
a. � b. c.
numbers that give number model for your estimate exact answer
the exact answer
2. Eighteen newborn hummingbirds weigh about 1 ounce. About how many of them
does it take to make 1 pound? (1 pound � 16 ounces)
a. � b. c.
numbers that give number model for your estimate exact answer
the exact answer
28820 � 20 � 4001618
73260 � 10 � 6001261
1,000,000s100,000s10,000s100s10s 1,000s
1,000,000s100,000s10,000s100s10s 1,000s
17 18184
Math Journal 1, p. 122
Student Page
Mental Math and Reflexes �Write multiplication problems on the board. Have students write number models to show their estimates. Suggestions:Sample answers are given.
Ongoing Assessment: Mental Math
and Reflexes �Recognizing Student Achievement
Use Mental Math and Reflexes to assess students’ ability to estimate
reasonable solutions to whole-number multiplication problems. Students are
making adequate progress if they can write appropriate number models for the
and problems. Some students may be able to estimate products for
the problems.
[Operations and Computation Goal 6]
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
Go over the answers. Ask:
● How would you solve 4 ∗ 29 in your head? Sample answer: Multiply 4 ∗ 30 and then subtract 4 from the product.
● How would you solve 803 ∗ 6 in your head? Sample answer: Multiply 800 ∗ 6 and 3 ∗ 6 and then add the two products.
� Estimating Products PARTNER ACTIVITY
(Math Journal 1, pp. 122 and 123)
Tell students that in this lesson they will apply the partial-products algorithm to multiply a 2-digit number by a 2-digit number.
Getting Started
Math MessageSolve the following problems on a computation grid:
4 ∗ 29 = 116 803 ∗ 6 = 4,818
3 ∗ 260 = 780 418 ∗ 7 = 2,926
Study Link 5�5 Follow-Up Have students compare answers and share how they decided whether an average person blinks more than or fewer than 100,000 times per day.
3 ∗ 52 3 ∗ 50 = 150
4 ∗ 26 4 ∗ 30 = 120
9 ∗ 74 10 ∗ 74 = 740
8 ∗ 632 8 ∗ 600 = 4,800
6 ∗ 569 6 ∗ 600 = 3,600
3 ∗ 248 3 ∗ 250 = 750
2 ∗ 7,414 2 ∗ 7,500 = 15,000
5 ∗ 8,299 5 ∗ 8,000 = 40,000
7 ∗ 6,172 7 ∗ 6,000 = 42,000
NOTE For additional practice
using a standard procedure for
rounding whole numbers to the
nearest ten and hundred, see
www.everydaymathonline.com.
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Multiplication Number Stories continuedLESSON
5�6
Date Time
3. A test found that a lightbulb lasts an average of 63 days after being turned on.
About how many hours is that?
a. 63 ∗ 24 b. 60 ∗ 20 = 1,200 c. 1,512 numbers that give number model for your estimate exact answer
the exact answer
4. A full-grown oak tree loses about 78 gallons of water through its leaves per day.
About how many gallons of water is that per year?
a. 78 ∗ 365 b. 80 ∗ 400 = 32,000 c. 28,470 numbers that give number model for your estimate exact answer
the exact answer
1,000,000s100,000s10,000s100s10s 1,000s
1,000,000s100,000s10,000s100s10s 1,000s
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Math Journal 1, p. 123
Student Page
Lesson 5�6 345
100s
∗
6
1
+
7
10s
6
1
0
1
2
3
1s
1
2
0
0
0
2
2
Ò 10 [60s] or 10 ∗ 60
Ò 10 [1s] or 10 ∗ 1
Ò 2 [60s] or 2 ∗ 60
Ò 2 [1s] or 2 ∗ 1
Problem 1: 12 ∗ 61 = ?
Adjusting the Activity
60 1
10 600 10
2 120 2
For each problem on pages 122 and 123, students first decide which two numbers need to be multiplied to give the exact answer (Step a). In Step b, they make a rough estimate of that product and write a number model that shows how they made that estimate. They should not do Step c at this time. Do Problem 1 as a class:
Step a An average person drinks about 61 cups of soda in 1 month. In 1 year, a person will drink 12 times that amount. To find the amount of soda a person drinks in one year, you would multiply 12 ∗ 61. Write 12 ∗ 61, but do not calculate the exact answer at this time.
