upper saddle river, new jersey grade 3: step up to grade...

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Glenview, Illinois • Boston, Massachusetts Chandler, Arizona • Shoreview, Minnesota Upper Saddle River, New Jersey

Grade 3: Step Up to Grade 4Teacher’s Guide• Teacher Notes and Answers

for Step-Up Lessons

• Practice

• Answers for Practice

• Test

• Answers for Test

45095_SLPSHEET_FSD 145095_SLPSHEET_FSD 1 6/6/08 3:57:25 PM6/6/08 3:57:25 PM

F8 Rounding Numbers Through Thousands

F9 Comparing and Ordering Numbers Through Thousands

F10 Place Value Through Millions

F11 Rounding Numbers Through Millions

F29 Patterns and Equations

G7 Estimating Sums

G42 Dividing with Objects

G59 Factoring Numbers

G66 Mental Math: Multiplying by Multiples of 10

G67 Estimating Products

H1 Equal Parts of a Whole

H2 Parts of a Region

H3 Parts of a Set

H14 Equivalent Fractions

H18 Mixed Numbers

I8 Congruent Figures and Motions

I10 Solids and Nets

I11 Views of Solid Figures

I13 Congruent Figures

I45 More Perimeter

45095_SLPSHEET_FSD 245095_SLPSHEET_FSD 2 6/6/08 3:57:30 PM6/6/08 3:57:30 PM

Math Diagnosis and Intervention SystemIntervention Lesson F8

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Rounding Numbers Through Thousands

Teacher Notes

Ongoing AssessmentAsk: What does 99,249 round to when rounded to the nearest hundred thousand? 100,000

Error InterventionIf students have trouble remembering place value,

then have the students make a table across the top of their page that looks like the following:

Hun

dre

d

Thou

sand

s

Ten

Thou

sand

s

Thou

sand

s

Hun

dre

ds

Tens

One

s

If You Have More TimeHave students list all the four-digit numbers that stay the same when rounded to the nearest thousand (the multiples of 1,000), the five-digit numbers that stay the same when rounded to the nearest ten thousand (the multiples of 10,000), and the six-digit numbers that stay the same when rounded to the nearest hundred thousand (the multiples of 100,000).


Rounding Numbers Through Thousands

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Intervention Lesson F8 71

Name

To round 34,853 to the nearest ten thousand, answer 1 to 6.

Materials 8 inches of yarn per pair

1. Plot 34,853 on the number line below.

2. Use the yarn to help you decide whether 34,853 is closer to 30,000 or 40,000. Which is it closer to?

3. So, what is 34,853 rounded to the nearest ten thousand?

4. Plot 37,421 on the number line above.

5. Use the yarn to help you decide whether 37,421 is closer to 30,000 or 40,000. Which is it closer to?

6. So, what is 37,421 rounded to the nearest ten thousand?

Round 739,218 to the nearest hundred thousand without using a number line. Answer 7 to 11.

7. Which digit is in the hundred thousands place?

8. What digit is to the right of the 7?

9. Is that digit less than 5, or is it 5 or greater?

If the digit to the right of the number is 5 or more, the number rounds up. If the digit is less than 5, the number rounds down.

10. Do you need to round up or down?

11. Keep the 7 and change the other digits to 0s. So, 739,218 rounds to .

30,000

30,000

40,000

40,000

7

3

less than 5

down

700,000

Round each number to the nearest ten.

12. 94,519 13. 537,681

Round each number to the nearest hundred.

14. 968,458 15. 58,326

Round each number to the nearest thousand.

16. 318,512 17. 21,236

Round each number to the nearest ten thousand.

18. 285,431 19. 184,032

Round each number to the nearest hundred thousand.

20. 735,901 21. 472,992

Use the information in the table for Exercises 22–23.

22. What is the price of the house rounded to the nearest hundred thousand?

23. What is the cost of repairs rounded to the nearest thousand?

24. Reasoning Write three numbers that would round to 44,000 when rounded to the nearest thousand.

25. Reasoning Explain how to round 496,275 to the nearest ten thousand.

72 Intervention Lesson F8

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Rounding Numbers Through Thousands (continued)

Name


Real Estate

Sale

Amount

in Dollars

Price of House 169,256

Advertising Fee 7,177

Repairs 5,873

94,520 537,680

968,500 58,300

319,000 21,000

290,000 180,000

700,000 500,000

200,000

6,000

Any numbers between 43,500 and 44,499

Sample answer: The digit in the ten thousands place is 9. The digit to the right of 9 is 6, which is 5 or greater. So, round up. Think of adding 1 to 49 to make 50. To the nearest ten thousand, 496,275 rounds to 500,000.

Intervention Lesson F8


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Comparing and Ordering Numbers Through Thousands

Teacher Notes

Ongoing AssessmentAsk: Why do you work from left to right instead of right to left when comparing or ordering numbers? Sample answer: The digits on the left have a higher value than the digits on the right.

Error InterventionIf students have trouble ordering numbers that are written horizontally,

then encourage them to write one number above the other, making sure they line up corresponding place values. Then compare the numbers in each column.

If You Have More TimeHave students write ordering problems for a partner to solve.


Comparing and Ordering Numbers Through Thousands

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Name

In a recent county election, Henderson received 168,356 votes. Juarez received 168,297 votes. Determine who received more votes by answering 1 to 7.

1. Write 168,356 and 168,297 in the place-value chart.

hundredthousands

tenthousands thousands hundreds tens ones

For Exercises 2–5, write �, �, or �.

2. Start with the left column in the chart. 100,000 100,000

3. Since the hundred thousands are equal, compare the ten thousands. 60,000 60,000

4. Since the ten thousands are equal, compare the thousands. 8,000 8,000

5. Since the thousands are equal, compare the hundreds. 300 200

6. Since 300 � 200, compare 168,356 and 168,297.

�

7. So, which candidate received more votes?

Order 346,217; 319,304; and 348,862 from least to greatest by answering 8 to 12.

8. Write 346,217; 319,304; and 348,862 in the place-value chart on the next page.

�

�

�

�

168,356 168,297

Henderson

1 6 8 3 5 61 6 8 2 9 7

hundredthousands


9. Start on the left. Write �, �, or �. 300,000 300,000 300,000

10. Since the hundred thousands are all equal, compare the ten thousands. Since 10,000 � 40,000, what is the least number?

11. Since 6,000 _____ 8,000, compare the thousands place

of the other two numbers. �

12. The numbers in order from least to greatest are:

Use � or � to compare each pair of numbers.

13. 8,112 8,221 14. 418,412 481,930

15. 321,159 312,147 16. 20,657 21,687

17. 118,111 118,147 18. 914,146 904,168

Order the numbers from least to greatest.

19. 8,200; 820; 7,980 20. 12,984; 12,875; 11,987

21. 200; 12,945; 2,309 22. 321,984; 345,879; 323,490

23. Reasoning When comparing 17,834 and 17,934, can you start by comparing hundreds? Explain.

No; Always compare the left-most digit first.74 Intervention Lesson F9

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Comparing and Ordering Numbers Through Thousands (continued)

Name


� �

319,304

348,862346,217

<

348,862346,217319,304

3 4 6 2 1 73 1 9 3 0 43 4 8 8 6 2

< <

> <

< >

820; 7,980; 8,200 11,987; 12,875; 12,984

200; 2,309; 12,945 321,984; 323,490; 345,879




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Place Value Through Millions

Teacher Notes

Ongoing AssessmentAsk: How does the number of zeros in the place value chart change as you move each place to the left? One zero is added to each place as you move left away from the ones.

Error InterventionIf students are having trouble remembering the number of zeros each value has,

then encourage students to write #00,000,000 above the heading hundred millions, #0,000,000 above the heading ten millions, #,000,000 above the heading millions, and so on. That way they know to place the number (#) and then the appropriate number of zeros.

If You Have More TimeHave students look up the population of the United States and write the number in standard form, expanded form, and word form.


Place Value Through Millions

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1. Write 462,397,158 in the place-value chart below.

Millions Thousands Ones

Hu

nd

red

M

illi

on

s

Ten

M

illi

on

s

Mil

lio

ns

Hu

nd

red

Th

ou

san

ds

Ten

Th

ou

san

ds

Tho

usa

nd

s

Hu

nd

red

s

Ten

s

On

es

2. Complete the table to find the value of each digit in 462,397,158.

Digit Place Value

4 hundred millions 400,000,000

6 ten millions

2

3

9

7

1

5

8

3. Use the table above to help you write 462,397,158 in expanded form.

400,000,000 � � � �

90,000 � � 100 � � .

4. Write the short word form of 462,397,158.

462 million, thousand,

5. Write 462,397,158 in word form.

4

millionshundred thousandsten thousandsthousandshundredstensones

60,000,000

6 2 3 9 7 1 5 8

60,000,0002,000,000

300,00090,000

7,000100

508

2,000,000 300,000

7,000 50 8

397 158

Four hundred sixty-two million, three hundred ninety-seven thousand, one hundred fifty-eight

Write the value of the underlined digit.

6. 4,562,398 7. 15,347,025 8. 37,814,956

9. 526,878,953 10. 782,354,065 11. 918,403,760

Write each number in word form and in short word form.

12. 2,160,500

13. 91,207,040

14. 510,200,450

15. An underground rail system in Osaka, Japan carries 988,600,000 passengers per year. Write this number in expanded form.

16. Reasoning What number would make the numbersentence below true?

3,589,000 � 3,000,000 � ■ � 80,000 � 9,000

17. Reasoning What number can be added to 999,990 to make 1,000,000?


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Place Value Through Millions (continued)

Name


Two million, one hundred sixty thousand, five hundred; 2 million, 160 thousand, 5 hundred

Ninety-one million, two hundred seven thousand, forty; 91 million, 207 thousand, 40

Five hundred ten million, two hundred thousand, four hundred fifty; 510 million, 200 thousand, 4 hundred, 50

4,0005,000,00060,000

10,000,00060500,000,000

900,000,000 � 80,000,000 � 8,000,000 � 600,000

500,000

10



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Rounding Numbers Through Millions

Teacher Notes

Ongoing AssessmentAsk: What is the smallest number that will round to 1,000,000 when rounded to the nearest million? 950,000

Error InterventionIf students are having trouble identifying the place values for rounding,

then have the students make a place value chart across the top of their page.

If students do not know the place values,

then use F10: Place Value Through Millions.

If You Have More TimeHave students round 5,830,957 to the nearest ten, hundred, thousand, ten thousand, hundred thousand, and million. Repeat with 9,999,999.

