Name Daily Spiral Review - Wikispaces7+masters.pdfDaily Spiral Review 7-1 Daily Spiral Review 7-1 ... W riting to Explain Dominic claims that when he multiplied 40 ! 50 he got an answer

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Daily Spiral Review 7-1

Daily Spiral Review

7-1

1. Micah collected shells on the beach during her summer vacation. If she collected 12 shells each day of her 5-day vacation, how many shells did she collect in all?A 48B 50C 60D 72

2. Susana has $30. She plans to buy a game that costs $16 and a game that costs $11. How much money will she have left over?A $27B $26C $4D $3

3. Mr. Horn, the band teacher, wants to split the band into 4 equal groups. There are 36 members in the band. Which operation will help him to quickly determine how many students will be in each group? A AdditionB SubtractionC MultiplicationD Division

4. Round the number 45,446 to the following places:

Ten: Hundred: Thousand

5. The distance from Michael’s house to his grandmother’s house is 240 miles, round trip. If Michael visits his grandmother 6 times a year, how many miles does he travel?

6. Write the next two numbers in the pattern.

8, 16, 32, ,

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Topic 7 21


Daily Spiral Review

7-1

1. Micah collected shells on the beach during her summer vacation. If she collected 12 shells each day of her 5-day vacation, how many shells did she collect in all?A 48B 50C 60D 72

2. Susana has $30. She plans to buy a game that costs $16 and a game that costs $11. How much money will she have left over?A $27B $26C $4D $3

3. Mr. Horn, the band teacher, wants to split the band into 4 equal groups. There are 36 members in the band. Which operation will help him to quickly determine how many students will be in each group? A AdditionB SubtractionC MultiplicationD Division


Ten: Hundred: Thousand

5. The distance from Michael’s house to his grandmother’s house is 240 miles, round trip. If Michael visits his grandmother 6 times a year, how many miles does he travel?

6. Write the next two numbers in the pattern.

8, 16, 32, , 64 128

About 1,400 miles

45,45045,40045,000


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Topic 7

Problem of the Day 7-1

7-1Problem of the DayProblem

of the Day

7-1

The zoo offers 5 boat tours and 8 train tours every day. How many tours will the train have made when the boat has made 35 tours? (Hint: Make a table.)

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1. Every day, 600 people eat at Franco’s diner. How many people eat there in a week?

A 420

B 4,200

C 42,000

D 420,000

3. There are 100 centimeters in a meter. If a classroom is 8 meters long, how long is it in centimeters?

A 80,000

B 8,000

C 800

D 80

2. Each of the 90 fourth-grade students at North Elementary read 30 books over the school year. How many books did they read altogether?

A 27

B 270

C 2,700

D 27,000

Quick Check

7-1Q

uick Check 7

-1

4. Writing to Explain Dominic claims that when he multiplied 40 ! 50 he got an answer of 200. Is Dominic correct? Explain why or why not.


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Topic 7 23

1. Every day, 600 people eat at Franco’s diner. How many people eat there in a week?

A 420

B 4,200

C 42,000

D 420,000

3. There are 100 centimeters in a meter. If a classroom is 8 meters long, how long is it in centimeters?

A 80,000

B 8,000

C 800

D 80

2. Each of the 90 fourth-grade students at North Elementary read 30 books over the school year. How many books did they read altogether?

A 27

B 270

C 2,700

D 27,000

Quick Check

7-1Q

uick Check 7

-1

4. Writing to Explain Dominic claims that when he multiplied 40 ! 50 he got an answer of 200. Is Dominic correct? Explain why or why not.

See student samples to the right.


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Reteaching

7-1Using Mental Math to Multiply 2-Digit NumbersYou can multiply with mental math by using basic facts and patterns.

Example A: 5 ! 5 " 25

5 ! 50 " 250

The product contains the number of zeros in each factor.

Example B: 5 ! 6 " 30

5 ! 60 " 300

50 ! 60 " 3,000

50 ! 600 " 30,000

When the product of a basic fact includes a zero, such as 5 ! 6 " 30, that zero is not part of the pattern.

Multiply. Use mental math.

1. 20 ! 20 " 2. 50 ! 10 " 3. 40 ! 40 "

4. 30 ! 80 " 5. 60 ! 600 " 6. 50 ! 900 "

7. 70 ! 300 " 8. 70 ! 600 " 9. 40 ! 500 "

10. Number Sense Tell what numbers go in the blanks.

To find 90 ! 300, multiply and .

Then write zeros at the end.


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Reteaching

7-1Using Mental Math to Multiply 2-Digit NumbersYou can multiply with mental math by using basic facts and patterns.

Example A: 5 ! 5 " 25

5 ! 50 " 250

The product contains the number of zeros in each factor.

Example B: 5 ! 6 " 30

5 ! 60 " 300

50 ! 60 " 3,000

50 ! 600 " 30,000

When the product of a basic fact includes a zero, such as 5 ! 6 " 30, that zero is not part of the pattern.

Multiply. Use mental math.

1. 20 ! 20 " 2. 50 ! 10 " 3. 40 ! 40 "

4. 30 ! 80 " 5. 60 ! 600 " 6. 50 ! 900 "

7. 70 ! 300 " 8. 70 ! 600 " 9. 40 ! 500 "

10. Number Sense Tell what numbers go in the blanks.

To find 90 ! 300, multiply and .

Then write zeros at the end.

400 500 1,600

2,400 36,000 45,000

21,000 42,000 20,000

9 33


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Topic 7 25

Practice 7-1

Practice

7-1Using Mental Math to Multiply 2-Digit NumbersMultiply. Use mental math.

1. 4 ! 30 " 2. 5 ! 90 "

3. 9 ! 200 " 4. 6 ! 500 "

5. 3 ! 600 " 6. 0 ! 600 "

7. 90 ! 70 " 8. 70 ! 400 "

9. 50 ! 800 " 10. 30 ! 800 "

11. 90 ! 500 " 12. 30 ! 4,000 "

13. Number Sense How many zeros are in the product of 60 ! 900? Explain how you know.

Truck A can haul 400 pounds in one trip. Truck B can haul 300 pounds in one trip.

14. How many pounds can Truck A haul in 9 trips?

15. How many pounds can Truck B haul in 50 trips?


A 280 B 2,800 C 28,000 D 280,000

17. Writing to Explain There are 9 players on each basketball team in a league. Explain how you can find the total number of players in the league if there are 30 teams.


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Topic 7 25

Practice 7-1

Practice

7-1Using Mental Math to Multiply 2-Digit NumbersMultiply. Use mental math.

1. 4 ! 30 " 2. 5 ! 90 "

3. 9 ! 200 " 4. 6 ! 500 "

5. 3 ! 600 " 6. 0 ! 600 "

7. 90 ! 70 " 8. 70 ! 400 "

9. 50 ! 800 " 10. 30 ! 800 "

11. 90 ! 500 " 12. 30 ! 4,000 "

13. Number Sense How many zeros are in the product of 60 ! 900? Explain how you know.

Truck A can haul 400 pounds in one trip. Truck B can haul 300 pounds in one trip.


15. How many pounds can Truck B haul in 50 trips?


A 280 B 2,800 C 28,000 D 280,000

17. Writing to Explain There are 9 players on each basketball team in a league. Explain how you can find the total number of players in the league if there are 30 teams.

1201,8001,8006,30040,00045,000

4503,000028,00024,000120,000

3,600 lb15,000 lb

Multiply the number of players on each team by the number of teams in the league. 9 ! 30 " 270 players.

There are three zeros, one from 60 and two from 900.


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Enrichment

7-1The World’s Greatest

World’s sleepiest animal

1. A koala sleeps about 20 hours each day. How many hours does it sleep in the month of June?

World’s number 1 milk drinking country

2. Each person in Ireland drinks about 700 cups of milk each year. How many cups would each person drink in 5 decades?

World’s fastest orbiting planet

3. Mercury orbits the sun in 88 days. The planet travels about 30 miles in 1 sec. How far does the planet travel in 1 minute?

World’s busiest airport

4. Hartsfield Atlanta International Airport in Georgia has about 2,000 airplanes depart and arrive each day. How many times do planes land and take off in April?

World’s coldest populated place

5. Norilsk is a small city in central Russia. The average temperature is 12.4°F. The city has 5 months without sunlight each year. How many months without sunlight occur in 1 century?

World’s heaviest land mammal

6. The African elephant weighs about 14,000 pounds. It eats about 50,000 pounds of twigs, foliage, grasses, and fruit every 3 months. How many pounds of food does it eat in 1 year?

1 min ! 60 sec

1 h ! 60 min

1 month ! 28–31 days

1 year ! 12 months

1 decade ! 10 years

1 century ! 100 years

Mental Math


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Enrichment

7-1The World’s Greatest

World’s sleepiest animal

1. A koala sleeps about 20 hours each day. How many hours does it sleep in the month of June?

World’s number 1 milk drinking country

2. Each person in Ireland drinks about 700 cups of milk each year. How many cups would each person drink in 5 decades?

World’s fastest orbiting planet

3. Mercury orbits the sun in 88 days. The planet travels about 30 miles in 1 sec. How far does the planet travel in 1 minute?

