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www.everydaymathonline.com
712 Unit 9 Multiplication and Division
�������
Advance PreparationPost the Guide to Solving Number Stories poster (Math Masters, page 406).
Teacher’s Reference Manual, Grades 1– 3 pp. 193 –195
Key Concepts and Skills• Find multiples of 10, 100, and 1,000.
[Number and Numeration Goal 3]
• Compare and order numbers.
[Number and Numeration Goal 6]
• Use multiplication facts to solve problems.
[Operations and Computation Goal 3]
• Solve number sentences involving the
symbols ×, ÷, and =.
[Patterns, Functions, and Algebra Goal 2]
Key ActivitiesChildren make up and solve multiplication
and division number stories about animal
weights. Children find products and quotients
involving multiples of 10, 100, and 1,000.
Ongoing Assessment: Informing Instruction See page 715.
Ongoing Assessment: Recognizing Student Achievement Use journal page 206. [Number and Numeration Goal 3]
MaterialsMath Journal 2, pp. 204–206
Math Masters, p. 406
slate � blank transparency (optional)
Playing Name That NumberStudent Reference Book, pp. 299
and 300
per group: 4 each of number cards
0–10 and 1 each of number cards
11–20 (from the Everything Math
Deck, if available)
Children use two or more operations
to find equivalent names for numbers.
Math Boxes 9�1Math Journal 2, p. 207
Children practice and maintain skills
through Math Box problems.
Home Link 9�1Math Masters, p. 267
Children practice and maintain skills
through Home Link activities.
READINESS
Extending Multiplication Fact PatternsMath Masters, p. 268
per partnership: base-10 blocks (longs, flats,
and big cubes)
Children explore patterns in multiples of 10,
100, and 1,000.
EXTRA PRACTICE
Minute Math +Minute Math ®+, pp. 128 and 131
Children solve number stories involving
multiplication and division.
ELL SUPPORT
Writing Multiplication and Division Number StoriesChildren write multiplication and division
number stories.
Teaching the Lesson Ongoing Learning & Practice
132
4
Differentiation Options
Multiply and Divide withMultiples of 10, 100, and 1,000
Objective To guide children as they multiply and divide
with multiples of 10, 100, and 1,000.w
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
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Lesson 9�1 713
Adult Weights of North American Animals cont.LESSON
9�1
Am
eric
an p
orcu
pine
20 lb
to 4
0 lb
Sea
otte
r48
lb to
99
lb
Pum
a15
0 lb
to 2
30 lb
Whi
te-ta
iled
deer
50 lb
to 4
80 lb
Pilo
t wha
le3,
200
lb to
6,4
00 lb
Atla
ntic
gre
en tu
rtle
250
lb to
450
lb
Wes
t Ind
ian
man
atee
500
lb to
1,1
00 lb
Am
eric
an a
lliga
tor
200
lb to
500
lbG
ray
fox
9 lb
to 1
6 lb Com
mon
dol
phin
200
lb to
300
lbR
ight
wha
le70
,000
lb to
140
,000
lb
Bot
tle-n
osed
dol
phin
350
lb to
430
lb
Gila
mon
ster
2lb
to 4
lb1 2
Gra
y w
hale
45,0
00 lb
to 7
2,00
0 lb
Date Time
Math Journal 2, p. 205
Student Page
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
(Math Journal 2, pp. 204 and 205)
According to the Adult Weights of North American Animals poster, a normal weight for a beaver is from 20 to 56 lb. Remind children that the abbreviation for pounds is lb. Any weight within this range is a correct response to the Math Message. Have children briefly share their observations from the poster.
NOTE The word range is used here to mean the series of numbers between
two given numbers. Children should not confuse this meaning with the data
landmark range, which means the difference between the largest (maximum) and
the smallest (minimum) numbers in a set of data. To support English language
learners, write range on the board twice with examples of both meanings.