Round 4,307,891 to the nearest million by answering 1 to 5.

1. What digit is in the millions place?


3. Is the digit to the right of 4 less than 5, or is it 5 or greater?

If the digit to the right of the number is 5 or more, the number rounds up. If the digit is less than 5, the number rounds down.


5. Keep the 4 and change the other digits to 0s. What is 4,307,891 rounded to the nearest million?

Round 6,570,928 to the nearest hundred thousand by answering 6 to 11.

6. Which digit is in the hundred thousands place?


8. Is the digit to the right of 5 less than 5, or is it 5 or greater?


10. Change the 5 to the next highest digit and change the other digits to 0s. What is 6,570,928 rounded to the nearest hundred thousand?

11. What is 6,570,928 rounded to the nearest thousand?



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Rounding Numbers Through Millions

4

3

less than 5

Down

4,000,000

5

7

5 or greater

Up

6,600,000

6,571,000

Round 1,581,267 to each place.

12. ten 13. hundred

14. thousand 15. ten thousand

16. hundred thousand 17. million

Round each number to the nearest ten.

18. 3,194,764 19. 8,967,001


20. 1,265,906 21. 6,906,294


22. 8,070,126 23. 9,264,431


24. 7,514,637 25. 2,437,894


26. 1,395,384 27. 3,992,460

Round each number to the nearest million.

28. 4,578,952 29. 5,022,121

30. 2,439,019 31. 8,888,888

32. Reasoning A number rounded to the nearest million is 4,000,000. One less than the same number rounds to 3,000,000 when rounded to the nearest million. What is the number?

Rounding Numbers Through Millions (continued)


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Name


3,194,760 8,967,000

1,265,900 6,906,300

8,070,000 9,264,000

7,510,000 2,440,000

1,400,000 4,000,000

5,000,000 5,000,000

2,000,000 9,000,000

1,581,270 1,581,300

1,581,000

1,600,000

1,580,000

2,000,000

3,500,000



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Patterns and Equations

Teacher Notes

Ongoing AssessmentAsk: If a rule for a table is x � 7, what equation represents the relationship between the inputs x and the outputs y? y � x � 7

Error InterventionIf students have trouble writing an expression for the pattern in the table,

then use F26: Expressions with Addition and Subtraction or F27: Expressions with Multiplication and Division.

If You Have More TimeHave students think of a real-world situation which can be represented by an equation, write the equation, and create a table.


Patterns and Equations

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1. Complete the table at the right. Cost of Food Order

c

Cost with Delivery

d

$8.50 $10.50

$9.25 $11.25

$10.47 $12.47$10.98 $12.98

$12.06 $14.06

2. What expression describes the cost with delivery for a food order costing c dollars?

c � 2

3. Set d equal to the expression to get an equation representing the relationship between the cost of the food order cand the cost with delivery d.

d � c � 2

4. Use the equation to find d, when c � $14.52. $16.52

5. Complete the table at the right. Number of Pretzels

p

Total Cost

c

2 $11.00

3 $16.50

5 $27.506 $33.00

7 $38.50

6. Write an equation representing the relationship between the number of pretzels p and the total cost c.

c � 5.5p

7. Use the equation to find c, when p � 4.

$22.00

8. A field goal in football is worth 3 points. Complete the table below to show the relationship between the number of field goals f and the number of points p.

Sample answers are shown in the table.

Field Goals (f) 1 2 3 4 5Points (p) 3 6 9 12 18

9. Write an equation to represent the relationship between the number of field goals f and points p. p � 3f

Write an equation to represent the relationship between x and y in each table. Then use the equation to complete the table.

10. x y

2 8

3 9

8 1414 20

21 27

11.x y

12 2

18 3

24 4

30 542 7

12. x y

4 32

5 40

7 568 64

10 80

y � x � 6 y � x � 6 y � 8x

13. x y

10 1

14 5

22 13

26 17

30 21

14.x y

2 4.8

3 7.2

4 9.6

6 14.47 16.8

15. x y

50 10

40 835 7

25 5

15 3

y � x � 9 y � 2.4x y � x � 5

16. x 2 2.5 3.2 3.8 4.7

y 9.8 10.3 11 11.6 12.5

y � x � 7.8

17. Reasoning If a rule is c � p � 5, what is c when p � 20? 25


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Patterns and Equations (continued)

Name


Intervention Lesson G7

Math Diagnosis and Intervention SystemIntervention Lesson G7

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Estimating Sums

Teacher Notes

Ongoing AssessmentAsk: When estimating 124 � 138, which would give a closer estimate, rounding to the nearest ten or to the nearest hundred? Rounding to the nearest ten.

Error InterventionIf students are having trouble with rounding the addends correctly,

then use F2: Rounding to Nearest Ten and Hundred.

If You Have More TimeHave students work with a partner to list ten different sums which are about 300 when estimated by rounding each addend to the nearest hundred.


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Intervention Lesson G7 91

Name

Estimating Sums

When Joseppi added 43 and 28, he got a sum of 71. To check that this answer is reasonable, use estimation.

1. Round each addend to the nearest ten.

43 rounded to the nearest ten is .

28 rounded to the nearest ten is .

2. Add the rounded numbers.

40 � 30 �

Since 71 is close to 70, the answer is reasonable.

When Ling added 187 and 242, she got a sum of 429. To check that this answer is reasonable, use estimation.

3. Round each addend to the nearest hundred.

187 rounded to the nearest hundred is .

242 rounded to the nearest hundred is .

4. Add the rounded numbers.

200 � 200 �

Since 429 is close to 400, the answer is reasonable.

40

70

200

30

200

400

92 Intervention Lesson G7

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Name


Estimating Sums (continued)

Estimate by rounding to the nearest ten.

5. 71 � 36 6. 24 � 81 7. 43 � 91 8. 54 � 66

9. 68 � 27 10. 19 � 93 11. 89 � 75 12. 54 � 33

Estimate by rounding to the nearest hundred.

13. 367 14. 791 15. 506 16. 458 _� 141 _� 632 _� 249 _� 891

17. 940 � 190 18. 675 � 460 19. 531 � 776

20. 369 � 481 21. 151 � 260 22. 705 � 936

23. Reasoning Jaimee was a member of the school chorus for 3 years. Todd was a member of the school band for 2 years. The chorus has 43 members and the band has 85 members. About how many members do the two groups have together?

24. Luis sold 328 sport bottles and Jorge sold 411. About how many total sport bottles did the two boys sell?

25. Reasoning What is the largest number that can be added to 46 so that the sum is 70 when both numbers are rounded to the nearest ten? Explain.

110

24; Since 46 rounds to 50, and 20 � 50 � 70, you need the largest number that rounds to 20, which is 24.

100 130 120

100 110 170 80

1,3001,2001,100

1,600500900

130

500 1,400 700 1,400

700



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Dividing with Objects

Teacher Notes

Ongoing AssessmentAsk: Why should the remainder always be less than the divisor? For example, when dividing 10 by 3, why can you not have a remainder of 4? If the remainder is equal to or greater than the divisor, then the quotient should be larger. For example, when dividing 10 counters into 3 equal groups, if 4 are left, there are enough to put another counter into each group.

Error InterventionIf students have trouble completing problems using counters or drawings,

then encourage them to use repeated subtraction to solve the problem. Continue to subtract until it can no longer be done. What is left is the remainder.

If You Have More TimeHave partners find all the division sentences that can be written if 8 is the dividend and the divisor is 1 to 8.


Dividing with Objects

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Materials 7 counters and 3 half sheets of paper for each student or pair

Andrew has 7 model cars to put on 3 shelves. He wants to put the same number of cars on each shelf. How many cars should Andrew put on each shelf? Answer 1 to 8.

Find 7 � 3.

1. Show 7 counters and 3 sheets of paper.

2. Put 1 counter on each piece of paper.

3. Are there enough counters to putanother counter on each sheet of paper? yes

4. Put another counter on each piece of paper.

5. Are there enough counters to putanother counter on each sheet of paper? no

6. How many counters are on each sheet? 2

7. How many counters are remaining, or left over? 1

So, 7 � 3 is 2 remainder 1, or 7 � 3 � 2 R1.

8. How many cars should Andrew put on each shelf? How many cars will be left over?

Andrew can put 2 cars on each shelf with 1 car left over.

Use counters or draw a picture to find each quotient and remainder.

9. 8 � 3 � 2 R2 10. 17 � 3 � 5 R2 11. 14 � 3 � 4 R2

12. 11 � 4 � 2 R3 13. 22 � 4 � 5 R2 14. 34 � 4 � 8 R2

15. 13 � 5 � 2 R3 16. 27 � 5 � 5 R2 17. 46 � 5 � 9 R1

18. 14 � 6 � 2 R2 19. 26 � 6 � 4 R2 20. 38 � 6 � 6 R2

21. 17 � 7 � 2 R3 22. 27 � 7 � 3 R6 23. 45 � 7 � 6 R3

24. 18 � 8 � 2 R2 25. 28 � 8 � 3 R4 26. 37 � 8 � 4 R5

27. 14 � 9 � 1 R5 28. 28 � 9 � 3 R1 29. 39 � 9 � 4 R3

30. 12 � 8 � 1 R4 31. 68 � 7 � 9 R5 32. 59 � 8 � 7 R3

33. 9 � 4 � 2 R1 34. 26 � 5 � 5 R1 35. 34 � 6 � 5 R4

36. 14 � 5 � 2 R4 37. 21 � 6 � 3 R3 38. 3 � 2 � 1 R1

39. Reasoning Grace is reading a book for school. The book has 26 pages and she is given 3 days to read it. How many pages should she read each day? Will she have to read more pages on some days than on others? Explain.

She should read 8–9 pages each day; she will read 9 pages on 2 days and 8 pages on 1 day.


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Dividing with Objects (continued)

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Factoring Numbers

Teacher Notes

Ongoing AssessmentAsk: What is the only even prime number? 2

Error InterventionIf students do not find all of the factors of a number,

then have them use manipulatives such as color tiles or counters to create arrays. Have them find all arrays methodically. Start with 1 row. See if the given number of counters can be put into 2 rows. Then see if they can be put into 3 rows and so on.

If You Have More TimeHave students write any number from 1 to 1,000 on a note card. Collect all of the cards and shuffle them. Have a student draw a card and explain why the number on the cards is either prime or composite. Repeat until all students have a turn.