World’s busiest airport

4. Hartsfield Atlanta International Airport in Georgia has about 2,000 airplanes depart and arrive each day. How many times do planes land and take off in April?

World’s coldest populated place

5. Norilsk is a small city in central Russia. The average temperature is 12.4°F. The city has 5 months without sunlight each year. How many months without sunlight occur in 1 century?

World’s heaviest land mammal

6. The African elephant weighs about 14,000 pounds. It eats about 50,000 pounds of twigs, foliage, grasses, and fruit every 3 months. How many pounds of food does it eat in 1 year?

1 min ! 60 sec

1 h ! 60 min

1 month ! 28–31 days

1 year ! 12 months

1 decade ! 10 years

1 century ! 100 years

Mental Math

600 h

35,000 c

1,800 mi

60,000 times

500 months

200,000 lb


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Topic 7 27

Daily Spiral Review

7-2Daily Spiral Review

7-2

Daily Spiral Review

7-2

Noah is starting a pet-sitting business. He made the chart below to show his rates for different types of jobs.

Noah’s Pet-Sitting ServiceJob Rate

Dog Walking $10 Cleaning Bird Cages $9 Cleaning Litter Boxes $8 Feeding Fish $2

Use the chart to answer Exercises 1–3.

1. If Noah walks 2 dogs each day, how much money does he earn in one week?A $180B $160C $140D $100

2. Last Saturday, Noah walked 1 dog, cleaned 2 litter boxes, and fed 5 ! sh. How much money did Noah earn? A $36B $38C $40D $44

3. Noah hopes to earn $72 by cleaning out bird cages this week. How many bird cages will Noah have to clean to earn $72? A 7B 8C 9D 10

Find the partial products and the product for Exercise 4.

4. 4 ! 27 "

Partial products:

Product:

5. Put the following numbers in order from least to greatest: 12,720; 12,718; 12,721; 12,684.

6. The principal at Tucker Elementary wants to order T-shirts for each student to wear on Field Day. There are 6 grades of students at Tucker Elementary. Each grade has almost 80 students. How many T-shirts does the principal need to order?



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Topic 7 27

Daily Spiral Review


7-2

Daily Spiral Review

7-2

Noah is starting a pet-sitting business. He made the chart below to show his rates for different types of jobs.

Noah’s Pet-Sitting ServiceJob Rate

Dog Walking $10 Cleaning Bird Cages $9 Cleaning Litter Boxes $8 Feeding Fish $2

Use the chart to answer Exercises 1–3.

1. If Noah walks 2 dogs each day, how much money does he earn in one week?A $180B $160C $140D $100

2. Last Saturday, Noah walked 1 dog, cleaned 2 litter boxes, and fed 5 ! sh. How much money did Noah earn? A $36B $38C $40D $44

3. Noah hopes to earn $72 by cleaning out bird cages this week. How many bird cages will Noah have to clean to earn $72? A 7B 8C 9D 10

Find the partial products and the product for Exercise 4.

4. 4 ! 27 "

Partial products:

Product:

5. Put the following numbers in order from least to greatest: 12,720; 12,718; 12,721; 12,684.

6. The principal at Tucker Elementary wants to order T-shirts for each student to wear on Field Day. There are 6 grades of students at Tucker Elementary. Each grade has almost 80 students. How many T-shirts does the principal need to order?


4 ! 20 " 804 ! 7 " 28

108

12,684; 12,718; 12,720; 12,721

480



28

Topic 7

Problem of the DayTell what operation. Solve.

Mr. Top is printing programs for the seats at the dinner theater. There are 50 tables that each seat 10 people. How many programs must he print?

Problem of the Day

7-2

7-2Problem of the Day 7-2


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1. Tyler read 94 pages a week. About how many pages will he read in 45 weeks?

A 3,600

B 4,000

C 4,500

D 5,000

2. During a fundraiser, the 22 members of Ms. Holzman’s class each raised about $28.00. Approximately how much money did the class raise altogether?

A $1,000

B $900

C $600

D $400

Quick Check

7-2Q

uick Check 7

-23. Annie drove for 15 hours. She drove 61 miles per hour. About how far did Annie drive?

A 600

B 900

C 950

D 1,500

4. Writing to Explain Why is it important to know how to estimate? Name two specific real-life situations when you might use estimation.


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1. Tyler read 94 pages a week. About how many pages will he read in 45 weeks?

A 3,600

B 4,000

C 4,500

D 5,000

2. During a fundraiser, the 22 members of Ms. Holzman’s class each raised about $28.00. Approximately how much money did the class raise altogether?

A $1,000

B $900

C $600

D $400

Quick Check

7-2Q

uick Check 7

-23. Annie drove for 15 hours. She drove 61 miles per hour. About how far did Annie drive?

A 600

B 900

C 950

D 1,500

4. Writing to Explain Why is it important to know how to estimate? Name two specific real-life situations when you might use estimation.



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Reteaching

7-2Estimating ProductsEstimate 11 ! 94.

Using rounding Using compatible numbers

Round 11 to 10. Replace 11 with 10.


10 ! 90 " 900 10 ! 100 " 1,000

11 ! 94 is about 900. 11 ! 94 is about 1,000.

Use rounding to estimate each product.

1. 62 ! 82 2. 59 ! 48 3. 74 ! 302

4. 47 ! 790 5. 498 ! 63 6. 687 ! 38

7. 18 ! 412 8. 385 ! 75 9. 62 ! 147

Use compatible numbers to estimate each product.

10. 32 ! 83 11. 37 ! 22 12. 51 ! 296

13. 65 ! 34 14. 108 ! 81 15. 43 ! 620

16. 426 ! 71 17. 59 ! 701 18. 87 ! 87

19. Number Sense To estimate the product of 37 ! 99,

Chris multiplied 40 ! 100. Tell how you know if this is an underestimate or an overestimate.


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7-2Estimating ProductsEstimate 11 ! 94.

Using rounding Using compatible numbers



10 ! 90 " 900 10 ! 100 " 1,000

11 ! 94 is about 900. 11 ! 94 is about 1,000.

Use rounding to estimate each product.

1. 62 ! 82 2. 59 ! 48 3. 74 ! 302

4. 47 ! 790 5. 498 ! 63 6. 687 ! 38

7. 18 ! 412 8. 385 ! 75 9. 62 ! 147


10. 32 ! 83 11. 37 ! 22 12. 51 ! 296

13. 65 ! 34 14. 108 ! 81 15. 43 ! 620

16. 426 ! 71 17. 59 ! 701 18. 87 ! 87

19. Number Sense To estimate the product of 37 ! 99,

Chris multiplied 40 ! 100. Tell how you know if this is an underestimate or an overestimate.

28,00030,00040,000

21,0003,0004,800

8,000 32,000 9,000

2,400 800 15,000

2,100 8,800 24,000

28,000 42,000 8,100

Overestimate, because both factors were increased.

Sample answers given for 1-18.


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Topic 7 31

Practice

7-2Practice 7

-2

Estimating ProductsUse rounding to estimate each product.

1. 38 ! 29 2. 71 ! 47

3. 54 ! 76 4. 121 ! 62

5. 548 ! 28 6. 823 ! 83

7. 67 ! 289 8. 183 ! 34


9. 28 ! 87 10. 673 ! 85

11. 54 ! 347 12. 65 ! 724

13. 81 ! 643 14. 44 ! 444

15. 72 ! 285 16. 61 ! 761

17. Vera has 8 boxes of paper clips. Each box has 275 paper clips. About how many paper clips does Vera have?

A 240 B 1,600 C 2,400 D 24,000

18. Writing to Explain A wind farm generates 330 kilowatts of electricity each day. About how many kilowatts does the wind farm produce in a week? Explain.


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Topic 7 31

Practice

7-2Practice 7

-2

Estimating ProductsUse rounding to estimate each product.

1. 38 ! 29 2. 71 ! 47

3. 54 ! 76 4. 121 ! 62

5. 548 ! 28 6. 823 ! 83

7. 67 ! 289 8. 183 ! 34


9. 28 ! 87 10. 673 ! 85

11. 54 ! 347 12. 65 ! 724

13. 81 ! 643 14. 44 ! 444

15. 72 ! 285 16. 61 ! 761

17. Vera has 8 boxes of paper clips. Each box has 275 paper clips. About how many paper clips does Vera have?

A 240 B 1,600 C 2,400 D 24,000

18. Writing to Explain A wind farm generates 330 kilowatts of electricity each day. About how many kilowatts does the wind farm produce in a week? Explain.

21,00015,0004,000

3,500

6,00064,0007,200

1,200

Sample answers given for 1–16.

1,600–2,700 48,000–63,00015,000–24,00048,000–63,00014,000–24,000

42,000–56,00016,000–25,00042,000–56,000

About 2,100 kilowatts; 330 rounds to 300 and there are 7 days in a week, so 7 ! 300 " 2,100.


