Upload
lamkhue
View
316
Download
4
Embed Size (px)
Citation preview
For the student For the teacher
Teacher Edition
Math on the Spot Video Tutor Online Assessment
System
Soar to Success Math Online Intervention
iTools Virtual Manipulatives
Digital ManagementCenter organizes program resources by TEKS!
Interactive Student Edition provides students
with an interactive learning environment!
Resources
e
Texas Essential Knowledge and Skills
Number and Operations—5.3.C Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm Also 5.3.A
MATHEMATICAL PROCESSES5.1.B Use a problem-solving model
Are You Ready?Access Prior KnowledgeUse the Are You Ready? 2.6 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.
Vocabulary
Go to Multimedia eGlossary at thinkcentral.com
2.6 Divide by 2-Digit Divisors How can you divide by 2-digit divisors?Essential Question?
Lesson OpenerMaking ConnectionsInvite students to tell you what they know about division of whole numbers.
When do we use division to solve a problem? (to find how many equal-sized groups are in a set of objects [partitive division], or how to find the number of groups of a given size within a set of objects [quotative division]) What is one way to estimate a quotient? (Possible answer: Divide compatible numbers.)
Using the Digital LessonTalk about using division to figure out calendar information. For example, if a student knows how many hours were spent doing homework in a month and needs to find about how many hours were spent doing homework in a day.
Learning Task• What information is given in this problem? (the number of miles a car traveled
and the number of miles the car travels on one gallon of gas—its MPG)
• What do we have to find? (about how many gallons of gas were used on the trip)
• What strategy can you use to solve the problem? (divide 1,407 by 32) Why? (Possible answer: I am looking for the number of equal groups of 32 in 1,407.)
Literacy and Mathematics• Write the acronym MPG on the board and explain what it means. Then, tell students
that different types of cars have different MPG ratings. Ask students how the MPG ratings of small cars and large cars may vary. Then, have students give reasons why a greater MPG rating is better than a lesser one.
• Tell students that a typical fuel tank in a compact car holds about 15 gallons of gas. Ask them to calculate about how many miles a car might go if its MPG rating was 45.
How can you divide by 2-digit divisors?
Lesson 2.6 85A
Essential Question?
Unlock the ProblemUnlock the Problem
Mathematical ProcessesMath Talk
Number and Operations—5.3.C Also 5.3.A
MATHEMATICAL PROCESSES5.1.B
2.6Name
How can you divide by 2-digit divisors?
Divide by 2-Digit Divisors
Mr. Yates owns a smoothie shop. To mix a batch of his famous smoothies,
he uses 18 ounces of orange juice. Each day he uses 560 ounces of orange
juice. How many batches of smoothies can Mr. Yates make in a day?
• Underline the sentence that tells you what you are trying to find.
• Circle the numbers you need to use.
Divide. 560 ÷ 18 Estimate. ___
STEP 1 Use the estimate to place the first digit in the quotient.
18 ) ‾ 560 The first digit of the quotient will be in the __ place.
STEP 2 Divide the tens.
3 18 ) ‾ 560
−54
2
56 tens ÷ 18Divide. ____
Multiply. ____
Subtract. ____
Check. 2 tens cannot be shared among 18 groups without regrouping.
STEP 3 Divide the ones.
31 18 ) ‾ 560
−54
20 −18
_
2
r2
Divide. ____
Multiply. ____
Subtract. ____
Check. ____
____
Since _ is close to the estimate of 30, the answer is reasonable.
So, Mr. Yates can make _ batches of smoothies each day.
Explain what the remainder 2 represents.
600 ÷ 20 = 30
tens
31
31
18 × 3 tens = 54 tens
56 tens − 54 tens
20 ones ÷ 18
18 × 1 one = 18 ones
The remainder represents the 2 ounces of orange juice left over after the 31 batches are made.
20 ones − 18 ones
2 ones cannot be shared
among 18 groups.
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
Module 2 85
English Language Learners Language SupportELL
9 8 2 92 1 ,
ELPS 2.I.3, 3.C.4, 3.D.2Leveled Activities ELPS
Beginning: Activity 19 1.A.1, 3.E, 4.F.7
Intermediate: Activity 22 1.A.1, 3.G.1, 4.C.1
Advanced: Activity 46 1.F, 2.I.4, 4.G.2
Advanced High: Activity 35 1.B.1, 1.F, 3.C.4, 3.G.2
Go to thinkcentral.com for the ELL Activity Guide containing these leveled activities.