Answers: Exercise 22 from page 196

6 � 3 � 18 2 � 9 � 18 3 � 6 � 18

1 � 18 � 18

9 � 2 � 18


Factoring Numbers

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Materials color tiles or counters, 24 for each student

The arrays below show all of the factors of 12.

1 � 12

2 � 6 3 � 4 4 � 3 6 � 2

1. What are all the factors of 12?

1 , 2 , 3 , 4 , 6 , 12

2. Create all the possible arrays you can with 17 color tiles.

3. What are the factors of 17? 1 , 17

Numbers which have only 2 possible arrays and exactly 2 factors are prime numbers.

4. Is 17 a prime number? yes

5. Is 12 a prime number? no

Numbers which have more than 2 possible arrays and more than 2 factors are composite numbers.

6. Is 17 a composite number? no

7. Is 12 a composite number? yes

8. What are all the factors of 24? 1, 2, 3, 6, 8, 12, 24

9. Is 24 a prime number or a composite number? composite

12 � 1

The order factors are listed may vary.

The order factors are listed may vary.


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Factoring Numbers (continued)

Name


Find all the factors of each number. Tell whether each is prime or composite.

10. 7 11. 8 12. 21

1, 7; 1, 2, 4, 8; 1, 3, 7, 21;

prime composite composite

13. 48 14. 51 15. 9

1, 2, 3, 4, 6, 8, 1, 3, 17, 51; 1, 3, 9;

12, 16, 24, 48; composite composite

16. 13 17. 26 18. 40

1, 13; 1, 2, 13, 26; 1, 2, 4, 5, 8,

prime composite 10, 20, 40;

19. 55 20. 70 21. 83

1, 5, 11, 55; 1, 2, 5, 7, 10, 1, 83;

composite 14, 35, 70; prime

22. Mr. Lee has 18 desks in his room. He would like them arranged in a rectangular array. Draw all the different possible arrays and write a multiplication sentence for each.

See answers on page 59.

23. Reasoning Lee says 53 is a prime number because it is an odd number. Is Lee’s reasoning correct? Give an example to prove your reasoning. No; 53 is a prime number not because it is an odd number, but because it only has 2 factors: 1 and 53. A counterexample is 15 is an odd number but it is not a prime number because 15 has more than 2 factors: 1, 3, 5, 15.

composite

composite

composite

18 � 1 � 18



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Mental Math: Multiplying by Multiples of 10

A publishing company ships a particular book in boxes with 6 books each. How many books are in 20 boxes? How many in 2,000 boxes?

Find 20 � 6 and 2,000 � 6 by filling in the blanks.

1. 20 � 6 � (10 � 2) � 6 2. 2,000 � 6 � (1,000 � 2) � 6

� 10 � ( 2 � 6) � 1,000 � ( 2 � 6)

� 10 � 12 � 1,000 � 12

� 120 � 12,000

3. How many books are in 20 boxes? 120 books

4. How many books are in 2,000 boxes? 12,000 books

The same publishing company ships a smaller book in boxes with 40 books each. How many books are in 50 boxes? How many are in 500 boxes?

Find 50 � 40 and 500 � 40 by filling in the blanks.

5. 50 � 40 � (5 � 10 ) � 6. 500 � 40 � (5 � 100 ) �

(4 � 10 ) (4 � 10 )

� 5 � 4 � 10 � 10 � 5 � 4 � 100 � 10

� 20 � 100 � 20 � 1,000

� 2,000 � 20,000

7. How many books are in 50 boxes? 2,000 books

8. How many books are in 500 boxes? 20,000 books



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Mental Math: Multiplying by Multiples of 10

Notice the pattern when multiplying multiples of 10.

9. 7 � 80 � 560 10. 4 � 60 � 240

70 � 80 � 5,600 40 � 60 � 2,400

70 � 800 � 56,000 40 � 600 � 24,000

Multiply.

11. 30 � 40 � 12. 10 � 600 � 13. 70 � 20 �

1,200 6,000 1,400

14. 50 � 400 � 15. 700 � 30 � 16. 40 � 800 �

20,000 21,000 32,000

17. 600 � 30 � 18. 40 � 90 � 19. 90 � 500 �

18,000 3,600 45,000

20. 70 � 500 � 21. 30 � 800 � 22. 200 � 70 �

35,000 24,000 14,000

23. 800 � 80 � 24. 30 � 600 � 25. 40 � 300 �

64,000 18,000 12,000

26. A class of 30 students is collecting pennies for a school fundraiser. If each of them collects 400 pennies, how many have they collected all together? 12,000 pennies

27. Reasoning Raul multiplied 60 � 500 and got 30,000. Since there are 4 zeros in the answer, he thought his answer was incorrect? Do you agree? Why or why not?

No, one of the zeros is from 6 � 5 which is 30.


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Teacher Notes

Ongoing AssessmentAsk: Will the number of zeros in the product always be the same as the sum of the number of zeros in the factors? No Why not? Sometimes the leading numbers in the factors will multiply to make another zero such as 4 � 5 � 20.

Error InterventionIf students are making mistakes with multiplication facts,

then use some of the intervention lessons on basic multiplication facts, G25 to G32.

If You Have More TimeHave students write and solve a word problem that involves multiplying multiples of ten.



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Estimating Products


Estimating Products

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Mrs. Wilson’s class at Hoover Elementary School is collecting canned goods. Their goal is to collect 600 cans. There are 21 students in the class and each student agrees to bring in 33 cans. Answer 1 to 7 to find if the class will meet their goal.

Estimate 21 � 33 and compare the answer to 600.

Round each factor to get numbers you can multiply mentally.

1. What is 21 rounded to the nearest ten? 20


3. Multiply the rounded numbers. 20 � 30 � 600

The answer is the same as the number needed to meet the goal.

4. 21 was rounded to 20. Was it rounded up or down? down

5. 33 was rounded to 30. Was it rounded up or down? down

6. Is 21 � 33 more or less than 20 � 30? more

7. Will the goal be reached? yes

Hoover Elementary School had a goal to collect 12,000 canned goods. There are 18 classes and each class collects 590 cans. Answer 8 to 13 to find if the school will meet their goal.

Estimate 18 � 590 and compare the answer with 12,000.

Round each factor to get numbers you can multiply mentally.


9. What is 590 rounded to the nearest hundred? 600

10. Multiply the rounded numbers. 20 � 600 � 12,000

The answer is the same as the number needed to meet the goal.

11. 18 was rounded to 20. Was it rounded up or down? up

590 was rounded to 600. Was it rounded up or down? up

12. Is 18 � 590 more or less than 20 � 600? less

13. Will the goal be reached? no

Round each factor so that you can estimate the product mentally.

14. 71 � 382 15. 27 � 62 16. 45 � 317

70 � 400 30 � 60 50 � 300

28,000 1,800 15,000

17. 58 � 176 18. 831 � 42 19. 16 � 768

60 � 200 800 � 40 20 � 800

12,000 32,000 16,000

20. 87 � 67 21. 373 � 95 22. 57 � 722

90 � 70 400 � 100 60 � 700

6,300 40,000 42,000

23. Debra spends 42 minutes each day driving to work. About how many minutes does she spend driving to work each month? 1,200 minutes

24. Reasoning If 64 � 82 is estimated to be 60 � 80, would the estimate be an overestimate or an underestimate? Explain.

It would be an underestimate because you are rounding both factors down.


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Estimating Products (continued)

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Teacher Notes

Ongoing AssessmentAsk: Why is it preferable to round 591 to the nearest hundred rather than the nearest ten? It is easier to multiply 600 than 590.

Error InterventionIf students have problems rounding numbers,

then use F2: Rounding to Nearest Ten and Hundred and F4: Numbers Halfway Between and Rounding.

If You Have More TimeHave students name situations when an estimate if sufficient and situations when an exact answer is needed.

Intervention Lesson H1

Math Diagnosis and Intervention SystemIntervention Lesson H1

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Equal Parts of a Whole

Teacher Notes

Ongoing AssessmentAsk: Looking at the names for shapes divided into 4, 5, 6, 8, 10, and 12 equal parts, what might be the name of a shape divided into seven equal parts? sevenths

Error InterventionIf children have trouble understanding the concept of equal parts,

then use A35: Equal parts.

If You Have More TimeHave students fold other rectangular sheets of paper and circular pieces of paper to find and name other equal parts.

Intervention Lesson H1 85


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Equal Parts of a Whole

Materials rectangular sheets of paper, 3 for each student; crayons or markers

1. Fold a sheet of paper so the two shorter edges fold

are on top of each other, as shown at the right.

2. Open up the piece of paper. Draw a line down the fold. Color each part a different color.

The table below shows special names for the equal parts. All parts must be equal before you can use these special names.

3. Are the parts you colored equal in size? yes

4. How many equal parts are there? 2 Number of Equal Parts

Name of Equal Parts

2 halves

3 thirds

4 fourths

5 fifths

6 sixths

8 eighths

10 tenths

12 twelfths

5. What is the name for the parts you colored?

halves

6. Fold another sheet of paper like above. Then fold it again so that it makes a long slender rectangle as shown below.

7. Open up the piece of paper. Draw lines down the folds. Color each part a different color.

8. Are the parts you colored equal in size? yes

9. How many equal parts are there? 4

10. What is the name for the parts you colored?

Newfold

Oldfold

fourths

11. Fold another sheet of paper into 3 parts that are not equal. Open it and draw lines down the folds. In the space below, draw your rectangle and color each part a different color.

Check that students draw unequal parts.

Tell if each shows parts that are equal or parts that are not equal. If the parts are equal, name them.

12. 13.

equal

not equal

fourths

14. 15.

equal

equal

thirds eighths

16. 17.

equal

not equal

twelfths

18. 19.

not equal

equal

fifths

20. 21.

equal

not equal

halves

22. 23.

equal

not equal

sixths

24. Reasoning If 5 children want to equally share a large pizza and each gets 2 pieces, will they need to cut the pizza into fifths, eighths, or tenths? tenths

86 Intervention Lesson H1

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Equal Parts of a Whole (continued)

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Parts of a Region

Teacher Notes

Ongoing AssessmentAsk: Janet said she ate 4 __

4 of an orange. Explain

why Janet could have said she ate the whole

orange. Sample answer: The orange would be cut

in 4 pieces and she ate 4 pieces, so she ate the

whole thing.

Error InterventionIf children have trouble writing fractions for parts of a region,

then use A36: Understanding Fractions to Fourths and A38: Writing Fractions for Part of a Region.

