Multiply with 5 and 10
Transcript of Multiply with 5 and 10
197A Chapter 4
About the MathProfessional Development
LESSON AT A GLANCE
Interactive Student Edition
Personal Math Trainer
Math on the Spot
Animated Math Models
iTools: Counters
iTools: Number Lines
HMH Mega Math
F C R Focus:Common Core State Standards3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement
quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Also 3.OA.A.1, 3.OA.C.7
MATHEMATICAL PRACTICESMP1 Make sense of problems and persevere in solving them. MP4 Model with mathematics.MP7 Look for and make use of structure.
F C R Coherence:Standards Across the GradesBefore2.OA.A.1
Grade 33.OA.A.3
After4.OA.A.2
Multiply with 5 and 10
LESSON 4.2
Teaching for DepthThis lesson presents different ways to represent multiplication with the factors 5 and 10. Different strategies, such as making jumps on a number line and skip counting by 5s or 10s, help students develop a deeper understanding of multiplication.
In this lesson, students further explore the concept of multiplication by finding unknown factors given the product and one factor or a picture and one factor.
The goals are to make multiplying by 5 or 10 flexible and fast and to deepen understanding of what multiplying by 5 or 10 means through visual representation, exploring strategies, and solving problems in context.
Professional Development Videos
FOCUS COHERENCE RIGOR
Learning ObjectiveUse skip counting, a number line, or a bar model to multiply with the factors 5 and 10.
Language ObjectiveStudents explain to a partner how you multiply with 5 and 10.
Materials MathBoard
F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your OwnLevel 3: Applications..................................Think Smarter and Go Deeper
F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 189J.
ENGAGE1
Lesson 4.2 197B
Daily RoutinesCommon Core
7 7 7 7 77 7 7 77
777 7 7
7
Books Read2 3 4 510
Fluency BuilderMaterials Multiplication Table (see eTeacher Resources)
Multiplication Table and Patterns Have students practice multiplication facts for 2 and 4. Give students copies of a blank multiplication table.
• Review how to fill in the table by pointing out that the numbers on the top and side are the factors and that the products are written in the boxes where the rows and columns meet.
• Have students complete the rows for 2 and 4.
• After students complete the rows, discuss any patterns they see.
Problem of the Day 4.2Hiro made a line plot to show the number of books read by the students in his class. How many people read more than 3 books?
Vocabulary multiple
Interactive Student EditionMultimedia Glossary e
with the Interactive Student Edition
Essential QuestionHow can you multiply with 5 and 10?
Making ConnectionsInvite students to tell you what they know about prairie dogs.
What is a prairie? a grassy, flat area What is a prairie dog? a small, furry animal Where do prairie dogs live? in the ground in grassy plains areas, or prairies How do prairie dogs live, alone or in groups? In groups, in the same burrows, and they have many burrows in one area
Learning ActivityWhat is the problem the students are trying to solve? Connect the story to the problem.
• How many burrows is Pedro looking at? 6 burrows
• Are the same number of prairie dogs in each burrow? yes
• How many prairie dogs are in each burrow? 10 prairie dogs
• What operation combines equal groups? multiplication
Literacy and MathematicsChoose one or more of the following activities.
• Ask students to read the question aloud and then restate it in their own words.
• Invite students to write a story about homes of other animals. Suggest that the number of animals in each home be the same so that students can multiply to find the total number of animals.
5
How can you multiply with 5 and 10?
EXPLORE2
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Unlock the ProblemUnlock the Problem
MATHEMATICAL PRACTICES 1MathTalk MATHEMATICAL PRACTICES 1MathTalk
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Chapter 4 197
Use skip counting.
Skip count by 5s until you say 6 numbers.
5, _, _, _, _, _
6 × 5 = _
So, Marcel needs _ strings in all.
Marcel is making 6 toy banjos. He needs 5 strings for each banjo. How many stringsdoes he need in all?
Multiply with 5 and 10Essential Question How can you multiply with 5 and 10?