Strategy: Describe• Students describe the process of solving a division
problem using the traditional algorithm.• Show students a division problem. Students take
turns describing how to solve the problem.• Have students focus on how to determine each digit in the quotient.
Lead them by asking, “How did you find this digit?” or “How do you know if this digit is too low or too high?”
Auditory Small Group
Unlock the ProblemDo you know what a smoothie is? Read the problem to learn the answer.
After students underline and circle the relevant information, ask:
• Why is division used to solve this problem? Possible answer: Division involves the number of groups, the number in each group, and the whole. In this problem, we know that 560 ounces is the whole and that there are 18 ounces in each group. So, we divide 560 by 18 to find the number of groups.
Discuss the solution.
• In Step 2, we divide the tens. Why can’t we divide the hundreds? Possible answer: 5 hundreds cannot be divided into 18 equal groups without regrouping.
• How many tens are we dividing in Step 2? Explain. We are dividing 56 tens; 5 hundreds 6 tens were regrouped as 50 tens 6 tens, or 56 tens altogether.
After discussing the solution, ask:
• Why wasn’t the remainder included as part of our answer? Possible answer: It is not reasonable for Mr. Yates to make a partial batch of smoothies.
Math Talk Use Math Talk to focus on students’ understanding of what remainders represent in various division problems.
Mathematical Processes
85 Module 2
Example
Share and ShowShare and Show
Every Wednesday, Mr. Yates orders fruit. He has set aside $1,250 to
purchase Valencia oranges. Each box of Valencia oranges costs $41.
How many boxes of Valencia oranges can Mr. Yates purchase?
You can use multiplication to check your answer.
Divide. 1,250 ÷ 41
DIVIDE CHECK YOUR WORK
Estimate. ___
41 1,2503030 r20
) ‾ × 4130–
+ +1,2001,250 –
So, Mr. Yates can buy _ boxes of Valencia oranges.
1. 28 ) ‾ 620 2. 64 ) ‾ 842 3. 53 ) ‾ 2,340
4. 723 ÷ 31 5. 1,359 ÷ 45 6. 7,925 ÷ 72
Divide. Check your answer.
1,200 ÷ 40 = 30
1,2301232020
1,230020
30
22 r4 13 r10 44 r8
23 r10 30 r9 110 r5
86
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.
Enrich VisualIndividual
• Many distance records have been set and then broken for hot-air balloons. Have students use the information below to find which balloon flight had the fastest average speed in miles per hour. (Hint: Speed = distance ÷ time) 2,900 ÷ 33 is 87 r29; 6,700 ÷ 47 is 142 r26; 26,542 ÷ 472 is 56 r110. So, the 1991 hot air balloon flight had the fastest average speed.
ExampleAsk the question shown below as you discuss the divide step of the solution.
• The division step shows the completed solution. Look at the first digit in the quotient. Explain how division, multiplication, and subtraction were used for that digit. Compatible numbers and division were used to identify and place the first digit in the quotient. Multiplication was used to find the amount we subtract. Then subtraction was used to continue the division.
Consider the same question for the second digit in the quotient.
Share and ShowThe first problem connects to the learning model. Have students use the MathBoard to explain their thinking.
Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.
1
2
3
a student misses the checked exercises
Quick Check
IF
THENDifferentiate Instruction withRtI Tier 1 Lesson 14
Hot-Air Balloon Distance Records
Year Distance Traveled (miles) Time (hours)
1987 2,900 33
1991 6,700 47
1999 26,542 472
Lesson 2.6 86
Problem SolvingProblem Solving
Problem SolvingProblem Solving
20 ounces cranberry juice10 ounces passion fruit juice
18 ounces orange juice12 ounces mango juice
22 ounces grape juice8 ounces apple juice
Royal Purple Smoothie
Orange Tango Smoothie
Crazy Cranberry Smoothie
Name
Use the list at the right to solve 14–16.
14. A smoothie shop receives a delivery of
980 ounces of grape juice. How many Royal
Purple smoothies can be made with the
grape juice?
15. Multi-Step
The shop has 1,260 ounces
of cranberry juice and
650 ounces of passion fruit
juice. If the juices are used
to make Crazy Cranberry
smoothies, which juice will run out first?
How much of the other juice will be left
over?
Practice: Copy and Solve Divide. Check your answer.
7. 775 ÷ 35 8. 820 ÷ 41 9. 805 ÷ 24
10. 1,166 ÷ 53 11. 1,989 ÷ 15 12. 3,927 ÷ 35
13. Why can you use multiplication to check division? Explain.
16. In the refrigerator, there are 680 ounces of orange juice
and 410 ounces of mango juice. How many Orange Tango smoothies can
be made? Explain your reasoning.