If You Have More TimeHave students design a rectangular flag (or rug, placemat, etc.) that is divided into equal parts. Have them color their flag and then on the back write the fractional parts of each color.


Parts of a Region

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Materials crayons or markers

1. In the circle at the right, color 2 of the equal parts blue and 4 of the equal parts red.

Write fractions to name the parts by answering 2 to 6.

2. How many total equal parts does the circle have? 6

3. How many of the equal parts of the circle are blue? 2

4. What fraction of the circle is blue?

2 ____

6 �

number of equal parts that are blue _____________________________ total number of equal parts � (numerator) ____________ (denominator)

Two sixths of the circle is blue.

5. How many of the equal parts of the circle are red? 4

6. What fraction of the circle is red?

4 ____

6 �

number of equal parts that are red ____________________________ total number of equal parts � (numerator) ____________ (denominator)

Four sixths of the circle is red.

Show the fraction 3 __ 8 by answering 7 to 9.

7. Color 3 __ 8 of the rectangle at the right.

8. How many equal parts doesthe rectangle have? 8

9. How many parts did youcolor? 3

Write the fraction for the shaded part of each region.

10. 11. 12.

2__3

1__4

4__5

13. 14. 15.

1__2

2__8

2__5

16. 17. 18.

1__3

3__5

5__8

Color to show each fraction.

19. 3 __ 4 20. 5 __ 6 21. 7 ___ 10

22. Math Reasoning Draw a picture to show 1 __ 3 . Then divide

each of the parts in half. What fraction of the parts does

the 1 __ 3 represent now? Check students’ drawings. 2__6

23. Ben divided a pie into 8 equal pieces and ate 3 of them. How much of the pie remains?

5__8


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Parts of a Region (continued)

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Parts of a Set


Parts of a Set

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Materials two-color counters, 20 for each pair; crayons or markers

1. Show 4 red counters and 6 yellow counters.

Write a fraction for the part that is red and the part that is yellow by answering 2 to 6.

2. How many counters are there in all? 10

3. How many of the counters are red? 4

4. What fraction of the group of counters is red?

4 ____

10 � number of counters that are red __________________________ total number of counters � (numerator) ____________ (denominator)

Four tenths of the group of counters is red

5. How many of the counters are yellow? 6

6. What fraction of the counters are yellow?

6 ____

10 �

number of counters that are yellow _____________________________ total number of counters � (numerator) ____________ (denominator)

Six tenths of the group of counters is yellow.Answer can vary on 7 and 8. Another correct set of answers is 12 and 10.

Show a group of counters with 5 __ 6 red by answering 7 to 9.

7. How many counters do you need in all? 6

8. How many of the counters need to be red? 5Check that students color 5 circles red.

9. Show the counters and color below to match.

Write the fraction for the shaded parts of each set.

10. 11.

2__3

1__2

12. 13.

3__4

4__5

14. 15.

2__5

4__6

Draw a set of shapes and shade them to show each fraction.

16. 5 __ 9 17. 6 ___ 10

Check students’ drawings.

18. Reasoning If Sally has 5 yellow marbles and 7 blue marbles. What fraction of her marbles are yellow? Draw a picture to justify your answer.5__12

; Students should draw 12 marbles with 5 blue.


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Parts of a Set (continued)

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Teacher Notes

Ongoing AssessmentAsk: What does it mean that 3 ___

12 of a group of

marbles are green? There are 3 green marbles out

of a total of 12 marbles.

Error InterventionIf children have difficulty describing parts of a set,

then use A37: Fractions of a Set and A39: Writing Fractions for Part of a Set.

If You Have More Time

Have students look around the classroom and

name different fractions they see. For example: 6 ___ 18

of the students have their math book out; 2 __ 5 of the

computers are turned off; 5 __ 9 of the boys have on

shorts.



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Equivalent Fractions


Equivalent Fractions

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Materials crayons or markers 1

1 __ 3 1 __ 3 1 __ 3

1 __ 6 1 __ 6 1 __ 6 1 __ 6 1 __ 6 1 __ 6

1. Show 2 __ 3 by coloring 2 of the 1 __ 3 strips.

2. Color as many 1 __ 6 strips as it takes

to cover the same region as the 2 __ 3 .

How many 1 __ 6 strips did you color? 4

3. So, 2 __ 3 is equivalent to four 1 __ 6 strips. 2 __ 3 � 4 ____ 6

You can use multiplication to find a fraction equivalent to 2 __ 3 . To do this, multiply the numerator and the denominator by the same number.

4. What number is the denominator � 2

2 __ 3 � 4 ____ 6

� 2

of 2 __ 3 multiplied by to get 6?

2

5. Since the denominator was multiplied by 2, the numerator must also be multiplied by 2. Put the product of 2 � 2 in the numerator of the second fraction above.

Multiply the numerator and denominator of each fraction by the same number to find a fraction equivalent to each.

6. � 3

2 __ 3 � 6 ____ 9

� 3

7. � 4

1 __ 2 � 4 ____ 8

� 4

8. Show 9 ___ 12 by coloring 9 of the 1 ___ 12 strips. 1

1 __ 4 1 __ 4 1 __ 4 1 __ 4

1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12 1 ___ 12

9. Color as many 1 __ 4 strips as it takes

to cover the same region as 9 ___ 12 .

How many 1 __ 4 strips did you color? 3

10. So, 9___12 is equivalent to three 1__

4 strips. 9___12 �

3____4

You can use division to find a fraction equivalent to 9___12 . To do this,

divide the numerator and the denominator by the same number.

11. What number is the denominator of � 3

9 ___ 12 � 3 ____ 4

� 3

9___12 divided by to get 4? 3

12. Since the denominator was divided by 3, the numerator must also be divided by 3. Put the quotient of 9 � 3 in the numerator of the second fraction above.

Divide the numerator and denominator of each fraction by the same number to find a fraction equivalent to each.

13. � 2

8 ___ 10 � 4 ____ 5

� 2

14. � 5

10 ___ 15 � 2 ____ 3

� 5

If the numerator and denominator cannot be divided by anything else, then the fraction is in simplest form.

15. Is 5___12 in simplest form? yes 16. Is 6__

8 in simplest form? no

Find each equivalent fraction.

17. 1__5 �

3____15 18. 8___

10 �4____5 19. 2__

8 �1____4

20. 7___10 �

14____20 21. 6___

14 �3____7 22. 8___

11 �16____22

Write each fraction in simplest form.

23. 6__8

3__4 24. 8___

12

2__3 25. 7___

35

1__5 26. 16___

24

2__3

27. Reasoning Explain why 4__6 is not in simplest form.

Sample answer: 4 and 6 have a common factor of 2. 112 Intervention Lesson H14

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Teacher Notes

Ongoing Assessment

Ask: Explain how you can tell 3 __ 7 is in simplest

form. 3 and 7 have only 1 as a common factor.

Error InterventionIf students do not understand how two fractions can be equivalent,

then use H7: Using Models to Find Equivalent Fractions.

If You Have More Time

Have students create and number a cube 2, 2, 3, 3,

6, and 6. Label 8 index cards: 1 __ 2 , 2 __

3 , 4 __

6 , 6 ___

18 , 6 ___

24 , 6 ___

10 , 6 ___

12 ,

and 3 __ 4 . Shuffle the index cards. One student rolls the

number cube and the other draws an index card.

Both students find a fraction equivalent to the one

on the index card by either multiplying or dividing

by the number rolled. Have students check each

others’ work. Sometimes either operation can be

done, sometimes only one can be used.



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Mixed Numbers

Teacher Notes

Ongoing AssessmentAsk: What is 15 ___

4 written as a mixed number? 3 3 __

4

Error InterventionIf students have difficulty dividing when converting from an improper fraction to a mixed number,

then use G42: Dividing with Objects and H15: Fractions and Division.

If students are changing a mixed number to an improper fraction and the students multiply the whole number and the numerator,

then, have the students write the word DoWN on their paper to remind them of the correct procedure: (D � W) � N.

If You Have More TimeHave students work in pairs. Have each student write 5 mixed numbers on index cards, one number per card. Then have students each write an improper fraction on an index card to match each mixed number written by the partner. Then the pair can play a memory game. Have the students shuffle the cards and lay them face down in an array. Have one student flip over two cards. If the cards are a match, then that player keeps the cards and can take another turn. If the cards are not a match, then the cards are turned back over and the other student has a chance to find a match. The game continues until all of the matches are found. The player with the most matches wins.


Mixed Numbers

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Materials fraction strips

A mixed number is a number written with a whole number and a fraction. An improper fraction is a fraction in which the numerator is greater than or equal to the denominator.

1. Circle the number that is a mixed number. 3 4 1 __ 3 8 __ 5

2. Circle the number that is an improper fraction. 3 __ 4 2 3 __ 5 9 __ 4

Write the improper fraction 7 __ 3 as a mixed number by answering 3 to 6.

3. Show seven 1 __ 3 fraction strips.

4. Use fraction strips. How many 1 strips can you make with

seven 1 __ 3 strips? 2

5. How many 1 __ 3 strips do you

have left over? 1

6. Write 7 __ 3 as a mixed

number. 21__

3

Write 7 __ 3 as a mixed number without fraction strips by answering 7 to 9.

7. Divide 7 by 3 at the right. 2 R1 3 � � 7

� 6

1

8. Fill in the missing numbers below.

Quotient 1

2 3

Remainder

Divisor

Notice, the quotient 2 tells how many one strips you can make.

The remainder 1 tells how many 1 __ 3 strips are left over.

9. Write 7 __ 3 as a mixed number. 21__

3

10. Since 14 � 5 � 2 R4, what is 14___5 as a mixed number?

24__5

Write 2 1__5 as an improper fraction by answering 11 to 13.

11. Show 2 1__5 with

fractions strips.

12. Use fraction

strips. How many 1__5 strips does it

take to equal 2 1__5?

11

13. What improper fraction equals 2 1__5 ?

11__5

Write 2 1__5 as an improper fraction without using fraction strips by

answering 14 to 16.

14. Fill in the missing numbers.

Whole Number � Denominator � Numerator

2 � 5 � 1 � 10 � 1 � 11

15. Write the 11 you found above over the denominator, 5.

11__5

16. What improper fraction equals 2 1__5 ?

11__5

Notice, 2 � 5 tells how many 1__5 strips equal 2 wholes. The 1 tells

how many additional 1__5 strips there are.

17. Since 6 � 4 � 3 � 27, what is 6 3__4 as an improper fraction?

27__4

Change each improper fraction to a mixed number or a whole number and change each mixed number to an improper fraction.