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Enrichment

7-2En

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-2

Vacation Estimation

It is 9:00 A.M. Your family vacation starts in New York City with a final destination in Miami. You travel 58 miles every hour if you do not stop for meals or attractions. You first head to Washington, D.C.

1. You must stop for a 1 hour lunch at noon. Use rounding to estimate how many miles you have traveled by noon.

2. Estimate how far away you are from Washington, D.C.

3. You arrive in Washington, D.C. You do some sightseeing, and at 5:00 P.M.

you continue your trip and drive until 7:00 P.M. You stop for dinner and rest for the evening. Estimate how many miles you have driven for the day.

4. Your family starts the second day at 9:00 A.M. and drives until

8:00 P.M. During that time, you stopped for 2 hours. Estimate how far you traveled for the day.

5. Estimate how far you are from Miami.

6. On the third day, about what time must you leave in the morning to get to

Miami around 5:00 P.M.? Remember, you will stop for a 1 hour lunch.

Mileage Between Cities

Miami New York City Pittsburgh Washington, D.C.Miami – 1,328 1,250 1,101New York City 1,328 – 386 229Pittsburgh 1,250 386 – 241Washington, D.C. 1,101 229 241 –

Estimation


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Enrichment

7-2En

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Vacation Estimation

It is 9:00 A.M. Your family vacation starts in New York City with a final destination in Miami. You travel 58 miles every hour if you do not stop for meals or attractions. You first head to Washington, D.C.

1. You must stop for a 1 hour lunch at noon. Use rounding to estimate how many miles you have traveled by noon.

2. Estimate how far away you are from Washington, D.C.

3. You arrive in Washington, D.C. You do some sightseeing, and at 5:00 P.M.

you continue your trip and drive until 7:00 P.M. You stop for dinner and rest for the evening. Estimate how many miles you have driven for the day.

4. Your family starts the second day at 9:00 A.M. and drives until

8:00 P.M. During that time, you stopped for 2 hours. Estimate how far you traveled for the day.

5. Estimate how far you are from Miami.

6. On the third day, about what time must you leave in the morning to get to

Miami around 5:00 P.M.? Remember, you will stop for a 1 hour lunch.

Mileage Between Cities

Miami New York City Pittsburgh Washington, D.C.Miami – 1,328 1,250 1,101New York City 1,328 – 386 229Pittsburgh 1,250 386 – 241Washington, D.C. 1,101 229 241 –

Estimation

Sample answers given for 1–6.

About 180 mi

About 50 mi

About 350 mi

About 540 mi

About 500 mi

Between 7:00 and 8:00 A.M.


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Daily Spiral Review

7-3

Carla is keeping track of the number of tomatoes that she picks in her garden. The chart below shows the number of tomatoes that she has picked each day this week.

Use the chart to answer Exercises 1 and 2.

1. What is the total number of tomatoes that Carla has picked so far this week?A 30B 31C 32D 33

2. The total number of tomatoes that Carla has picked this summer is 4 times the number she picked on Wednesday and Thursday combined. How many tomatoes has she picked this summer?A 64B 62C 60D 16

3. Put the following numbers in order from least to greatest:

274; 290; 234; 302; 220

4. Jorge went to the store with $200. He bought a sweatshirt for $22 and shoes for $27. How much money did he have left after those purchases?

5. What are the next three numbers in the following pattern?

6, 12, 18, 24, , ,

6. Ted has 16 pigs on his farm. He wants to put the same number of pigs in each of his 4 pens. How many pigs will he put in each pen?

Tomatoes PickedDay Number of Tomatoes

Monday 6Tuesday 4Wednesday 7Thursday 9Friday 6



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Topic 7 33

Daily Spiral Review

7-3

Carla is keeping track of the number of tomatoes that she picks in her garden. The chart below shows the number of tomatoes that she has picked each day this week.

Use the chart to answer Exercises 1 and 2.

1. What is the total number of tomatoes that Carla has picked so far this week?A 30B 31C 32D 33

2. The total number of tomatoes that Carla has picked this summer is 4 times the number she picked on Wednesday and Thursday combined. How many tomatoes has she picked this summer?A 64B 62C 60D 16

3. Put the following numbers in order from least to greatest:

274; 290; 234; 302; 220

4. Jorge went to the store with $200. He bought a sweatshirt for $22 and shoes for $27. How much money did he have left after those purchases?

5. What are the next three numbers in the following pattern?

6, 12, 18, 24, , ,

6. Ted has 16 pigs on his farm. He wants to put the same number of pigs in each of his 4 pens. How many pigs will he put in each pen?

Tomatoes PickedDay Number of Tomatoes

Monday 6Tuesday 4Wednesday 7Thursday 9Friday 6


220, 234, 274, 290, 302

$151

30 36 42

4



34

Topic 7

7-3Problem of the DayIt takes Lorraine 48 minutes to drive to and from her grandmother’s house. About how many minutes will she drive if she visits her grandmother 12 times?

Problem of the Day 7-3Problem

of the Day

7-3


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1. The 27 students in Mr. Whitman’s class each brought in 48 aluminum cans during the class recycling drive. How many aluminum cans did Mr. Whitman’s class collect altogether?

A 1,286

B 1,296

C 1,396

D 2,296

2. There are 29 students in Mrs. Langley’s class. Each student does 35 math homework problems each night. How many math problems does the class do altogether in one night?

A 1,015

B 955

C 815

D 775 Quick C

heck 7-3

Quick Check

7-3

3. Writing to Explain Molly had the following work on her paper:

80 640 3,200 2402 160 12

What multiplication problem is Molly trying to solve? How do you know?


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Topic 7 35

1. The 27 students in Mr. Whitman’s class each brought in 48 aluminum cans during the class recycling drive. How many aluminum cans did Mr. Whitman’s class collect altogether?

A 1,286

B 1,296

C 1,396

D 2,296

2. There are 29 students in Mrs. Langley’s class. Each student does 35 math homework problems each night. How many math problems does the class do altogether in one night?

A 1,015

B 955

C 815

D 775 Quick C

heck 7-3

Quick Check

7-3

3. Writing to Explain Molly had the following work on her paper:

80 640 3,200 2402 160 12

What multiplication problem is Molly trying to solve? How do you know?



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Reteaching

7-3Arrays and an Expanded AlgorithmHere is how to find the product of 12 ! 24 using an array.

Draw a rectangle 24 units long by 12 units wide.

Divide the rectangle by tens and ones for each factor. Find the number of squares in each smaller square.

Then add the numbers of the squares in the four rectangles:

200 " 40 " 40 " 8 # 288

So, 12 ! 24 # 288.

Divide the rectangle by tens and ones for each factor. Then complete the calculation.

1.

2 20 40

10 20 200

10 4 40

2 4 8

10

20 4

2

2 21 1

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36 Topic 7

Reteaching

7-3Arrays and an Expanded AlgorithmHere is how to find the product of 12 ! 24 using an array.

Draw a rectangle 24 units long by 12 units wide.

Divide the rectangle by tens and ones for each factor. Find the number of squares in each smaller square.

Then add the numbers of the squares in the four rectangles:

200 " 40 " 40 " 8 # 288

So, 12 ! 24 # 288.

Divide the rectangle by tens and ones for each factor. Then complete the calculation.

1.

2 20 40

10 20 200

10 4 40

2 4 8

10

20 4

2

2 21 1

Rete

achi

ng 7-3

22 02 0

2 0 0

2 2 0 2 02 0 02 4 2

!


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Topic 7 37

Practice

7-3Arrays and an Expanded AlgorithmUse the grid to help you complete the calculation.

1.

2. 3. 4.

5. 24 ! 57 " 6. 44 ! 48 "

7. A red kangaroo can cover 40 feet in 1 jump. How many feet can the red kangaroo cover in 12 jumps?

8. Barb exercises for 14 hours in 1 week. How many hours does she exercise in 32 weeks?

A 496 h B 448 h C 420 h D 324 h

9. Writing to Explain How is breaking apart the problem 16 ! 34 like solving four simpler problems?

3 11 9

2 62 2

3 31 4

2 31 7

Practice 7-3


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Topic 7 37

Practice

7-3Arrays and an Expanded AlgorithmUse the grid to help you complete the calculation.

1.

2. 3. 4.

5. 24 ! 57 " 6. 44 ! 48 "

7. A red kangaroo can cover 40 feet in 1 jump. How many feet can the red kangaroo cover in 12 jumps?

8. Barb exercises for 14 hours in 1 week. How many hours does she exercise in 32 weeks?

A 496 h B 448 h C 420 h D 324 h

9. Writing to Explain How is breaking apart the problem 16 ! 34 like solving four simpler problems?

3 11 9

2 62 2

3 31 4

2 31 7

Practice 7-3

480 ft

2,1121,368

92 7 0

1 03 0 05 8 9

1 24 0

1 2 04 0 05 7 2

1 21 2 0

3 03 0 04 6 2

Breaking apart makes four problems with easier numbers.