Ask children to name other animals on the poster and to tell their normal adult weight ranges. Have children give numbers within these ranges. For example, the weight range for an arctic fox is 7 lb to 20 lb. Ask: Could an arctic fox weigh 15 lb? yes 22 lb? no
� Modeling How to Solve WHOLE-CLASS ACTIVITY
Multiplication and Division Number Stories(Math Journal 2, pp. 204 and 205; Math Masters, p. 406)
Explain that the class will solve multiplication and division number stories. Refer children to the Guide for Solving Number Stories poster (Math Masters, page 406) and the animal posters in their journals (Math Journal 2, pages 204 and 205). Write the following problem on the board or transparency. Which animal could weigh 30 times as much as a 50-pound sea otter?
ELL
Getting Started
Math MessageUse journal pages 204 and 205 to find out how much an adult beaver might weigh. Write the answer on your slate. Talk to a partner about information on the map.
Mental Math and ReflexesPose problems like the following. Children answer on their slates:
How much are 7 [30s]? 210
What number is 50 times as much as 6? 300
How many 9s equal 540? 60
How much are 70 [30s]? 2,100
What number is 50 times as much as 60? 3,000
How many 90s make 5,400? 60
How much are 30 [700s]? 21,000
What number is 60 times as much as 500? 30,000
How many 60s make 54,000? 900
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714 Unit 9 Multiplication and Division
Guide to Solving Number Stories
Name Date Time
1. What do you understand from the story?
� Read the story. What do you want to find out?
� What do you know?
2. What will you do?
� Add?
� Subtract?
� Multiply?
� Divide?
� Draw a picture?
� Make tallies?
� Use counters or base-10 blocks?
� Use a number grid or number line?
� Make a table?
� Draw a diagram?
� Write a number model?
3. Answer the question.
� Solve the problem. Record your work.
� Write the answer with the units.
4. Check.
� Does your answer make sense? How do you know?
EM3MM_G3_U02_036-063.indd 406 12/29/10 5:57 PM
Math Masters, p. 406
Teaching Aid Master
?30 [50s] = ?
30 [50s] = 1,500
One polar bear weighs as much as 30 sea otters.
1. What do you understand from the story? Think:
● What do you want to find out? Which animal could weigh 30 times as much as the sea otter?
● What information do you know from reading the story? A sea otter weighs 50 lb. There is an animal that weighs about 30 times as much as a sea otter.
2. What could you do to find which animal weighs about 30 times as much as the sea otter? You could multiply 30 times 50 lb and then find an animal that weighs about that much.
● Write a number model to represent the story. Possible number models: ? = 30 × 50; 30 × 50 = ?
NOTE Remind children that they can use either a question mark or a letter for
the unknown quantity in a number model.
3. Answer the question. 30 times 50 lb is 1,500 lb. A polar bear could weigh from 650 to 1,750 lb; and 1,500 lb is in that range.
Allow time for children to write solution strategies on the board and explain them to the class. Possible strategies may include: I added 50 ten times to get 500 and then added 500 three times to get 1,500; I know that 50 × 30 = 1,500 is an extension of the basic fact 5 × 3 = 15; I added 30 fifty times to get 1,500.
4. Does your answer make sense? How do you know? Sample answer: I know that 10 sea otters weigh 500 lb. 30 sea otters would weigh 3 times that amount, about 1,500 lb; which is in the weight range for polar bears.
● Does your answer make the number model true? yes Write a summary number model on the board: 1,500 = 30 × 50.
Write the following problem on the board or transparency: How many 50-pound sea otters together would weigh about 1 ton? (1 ton = 2,000 lb)
1. What do you understand from the story? Think:
● What do you want to find out? The number of 50-pound sea otters whose total weight would be 2,000 lb
● What information do you know from reading the story? A sea otter weighs 50 lb. An unknown number of sea otters weigh 2,000 lb.
2. What could you do to find the number of 50-pound sea otters whose total weight would be 2,000 pounds? Children may think of this problem in terms of multiplication (What number times 50 equals 2,000?) or division (How much is 2,000 divided by 50?).