44 smoothies
cranberry juice; 20 ounces of passion fruit juice will be left over
34 smoothies; Possible explanation: The orange juice can be used in 37 Orange Tango
smoothies, and the mango juice can be used to make 34 Orange Tango smoothies. You
will run out of mango juice after 34 smoothies.
22 r5 20 33 r13
22 132 r9 112 r7
Possible answer: Since multiplication is the inverse operation of division, the product
should be close to the dividend, even without adding the remainder.
Module 2 • Lesson 6 87
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
5.3.C
Name
When you divide by a 2-digit divisor, you can use estimation to help you place the first digit in the quotient. Then you can divide.
Divide. 53 ) - 2,369
Step 1 Use compatible numbers to estimate the quotient. Then use the estimate to place the first digit in the quotient.
The first digit will be in the tens place.
Step 2 Divide the tens.
Step 3 Bring down the 9 ones.Then divide the ones.
So, 2,369 ÷ 53 is .
Divide. Check your answer.
1. 52 ) -
612 2. 63 ) -
917 3. 89 ) -
1,597
4. 43 ) -
641 5. 27 ) -
4,684 6. 64 ) -
8,455
Divide by 2-Digit DivisorsOBJECTIVE Divide by 2-digit divisors.
LESSON 14
Think:
Divide: 236 tens ÷ 53
Multiply: 53 × 4 tens = 212 tens
Subtract: 236 tens - 212 tens
Compare: 24 < 53, so the first digit of the quotient is reasonable.
Think:
Divide: 249 ones ÷ 53
Multiply: 53 × 4 ones = 212 ones
Subtract: 249 ones - 212 ones
Compare: 37 < 53, so the second digit of the quotient is reasonable.
Write the remainder to the right of the whole number part of the quotient.
44 r37
50 ) - 2,000
53 )- 2,369 -212
24
53 ) - 2,369 -212
249-212
37
40
4
44 r37
11 r40
14 r39
14 r35
173 r13
17 r84
132 r7
Check students’ work.
Number and Operations 27 © Houghton Mifflin Harcourt Publishing Company
Name
E14
Enrich 14
Enrich
14 366) ———
START
5
5 r12
27 951)—–––
58 933)———
18 1,981)—————
39 1,600)—————45 548)————
48 3,120)————
66 4,800)————
79 1,264)————
15 1,230)—————
65
12
64
35 r635 r16
111
110 r1
16 r16
16 r5
80 r2
16
17
72 r48
72 r58
12 r8
22 122)————
41 r1
FINISH
40 r38
16
26 r2
A-Mazing Division
Solve each division problem, beginning at START. Draw a line from
the problem to the correct quotient. Continue until you reach FINISH.
If you reach a dead end, go back and try again.
82
Enrich 14RtI Tier 1 Lesson 14
COMMON ERRORSError When dividing, subtraction produces a number that is greater than or equal to the divisor.
Example
Springboard to Learning Point out that the division cannot continue when the difference is greater than or equal to the divisor. Have these students compute the result of increasing the corresponding digit in the quotient by 1.
CE
Problem SolvingBefore students complete the exercises, ask them to describe two different ways to check their answers. One way is to compare the exact answer to the estimate that was used to place the first digit and decide if the exact answer is reasonable. Another way is to multiply the divisor by the quotient, add the remainder to the product, and see if the result is equal to the dividend.
ProblemProblem 16 requires students to analyze the recipes to determine the number of smoothies that can be made with the given ingredients.
63 ) ‾ 1,953 −1 26 69
2
Math on the Spot Video Tutor
Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and H.O.T. problems, students will build skills needed in the TEXAS assessment.
MV
Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.
1
2
3
87 Module 2
Daily Assessment TaskDaily Assessment Task
Mathematical Processes
TEXAS Test Prep 20. James has 1,836 marbles. He decides to divide them equally among
23 boxes. How many marbles will James have left over?
A 19
B 23
C 90
D 79
Fill in the bubble completely to show your answer.
17. A shipment of 572 scented erasers has arrived at the school store.
You want to sell them in sets of 15. How many full sets of erasers
can you make?
A 40 C 39
B 38 D 37
18. Darius counted that he walks 864 steps from his house to the bookstore.
If Darius takes 52 steps each minute, about how long will it take him to
reach the bookstore?