2 11 4 0

3 02 0 03 9 1

!

!! !


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38 Topic 7

Enrichment

7-3Crazy CubesWrite the letter of the cube that is not the same as the others in the group. Each cube has 6 distinct faces.

1.

2.

3.

4.

A B C D

A

B

C

D

A B C

D E F

A B C

D E F

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Reasoning


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38 Topic 7

Enrichment

7-3Crazy CubesWrite the letter of the cube that is not the same as the others in the group. Each cube has 6 distinct faces.

1.

2.

3.

4.

A B C D

A

B

C

D

A B C

D E F

A B C

D E F

Enric

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Reasoning

C

C

F

E


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Topic 7 39


Daily Spiral Review

7-4

1. Mallory went to the store with $10.00. She bought a bottle of shampoo for $3.25. How much money did she have left? A $7.75B $7.25C $6.75D $5.75

2. Bill was counting off members of his team by fours. The ! rst number he said was 4, then 8, and then 12. What are the next three numbers in the pattern? A 15, 18, 21B 14, 16, 18C 16, 18, 20D 16, 20, 24

3. Doug and his mother are driving to visit his uncle. They drive 271 miles per day for 3 days. How many miles do they drive altogether? A 923 milesB 813 milesC 713 milesD 621 miles

4. What is the place value of the underlined digit?

8,065,123

5. A number has a 7 in the tens place, a 2 in the tenths place, a 1 in the hundredths place, and a 0 in the ones place. What is the number?

6. Lucy’s Diner ordered 4 boxes of plastic forks. Each box contained 125 plastic forks. How many plastic forks did Lucy’s Diner order?


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Topic 7 39


Daily Spiral Review

7-4

1. Mallory went to the store with $10.00. She bought a bottle of shampoo for $3.25. How much money did she have left? A $7.75B $7.25C $6.75D $5.75

2. Bill was counting off members of his team by fours. The ! rst number he said was 4, then 8, and then 12. What are the next three numbers in the pattern? A 15, 18, 21B 14, 16, 18C 16, 18, 20D 16, 20, 24

3. Doug and his mother are driving to visit his uncle. They drive 271 miles per day for 3 days. How many miles do they drive altogether? A 923 milesB 813 milesC 713 milesD 621 miles

4. What is the place value of the underlined digit?

8,065,123

5. A number has a 7 in the tens place, a 2 in the tenths place, a 1 in the hundredths place, and a 0 in the ones place. What is the number?

6. Lucy’s Diner ordered 4 boxes of plastic forks. Each box contained 125 plastic forks. How many plastic forks did Lucy’s Diner order?

millions place

70.21

500 plastic forks



40

Topic 7


Problem of the DayProblem

of the Day

7-4

What simpler multiplication problems can you use to solve 46 ! 49?

7-4


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Topic 7 41

1. Marvin drinks 74 ounces of water a day. How much water does he drink over 40 days?

A 2,860 ounces

B 2,880 ounces

C 2,960 ounces

D 2,980 ounces

3. 17 students each brought in 20 cookies for the school bake sale. How many cookies were there at the bake sale?

A 400

B 380

C 360

D 340

2. Lincoln can type 58 words a minute. How many words can he type in an hour?

A 3,420

B 3,480

C 3,980

D 4,980

Quick Check

7-4Q

uick Check 7

-4

4. Writing to Explain Use a grid to find the product of 29 ! 30. Then, explain how you can use a grid to find partial products and the product.


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Topic 7 41

1. Marvin drinks 74 ounces of water a day. How much water does he drink over 40 days?

A 2,860 ounces

B 2,880 ounces

C 2,960 ounces

D 2,980 ounces

3. 17 students each brought in 20 cookies for the school bake sale. How many cookies were there at the bake sale?

A 400

B 380

C 360

D 340

2. Lincoln can type 58 words a minute. How many words can he type in an hour?

A 3,420

B 3,480

C 3,980

D 4,980

Quick Check

7-4Q

uick Check 7

-4

4. Writing to Explain Use a grid to find the product of 29 ! 30. Then, explain how you can use a grid to find partial products and the product.



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42 Topic 7

Rete

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Reteaching

7-4Multiplying 2-Digit Numbers by Multiples of TenTo find the product of 60 and 26, you can use breaking apart.

Mark off a section of a grid to show 60 ! 26.

Count the number of rows. Count the number of squares in each row.

There are 60 rows. There are 26 squares per row.

Draw a line to separate the factor 26 into the tens place and the ones place. Show 26 as 20 " 6.

Into how many sections have you divided the larger section?

There are 2 sections. Mark one section 60 ! 20 and the other section 60 ! 6.

Multiply to find the products.

60 rows of 20 Add. 60 rows of 6

1,200" 360

1,560

For Exercises 1 through 5, use grid models to break apart each product and solve.

1. 23 ! 40

2. 16 ! 30

3. 34 ! 50

4. 60 ! 47

5. 17 ! 80

60

20 6

60 20 1,20060 6 360

60

20 6


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42 Topic 7

Rete

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ng 7-4

Reteaching

7-4Multiplying 2-Digit Numbers by Multiples of TenTo find the product of 60 and 26, you can use breaking apart.

Mark off a section of a grid to show 60 ! 26.

Count the number of rows. Count the number of squares in each row.

There are 60 rows. There are 26 squares per row.

Draw a line to separate the factor 26 into the tens place and the ones place. Show 26 as 20 " 6.

Into how many sections have you divided the larger section?

There are 2 sections. Mark one section 60 ! 20 and the other section 60 ! 6.

Multiply to find the products.

60 rows of 20 Add. 60 rows of 6

1,200" 360

1,560

For Exercises 1 through 5, use grid models to break apart each product and solve.

1. 23 ! 40

2. 16 ! 30

3. 34 ! 50

4. 60 ! 47

5. 17 ! 80

60

20 6

60 20 1,20060 6 360

60

20 6

Check students’ models.

800 and 120; 920300 and 180; 4801,500 and 200; 1,7002,400 and 420; 2,820800 and 560; 1,360


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Topic 7 43

Practice 7-4

Practice

7-4Multiplying 2-Digit Numbers by Multiples of TenUse the grid to show the partial products. Multiply to find the product.

1. 23 ! 50 2. 30 ! 82

3. 14 ! 40 4. 20 ! 63


5. Martika works as a legal secretary. She earns $20 an hour. How much

does Martika earn if she works 32 hours? 6. Which numbers are the partial products of 77 ! 30?

A 210 and 700 B 2,100 and 210 C 511 and 2,100 D 4,900 and 210

7. Writing to Explain Explain how you can find the product of 40 ! 16 by breaking apart the numbers.

30 80 2,400

30 2 60

30

80 250

20 50 1,00020

3 3 50 150

20 60 1,20020

60 3

20 3 60

40 10 40040 4 16040

10 4


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Topic 7 43

Practice 7-4

Practice

7-4Multiplying 2-Digit Numbers by Multiples of TenUse the grid to show the partial products. Multiply to find the product.

1. 23 ! 50 2. 30 ! 82

3. 14 ! 40 4. 20 ! 63


5. Martika works as a legal secretary. She earns $20 an hour. How much

does Martika earn if she works 32 hours? 6. Which numbers are the partial products of 77 ! 30?

A 210 and 700 B 2,100 and 210 C 511 and 2,100 D 4,900 and 210

7. Writing to Explain Explain how you can find the product of 40 ! 16 by breaking apart the numbers.

30 80 2,400

30 2 60

30

80 250

20 50 1,00020

3 3 50 150

20 60 1,20020

60 3

20 3 60

40 10 40040 4 16040

10 4

1,000 " 150; 1,150 2,400 " 60; 2,460

400 " 160; 560 1,200 " 60; 1,260

$640

Sample answer: To find the product of 40 ! 16, you can add 40 ! 10 to 40 ! 6. 40 ! 10 " 400 and 40 ! 6 " 240.400 # 240 " 640


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44 Topic 7

Enric

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Enrichment

7-4A Finished Product!Find each partial product. Then, use numbers from the number sentences to complete the word sentences.

1. 30 ! 20 "

30 ! 4 "

30 ! 24 "

2. 60 ! 80 "

60 ! 3 "

60 ! 83 "

3. 90 ! 70 "

90 ! 4 "

90 ! 74 "

4. 80 ! 80 "

80 ! 5 "

80 ! 85 "

5. 40 ! 50 "

40 ! 2 "

40 ! 52 "

Marie had songs on her mp3 player.

She added more songs.

Now Marie has a total of mp3 songs.

A sporting manufacturer shipped out

bowling pins and bowling balls to an

alley. There were items altogether.

The population of Desertvale was recorded at

in January. There were more

people added in a year. The following January,

the population of Desertvale was .

Jed estimated that there were

jellybeans in a jar. When the jellybeans were finally

counted Jed found there were actually

more. In fact, there were jellybeans in all.

Now, create your own word sentences using the number sentences in Exercise 5.