Step b To estimate the answer, round 12 to 10 and write a number model for the rough estimate: 10 ∗ 61 = 610. Or round 61 to 60 and write a number model for the rough estimate: 12 ∗ 60 = 720. Looking at the number models, you can tell that the answer will be in the hundreds, so circle “100s.”
Have students work with a partner to complete Steps a and b for the rest of the problems.
� Extending the Partial-Products WHOLE-CLASS ACTIVITY
Algorithm to 2-Digit Multipliers(Math Journal 1, pp. 122 and 123)
Demonstrate how to use the partial-products algorithm to find the exact answer and check the estimate for Problem 1 on journal page 122. (See margin.) Work from left to right. Point out that each part of one factor is multiplied by each part of the other factor.
Ongoing Assessment: Informing Instruction
As students say each step, watch for those who say, for example “1 times 6”
instead of “10 sixties” or “10 times 60.” Remind students to consider the value of
each digit.
Do several more problems with the class. Suggestions:
● 18 ∗ 52 = 936 ● 29 ∗ 73 = 2,117
● 26 ∗ 34 = 884 ● 28 ∗ 434 = 12,152
Organize the multiplication problems as follows:12 ∗ 61 = (10 + 2) ∗ (60 + 1)
Students then add the partial products in the table to find the total:
600 + 10 + 120 + 2 = 732.
A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L
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346 Unit 5 Big Numbers, Estimation, and Computation
Adjusting the Activity
121
Math Boxes LESSON
5 � 6
Date Time
1. a. Measure the line segment to the nearest �1
4� inch.
About inches
b. Draw a line segment that is half as long as the one above.
c. How long is the line segment you drew? About inches2�
12
�
5
2. Estimate the product. Write a number
model to show how you estimated.
a. 48 � 21
Number model:
b. 98 � 72
Number model:
100 � 70 � 7,000
50 � 20 � 1,000
4. Write each number using digits.
a. three hundred forty-two thousandths
b. six and twenty-five hundredths
6.25
0.342
5. If you remove 7 gallons per day from a
65-gallon water tank, how many days will
it take to empty the tank?
About 10 days
3. Multiply. Use the partial-products method.
� 52 � 432,236
128
184 18
27 28 175
Sample answers:
32 626
25
8 0
025 01
º
�
00
4 3
Math Journal 1, p. 121
Student Page
Links to the FutureDo not expect all students to master the
partial-products algorithm for two 2-digit
multipliers at this time. This algorithm will
be practiced and reinforced throughout
Fourth Grade Everyday Mathematics.
Fluently multiplying whole numbers using
the standard algorithm is expected in
Grade 5.
Lesson 9-8 introduces multiplication of
decimals. This is a Grade 5 Goal.
� Using the Partial-Products PARTNER ACTIVITY
Algorithm(Math Journal 1, pp. 122 and 123)
Students complete the remaining problems on journal pages 122 and 123 in the same way. They check their estimates and complete Step c by finding the exact answer using the partial-products algorithm.
Ask students to respond to the following question in a Math Log
or on an Exit Slip (Math Masters, page 388 or 389): Explain how the
partial-products algorithm is similar to finding a team’s score in a game of
Multiplication Wrestling.
Look for students to note that every part of one factor is multiplied by every part
of the other factor.
A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L
2 Ongoing Learning & Practice
� Playing Name That Number PARTNER ACTIVITY
(Student Reference Book, p. 254; Math Masters, p. 489)
Students play Name That Number to practice representing numbers in different ways. See Lesson 2-2 for additional information.
� Math Boxes 5�6 INDEPENDENTACTIVITY
(Math Journal 1, p. 121)
Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 5-8 and 5-10. The skill in Problem 5 previews Unit 6 content.
Writing/Reasoning Have students write a response to the following: Devon wrote 342,000 for Problem 4a. Explain the error he might have made. Sample answer: He wrote 342 thousands, not 342 thousandths.
� Study Link 5�6 INDEPENDENTACTIVITY
(Math Masters, p. 154)
Home Connection Students practice using the partial-products algorithm with 2-digit multipliers.
Algorithm Project The focus of this
lesson is partial products. To teach U.S.
traditional multiplication, see Algorithm
Project 5 on page A21.
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STUDY LINK
5�6 More Multiplication
Name Date Time
18
Multiply using the partial-products algorithm. Show your work.