Lesson 4.2
• How many banjos is Marcel
making? __• How many strings does each
banjo have? __
Example 1 Use a number line.
Each string is 10 inches long. How many inches of string will Marcel use for each banjo?
Think: 1 jump = 10 inches
• Draw 5 jumps for the 5 strings. Jump 10 spaces at a time for the length of each string.
• You land on 10,_, _, _, and _. 5 × 10 = _
The numbers 10, 20, 30, 40, and 50 are multiples of 10.
So, Marcel will use _ inches of string for each banjo.
A multiple of 10 is any product that has 10 as one of its factors.
Operations and Algebraic Thinking—3.OA.A.3 Also 3.OA.A.1, 3.OA.C.7
MATHEMATICAL PRACTICESMP1, MP4, MP7
Analyze What do you notice about the multiples of 10?
50403020
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10 15 20 25 30
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6 banjos
5 strings
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Possible answer: the ones digit in the multiples of 10 is zero.
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5. How are all of the products in Exercise 4 alike?
7 10 10 2
6 60 70 1
3 5 0 5
0 9 5 25
4 10 10 2
7 20 90 9
6 5 7 5
1 5 8 40
1. 5 3 5
3 5 30
5 3 5
3 5 35
2. 3 5 70
10 3 5
10 3 5
3 5 40
3. 5 3 5
5 3 5
3 5 45
3 5 15
4. 3 5 20
10 3 5
3 5 10
10 3 5
Unknown Numbers
Use the numbers in each oval to complete four different number sentences. Use each number in the oval only once.
Lesson 4.2Enrich
Possible answers are shown. 8
51
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Possible answer: they are all even. The ones digit is always 0.
4-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Multiply with 5 and 10
You can use an array to multiply with 5.
Find the product. 5 3 4
Step 1 Make an array to show 5 3 4.Show 5 rows of 4 tiles.
Step 2 Count the tiles.5 rows of 4 tiles 5 20 tiles
So, 5 3 4 5 20.
You can use doubles to multiply with 10.
Find the product. 6 3 10
Think: 5 1 5 5 10
Multiply with 5. 6 3 5 5 30
Then double the product. 30 1 30 5 60
So, 6 3 10 5 60.
Find the product.
1. 2 3 5 5 2. 10 3 2 5 3. 5 3 5 5 4. 5 3 1 5
5. 10 3 1 5 6. 10 3 5 5 7. 3 3 5 5 8. 10 3 7 5
9. 10 3 4
_
40
10. 6 3 5
_
30
11. 9 3 5
_
45
12. 10 3 3
_
30
13. 5 3 2
_
10
14. 10 3 6
_
60
15. 8 3 5
_
40
16. 10 3 8
_
80
Lesson 4.2Reteach
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4-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
DifferentiatedInstruction1
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Enrich 4.2Reteach 4.2
Unlock the ProblemMATHEMATICAL PRACTICES
Be sure students understand what the numbers in the problem represent. MP2 Reason abstractly and quantitatively. • If there were 5 instruments with 6 strings
each, how would the skip counting be different? Possible answer: I would count by 6s instead of by 5s.
Example 1Help students see that each jump represents one string. Have them count aloud as they make each jump.A counting number is a whole number that can be used to count a set of objects (1, 2, 3, and so on). Explain that a multiple is a number that is the product of a given number and a counting number. Give examples of multiples of 5: 5, 10, 15, 20, 25; and multiples of 10: 10, 20, 30, 40, 50.• Why are multiples of 10 also multiples of 5?
Since 5 is a factor of 10, 10 is a multiple of 5. So, every multiple of 10 is also a multiple of 5.
MP3 Construct viable arguments and critique the reasoning of others.• When you multiply with 10, you can multiply
with 5 and then double the product. Explain how you would find the product 6 × 10 using this strategy. Possible answer: I would multiply 6 × 5 = 30. Then I can double 30. Since 30 + 30 = 60, the product 6 × 10 = 60.