Mental Math


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44 Topic 7

Enric

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Enrichment

7-4A Finished Product!Find each partial product. Then, use numbers from the number sentences to complete the word sentences.

1. 30 ! 20 "

30 ! 4 "

30 ! 24 "

2. 60 ! 80 "

60 ! 3 "

60 ! 83 "

3. 90 ! 70 "

90 ! 4 "

90 ! 74 "

4. 80 ! 80 "

80 ! 5 "

80 ! 85 "

5. 40 ! 50 "

40 ! 2 "

40 ! 52 "

Marie had songs on her mp3 player.

She added more songs.

Now Marie has a total of mp3 songs.

A sporting manufacturer shipped out

bowling pins and bowling balls to an

alley. There were items altogether.

The population of Desertvale was recorded at

in January. There were more

people added in a year. The following January,

the population of Desertvale was .

Jed estimated that there were

jellybeans in a jar. When the jellybeans were finally

counted Jed found there were actually

more. In fact, there were jellybeans in all.

Now, create your own word sentences using the number sentences in Exercise 5.

Mental Math

2,000 80 2,080

6,800 400 6,400

6,660 360 6,300

4,980 180 4,800

720 120 600

4,980

720

360

Check students’ sentences

6,300

6,660

1804,800

120600

6,800400

6,400


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Topic 7 45

Daily Spiral Review

7-5

1. What is the number seven million, three hundred ! fty thousand, nine hundred nine written in standard form? A 7,305,909 B 7,305,990C 7,350,909D 7,350,990

2. A basketball arena can hold approximately 7,000 people. Fans bought 5,134 tickets prior to the game. About how many more seats are there left to ! ll before the game?A 5,000B 2,000C 1,500D 1,000

3. Doreen is organizing her CD collection into bins. Each bin holds 25 CDs. Doreen has completely ! lled 5 bins. How many CDs does she have? A 50B 75C 100D 125

4. The school buses for King Philip Elementary School carry 40 students per bus. The buses go between 25 and 35 miles per hour on the way to school. There are 12 buses that bring students to school each day.

What piece of information is NOT needed if you want to determine how many students take the bus to school each day?

5. It is approximately 3,000 miles from New York City to Los Angeles. Suppose a pilot travels between New York and Los Angeles 6 times in one week. About how many miles did she travel?



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Topic 7 45

Daily Spiral Review

7-5

1. What is the number seven million, three hundred ! fty thousand, nine hundred nine written in standard form? A 7,305,909 B 7,305,990C 7,350,909D 7,350,990

2. A basketball arena can hold approximately 7,000 people. Fans bought 5,134 tickets prior to the game. About how many more seats are there left to ! ll before the game?A 5,000B 2,000C 1,500D 1,000

3. Doreen is organizing her CD collection into bins. Each bin holds 25 CDs. Doreen has completely ! lled 5 bins. How many CDs does she have? A 50B 75C 100D 125

4. The school buses for King Philip Elementary School carry 40 students per bus. The buses go between 25 and 35 miles per hour on the way to school. There are 12 buses that bring students to school each day.

What piece of information is NOT needed if you want to determine how many students take the bus to school each day?

5. It is approximately 3,000 miles from New York City to Los Angeles. Suppose a pilot travels between New York and Los Angeles 6 times in one week. About how many miles did she travel?


The buses go between 25 and 35 miles per hour on the way to school.

18,000 miles



46

Topic 7

7-5Problem of the DayProblem

of the Day

7-5


Melanie earns $10 an hour babysitting. She made a chart to show how many hours she babysat last week. How much money did Melanie earn last week? Write two number sentences that you can use to solve this problem. Then solve.

Day Hours of babysittingThursday 4Friday 3Saturday 7Sunday 4


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Topic 7 47

Quick C

heck 7-5

1. Jacob reads 68 pages a night. How many pages does Jacob read in a month with 31 days?

A 2,108

B 2,208

C 2,618

D 2,868

2. Mrs. Jackson’s classroom is 24 feet by 22 feet. How many square feet is her rectangular classroom? Hint: The area of a rectangle is length ! width.

A 628

B 620

C 538

D 528

Quick Check

7-5

3. Writing to Explain How is using partial products to find the product of a 2-digit by 2-digit problem similar to how you have used partial products in the past? How is it different?


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Topic 7 47

Quick C

heck 7-5

1. Jacob reads 68 pages a night. How many pages does Jacob read in a month with 31 days?

A 2,108

B 2,208

C 2,618

D 2,868

2. Mrs. Jackson’s classroom is 24 feet by 22 feet. How many square feet is her rectangular classroom? Hint: The area of a rectangle is length ! width.

A 628

B 620

C 538

D 528

Quick Check

7-5

3. Writing to Explain How is using partial products to find the product of a 2-digit by 2-digit problem similar to how you have used partial products in the past? How is it different?



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48 Topic 7

Reteaching

7-5Multiplying 2-Digit by 2-Digit NumbersThere are 24 cars in the race. Each car has a 13-person crew in the pit area. How many pit-area workers are at the race?

1. 2. 3. 4.

5. Number Sense Corina multiplied 62 ! 22 and got a product of 1,042. Explain why Corina’s answer is not reasonable.

Step 3Step 2Step 1

Multiply the ones.

Regroup if necessary.

Multiply the tens.


Add the partial products.

241372

240312

24 13 312, so thereare 312 pit-area workersat the race.

1241372

1241372

240

1

38! 26

67! 27

47! 85

88! 32Re

teac

hing

7-5


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48 Topic 7

Reteaching

7-5Multiplying 2-Digit by 2-Digit NumbersThere are 24 cars in the race. Each car has a 13-person crew in the pit area. How many pit-area workers are at the race?

1. 2. 3. 4.

5. Number Sense Corina multiplied 62 ! 22 and got a product of 1,042. Explain why Corina’s answer is not reasonable.

Step 3Step 2Step 1

Multiply the ones.


Multiply the tens.


Add the partial products.

241372

240312

24 13 312, so thereare 312 pit-area workersat the race.

1241372

1241372

240

1

38! 26

67! 27

47! 85

88! 32Re

teac

hing

7-5

988 1,809 3,995 2,816

Sample answer: Corina’s answer is not reasonable because even when both factors are rounded down, her answer is still low.


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Topic 7 49

Practice

7-5Multiplying 2-Digit by 2-Digit Numbers1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. A carton holds 24 bottles of juice. How many juice bottles are in 15 cartons?

14. How much do 21 bushels of sweet corn weigh?

15. How much do 18 bushels of asparagus weigh?

16. How much more do 13 bushels of beets weigh than 13 bushels of carrots?

17. Which of the following is a reasonable answer for 92 ! 98?

A 1,800 B 9,000 C 10,000 D 90,000

18. Writing to Explain Garth is multiplying 29 ! 16. He has 174 after multiplying the ones and 290 after multiplying the tens. Explain how Garth can find the final product.

54! 17

36! 20

53! 12

48! 46

37! 83

62! 17

91! 49

28! 56

70! 39

58! 90

97! 42

64! 88

Vegetable Weight of 1 BushelAsparagus 24 lbBeets 52 lbCarrots 50 lbSweet corn 35 lb

Practice 7-5


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Topic 7 49

Practice

7-5Multiplying 2-Digit by 2-Digit Numbers1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. A carton holds 24 bottles of juice. How many juice bottles are in 15 cartons?

14. How much do 21 bushels of sweet corn weigh?

15. How much do 18 bushels of asparagus weigh?

16. How much more do 13 bushels of beets weigh than 13 bushels of carrots?

17. Which of the following is a reasonable answer for 92 ! 98?

A 1,800 B 9,000 C 10,000 D 90,000

18. Writing to Explain Garth is multiplying 29 ! 16. He has 174 after multiplying the ones and 290 after multiplying the tens. Explain how Garth can find the final product.

54! 17

36! 20

53! 12

48! 46

37! 83

62! 17

91! 49

28! 56

70! 39

58! 90

97! 42

64! 88

Vegetable Weight of 1 BushelAsparagus 24 lbBeets 52 lbCarrots 50 lbSweet corn 35 lb

Practice 7-5

918 720 636 2,208

3,071 1,054 4,459 1,568

2,730 5,220 4,074 5,632

360 bottles of juice

Sample answer:

Garth can add 174 and 290 to get 464.

735 lb

432 lb

26 lb


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50 Topic 7

Enrichment

7-5

Decision Making

Enric

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Food for ThoughtYou work at a pet shop. One of your jobs is to feed all the animals. Answer the questions below using the chart at the right.

First thing in the morning you feed the fish. The 12 fish tanks have a total of 26 large fish.You can choose between two kinds of pellets.

1. Which kind of pellets do you choose? Estimate the number of pellets you need. Explain your method.

2. What is the exact amount?

You feed the puppies next. There are 10 cages of large-breed puppies. Each cage can hold 3 puppies, but 2 of the cages only have 2 puppies each. You need to decide which food to give the puppies.