18. 3 2__7

23__7 19. 7__

3

21__3 20. 7__

2

31__2 21. 1 1___

10

11__10


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Mixed Numbers (continued)

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Intervention Lesson I8

Math Diagnosis and Intervention SystemIntervention Lesson I8

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Congruent Figures and Motions

Teacher Notes

Ongoing AssessmentAsk: Why are all squares not congruent? Congruent figures must have the same size and shape. Squares can be different sizes.

Error InterventionIf students have trouble understanding congruency,

then use D54: Same Size, Same Shape.

If students have trouble differentiating between slides, flips, and turns,

then use D55: Ways to Move Shapes.

If students understand congruency, but have trouble deciding if two figures are congruent,

then have students trace one of the figures and place the tracing over the other figure to see if it has the same size and shape.

If You Have More TimeHave students write their name using letters that have been flipped, turned, or slid. Exchange with a partner and have the partner identify what motion was used on each letter. Show the students that some letters can look like a slide and a flip. For example, the letter “I” looks the same when it is flipped and slid to the right.


Congruent Figures and Motions

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Materials construction paper, markers, and scissors

Follow 1–10.

1. Cut a scalene triangle out of construction paper.

2. Place your cut-out triangle on the bottom left side of another piece of contruction paper. Trace the triangle

Slide

with a marker.

3. Slide your cut-out triangle to the upper right of the same paper and trace the triangle again.

4. Look at the two triangles that you just traced. Are the two triangles the same size and shape? yes

When a figure is moved up, down, left, or right, the motion is called a slide, or translation.

Figures that are the exact same size and shape are called congruent figures.

5. On a new sheet of paper, draw a straight dashed line as Flipshown at the right. Place your cut-out triangle on the left side of the dashed line. Trace the triangle with a marker.

6. Pick up your triangle and flip it over the dashed line, like you were turning a page in a book. Trace the triangle again.

7. Look at the two triangles that you just traced. Are the two triangles congruent? yes

When a figure is picked up and flipped over, the motion is called a flip, or reflection.

8. On a new sheet of paper, draw a point in the middle of Turn

the paper. Place a vertex of your cut-out triangle on the point. Trace the triangle with a marker.

9. Keep the vertex of your triangle on the point and move the triangle around the point like the hands on a clock. Trace the triangle again.

10. Look at the two triangles you just traced. Are the two triangles congruent? yes

When a figure is turned around a point, the motion is a turn, or rotation.

Write slide, flip, or turn for each diagram.

11. 12. 13.

slide flip turn

14. 15. 16.

turn flip slide

For Exercises 17 and 18, use the figures to the right.

17. Are Figures 1 and 2 related by a slide, a flip, or a turn? slide

18. Are Figures 1 and 3 related by a slide, a flip, or a turn? flip

19. Reasoning Are the polygons at the right congruent? If so, what motion could be used to show it?

Yes; one is a turn of the other.

106 Intervention Lesson I8

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Congruent Figures and Motions (continued)

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Solids and Nets

Teacher Notes

Ongoing AssessmentAsk: What solid best represents a can of corn? cylinder

Error InterventionIf students have trouble identifying solids,

then use I1: Solid Figures.

If You Have More TimeIn pairs, have students play Guess My Solid. One student should select a solid made from the nets; make sure the other student cannot see which solid the partner picks. The second student asks yes-or-no questions such as, Does it have more than 5 vertices? Does it have at least one square face? and then tries to guess what the solid is using the clues.


Solids and Nets

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Materials tape, scissors, copy of nets for all prisms, square and rectangular pyramids from Teaching Tool Masters

Cut out and tape each net to help complete the tables. Each group should make 7 solids.

Solid Faces Edges Vertices Shapes of Faces1. Pyramid

5 8 5

1 square

4 triangles

2. Rectangular Pyramid

5 8 51 rectangle, 4 triangles

3. Cube

6 12 8 6 squares

4. Rectangular Prism

6 12 86

rectangles

5. Triangular Prism

5 9 62 triangles,

3 rectangles

What solid will each net form?

6. 7.

cylinder cube

8. 9.

rectangular prism triangular prism

10. 11.

cone square pyramid

12. Reasoning Is the figure a net for a cube? Explain.

No; the net only has five faces and a cube has six faces.


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Solids and Nets (continued)

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Views of Solid Figures

Teacher Notes

Ongoing AssessmentAsk: Which views would change if a cube were added behind the far, back, left cube in a solid? The top view and the side view would change. The front view would not change.

Error InterventionIf students have trouble seeing the views using blocks or small cubes,

then use larger boxes to illustrate the solids in front of the class.

If You Have More TimeHave student work in pairs. One student draws a top, side, or front view and the other student constructs a possible solid having the given view with blocks or small cubes.


Views of Solid Figures

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Materials 6 blocks or small cubes from place-value blocks for each pair or group, crayons or markers

Stack blocks to model the solid shown at the Top View

Side View

Front View

right. Assume that there are only 6 cubes in the solid so that none are hidden.

The top view of the solid is the image seen when looking straight down at the figure.

Draw the top view of the solid at the right by answering 1 and 2.

1. How many cubes can you see when you look straight down at the solid? 3

2. Color in squares on the grid to indicate the blocks seen from the top view.

The front view is the image seen when looking straight at the cubes.

Draw the front view of the solid above by answering 3 and 4.

3. How many cubes can you see when you look straight at the solid? 6

4. Color in squares on the grid to indicate the blocks seen from the front view.

The side view is the image seen when looking at the side of the cubes.

Draw the side view of the solid above by answering 5 and 6.

5. How many cubes can you see when you look at the solid from the side? 3

6. Color in squares on the grid to indicate the blocks seen from the side view.

Draw the front, right, and top views of each solid figure. There are no hidden cubes.

7. 8.

TopFront Side

TopSideFront

9. 10. 11.

Top

Front

Side

Top

Front

Side

Top

Front

Side

12. Reasoning If a cube is added to the top of the solid in Exercise 11, what views would change? What view would not change?

The front and side views would change but the top view would not.


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Views of Solid Figures (continued)

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Congruent Figures

Teacher Notes

Ongoing AssessmentAsk: Do figures have to be facing the same way in order to be considered congruent? No, they have to be the same size and the same shape but they can be turned in different directions and still be considered congruent.

Error InterventionIf students have trouble identifying shapes that are the same size,

then have students trace one figure and move the tracing over the other figure.

If You Have More TimeHave student work in pairs to find congruent objects in the classroom.


Congruent Figures

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Materials tracing paper and scissors

Two figures that have exactly the same size and shape are congruent.

1. Place a piece of paper over Figure A and trace the shape. Is the figure you drew congruent to Figure A? yes

Cut out the figure you traced and use it to answer 2 to 10. Figure A

Figure B Figure C Figure D

2. Place the cutout on top of Figure B. Is Figure B the same size as Figure A? no

3. Is Figure B congruent to Figure A? no

4. Place the cutout on top of Figure C. Is Figure C the same shape as Figure A? no

5. Is Figure C congruent to Figure A? no

6. Place the cutout on top of Figure D. Is Figure D the same size as Figure A? yes

7. Is Figure D the same shape as Figure A? yes

8. Is Figure D congruent to Figure A? yes

9. Circle the figure that is congruent to the figure at the right.

Tell if the two figures are congruent. Write Yes or No.

10. 11. 12.

yes no yes

13. 14. 15.

yes no no

16. 17. 18.

yes no no

19. Divide the isosceles triangle shown at the right into 2 congruent right triangles.

20. Divide the hexagon shown at the right into 6 congruent equilateral triangles.

21. Divide the rectangle shown at the right into 2 pairs of congruent triangles.

22. Reasoning Are the triangles at the right congruent? Why or why not?

No; the triangles are the same shape, but they are not the same size.


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Congruent Figures (continued)

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More Perimeter

Teacher Notes

Ongoing AssessmentAsk: Why is the formula for the perimeter of a square P � 4s? Because all of the sides of a square are equal, you can just multiply one side by 4 instead of adding each side.

Error InterventionIf students do not know the properties of rectangles,

then use I7: Quadrilaterals.

If students are having trouble remembering the formula for the perimeter of a square and the formula of the perimeter of a rectangle,

then have students create formula cards on note cards including examples of how to use the formula correctly.

If You Have More TimeHave students work in pairs to create a stack of 16 index cards with numbers 2 to 9 each written on cards. Have students draw two cards from the deck. The first card represents the length and the second card represents the width. The students work together to find the perimeter of a rectangle with the given dimensions. Have the students draw from the deck at least five different times and record their work.


More Perimeter

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Jonah’s pool is a rectangle. The pool is 15 feet long and 10 feet wide. What is the perimeter of the pool?

Find the perimeter of the pool by answering 1 to 3.

1. Write in the missing measurements on the pool 15 ft

10 ft 10 ft

15 ft

shown at the right.

2. Add the lengths of the sides.

10 ft � 10 ft � 15 ft � 15 ft � 50 ft

3. What is the perimeter of the pool? 50 ft

Find a formula for the perimeter of a rectangle by answering 4 to 10.

8 in.

3 in.Rectangle A

5 ft

4 ftRectangle

B

4. Write the side lengths of the rectangle. 7. Write the side lengths of the rectangle.

8 � 3 � 8 � 3 � 22 in. 5 � 4 � 5 � 4 � 18 ft

5. Rearrange the numbers. 8. Rearrange the numbers.

8 � 8 � 3 � 3 � 22 in. 5 � 5 � 4 � 4 � 18 ft

6. Rewrite the number sentence. 9. Rewrite the number sentence.

2(8) � 2 ( 3 ) � 22 in. 2(5) � 2( 4 ) � 18 ft

16 � 6 � 22 in. 8 � 10 � 18 ft

10. Complete the table.

Rectangle Length Width Perimeter

A 8 3 2( 8 ) � 2(3)

B 5 4 2(5) � 2(4)

Any � w 2� � 2 w

The formula for the perimeter of a rectangle is P � 2� � 2w

11. Reasoning Use the formula to find the perimeter of Jonah’s pool.

P � 2� � 2w

P � 2 ( 15 ) � 2( 10 ) � 30 � 20 � 50 ft

12. Is the perimeter the same as you found on the previous page? yes

A square is a type of rectangle where all of the side lengths are equal.

Find a formula for the perimeter of the square by answering 13 to 15.