MathTalk Use Math Talk to focus on students’
understanding that multiples of 10 always have 0 in the ones place.
ELL Strategy: Elicit Prior KnowledgeRemind students of previous learning by having them use a number line to skip count aloud by 2s, while they draw the jumps from 0–12.• Have students count the number of jumps it
took to get to 12.
• How many jumps by 2s did it take to reach 12 on the number line? 6
• Model the multiplication equation, 2 × 6 = 12.
• Have students follow the steps to skip count by 4s.
LESSON 4.23.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
COMMON ERRORS
COMMON ERRORS
EXPLAIN3
Quick Check
If
Rt I RR1
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Quick Check
If
Rt I 1
2
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Then
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MathTalk MATHEMATICAL PRACTICES 3
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Example 2 Use a bar model.
Marcel bought 3 packages of strings. Each package cost 10¢. How much did the packages cost in all?
So, the packages of strings cost _ in all.
Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and Show MATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD
1. How can you use this number line to find 8 × 5?
2. 2 × 5 = _ 3. _ = 6 × 10 4. _ = 5 × 5 5. 10 × 7 = _
Find the product.
6. 10 × 4
_
7. 5 × 6
_
8. 10 × 0
_
9. 5 × 3
_
10. 7 × 5
_
11. 5 ×10
_
12. 4 × 5
_
13. 9 ×10
_
THINK
1 unit → 10¢
3 units → _ × _
RECORD
_ × _ = _
MODEL
Apply How can knowing 4 × 5 help you find 4 × 10?
Possible answer: start at 0, make 8 jumps of 5 spaces each. 5, 10, 15, 20, 25, 30, 35, 40,
so 8 × 5 = 40.
Possible explanation: if you know 4 × 5 = 20, you can double 20 to fi nd the product of 4 and 10; 20 + 20 = 40, so 4 × 10 = 40.
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3 10¢ 3 10¢ 30¢
30¢
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Lesson 4.2 198
Error Students may write incorrect products for multiplications with 5 because they skip counted incorrectly.
Example In Exercise 7, students may write 6 × 5 = 35, instead of 6 × 5 = 30.Springboard to Learning Remind students to keep track of the number of times they skip count. The other factor tells them how many times to skip count.
Example 2Ask students to point to the bar model and say aloud what each section represents. Make sure students understand that each section represents one package of string. Then discuss what the total length of the bar represents.
Share and Show MATHBOARDMATHBOARDMBOARDMMMMBOARDBOARDBOARDBOARDMATHATHABOARDMMMMAAAATHATHATHTHTHATHATHATHAATHAAAATHAAATHATHTHTHATHATHAAATHATHATHAAATHABOARDBOARDBOARDBOARD
The first problem connects the learner to the learning model. Have students use the MathBoard to explain their thinking.
MathTalk Use Math Talk to reinforce the
doubles strategy students learned in the previous lesson. Students should recognize that the same reasoning that allows them to use doubles when multiplying with 4 can be used when multiplying with 10. • Explain how knowing 7 × 3 can help you find
7 × 6. If you know 7 × 3 = 21, you can double 21 to find the product of 7 and 6; 21 + 21 = 42, so 7 × 6 = 42.
Use the checked excercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.
a student misses the checked excercises
Differentiate Instruction with • Reteach 4.2 • Personal Math Trainer 3.OA.A.3 • RtI Tier 1 Activity (online)
VisualIndividual
Materials Analog Clockface (see eTeacher Resources)
• Ask students how each minute is shown on the clock. short lines between the numbers and at the numbers
• How many spaces are there between 12 and 1 on the clock? 5 spaces How many minutes does this represent? 5 minutes
• How many spaces are there between 12 and 2 on the clock? 10 spaces How many minutes does this represent? 10 minutes
• Have students write the related multiplication facts for each number on the clock using a factor of 5. 1 × 5 = 5, 2 × 5 = 10, 3 × 5 = 15, etc.