3. What kind of puppy food do you choose? Estimate the amount of puppy food you need. Explain your method.


Daily Feeding Chart

Fish10 super pellets each

or21 mini pellets each

Puppies16 oz dry food each

or14 oz wet food each


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50 Topic 7

Enrichment

7-5

Decision Making

Enric

hmen

t 7-5

Food for ThoughtYou work at a pet shop. One of your jobs is to feed all the animals. Answer the questions below using the chart at the right.

First thing in the morning you feed the fish. The 12 fish tanks have a total of 26 large fish.You can choose between two kinds of pellets.

1. Which kind of pellets do you choose? Estimate the number of pellets you need. Explain your method.


You feed the puppies next. There are 10 cages of large-breed puppies. Each cage can hold 3 puppies, but 2 of the cages only have 2 puppies each. You need to decide which food to give the puppies.

3. What kind of puppy food do you choose? Estimate the amount of puppy food you need. Explain your method.


Daily Feeding Chart

Fish10 super pellets each

or21 mini pellets each

Puppies16 oz dry food each

or14 oz wet food each

Food choice and estimates vary; super pellets, about 300; mini fish pellets, about 600

260 super pellets, 546 mini pellets

Food choice and estimates vary; 600 oz of dry food; 300 oz of wet food

448 oz of dry food, 392 oz of wet food


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Topic 7 51

1. Luis’s family is going to the amusement park. Tickets cost $26 for each child. There are 7 children going. How much will all of their tickets cost?A $142B $162C $182D $202

2. Traci wants to put the same number of books on each shelf on her bookcase. Which would be the quickest operation to use to ! gure out how many books go on each shelf? A AdditionB Subtraction C MultiplicationD Division

3. Pedro collects baseball cards. He had 192. His friend Kevin gave him 267 more. His friend Shannon gave him 212 more. How many baseball cards does Pedro have now?A 771B 679C 671D 579


Ten:

Hundred:

Thousand:

5. Write the following number: four hundred six million, seven hundred seventy-eight thousand, thirty-nine.

6. Warren planted 7 rows of summer squash in his garden. Each row had 5 plants in it. How many summer squash plants were there in Warren’s garden?

7. Jodie drove 4 hours to visit her grandmother. She averaged 60 miles per hour during her trip. How many miles did Jodie travel to see her grandmother?


Daily Spiral Review

7-6


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Topic 7 51

1. Luis’s family is going to the amusement park. Tickets cost $26 for each child. There are 7 children going. How much will all of their tickets cost?A $142B $162C $182D $202

2. Traci wants to put the same number of books on each shelf on her bookcase. Which would be the quickest operation to use to ! gure out how many books go on each shelf? A AdditionB Subtraction C MultiplicationD Division

3. Pedro collects baseball cards. He had 192. His friend Kevin gave him 267 more. His friend Shannon gave him 212 more. How many baseball cards does Pedro have now?A 771B 679C 671D 579


Ten:

Hundred:

Thousand:

5. Write the following number: four hundred six million, seven hundred seventy-eight thousand, thirty-nine.

6. Warren planted 7 rows of summer squash in his garden. Each row had 5 plants in it. How many summer squash plants were there in Warren’s garden?

7. Jodie drove 4 hours to visit her grandmother. She averaged 60 miles per hour during her trip. How many miles did Jodie travel to see her grandmother?


Daily Spiral Review

7-6

406,778,039

35

240

40,54040,50041,000



Problem of the DayProblem

of the Day

7-6

7-6

52

Topic 7


How much greater is the area of Figure A than Figure B? To find the area, multiply length times width.

Figure A Figure B

13 in. 14 in.

12 in.16 in.


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Topic 7 53

Quick Check

7-6

Multiply to find the product.

1. At the Computer City warehouse, there are 50 cases of blank CDs. Each case has 800 CDs in it. How many CDs are there in the warehouse?

A 4,000

B 40,000

C 45,000

D 400,000

2. Laura does 55 sit-ups a day. How many sit-ups does she do in 30 days?

A 1,650

B 1,550

C 165

D 155

3. Writing to Explain Why does it make sense to solve multiplication problems with greater numbers the way it was taught in this lesson rather than with arrays or grids?

Quick C

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Topic 7 53

Quick Check

7-6

Multiply to find the product.

1. At the Computer City warehouse, there are 50 cases of blank CDs. Each case has 800 CDs in it. How many CDs are there in the warehouse?

A 4,000

B 40,000

C 45,000

D 400,000

2. Laura does 55 sit-ups a day. How many sit-ups does she do in 30 days?

A 1,650

B 1,550

C 165

D 155

3. Writing to Explain Why does it make sense to solve multiplication problems with greater numbers the way it was taught in this lesson rather than with arrays or grids?

Quick C

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54 Topic 7

Special CasesMultiply 600 ! 40.

1. 2. 3.

4. Explain how to use mental math to find 3,000 ! 25.

10,000! 25

500! 40

110! 25

Another WayOne Way Use a pattern.

600 40

6 4 24

There are three zeros in the factors.

600 40

600 40 24,000

6 4 24 60 4 240

600 4 2,400600 40 24,000

Rete

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ng 7-6

28447_ANC-NATGR4_T7-6_working.in54 54 2/5/08 9:03:06 AM

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54 Topic 7

Special CasesMultiply 600 ! 40.

1. 2. 3.

4. Explain how to use mental math to find 3,000 ! 25.

10,000! 25

500! 40

110! 25

Another WayOne Way Use a pattern.

600 40

6 4 24

There are three zeros in the factors.

600 40

600 40 24,000

6 4 24 60 4 240

600 4 2,400600 40 24,000

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ng 7-6

First multiply: 25 ! 3 " 75. Then count the zeros from the factors, and write them after 75. 3,000 ! 25 " 75,000.

2,750 20,000 250,000

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Topic 7 55

Practice

7-6

Pencils 144Pens 115

Supplies Per Box

Practice 7-6

Special Cases1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. Number Sense Would the answer to 20 ! 500 have three zeroes or 4? Explain.

Use the table at right for problems 14 and 15.

14. How many pencils are in 30 boxes?

15. How many pens are in 200 boxes?

16. Hailey sold 120 bottles of water in 1 week. How many bottles could she sell in 20 weeks?

A 240 B 1,220 C 2,400 D 24,000

17. Writing to Explain How could you use the product of10 ! 42 " 420 to find the product of 5 ! 42?

800! 15

300! 50

600! 50

100! 60

800! 50

500! 70

800! 70

325! 30

400! 80

300! 25

200! 20

200! 30

Pencils 150Pens 190

Supplies Per Box


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Topic 7 55

Practice

7-6

Pencils 144Pens 115

Supplies Per Box

Practice 7-6

Special Cases1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. Number Sense Would the answer to 20 ! 500 have three zeroes or 4? Explain.

Use the table at right for problems 14 and 15.

14. How many pencils are in 30 boxes?

15. How many pens are in 200 boxes?

16. Hailey sold 120 bottles of water in 1 week. How many bottles could she sell in 20 weeks?

A 240 B 1,220 C 2,400 D 24,000

17. Writing to Explain How could you use the product of10 ! 42 " 420 to find the product of 5 ! 42?

800! 15

300! 50

600! 50

100! 60

800! 50

500! 70

800! 70

325! 30

400! 80

300! 25

200! 20

200! 30

Pencils 150Pens 190

Supplies Per Box

6,000 4,000 7,500 32,000

9,750 56,000 35,000 40,000

12,000 15,000 30,000 6,000

4 zeroes because 2 ! 5 " 10 and that gets three zeroes added to the end of it to get 10,000.

4,500 pencils

38,000 pens

The product of 5 ! 42 would be half of 10 ! 42


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Enrichment

7-6

56 Topic 7

Treasure! Benjamin is a treasure hunter. He and his crew recently found the treasure of a sunken ship from the past. The chests contained gold, silver, and jewels.

Benjamin’s ship can carry a maximum weight of 10,000 lb without sinking.

1. What is the total weight of the gold chests?

2. What is the total weight of the silver chests?

3. What is the total weight of the jewel chests?

4. How many trips does Benjamin need to take to carry all of the chests to shore? How do you know?

5. Suppose Benjamin only carries gold chests on his last trip. If Benjamin carried full loads on the first two trips, about how many gold chests will he carry on the last trip?

Treasure Found

Type of Chest Weight of Each Chest Number of Each ChestGold 180 lb 60Silver 150 lb 50Jewels 120 lb 30

Enric

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Number Sense


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56 Topic 7

Treasure! Benjamin is a treasure hunter. He and his crew recently found the treasure of a sunken ship from the past. The chests contained gold, silver, and jewels.

Benjamin’s ship can carry a maximum weight of 10,000 lb without sinking.

1. What is the total weight of the gold chests?

2. What is the total weight of the silver chests?

3. What is the total weight of the jewel chests?

4. How many trips does Benjamin need to take to carry all of the chests to shore? How do you know?

5. Suppose Benjamin only carries gold chests on his last trip. If Benjamin carried full loads on the first two trips, about how many gold chests will he carry on the last trip?