A 31 minutes
B 17 minutes
C 13 minutes
D 20 minutes
19. Multi-Step The school store has 1,262 bouncy balls. The bouncy
balls are packaged in sets. Any single bouncy ball is sold for $1.
If all the bouncy balls sell, which of the following will give the store
the best profit?
A Sets of 25 for $13
B Sets of 16 for $9
C Sets of 12 for $7
D Sets of 10 for $6
88
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
Differentiated Centers Kit
THENIF
YES
NO
Daily Assessment Task 1
2
3
• Enrich 14
• Homework and Practice Lesson 2.6
• Soar to Success MathWarm-Up 13.39
LiteratureA Drive Through HistoryStudents read about how the Alverez family uses multiplication and division to plan their vacation
ActivitiesDecide and DivideStudents complete purple Activity Card 15 by estimating quotients and then dividing 3-digit dividends by 2-digit divisors.
ActivitiesDivide and ConquerStudents complete orange Activity Card 15 by making and solving problems with 3-digit dividends and 2-digit divisors.
TEXAS Test Prep CoachIn the Test Prep exercise, if students selected:
B They used the divisor instead of the remainder.
C They used estimation.
D They used the quotient instead of the remainder.
Essential Question? WriteMathWriteMath
How can you divide by 2-digit divisors? Possible answer: First, I use compatible numbers and an estimate to place the first digit. Then, I repeat these steps: divide, multiply, subtract and compare, and then regroup when necessary.
Can students divide by 2-digit numbers?
Lesson 2.6 88
TEXAS Test PrepLesson CheckLesson Check
13. Tamera has a rubber band ball made of
3,241 rubber bands. How many complete
smaller rubber band balls can she make if
each small ball is made of 80 bands?
A 28
B 40
C 53
D 41
14. Sam picks out a book that has 468 pages. He
wants to finish the book in 36 days. If he reads
the same number of pages each day, how
many pages should he read?
A 23
B 17
C 13
D 11
15. A baker has 834 fluid ounces of muffin batter.
Each muffin needs 12 fluid ounces of batter.
How many muffins can the baker make?
A 70
B 69
C 68
D 65
16. Springfield has an aquarium that holds
336 gallons of water. It takes 24 hours to fill
the aquarium. How many gallons of water
fill the aquarium each hour?
A 16 gallons
B 14 gallons
C 15 gallons
D 13 gallons
17. Multi-Step A juice bar has 768 ounces of
passion fruit juice and 810 ounces of berry
juice. Passion fruit juice is sold in 16-ounce
cups. Berry juice is sold in 18-ounce cups.
Which statement is true?
A The juice bar can sell 3 more cups of
berry juice than passion fruit juice.
B The juice bar can sell the same number
of cups of berry juice and passion fruit
juice.
C The juice bar can sell fewer than 90 total
cups of berry juice and passion fruit
juice.
D The juice bar can sell 3 more cups of
passion fruit juice than berry juice.
18. Multi-Step A city has 7,204 recycle bins. The
city gives half of the recycle bins to its citizens.
The rest of the recycle bins are divided into
23 equal groups for city parks. How many
recycle bins are left over?
A 14
B 156
C 138
D 28
Fill in the bubble completely to show your answer.
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
90
Problem SolvingProblem Solving
Name
Homeworkand Practice
Divide. Check your answer.
1. 18 ) ‾ 783 2. 22 ) ‾ 4,722 3. 56 ) ‾ 891
4. 19 ) ‾ 3,192 5. 63 ) ‾ 173 6. 43 ) ‾ 8,382
7. 39 ) ‾ 5,109 8. 32 ) ‾ 832 9. 14 ) ‾ 573
Explain.
10. You can check your answer to a division problem by using multiplication.
How can you check the answer when a division problem has a remainder?
11. Leon has 1,353 bottle caps in his collection.
He decides to divide them evenly among
47 boxes. How many bottle caps will Leon
have left over?
12. It takes 48 ounces of vegetable broth to make
a pot of Chef Zoe’s minestrone soup. How
many pots of soup can be made with
432 ounces of broth?
2.6 Divide by 2-Digit Divisors
Number and Operations—5.3.CAlso 5.3.AMATHEMATICAL PROCESSES 5.1.B
43 r9
168
131
214 r14
2 r47
26
15 r51
194 r40
40 r13
Possible answer: After the quotient and divisor are multiplied, the remainder
must be added to get the dividend.
37 bottle caps 9 pots
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
Module 2 • Lesson 6 89
555555555
Homework and PracticeUse the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson.
89-90 Module 2