13. Add to find the perimeter of the square shown at the right. 5 cm

5 � 5 � 5 � 5 � 20

14. What could you multiply to find the perimeter of the square? 4 � 5

15. If s equals the length of a side of a square, how could you find the perimeter? P � 4s

Find the perimeter of the rectangle with the given dimensions.

16. � � 9 mm, w � 12 mm 17. � � 13 in., w � 14 in.

42 mm 54 in.

18. � � 2 ft, w � 15 ft 19. � � 17 cm, w � 25 cm

34 ft 84 cm

Find the perimeter of the square with the given side.

20. s � 2 yd 21. s � 10 in. 22. s � 31 km 23. s � 11 m

8 yd 40 in. 124 km 44 m

24. Reasoning Could you use the formula for the perimeter of a rectangle to find the perimeter of a square? Explain your reasoning.

Yes; the formula for the perimeter of a rectangle can be used to find the perimeter of a square because a square is a rectangle.


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Name

Practice F8

Rounding Numbers Through ThousandsRound each number to the nearest ten.

1. 326 2. 825 3. 162 4. 97


5. 1,427 6. 8,136 7. 1,308 8. 3,656


9. 18,366 10. 408,614 11. 29,430 12. 63,239


13. 12,108 14. 70,274 15. 33,625 16. 17,164

17. What is 681,542 rounded to the nearest hundred thousand?

A 600,000 B 680,000 C 700,000 D 780,000

18. Mrs. Kennedy is buying pencils for each of 315 students at Hamilton Elementary. The pencils are sold in boxes of tens. How can she use rounding to decide how many pencils to buy?

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Practice

F8

Name

Practice F9

Practice

F9Comparing and Ordering Numbers Through ThousandsUse the chart for help if you need to.

hundredthousands


Compare. Write � or � for each .

1. 54,376 45,763 2. 6,789 9,876

3. 9,635 9,536 4. 4,125 3,225


5. 959,211 936,211 958,211

6. 456,318 408,405 459,751

7. Write three numbers that are greater than 43,000 and less than 44,000.

8. Which number has the greatest value?

A 86,543,712 B 86,691,111 C 86,381,211 D 86,239,121

9. Tell how you could use a number line to determine which of two numbers is greater.

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Practice F10

Place Value Through MillionsWrite the number in standard form and in word form.

1. 300,000,000 � 70,000,000 � 2,000,000 � 500,000 � 10,000 � 2,000 � 800 � 5

Write the word form and tell the value of the underlined digit for each number.

2. 4,600,028

3. 488,423,046

4. Number Sense Write the number that is one hundred million more than 15,146,481.

5. The population of a state was estimated to be 33,871,648. Write the word form.

86. Which is the expanded form for 43,287,005?

A 4,000,000 � 300,000 � 20,000 � 8,000 � 700 � 5

B 40,000,000 � 3,000,000 � 200,000 � 80,000 � 7,000 � 5

C 400,000,000 � 30,000,000 � 2,000,000 � 8,000 � 500

D 4,000,000 � 30,000 � 2,000 � 800 � 70 � 5

7. In the number 463,211,889, which digit has the greatest value? Explain.

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Practice

F10

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Practice F11

Practice

F11Rounding Numbers Through MillionsRound each number to the nearest thousand.

1. 6,326 2. 2,825 3. 2,162 4. 4,097


5. 31,427 6. 68,136 7. 76,308 8. 93,656


9. 618,366 10. 409,614 11. 229,930 12. 563,239


13. 12,108,219 14. 7,570,274 15. 9,333,625 16. 4,307,164

17. What is1,486,428 rounded to the nearest million?

A 1,000,000 B 1,250,000 C 1,500,000 D 2,000,000


A 600,000 B 680,000 C 700,000 D 780,000

19. Round 2,672,358 to each place value?

ten hundred

thousand ten thousand

hundred thousand million

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Practice F29

Practice

F29Patterns and EquationsFor 1 through 6, complete each table. Find each rule.

1. 2. 3. 4.

Rule: Rule: Rule: Rule:

5. 6.

Rule: Rule:

7. Lucas recorded the growth of a plant. How tall will the plant be on Day 5?

Day 1 2 3 4 5 Height in inches 6 12 18 24 ?

8. Danielle made a table of the rental fees at a video store. What is the rule?

x 1 2 3 4 y $3 $6 $9 $12

A y � 3x C y � x � 3 B y � 6x D y � 4x

9. Curtis found a rule for a table. The rule he made is y � 7x. What does the rule tell you about every y-value?

x y81 963 745 527 ?

x y6 428 5610 7012 ?

x y36 642 748 854 ?

x y10 3015 4520 6025 ?

x 2 4 6 8y 22 44 66 ?

x 9 12 15 18y 3 4 5 ?

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Practice G7

Estimating SumsEstimate by rounding to the nearest ten.

1. 51 � 46 2. 34 � 71 3. 33 � 81 4. 53 � 69

5. 58 � 47 6. 39 � 64 7. 88 � 76 8. 33 � 23


9. 478 10. 680 11. 617 12. 569_ � 252 _ � 743 _ � 358 _ � 780

13. 840 � 501 14. 764 � 571 15. 421 � 887

16. 458 � 681 17. 141 � 370 18. 605 � 825

19. Corey was a member of the baseball team for 4 years. Dan was a member of the football team for 3 years. The baseball team has 51 members and the football team has 96 members. About how many members do the two groups have together?

20. Karen sold 534 magazines and Carly sold 308. About how many total magazines did the two girls sell?

21. What is the largest number that can be added to 28 so that the sum is 50 when both numbers are rounded to the nearest ten? Explain.

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Practice G42

Practice

G42Dividing with ObjectsDivide. You may use counters or pictures to help.

1. 27 � 4 2. 32 � 6 3. 17 � 7 4. 29 � 9

5. 27 � 8 6. 27 � 3 7. 28 � 5 8. 35 � 4

9. 19 � 2 10. 30 � 7 11. 17 � 3 12. 16 � 9

If you arrange these items into equal rows, tell how many will be in each row and how many will be left over.

13. 26 shells into 3 rows

14. 19 pennies into 5 rows

15. 17 balloons into 7 rows

16. Ms. Nikkel wants to divide her class of 23 students into 4 equal teams. Is this reasonable? Why or why not?

17. Which is the remainder for the quotient of 79 � 8?

A 7 B 6 C 5 D 4

18. Pencils are sold in packages of 5. Explain why you need 6 packages in order to have enough for 27 students.

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Practice G59

Practice

G59Factoring NumbersIn 1 through 12, find all the factors of each number. Tell whether each number is prime or composite.

1. 81 2. 43 3. 572 4. 63

5. 53 6. 87 7. 3 8. 27

9. 88 10. 19 11. 69 12. 79

13. 3,235 14. 1,212 15. 57 16. 17

17. Mr. Gerry’s class has 19 students, Ms. Vernon’s class has 21 students, and Mr. Singh’s class has 23 students. Whose class has a composite number of students?

18. Every prime number larger than 10 has a digit in the ones place that is included in which set of numbers below?

A 1, 3, 7, 9 C 0, 2, 4, 5, 6, 8

B 1, 3, 5, 9 D 1, 3, 7

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Practice G66

Practice

G66Mental Math: Multiplying by Multiples of 10Multiply. 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 lb in one trip. Truck B can haul 300 lb 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. 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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Practice G67

Practice

G67Estimating ProductsRound each factor so that you can estimate the product mentally.Use 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

Use compatible numbers to estimate each product.

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. Ana can put 27 stickers on each page of her scrapbook. The scrapbook has 112 pages. About how many stickers can Ana put in the scrapbook?

A 6,000 B 4,000 C 3,000 D 2,000

19. 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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Practice H1

Practice

H1Equal Parts of a WholeTell if each shows equal or unequal parts. If the parts are equal, name them.

1. 2. 3. 4.

Name the equal parts of the whole.

5. 6. 7. 8.

Use the grid to draw a region showing the number of equal parts named.

9. tenths 10. sixths

11. Geometry How many equal parts does this figure have?

12. Which is the name of 12 equal parts of a whole?

halves tenths sixths twelfths

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cheesegreenpeppers

mushrooms

Region BRegion A

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Practice H2

Practice

H2Parts of a RegionWrite a fraction for the part of the region below that is shaded.

1. 2.

Shade in the models to show each fraction.

3. �24� 4. 7

__ 10

5. What fraction of the pizza is cheese?

6. What fraction of the pizza is mushroom?

7. Number Sense Is �14� of 12 greater than �

14� of 8? Explain your

answer.

8. A set has 12 squares. Which is the number of squares in �13� of

the set?

A 3 B 4 C 6 D 9

9. Explain why �12� of Region A is not larger than �

12� of Region B.

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Practice H3

Practice

H3Parts of a Set

1. Draw a group of squares with 9 ___ 10 shaded.

2. How many squares do you need to draw altogether.

3. How many should be shaded?

Write the fraction for each shaded model.

4. 5.

6. 7.

8. 9.

Draw a model and shade it in to show each fraction.

10. 8 ___ 12 11. 15 ___ 20

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Practice H14

Practice

H14Equivalent FractionsTo find an equivalent fraction by To find the equivalent fraction by multiplying, use this example. dividing, use this example.

� 2

2 __ 3 � ____ 6 � 2

� 5

10 ___ 15 � ____ 3 � 5

Find the equivalent fraction.

1. 1 __ 6 � ____ 18 2. 6 ___ 10 � ____ 5 3. 6 __ 8 � ____ 4

4. 6 ___ 10 � ____ 20 5. 8 ___ 14 � ____ 7 6. 9 ___ 11 � ____ 22


7. 9 ___ 12

8. 5 ___ 10

9. 5 ___ 25

10. 24 ___ 36

Multiply or divide to find an equivalent fraction.

11. 11 ___ 22 12. 6 ___ 36 13. 9 ___ 10 14. 5 ___ 35 15. 7 ___ 12

16. At the air show, 1 _ 3 of the airplanes were gliders. Which fraction is not an equivalent fraction for 1 _ 3 ?

A 5 ___ 15 B 7 ___ 21 C 6 ___ 24 D 9 ___ 27

17. In Missy’s sports-cards collection, 5 _ 7 of the cards are baseball. In Frank’s collection, 12

__ 36 are baseball. Frank says they have the same fraction of baseball cards. Is he correct?

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Practice H18

Practice

H18Mixed NumbersWrite 5 _ 2 as a mixed number without using fraction strips.

1. Divide 5 by 2 at the right. 2 � � 5

�


Quotient

Remainder

Divisor

3. Write 5 _ 2 as a mixed number.

Write each improper fraction as a mixed number.