● Write a number model for the story. Possible number models: ? × 50 = 2,000; 2,000 ÷ 50 = ?
3. Answer the question. 50 times 40 is 2,000, so forty 50-pound sea otters together weigh a ton.
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Lesson 9�1 715
Allow time for children to share solution strategies. Possible strategies may include: I know the basic fact 4 × 5 = 20. 40 × 50 = 2,000 and 2,000 ÷ 50 = 40 are extensions of the basic fact. From the first story, I knew that 30 sea otters were 1,500 lb and that 10 sea otters were 500 lb, so I added and found that 40 sea otters weigh 2,000 lb.
4. Does your answer make sense? How do you know? Possible answer: One sea otter weighs 50 lb, so two weigh 100 lb. There are ten 100s in 1,000 and twenty 100s in 2,000, so 40 sea otters weigh 2,000 lb.
● Does your answer make the number model true? yes Write a summary number model on the board: 40 × 50 = 2,000.
� Writing and Solving Number WHOLE-CLASS ACTIVITY
Stories with Multiples of 10, 100, and 1,000(Math Journal 2, pp. 204 and 205)
Use the Adult Weights of North American Animals poster as a basis for multiplication and division number stories. Choose any numbers that fall within the weight ranges. Record the problems on the board.
Suggestions:
● Which animal could weigh about 10 times as much as a 34-pound American porcupine? Harp seal, northern fur seal, American alligator, white-tailed deer, Atlantic green turtle, or black bear
● Which animal could weigh about 30 times as much as a 5-pound snowshoe hare? Puma or white-tailed deer
● How many 300-pound northern fur seals weigh as much as a 6,000-pound pilot whale? 20
● How many 80-pound white-tailed deer weigh as much as a 560-pound black bear? 7
Invite children to tell their own multiplication and division number stories for the class to solve.
Ongoing Assessment: Informing Instruction
Watch for children who tell addition or subtraction number stories. Accept and
solve these types of problems, but continue to model multiplication and division
number stories, emphasizing that multiplication is a way to find the total number
of things when equal groups are put together.
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BBBBBBBBBBBBBBBBBBBB ELEELEEMMMMMMMMMOOOOOOOOOBBBLBLBLBBLBBBLOOORORORORORORORORORORORO LELELELEEEEEELEMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINVINNNNVINVINVINNVINVINVINVINVV GGGGGGGGGGGOLOOOLOOLOLOLOO VVINVINLLLLLLLLLVINVINVINVINVINNVINVINVINVINVINVINNGGGGGGGGGGOOOLOLOLOLOLOLLOO VVVLLLLLLLLLLVVVVVVVVOSOSOSOOSOSOSOSOSOSOOSOSOSOSOOOSOSOOSOSOSOSOSOSOSOSOOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVLLLLLLLLVVVVVVVVVLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING
Adjusting the Activity Pose problems that require two
steps. Suggestion:
Which animal could weigh about 1,000 times
as much as the combined weight of a
75-pound sea otter and a 45-pound sea
otter? Right whale
AUDITORY � KINESTHETIC � TACTILE � VISUAL
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Links to the Future
Date Time
Multiples of 10, 100, and 1,000LESSON
9 �1
Solve each problem.
1. a. 7 [40s] = 280 b. 7 × 40 = 280
2. a. 6 [70s] = 420 b. 6 × 70 = 420
3. a. 60 [20s] = 1,200 b. 60 × 20 = 1,200
4. How many 50s are in 4,000? 80
5. How many 800s are in 2,400? 3
6. a. How many 3s are in 270? 90 b. 90 × 3 = 270
c. 270 ÷ 3 = 90
7. a. 40 × 300 = 12,000 b. 12,000 ÷ 40 = 300
For Problems 8 through 10, use the information on pages 204 and 205.
8. a. Which animal might weigh about
20 times as much as a 30-pound raccoon? Black bear
b. Can you name two other animals that might
weigh 20 times as much as a 30-pound raccoon?