Treasure Found

Type of Chest Weight of Each Chest Number of Each ChestGold 180 lb 60Silver 150 lb 50Jewels 120 lb 30

Enric

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Number Sense

10,800 lb

7,500 lb

3,600 lb

3 trips; He has to carry a total of about22,000 lb. On each trip he can only carry up to 10,000 lb.

About 11 gold chests; He will have about 2,000 lb left to carry on the last trip.


Daily Spiral Review


7-7

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Topic 7 57

1. Michelle has a spinner with ! ve equal-sized sections. Which of the following is true?

15 2

34

A It is likely Michelle will spin a 6.B It is impossible for Michelle

to spin a 5.C Michelle is likely to spin an

odd number.D Michelle is certain to spin an

odd number.

2. Andrew has 36 model airplanes. The airplanes hang in groups of 6 from his ceiling. Which model shows how many groups of 6 he has? A 36

8 8

B 36

12 1212

C 36

9 99 9

D 36

6 66 666

3. Mark has 108 books. Erika has 211 books. Christina has 303 books. How many books do they have altogether?

4. There are 12 houses in Carlos’s neighborhood. Each house has 16 windows. How many windows are there altogether?

5. Vasudha lives 83 miles from Gabriella’s house. Rounded to the nearest hundred, about how far does Vasudha live from Gabriella?

6. There are 3 blue marbles, 6 red marbles, and 2 green marbles in a bag. What is the likelihood that Javier will draw a yellow marble from the bag without looking?


Daily Spiral Review


7-7

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Topic 7 57

1. Michelle has a spinner with ! ve equal-sized sections. Which of the following is true?

15 2

34

A It is likely Michelle will spin a 6.B It is impossible for Michelle

to spin a 5.C Michelle is likely to spin an

odd number.D Michelle is certain to spin an

odd number.

2. Andrew has 36 model airplanes. The airplanes hang in groups of 6 from his ceiling. Which model shows how many groups of 6 he has? A 36

8 8

B 36

12 1212

C 36

9 99 9

D 36

6 66 666

3. Mark has 108 books. Erika has 211 books. Christina has 303 books. How many books do they have altogether?

4. There are 12 houses in Carlos’s neighborhood. Each house has 16 windows. How many windows are there altogether?

5. Vasudha lives 83 miles from Gabriella’s house. Rounded to the nearest hundred, about how far does Vasudha live from Gabriella?

6. There are 3 blue marbles, 6 red marbles, and 2 green marbles in a bag. What is the likelihood that Javier will draw a yellow marble from the bag without looking?

192 windows

100 miles

impossible

622



Problem of the Day 7-7Problem

of the Day

7-7

58

Topic 7

7-7Winston reads 124 pages a month for 5 months. Lana reads 95 pages a month for 7 months. Who reads more?

Problem of the Day


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Topic 7 59

Quick Check

7-7C

enter Activity 7

-7

1. Doug spent 16 days at summer camp. Each day he spent 4 hours at arts and crafts. Each hour at arts and crafts he made 3 drawings. How many drawings did he make while at summer camp?

A 192

B 112

C 48

D 12

3. Mr. Rivera teaches 6 classes per day. Each class has 15 students. At school he coaches the baseball team. There are 12 students on the baseball team that do not have a class with him. How many students does Mr. Rivera work with each day?

A 90

B 102

C 162

D 180

2. Margo has 8 different kinds of tea in her pantry. Each kind of tea is in a different box, and there are 14 packets of tea in each box. Her friend Liz has the same number of tea packets. How many tea packets do they have altogether?

A 112

B 168

C 224

D 448

4. There are 22 tables in the cafeteria. Each table can sit 8 students. There are 4 lunch periods each day. How many students can the cafeteria serve each day?

A 822

B 704

C 264

D 176

5. Writing to Explain Ernie spends 6 hours reading each weekend. Ernie has 3 sisters. Each sister reads the same amount Ernie does each weekend. How many hours do Ernie and his sisters read combined?

Quick C

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Topic 7 59

Quick Check

7-7C

enter Activity 7

-7

1. Doug spent 16 days at summer camp. Each day he spent 4 hours at arts and crafts. Each hour at arts and crafts he made 3 drawings. How many drawings did he make while at summer camp?

A 192

B 112

C 48

D 12

3. Mr. Rivera teaches 6 classes per day. Each class has 15 students. At school he coaches the baseball team. There are 12 students on the baseball team that do not have a class with him. How many students does Mr. Rivera work with each day?

A 90

B 102

C 162

D 180

2. Margo has 8 different kinds of tea in her pantry. Each kind of tea is in a different box, and there are 14 packets of tea in each box. Her friend Liz has the same number of tea packets. How many tea packets do they have altogether?

A 112

B 168

C 224

D 448

4. There are 22 tables in the cafeteria. Each table can sit 8 students. There are 4 lunch periods each day. How many students can the cafeteria serve each day?

A 822

B 704

C 264

D 176

5. Writing to Explain Ernie spends 6 hours reading each weekend. Ernie has 3 sisters. Each sister reads the same amount Ernie does each weekend. How many hours do Ernie and his sisters read combined?

Quick C

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Reteaching

7-7Re

teac

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7-7

Problem Solving: Two-Question Problems

Solve. Use the answer from Problem 1 to solve Problem 2.

1. Problem 1: April made 16 baskets and glued 5 flowers on each one. How many flowers did she use altogether?

Problem 2: Each flower April used had 8 petals. How many petals were there on all the flowers she used?

2. Problem 1: Jorge washed cars for four hours on Saturday. In the first hour, he washed 4 cars. In the second hour, he washed 9 cars. In the third hour, he washed 12 cars. How many cars did he wash altogether in the first three hours?

Problem 2: Jorge washed the same number of cars in the fourth hour as he did in the first three hours combined. How many cars did he wash altogether in four hours?

Read and Understand Problem 1: Gina gave 3 sheets of paper to each of the 12 students in her class. How many sheets of paper did she give out?

Problem 2: Each sheet of paper had 3 paper clips attached to it. How many paper clips did she give out?

Answer Problem 1 first.

? sheets of paper12 12 12

12 students ! 3 sheets of paper " 36 sheets of paperGina gave out 36 sheets of paper.

Plan and Solve Use the answer from Problem 1 to solve Problem 2.

? paper clips36 36 36

36 sheets of paper ! 3 paper clips " 108 paper clipsGina gave out 108 paper clips.


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Reteaching

7-7Re

teac

hing

7-7

Problem Solving: Two-Question Problems

Solve. Use the answer from Problem 1 to solve Problem 2.

1. Problem 1: April made 16 baskets and glued 5 flowers on each one. How many flowers did she use altogether?

Problem 2: Each flower April used had 8 petals. How many petals were there on all the flowers she used?

2. Problem 1: Jorge washed cars for four hours on Saturday. In the first hour, he washed 4 cars. In the second hour, he washed 9 cars. In the third hour, he washed 12 cars. How many cars did he wash altogether in the first three hours?

Problem 2: Jorge washed the same number of cars in the fourth hour as he did in the first three hours combined. How many cars did he wash altogether in four hours?

Read and Understand Problem 1: Gina gave 3 sheets of paper to each of the 12 students in her class. How many sheets of paper did she give out?

Problem 2: Each sheet of paper had 3 paper clips attached to it. How many paper clips did she give out?

Answer Problem 1 first.

? sheets of paper12 12 12

12 students ! 3 sheets of paper " 36 sheets of paperGina gave out 36 sheets of paper.

Plan and Solve Use the answer from Problem 1 to solve Problem 2.

? paper clips36 36 36

36 sheets of paper ! 3 paper clips " 108 paper clipsGina gave out 108 paper clips.

25 cars; 50 cars

80 flowers; 640 petals


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Topic 7 61

Practice

7-7Practice 7

-7

Problem Solving: Two-Question ProblemsFor 1 and 2, use the answer from the first problem to solve the second problem.

1. Problem 1: Francisco reads 75 pages every week for a summer reading program. If there are about 4 weeks in a month, then how many pages can Francisco read in a month?

Problem 2: How many pages will Francisco read in the three

months of summer?

2. Problem 1: Mr. Dunn drives a 15-mile round trip every day

to work. If Mr. Dunn works five days a week how many miles does he drive?

Problem 2: Mr. Dunn estimates he uses 3 gallons of gas over

the course of a week. How many miles per gallon does his car get?

3. A company buys printer paper in a box which contains

8 packages. If each package of paper costs 3 dollars, how much does a box of paper cost? Which equation shows how much 12 boxes will cost?

A 8 ! 3 " 12 B 24 # 12 C 24 ! 12 D 24 " 12

4. Writing to Explain There are 12 plots in a community garden. What information would you need to know if you wanted to know how much area can be farmed in the community garden? Explain.


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Topic 7 61

Practice

7-7Practice 7

-7

Problem Solving: Two-Question ProblemsFor 1 and 2, use the answer from the first problem to solve the second problem.