4. 12 ___ 7

5. 7 __ 3

6. 9 __ 7

7. 9 __ 4

8. 29 ___ 13

9. 34 ___ 8

10. Write 2 4 _ 5 as an improper fraction.

Whole Number � Denominator � Numerator __________________________________________ Denominator �

2 � � 4 � 10 � ____________________________________________

� _______

Change each mixed number to an improper fraction.

11. 2 4 __ 5

12. 8 7 __ 9

13. 3 6 __ 7

14. 7 1 __ 8

15. 4 3 __ 7

16. 5 1 __ 4

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Practice

I8Congruent Figures and MotionsCongruent figures have the same size and shapes, although they may face different directions.

Write yes or no to tell if the figures are congruent.

1. 2. 3.

4. 5. 6.

Slide

Flip

Turn


6. 7. 8.

10. 11. 12.

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Practice I10

Practice

I10Solids and NetsFor 1 and 2, predict what shape each net will make.

1. 2.

For 3–5, tell which solid figures could be made from the descriptions given.

3. A net that has 6 squares 4. A net that has 4 triangles 5. A net that has 2 circles and a rectangle 6. Which solid can be made by a net that has exactly one circle in it?

A Cone B Cylinder C Sphere D Pyramid

7. Draw a net for a triangular pyramid. Explain how you know your diagram is correct.

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Practice I11

Practice

I11Views of Solid FiguresDraw the front, right, and top views of each solid figure.

1. 2.

Top Front Side Top Side Front

3. 4.

Top Front Side Top Side Front

5.

Top Front Side

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Practice I13

Practice

I13Congruent FiguresCongruent figures have the same size and shape, although they may face different directions.

Tell if the figures are congruent.

1. 2. 3.

4. 5. 6.

7. Divide this shape into 8. Divide this shape into 4 congruent shapes. 2 congruent shapes.


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Practice I45

Practice

I45PerimeterLook at Rectangle A and Rectangle B. Complete the table.

9 in.

3 in.Rectangle A

6 ft

4 ftRectangle

B


A

B

So, Any � w 2� � 2w

Find the perimeter of these rectangles.

1. � � 9 w � 2 2. � � 6 w � 7

3. � � 11 w � 12 4. � � 10 w � 5


5. s � 4 6. s � 2

7. s � 9 8. s � 6

9. s � 20 10. s � 5

11. s � 8 12. s � 10

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F8 F9

F10 F11Answers: F8, F9, F10, F11

Answers for Practice

F8, F9, F10, F11

330 830 160 100

1,400 8,100 1,300 3,700

18,000 409,000 29,000 63,000

10,000 70,000 30,000 20,000

Round to the nearest 10.

Name

Practice F8

Rounding Numbers Through ThousandsRound each number to the nearest ten.

1. 326 2. 825 3. 162 4. 97


5. 1,427 6. 8,136 7. 1,308 8. 3,656


9. 18,366 10. 408,614 11. 29,430 12. 63,239


13. 12,108 14. 70,274 15. 33,625 16. 17,164


A 600,000 B 680,000 C 700,000 D 780,000

18. Mrs. Kennedy is buying pencils for each of 315 students at Hamilton Elementary. The pencils are sold in boxes of tens. How can she use rounding to decide how many pencils to buy?

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Practice

F8

45095_Practice_F8-I45.indd F8 6/30/08 12:01:54 PM

<>>

936,211 958,211

Answers will vary.

>

959,211

408,405 456,318 459,751

Answers will vary.

Name

Practice F9

Practice

F9Comparing and Ordering Numbers Through ThousandsUse the chart for help if you need to.

hundredthousands


Compare. Write � or � for each .

1. 54,376 45,763 2. 6,789 9,876

3. 9,635 9,536 4. 4,125 3,225


5. 959,211 936,211 958,211

6. 456,318 408,405 459,751

7. Write three numbers that are greater than 43,000 and less than 44,000.

8. Which number has the greatest value?

A 86,543,712 B 86,691,111 C 86,381,211 D 86,239,121

9. Tell how you could use a number line to determine which of two numbers is greater.

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372,512,805; three hundred seventy-two million, five hundred twelve thousand, eight hundred five

Four million, six hundred thousand, twenty-eight; six hundred thousand

Thirty-three million, eight hundred seventy-one thousand, six hundred forty-eight

4; it is in the hundred millions place.

Four hundred eighty-eight million, four hundred twenty-three thousand, forty-six; forty

115,146,481

Name

Practice F10

Place Value Through MillionsWrite the number in standard form and in word form.

1. 300,000,000 � 70,000,000 � 2,000,000 � 500,000 � 10,000 � 2,000 � 800 � 5

Write the word form and tell the value of the underlined digit for each number.

2. 4,600,028

3. 488,423,046

4. Number Sense Write the number that is one hundred million more than 15,146,481.

5. The population of a state was estimated to be 33,871,648. Write the word form.

86. Which is the expanded form for 43,287,005?

A 4,000,000 � 300,000 � 20,000 � 8,000 � 700 � 5

B 40,000,000 � 3,000,000 � 200,000 � 80,000 � 7,000 � 5

C 400,000,000 � 30,000,000 � 2,000,000 � 8,000 � 500

D 4,000,000 � 30,000 � 2,000 � 800 � 70 � 5

7. In the number 463,211,889, which digit has the greatest value? Explain.

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Practice

F10


6,000 3,000 2,000 4,000

30,000 70,000 80,000 90,000

600,000 400,000 200,000 600,000

9,000,00012,000,000 8,000,000 4,000,000

2,672,360 2,672,4002,672,000 2,670,000

2,700,000 3,000,000

Name

Practice F11

Practice

F11Rounding Numbers Through MillionsRound each number to the nearest thousand.

1. 6,326 2. 2,825 3. 2,162 4. 4,097


5. 31,427 6. 68,136 7. 76,308 8. 93,656


9. 618,366 10. 409,614 11. 229,930 12. 563,239


13. 12,108,219 14. 7,570,274 15. 9,333,625 16. 4,307,164

17. What is1,486,428 rounded to the nearest million?

A 1,000,000 B 1,250,000 C 1,500,000 D 2,000,000


A 600,000 B 680,000 C 700,000 D 780,000

19. Round 2,672,358 to each place value?

ten hundred

thousand ten thousand

hundred thousand million

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F29 G7

G42 G59Answers: F29, G7, G42, G59


F29, G7, G42, G59

x � 9 7x x � 6 3x

11x x � 3

30 inches

The y-value is 7 times greater than the x-value.

3 84 9 75

88 6

Name

Practice F29

Practice

F29Patterns and EquationsFor 1 through 6, complete each table. Find each rule.

1. 2. 3. 4.

Rule: Rule: Rule: Rule:

5. 6.

Rule: Rule:

7. Lucas recorded the growth of a plant. How tall will the plant be on Day 5?

Day 1 2 3 4 5 Height in inches 6 12 18 24 ?

8. Danielle made a table of the rental fees at a video store. What is the rule?

x 1 2 3 4y $3 $6 $9 $12

A y � 3x C y � x � 3 B y � 6x D y � 4x

9. Curtis found a rule for a table. The rule he made is y � 7x.What does the rule tell you about every y-value?

x y81 963 745 527 ?

x y6 428 5610 7012 ?

x y36 642 748 854 ?

x y10 3015 4520 6025 ?

x 2 4 6 8y 22 44 66 ?

x 9 12 15 18y 3 4 5 ?

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100

24; 28 rounds to 30, so the second number must round to 20, 30 � 20 � 50

100 110 120

110 100 170 50

1,3001,4001,300

1,4005001,200

150members

800 1,400 1,000 1,400

800magazines

Name

Practice G7

Estimating SumsEstimate by rounding to the nearest ten.

1. 51 � 46 2. 34 � 71 3. 33 � 81 4. 53 � 69

5. 58 � 47 6. 39 � 64 7. 88 � 76 8. 33 � 23


9. 478 10. 680 11. 617 12. 569_� 252 _� 743 _� 358 _� 780

13. 840 � 501 14. 764 � 571 15. 421 � 887

16. 458 � 681 17. 141 � 370 18. 605 � 825

19. Corey was a member of the baseball team for 4 years. Dan was a member of the football team for 3 years. The baseball team has 51 members and the football team has 96 members. About how many members do the two groups have together?

20. Karen sold 534 magazines and Carly sold 308. About how many total magazines did the two girls sell?

21. What is the largest number that can be added to 28 so that the sum is 50 when both numbers are rounded to the nearest ten? Explain.

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Practice

G7

45095_Practice_F8-I45.indd G7 6/30/08 12:02:02 PM

6 R3 5 R2 2 R3 3 R2

3 R3 9 5 R3 8 R3

9 R1 4 R2 5 R2 1 R7

No. The teams will not be even.23 � 4 � 5R3

6 � 5 � 30 5 � 5 � 25 (not enough)

2 rows; 3 left over3 rows; 4 left over8 rows; 2 left over

Name

Practice G42

Practice

G42Dividing with ObjectsDivide. You may use counters or pictures to help.

1. 27 � 4 2. 32 � 6 3. 17 � 7 4. 29 � 9

5. 27 � 8 6. 27 � 3 7. 28 � 5 8. 35 � 4

9. 19 � 2 10. 30 � 7 11. 17 � 3 12. 16 � 9

If you arrange these items into equal rows, tell how many will be in each row and how many will be left over.

13. 26 shells into 3 rows

14. 19 pennies into 5 rows

15. 17 balloons into 7 rows

16. Ms. Nikkel wants to divide her class of 23 students into 4 equal teams. Is this reasonable? Why or why not?

17. Which is the remainder for the quotient of 79 � 8?

A 7 B 6 C 5 D 4

18. Pencils are sold in packages of 5. Explain why you need 6 packages in order to have enough for 27 students.

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Ms. Vernon’s

1, 3, 9, 27, 81 1, 43 1, 2, 4, 11, 13, 22, 26, 44, 52, 143, 286, 572

1, 3, 7, 9,

21, 63

1, 53 1, 3, 29, 87 1, 3 1, 3, 9, 27

1, 2, 4, 8, 11,

22, 44, 88

1, 19 1, 3, 23, 69 1, 79

compositecomposite composite

prime

compositeprime compositeprime

compositeprimecomposite

prime

composite compositecomposite prime

1, 5, 647,

3235

1, 2, 4, 6, 12, 101, 202, 303, 606, 1212

1, 3, 19, 57 1, 17

Name

Practice G59

Practice

G59Factoring NumbersIn 1 through 12, find all the factors of each number. Tell whether each number is prime or composite.