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Chapter 4 • Lesson 2 199
Name
On Your OwnOn Your Own
Find the product.
14. 5 × 1 = _
18. 10 × 0 = _
15. _ = 10 × 2
19. 10 × 5 = _
16. _ = 4 × 5
20. _ = 1 × 5
17. 10 × 10 = _
21. _ = 5 × 9
22. 3 × 4
_
23. 5 × 0
_
24. 4 × 8
_
25. 10 × 5
_
MATHEMATICALPRACTICE 7 Identify Relationships Algebra Use the pictures
to find the unknown numbers.
MATHEMATICALPRACTICE 4 Use a Diagram Complete the bar model to solve.
3 × _ = _ _ × 3 = _
______ ______
26. 27.
28. Marcel played 5 songs on the banjo. If each song lasted 8 minutes, how long did he play?
29. There are 6 banjo players. If each player needs 10 sheets of music, how many sheets of music are needed?
30. DEEPER Chris has 5 stacks of DVDs on a shelf. Each stack has 10 DVDs. If Chris adds 2 more identical stacks of DVDs to the shelves, how many DVDs will Chris have?
31. DEEPER Mark is making 10 kites. He uses 5 yards of ribbon for each kite. He has already made 2 of the kites. How many yards of ribbon will Mark need to make the rest of the kites?
50 5
20
45
5
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20 100
012 5032
155 3010
40 minutes
70 DVDs
60 sheets of music
40 yards
199 Chapter 4
On Your OwnIf students complete the checked excercises correctly, they may continue with the On Your Own section. MP7 Look for and make use of structure. Exercises 26 and 27 require students to interpret pictures to find unknown factors in multiplication sentences.MP4 Model with mathematics. Exercises 28 and 29 require students to label a bar model and use it to answer the question.MP3 Construct viable arguments and critique the reasoning of others. Discuss different strategies that can be used to find unknown factors. Write × 5 = 25 on the board. Tell students that one strategy they can use to find the unknown factor in this problem is to find how many 5s are in 25. Have students use this strategy by starting at 0, counting on by 5s to 25, and keeping track of how many 5s are counted.
ELABORATE4
Differentiated Centers Kit
DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESDEVALUATE5 Formative
Assessment
Stringed Instruments
Guitar 6
5
8
4
Banjo
Mandolin
Violin
Instrument Strings
MATHEMATICAL PRACTICES M
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Use the table for 32–34.
32. John and his dad own 7 banjos. They want to replace the strings on all of them. How many strings should they buy? Write a multiplication sentence to solve.
33. DEEPER Mr. Lemke has 5 guitars, 4 banjos, and 2 mandolins. What is the total number of strings on Mr. Lemke’s instruments?
34. SMARTER The orchestra has 5 violins and 3 guitars that need new strings. What is the total number of strings that need to be replaced? Explain.
35. WRITE Math What’s the Error? Mr. James has 3 banjos. Mr. Lewis has 5 times the number of banjos Mr. James has. Riley says Mr. Lewis has 12 banjos. Describe her error.
36. SMARTER Circle the number that makes the multiplication sentence true.
5 × 789
= 45
7 × 5 = 35; 35 strings
66 strings
Possible answer: Riley multiplied 4 × 3
38 strings; possible explanation: the violins will need
instead of 5 × 3. Mr. Lewis has 15 banjos.
5 × 4 = 20 strings; the guitars will need 3 × 6 = 18 strings.
Then add 20 + 18 = 38.
Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.
SMARTER
Lesson 4.2 200
Students read the book and determine how to use multiplication to find the total number of objects in each collection.
Students complete purple Activity Card 7 by using randomly generated factors to practice multiplication facts for 1, 2, 4, and 5.
Students complete blue Activity Card 7 by using nickels to practice counting by fives.