Northern fur seal and West Indian manatee
9. About how many 200-pound American alligators
weigh about as much as a 3,200-pound
beluga whale? 16 American alligators
10. Which animal might weigh about 100 times as much as
the combined weights of a 15-pound
arctic fox and a 10-pound arctic fox? Beluga whale or walrus
� �� �
Try This
204-239_EMCS_S_MJ2_G3_U09_576418.indd 206 2/18/11 1:53 PM
Math Journal 2, p. 206
Student Page
716 Unit 9 Multiplication and Division
Date Time
Math BoxesLESSON
9�1
5. Use bills and coins.
Share $45.90 equally among
3 people.
Each gets $ 15.30 .
Share $49.20 equally among
4 people.
Each gets $ 12.30 .
3. Write equivalent fractions.
1 _ 2 =
1 _ 4 =
2. Put these numbers in order from
smallest to largest.
998,752 750,999
1,000,008 998,752
750,999 1,000,008
1,709,832 1,709,832
4. Pencils cost $1.99 for a package
of 24. Estimate. About how much
do 4 packages cost?
about $8.00
6. Measure the line segment to the
nearest 1 _ 2 inch.
about 1 in.
Draw a line segment that is
1 1 _ 2 inches long.
1. If I wanted to take out a square
about 4 times as often as a circle,
I would put in 20 square(s).
20
19127–30
73 143 144
Sample answers:3
6
3
12
204-239_EMCS_S_MJ2_G3_U09_576418.indd 207 3/29/11 5:52 PM
Math Journal 2, p. 207
Student Page
� Finding Products and INDEPENDENTACTIVITY
Quotients Involving Multiples of 10, 100, and 1,000(Math Journal 2, pp. 204–206)
Children complete journal page 206. Circulate and assist as necessary.
Ongoing Assessment: Journal page 206 �Problems 1 and 2Recognizing Student Achievement
Use journal page 206, Problems 1 and 2 to assess children’s progress toward
solving problems involving multiples of 10, 100, and 1,000. Children are making
adequate progress if they are able to complete Problems 1 and 2. Some children
may be able to solve problems involving multiples of 100 and 1,000.
[Number and Numeration Goal 3]
In this lesson, children make up and solve multiplication and division number stories involving multidigit numbers. Many children will use basic facts, multiples of 10, and mental math to solve these problems. However, using and explaining strategies for solving number stories involving multiplication of multidigit whole numbers by a 2-digit whole number is a Grade 4 Goal. Using and explaining strategies for solving number stories involving division of multidigit whole numbers is a Grade 5 Goal.
2 Ongoing Learning & Practice
� Playing Name That Number SMALL-GROUP ACTIVITY
(Student Reference Book, pp. 299 and 300)
Children play Name That Number. They use two or more operations to find equivalent names for numbers. For game instructions, see Lesson 1-6 or pages 299 and 300 in the Student Reference Book.
� Math Boxes 9�1 INDEPENDENTACTIVITY
(Math Journal 2, p. 207)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-3. The skill in Problem 6 previews Unit 10 content.
Writing/Reasoning Have children write an answer to the following: Explain how you solved Problem 4. Sample answer: $1.99 is close to $2.00. I multiplied $2.00 × 4 to get $8.00.
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Name Date Time
Who Am I?HOME LINK
9�1
The problems in this Home Link involve children solving whole-number riddles. Your childwill use place-value concepts, number sense, and computation skills to solve the riddles. Toprovide practice with basic and extended facts, multiplication fact practice is added at thebottom of this Home Link.
Please return this Home Link to school tomorrow.
FamilyNote
In each riddle, I am a different whole number. Use the clues to find out who I am.
1. Clue 1: I am greater than 30 and less than 40. Who am I?Clue 2: The sum of my digits is less than 5.
2. Clue 1: I am greater than 15 and less than 40. Who am I?Clue 2: If you double me, I become
a number that ends in 0.
Clue 3: �15
� of me is equal to 5.
3. Clue 1: I am less than 100. Who am I?Clue 2: The sum of my digits is 4.
Clue 3: Half of me is an odd number.