1. Problem 1: Francisco reads 75 pages every week for a summer reading program. If there are about 4 weeks in a month, then how many pages can Francisco read in a month?

Problem 2: How many pages will Francisco read in the three

months of summer?

2. Problem 1: Mr. Dunn drives a 15-mile round trip every day

to work. If Mr. Dunn works five days a week how many miles does he drive?

Problem 2: Mr. Dunn estimates he uses 3 gallons of gas over

the course of a week. How many miles per gallon does his car get?

3. A company buys printer paper in a box which contains

8 packages. If each package of paper costs 3 dollars, how much does a box of paper cost? Which equation shows how much 12 boxes will cost?

A 8 ! 3 " 12 B 24 # 12 C 24 ! 12 D 24 " 12

4. Writing to Explain There are 12 plots in a community garden. What information would you need to know if you wanted to know how much area can be farmed in the community garden? Explain.

You would need to know the area of one of the plots because you already know the number of plots.

Mr. Dunn’s car gets 25 miles per gallon.

Mr. Dunn drives 75 miles a week.

Francisco will read 900 pages over the summer.

Francisco can read 300 pages in a month.


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62 Topic 7

Enrichment

7-7En

richm

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-7

Something’s MissingFind the missing number that makes the number sentence true.

1. 2,323 ! " 2,091 2. # 10 " 100

3. 123 $ " 168 4. 730 $ " 803

5. ! 9 " 825 6. 4 # 6 % " 8

7. $ 282 " 290 8. 759 # " 0

9. % 4 # 9 " 27 10. 16 ! $ 9 " 20

11. 3 # 4 % " 6 12. 690 # " 690

13. 48 % $ " 14 14. 999 ! " 0

15. Use each of the numbers in the box once to complete the number sentences.

% 3 " 3 9 25

6 2 # 3 "

8 ! " 3

# 5 " 10

Write some number sentences with missing operation signs. Give them to a partner to solve.

16.

17.

18.

19.

20.

Reasoning


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Enrichment

7-7En

richm

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-7

Something’s MissingFind the missing number that makes the number sentence true.

1. 2,323 ! " 2,091 2. # 10 " 100

3. 123 $ " 168 4. 730 $ " 803

5. ! 9 " 825 6. 4 # 6 % " 8

7. $ 282 " 290 8. 759 # " 0

9. % 4 # 9 " 27 10. 16 ! $ 9 " 20

11. 3 # 4 % " 6 12. 690 # " 690

13. 48 % $ " 14 14. 999 ! " 0

15. Use each of the numbers in the box once to complete the number sentences.

% 3 " 3 9 25

6 2 # 3 "

8 ! " 3

# 5 " 10

Write some number sentences with missing operation signs. Give them to a partner to solve.

16.

17.

18.

19.

20.

Reasoning

45232

834812

28 8

10733

051999

96

52

Check students’ work.


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Topic 7 63

Topic 7M

ultiple-Choice Test

1. To find 500 ! 800, Sean first found 5 ! 8 " 40. How many zeros should Sean include in the product? (7-1)

A 0

B 1

C 3

D 5

2. There are forty-one chapters in the book Ted has to read for class. Each chapter is 38 pages long. Which shows the best way to estimate how many pages there are in the entire book? (7-2)

A 30 ! 40

B 30 ! 50

C 40 ! 30

D 40 ! 40

3. Peter has 23 pages in his photo album. Each page has 14 photos. Peter is using the table below to calculate how many photos he has in his album. Which number is missing from the table? (7-3)

20 310 200 ?4 80 12

A 30

B 34

C 37

D 122

4. Which partial products can be used to find 40 ! 58? (7-5)

A 320 and 200

B 220 and 2,000

C 320 and 2,000

D 320 and 2,008

5. There are 12 inches in a foot. A field at school is 360 feet long. Which is the best estimate in inches of the field? (7-2)

A 1,200

B 4,000

C 5,000

D 6,000

6. The video store ordered 40 copies of a new movie. Each copy has 3 DVDs. How many DVDs did the video store order? (7-4)

A 120

B 112

C 110

D 12

Mark the best answer.

Topic 7 Multiple-Choice

Test


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Topic 7 63

Topic 7M

ultiple-Choice Test

1. To find 500 ! 800, Sean first found 5 ! 8 " 40. How many zeros should Sean include in the product? (7-1)

A 0

B 1

C 3

D 5

2. There are forty-one chapters in the book Ted has to read for class. Each chapter is 38 pages long. Which shows the best way to estimate how many pages there are in the entire book? (7-2)

A 30 ! 40

B 30 ! 50

C 40 ! 30

D 40 ! 40

3. Peter has 23 pages in his photo album. Each page has 14 photos. Peter is using the table below to calculate how many photos he has in his album. Which number is missing from the table? (7-3)

20 310 200 ?4 80 12

A 30

B 34

C 37

D 122

4. Which partial products can be used to find 40 ! 58? (7-5)

A 320 and 200

B 220 and 2,000

C 320 and 2,000

D 320 and 2,008

5. There are 12 inches in a foot. A field at school is 360 feet long. Which is the best estimate in inches of the field? (7-2)

A 1,200

B 4,000

C 5,000

D 6,000

6. The video store ordered 40 copies of a new movie. Each copy has 3 DVDs. How many DVDs did the video store order? (7-4)

A 120

B 112

C 110

D 12

Mark the best answer.

Topic 7 Multiple-Choice

Test


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66 Topic 7

Topic 7Free-Response Test

Topi

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Free

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Multiply using mental math.

1. 30 ! 80

2. 70 ! 40

3. 60 ! 500

4. 200 ! 90

Use rounding or compatible numbers to estimate each product.

5. 62 ! 33

6. 48 ! 132

7. 302 ! 76

8. 476 ! 89

Draw an array for each problem. Write the partial products and solve.

9. 12! 15

10. 18! 13

Give each answer.


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66 Topic 7

Topic 7Free-Response Test

Topi

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Free

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Multiply using mental math.

1. 30 ! 80

2. 70 ! 40

3. 60 ! 500

4. 200 ! 90

Use rounding or compatible numbers to estimate each product.

5. 62 ! 33

6. 48 ! 132

7. 302 ! 76

8. 476 ! 89

Draw an array for each problem. Write the partial products and solve.

9. 12! 15

10. 18! 13

Give each answer.

20 10

100 50

2,400

2,800

30,000

18,000

1,800

5,000 or 6,500

24,000

45,000

100! 20! 50! 10 180

100! 80! 30! 24 234

30

24

100

80


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Do the following to find the approximate and actual costs of your textbooks as well as those of the entire class. The table shows sample prices.

Type of Textbook

Cost of One Textbook

Cost for Your Class Students

Estimate Actual

Science $37

Social Studies $39

Reading $44

Language $32

Mathematics $45

Spelling $25

Total

1. Put a mark next to each textbook in the table that your class has. Cross out the other textbooks. Find the total cost of your own textbooks. Write your answer in the table.

2. Use the total cost of your textbooks to estimate the total cost of textbooks for your entire class. Then find the actual cost. Write your answers in the table. Explain how you estimated.

3. Estimate the cost of each type of book for your entire class. Record your estimates in the table.

4. Find the actual cost of each type of book for your entire class to complete the table.

5. Use the estimates to decide whether or not the actual costs you found for each book for the entire class are reasonable. Explain for one book.

Topic 7Performance Assessment

Topi

c 7

Pe

rform

ance

Ass

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ent

68 Topic 7


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Do the following to find the approximate and actual costs of your textbooks as well as those of the entire class. The table shows sample prices.

Type of Textbook

Cost of One Textbook

Cost for Your Class Students

Estimate Actual

Science $37

Social Studies $39

Reading $44

Language $32

Mathematics $45

Spelling $25

Total

1. Put a mark next to each textbook in the table that your class has. Cross out the other textbooks. Find the total cost of your own textbooks. Write your answer in the table.

2. Use the total cost of your textbooks to estimate the total cost of textbooks for your entire class. Then find the actual cost. Write your answers in the table. Explain how you estimated.

3. Estimate the cost of each type of book for your entire class. Record your estimates in the table.

4. Find the actual cost of each type of book for your entire class to complete the table.

5. Use the estimates to decide whether or not the actual costs you found for each book for the entire class are reasonable. Explain for one book.

Topic 7Performance Assessment

Topi

c 7

Pe

rform

ance

Ass

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68 Topic 7

I rounded $165 to $170 then multiplied by 20.

Yes, my actual costs for my class are reasonable and close to my estimates. For example, my estimate for the Reading textbooks was $900 and my actual cost was $880.

!!!

!

!!

20$800$800$900

$900

$3,400$165

$740$780$880

$900

$3,300


Documents

Name Daily Spiral Review - Wikispaces7+masters.pdfDaily Spiral Review 7-1 Daily Spiral Review 7-1 ... W riting to Explain Dominic claims that when he multiplied 40 ! 50 he got an answer