LiteratureCollections Times Four
ActivitiesFactor Spin
ActivitiesLine ’Em Up
Essential QuestionUsing the Language ObjectiveReflect Have students explain to a partner to answer the Essential Question. How can you multiply with 5 and 10? Possible answers: skip count; use a number line; use a bar model; draw a picture
Math Journal WRITE MathMichelle bought some pinwheels for a dollar and paid in dimes. How many dimes did she use? Explain.
MATHEMATICAL PRACTICES
MP1 Make sense of problems and persevere in solving them. Have students read the first problem and discuss how they will solve it. You may need to remind them to use the data in the table.
DEEPER
Exercise 33 requires students to organize their work so they can find the numbers they need to answer the question.
SMARTER
This item gives students a menu of three numbers from which to choose the missing factor. Students must demonstrate a knowledge of multiplying with 5 to make the multiplication sentence true.
Math on the Spot Video TutorUse this video to help students model and solve this type of Think Smarter problem.
Problem Solving • Applications
Cross-Curricular
Problem SolvingProblem Solving
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Multiply with 5 and 10
Find the product.
17. Ginger takes 10 nickels to buy some pencils at the school store. How many cents does Ginger have to spend?
_______
18. The gym at Evergreen School has three basketball courts. There are 5 players on each of the courts. How many players are there?
_______
Chapter 4 201
9. 5 × 6
_
10. 10 × 7
_
11. 5 × 3
_
12. 10 × 4
_
13. 5 × 0
_
14. 10 × 8
_
15. 5 × 2
_
16. 10 × 6
_
5. 1× 10 = ______ 6. ______ = 4 × 5 7. 5× 10 = ______ 8. 7× 5 = ______
1. 5× 7 = ______ 2. 5× 1 = ______ 3. 2 × 10 = ______ 4. ______ = 8 × 5
COMMON CORE STANDARD—3.OA.A.3 Represent and solve problems involving multiplication and division.
Lesson 4.2Practice and Homework
70 15 40
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50 cents
Check students’ work.
15 players
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19. WRITE Math Michelle bought some pinwheels for a dollar and paid in dimes. How many dimes did she use? Explain.
201 Chapter 4
Practice and HomeworkUse the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers.
SCIENCE SOCIAL STUDIES
Materials pictures of ants, ladybugs, and other insects
• Insects are arthropods. An arthropod is an invertebrate (an animal with no backbone) that has a segmented body.
• The insect body has 3 parts: the head, the thorax, which is the middle of the body, and the abdomen, which is the back. Insects have 6 legs.
• The mass of an object is the amount of matter the object has. An ant can carry 5, 10, and even 30 times its mass.
• Have students write and solve word problems. For example: If an ant has a mass of 3 milligrams, how much can it carry? 5 3 3 5 15 mg; 10 3 3 5 30 mg
• The United States and Canada use dollars that are worth 100 cents.
• Mexico uses new (nuevo) pesos. One peso is equal to 100 centavos. There are coins worth 5, 10, 20, and 50 centavos.
• Both Canada and the United States have nickels worth 5 cents. If you had 4 nickels, how many cents would you have? 20 cents
• If you had 6 five-centavos coins, how many centavos would you have? 30 centavos
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Zoo
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Field Trip Choices
Key: Each = 2 votes.
Personal Math Trainer
FOR MORE PRACTICE GO TO THE
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Lesson Check (3.OA.A.3)
1. Mrs. Hinely grows roses. There are 6 roses on each of her 10 rose bushes. How many roses in all are on Mrs. Hinely’s rose bushes?
2. Find the product.
5 × 8
_
Spiral Review (3.OA.D.9, 3.NBT.A.1, 3.MD.B.3)
3. Mr. Miller’s class voted on where to go for a field trip. Use the picture graph to find which choice had the most votes.
4. Zack made this table for his survey.
How many votes were cast?
5. Which of the following is an even number?
25, 28, 31, 37
6. Estimate the sum.
202
479 + 89
__
60 roses
zoo
28
47 votes
Possible answer: about 600
40
Lesson 4.2 202
Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.