1. 582 º 7 � 2. 56 º 30 �
3. 42 º 50 � 4. � 27 º 18
5. � 46 º 71 6. 340 º 50 � 17,0003,2664862,100
1,6804,074
Try This
7. � 241 º 31 8. � 768 º 4937,6327,471
9. � 283 � 5,439 10. 6,473 � 4,278 �
11. 5,583 � 4,667 � 12. � 9,141 � 6,3722,76991610,7515,722
Practice
Math Masters, p. 154
Study Link Master
Lesson 5�6 347
3 Differentiation Options
READINESS SMALL-GROUP ACTIVITY
� Modeling Multiplication 15–30 Min
with Base-10 Blocks(Math Masters, pp. 432 and 433)
To explore the partial-products algorithm using a concrete model, have students use base-10 blocks to model multiplication problems involving two 2-digit numbers.
Place taped transparencies of Math Masters, pages 432 and 433 on a table. To model 17 * 32, use an erasable marker to mark off a portion of the grid that is 17 squares high and 32 squares wide (17 by 32).
Start here.
Array model of 17 ∗ 32
Ask students to cover the array using as few base-10 blocks (flats, longs, and cubes) as possible.
Start here.
Base-10 block model of 17 ∗ 32
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348 Unit 5 Big Numbers, Estimation, and Computation
LESSON
5�6
Name Date Time
Sorting Numbers
Study the Venn diagrams in Problems 1 and 2. Label each circle and add at least one
number to each section.
1.
Try This
2.
720
2,400
300
180
4,200
4,000 240 2,100
80
5,600
160
p
multiples of 30divisible by 80
Sample answers:
990
1,230
360
120
1,500 420
2,000 3,500 770
1,050
750
1,200
210
840
4,200
6,300
350
7,000
250
4,000
650
560
490
280
30 as a factor
build arrays with
50 rows
multiples of 70
Sample answers:Sample answers:
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Math Masters, p. 156
Teaching Master
LESSON
5�6
Name Date Time
A Dart Game
Vanessa played a game of darts. She threw 9 darts.
Each dart hit the target. She scored 550 points.
Where might each of her 9 darts have hit? Use the
table to show all possible solutions.
200
100
50
25
111
12234
63
741
246
24
200 100 50 25
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Math Masters, page 155
Now match each part of the 17-by-32 array with a partial product.
� Match the 3 flats with 10 ∗ 30 = 300. These cover 300 squares.
� Match the 2 vertical longs with 10 ∗ 2 = 20. These cover 20 squares.
� There are 7 rows with 3 longs in each row. These cover 7 ∗ 30 = 210 squares.
� There are 7 rows with 2 cubes in each row. These cover 7 ∗ 2 = 14 squares.
� There are 544 (300 + 20 + 210 + 14) cubes in all.
Erase the transparencies. Use the transparencies and base-10 blocks to model and solve other 2-digit-times-2-digit problems.
ENRICHMENT INDEPENDENTACTIVITY
� Scoring a Dart Game 5–15 Min
(Math Masters, p. 155)
To apply students’ multidigit multiplication skills, have them use various strategies to solve a multistep number story involving a dart game with more than one possible answer. Ask students to explain how they know they found all the solutions.
ENRICHMENT PARTNER ACTIVITY
� Solving Venn Diagram Puzzles 5–15 Min
(Math Masters, p. 156)
To apply students’ understanding of extended multiplication and division facts, have them solve Venn diagram puzzles based on factors.
ENRICHMENT PARTNER ACTIVITY
� Writing Multiplication 5–15 Min
Number StoriesTo apply students’ understanding of multiplication algorithms, have them write and solve multistep multiplication number stories. Then have them record a number model using a letter for the unknown. Some students may be interested in writing and solving problems that involve distances, intervals of time, liquid volumes, masses of objects, or money. Stories may look similar to the following:
� Simon is filling the ketchup bottles at his restaurant. Each bot-tle holds 16 ounces of ketchup. There are 12 tables in each room and 3 rooms in the restaurant. How many ounces of ketchup will he need to fill one bottle for each table? Answer: 576 oz; Number model with unknown: (12 ∗ 3) ∗ 16 = n; Number model with answer: (12 ∗ 3) ∗ 16 = 576
Provide opportunities for students to revise and share their writing. Then have partners solve each other’s problems.
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