4. Clue 1: If you multiply me by 2, I become Who am I?a number greater than 20 and less than 40.
Clue 2: If you multiply me by 6, I end in 8.
Clue 3: If you multiply me by 4, I end in 2.
5. Clue 1: Double my tens digit to get Who am I?my ones digit.
Clue 2: Double me and I am less than 50.
Solve.
6. 8 � 7 � 7. 5 � 4 �
80 � 7 � 5 � 40 �
800 � 7 � 50 � 400 � 20,0005,600
200560
2056
Practice
31
25
22
13 or 18
12 or 24
Math Masters, p. 267
Home Link Master
Lesson 9�1 717
Name Date Time
LESSON
9�1 Extending Multiplication Fact Patterns
Fill in the missing numbers.
1. 1 � 10 � 1 � 100 �
2 � 10 � 2 � 100 �
3 � 10 � 3 � 100 �
4 � 10 � 4 � 100 �
5 � 10 � 5 � 100 �
2. 6 � 100 � 6 � 1,000 �
7 � 100 � 7 � 1,000 �
8 � 100 � 8 � 1,000 �
9 � 100 � 9 � 1,000 �
3. 1 [10] � 1 [100] �
2 [10s] � 2 [100s] �
7 [10s] � 7 [100s] �
5 [10s] � 5 [100s] �
8 [10s] � 8 [100s] �
4. Explain how you can use the patterns above to find the answer to 8 [1,000s].
Sample answer: I know that 8 [1s] are 8. 8 [1,000s] are 1,000times as much, or 8,000. I know that 8 [10s] are 80 and
8 [100s] are 800; so 8 [1,000s] must be 8,000.
5. 10 � 100 � 10 [100s] �
10 � 1,000 � 10 [1,000s] �
Try This
1020304050
100200300400500
6,0007,0008,0009,000
600700800900
1020705080
100200700500800
1,000 1,00010,00010,000
Math Masters, p. 268
Teaching Master
� Home Link 9�1 INDEPENDENTACTIVITY
(Math Masters, p. 267)
Home Connection Children solve whole-number riddles.
3 Differentiation Options
READINESS PARTNER ACTIVITY
� Extending Multiplication 5–15 Min
Fact Patterns(Math Masters, p. 268)
To explore patterns in multiples of 10, 100, and 1,000, have children complete Math Masters, page 268. Children can model the problems with base-10 longs, flats, and big cubes.
EXTRA PRACTICE SMALL-GROUP ACTIVITY
� Minute Math+ 5–15 Min
To offer children more experience with multiplication and division number stories, see the following pages in Minute Math+:
Number Stories: pp. 128 and 131.
ELL SUPPORT SMALL-GROUP ACTIVITY
� Writing Multiplication and 15–30 Min
Division Number StoriesTo provide language support for multiplication and division, have children write multiplication and division number stories for others to solve. Also provide them
with opportunities to write a paragraph describing how they solved a particular problem. Provide English language learners with feedback on their mathematical writing and offer them multiple opportunities to revise their writing. This activity will support not only their problem-solving efforts, but also their communication skills.
NOTE Remind children to continue to record the sunrise, sunset, and length of
day in their journals on pages 279–281. They should also continue to record the
national high and low temperatures on journal page 175 and then graph the
temperature range on journal page 177.
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Copyrig
ht ©
Wrig
ht G
roup/M
cG
raw
-Hill
406
Guide to Solving Number Stories
Name Date Time
1. What do you understand from the story?
� Read the story. What do you want to find out?
� What do you know?
2. What will you do?
� Add?
� Subtract?
� Multiply?
� Divide?
� Draw a picture?
� Make tallies?
� Use counters or base-10 blocks?
� Use a number grid or number line?
� Make a table?
� Draw a diagram?
� Write a number model?
3. Answer the question.
� Solve the problem. Record your work.
� Write the answer with the units.
4. Check.
� Does your answer make sense? How do you know?
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