1. 81 2. 43 3. 572 4. 63

5. 53 6. 87 7. 3 8. 27

9. 88 10. 19 11. 69 12. 79

13. 3,235 14. 1,212 15. 57 16. 17

17. Mr. Gerry’s class has 19 students, Ms. Vernon’s class has 21 students, and Mr. Singh’s class has 23 students. Whose class has a composite number of students?

18. Every prime number larger than 10 has a digit in the ones place that is included in which set of numbers below?

A 1, 3, 7, 9 C 0, 2, 4, 5, 6, 8

B 1, 3, 5, 9 D 1, 3, 7

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G66, G67, H1, H2

G66 G67

H1 H2Answers: G66, G67, H1, H2

1201,8001,8006,300

40,00045,000

4503,000

028,00024,000120,000

3,600 lb15,000 lb

Answers will vary. Sample answer: Multiply 3 � 9 � 27; 27 � 10 � 270

3 Answers will vary.

Name

Practice G66

Practice

G66Mental Math: Multiplying by Multiples of 10Multiply. 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 lb in one trip. Truck B can haul 300 lb 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. 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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21,00015,0004,000

3,500

6,00064,0006,000

1,200

30 � 90; 2,700 700 � 90; 6,30050 � 300; 15,00080 � 600; 48,00070 � 300; 21,000

70 � 700; 49,00040 � 400; 16,00060 � 800; 48,000

7 � 300 � 2,100 kilowatts Multiply 7 days in one week � 300.(300 is incompatible to 330)

Answersmay vary.

Name

Practice G67

Practice

G67Estimating ProductsRound each factor so that you can estimate the product mentally.Use 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

Use compatible numbers to estimate each product.

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. Ana can put 27 stickers on each page of her scrapbook. The scrapbook has 112 pages. About how many stickers can Ana put in the scrapbook?

A 6,000 B 4,000 C 3,000 D 2,000

19. 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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Equal,halves

Unequal Equal,eighths

Equal,fourths

eighths thirds fifths sixths

Answers will vary.

4

Name

Practice H1

Practice

H1Equal Parts of a WholeTell if each shows equal or unequal parts. If the parts are equal, name them.

1. 2. 3. 4.

Name the equal parts of the whole.

5. 6. 7. 8.

Use the grid to draw a region showing the number of equal parts named.

9. tenths 10. sixths

11. Geometry How many equal parts does this figure have?

12. Which is the name of 12 equal parts of a whole?

halves tenths sixths twelfths

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45095_Practice_F8-I45.indd H1 6/30/08 12:02:10 PM

cheesegreenpeppers

mushrooms

Region BRegion A

�48��

34�

or

Yes. Answers will vary. �14� of 12 is 3 and �

14� of 8 is 2; 3 > 2.

They each have the same region shaded for

1_2

3_8

2_8

1_2

Name

Practice H2

Practice

H2Parts of a RegionWrite a fraction for the part of the region below that is shaded.

1. 2.

Shade in the models to show each fraction.

3. �24� 4. 7__

10

5. What fraction of the pizza is cheese?

6. What fraction of the pizza is mushroom?

7. Number Sense Is �14� of 12 greater than �

14� of 8? Explain your

answer.

8. A set has 12 squares. Which is the number of squares in �13� of

the set?

A 3 B 4 C 6 D 9

9. Explain why �12� of Region A is not larger than �

12� of Region B.

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H3, H14, H18, I8

H3 H14

H18 I8Answers: H3, H14, H18, I8

Answers will vary.

Answers will vary.

109

4_5

2_3

6_8

2_5

7_9

4__16

Name

Practice H3

Practice

H3Parts of a Set

1. Draw a group of squares with 9___10 shaded.

2. How many squares do you need to draw altogether.

3. How many should be shaded?

Write the fraction for each shaded model.

4. 5.

6. 7.

8. 9.

Draw a model and shade it in to show each fraction.

10. 8___12 11. 15___

20

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4 3

3 3 3

12 4 18

3_4

1_2

1_5

14__24

1_7

18__20

1_6

1_2

In simplest form, 12__36 � 1_

3. The fraction 5_7

is already in simplest form. Since 1_3 � 5_

7,Frank and Missy do not have the same fraction of baseball cards.

2_3

Sample answers given

Name

Practice H14

Practice

H14Equivalent FractionsTo find an equivalent fraction by To find the equivalent fraction by multiplying, use this example. dividing, use this example.

� 2

2__3 � ____

6 � 2

� 5

10___ 15 � ____ 3 � 5

Find the equivalent fraction.

1. 1__6 � ____

18 2. 6___10 � ____

5 3. 6__8 � ____

4

4. 6___10 � ____

20 5. 8___14 � ____

7 6. 9___11 � ____

22


7. 9___12 8. 5___

10 9. 5___25 10. 24___

36

Multiply or divide to find an equivalent fraction.

11. 11___22 12. 6___

36 13. 9___10 14. 5___

35 15. 7___12

16. At the air show, 1_3 of the airplanes were gliders. Which fraction

is not an equivalent fraction for 1_3?

A 5___15 B 7___

21 C 6___24 D 9___

27

17. In Missy’s sports-cards collection, 5_7 of the cards are baseball.

In Frank’s collection, 12__36 are baseball. Frank says they have

the same fraction of baseball cards. Is he correct?

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15_7 2 1_7 1 2_7

21_4 2 3__

13 4 2_8; 4 1_4

14__5

79__9

27__7

57__8

31__7

21__4

221

2

41

21_2

55

4 1415

Name

Practice H18

Practice

H18Mixed NumbersWrite 5_

2 as a mixed number without using fraction strips.

1. Divide 5 by 2 at the right.

2 � � 5

�


Quotient

Remainder

Divisor

3. Write 5_2 as a mixed number.

Write each improper fraction as a mixed number.

4. 12___7 5. 7__

3 6. 9__7

7. 9__4 8. 29___

13 9. 34___8

10. Write 2 4_5 as an improper fraction.Whole Number � Denominator � Numerator__________________________________________

Denominator �

2 � � 4 � 10 �____________________________________________ � _______

Change each mixed number to an improper fraction.

11. 24__5 12. 87__

9 13. 36__7

14. 71__8 15. 43__

7 16. 51__4©

Pea

rson

Ed

ucat

ion,

Inc.

3


No Yes No

Yes No Yes

slide turn fl ip

turn slide fl ip

Name

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Practice I8

Practice

I8Congruent Figures and MotionsCongruent figures have the same size and shapes, although they may face different directions.

Write yes or no to tell if the figures are congruent.

1. 2. 3.

4. 5. 6.

Slide Flip Turn


6. 7. 8.

10. 11. 12.

45095_Practice_F8-I45.indd I8 7/1/08 11:40:17 AM

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I10, I11, I13, I45

I10 H11

I13 I45Answers: I10, I11, I13, I45

rectangular prism square pyramid

cubetriangular pyramid

cylinder

Answers will vary.

Name

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Practice I10

Practice

I10Solids and NetsFor 1 and 2, predict what shape each net will make.

1. 2.

For 3–5, tell which solid figures could be made from the descriptions given.

3. A net that has 6 squares

4. A net that has 4 triangles

5. A net that has 2 circles and a rectangle

6. Which solid can be made by a net that has exactly one circle in it?

A Cone B Cylinder C Sphere D Pyramid

7. Draw a net for a triangular pyramid. Explain how you know your diagram is correct.

45095_Practice_F8-I45.indd I10 6/30/08 12:02:23 PM

Name

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Practice I11

Practice

I11Views of Solid FiguresDraw the front, right, and top views of each solid figure.

1. 2.

TopFront Side TopSideFront

3. 4.

TopFront Side TopSideFront

5.

TopFront Side


7–10: Answers will vary.

yes no no

no yes yes

Name

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Practice I13

Practice

I13Congruent FiguresCongruent figures have the same size and shape, although they may face different directions.

Tell if the figures are congruent.

1. 2. 3.

4. 5. 6.




9 3 246 4 20

16

P � 22 P � 26

P � 30P � 46

36

8

24

80 20

32 40

Name

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Practice I45

Practice

I45PerimeterLook at Rectangle A and Rectangle B. Complete the table.

9 in.

3 in.Rectangle A

6 ft

4 ftRectangle

B


A

B

So, Any � w 2� � 2w

Find the perimeter of these rectangles.

1. � � 9 w � 2 2. � � 6 w � 7

3. � � 11 w � 12 4. � � 10 w � 5


5. s � 4 6. s � 2

7. s � 9 8. s � 6

9. s � 20 10. s � 5

11. s � 8 12. s � 10


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Name Grade 3

Step Up to Grade 4 Test

T1

1. Round 43,864 to the nearest ten

thousand.

A 40,000

B 43,000

C 43,900

D 44,000

2. Which is the expanded form of

4,321,189?

A 4,000,000 � 300,000 � 20,000 �

1,000 � 100 � 80 � 9

B 4,000,000 � 300,000 � 21,000 �

100 � 89

C 4,000,000 � 300,000 � 20,000 �

1,000 � 90 � 9

D 400,000 � 300,000 � 21,000 �

1,000 � 100 � 80 � 9

3. Which digit is in the thousands place?

128,698,473

A 1

B 2

C 6

D 8

4. Round this number to the nearest

ten million. 15,679,841

A 5,000,000

B 11,000,000

C 15,000,000

D 16,000,000

5.

If x = 35, what is the value of y?

A 30

B 27

C 25

D 23

6. Estimate by rounding to the nearest

hundred. 689 � 228

A 628

B 800

C 889

D 900

x 20 25 30 35y 12 17 22 ?

Name Grade 3


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T2

7. Find the quotient and the remainder.

26 � 4

A 4 R 2

B 6 R 2

C 6 R 4

D 8 R 2


A 1, 6, 12

B 1, 2, 6, 12

C 1, 2, 3, 6, 12

D 1, 2, 3, 4, 6, 12

9. The comic book store packs 30 comic

books into one envelope. How many

comic books will be packed into

30 envelopes?

A 90

B 300

C 600

D 900

10. Estimate the product by rounding

each factor.

28 � 23

A 900

B 600

C 500

D 400

11. Name the equal parts of the whole.

A fifths

B fourths

C thirds

D halves

12. Write the fraction for the shaded part

of the region.

A 4 _ 5

B 5 _ 8

C 6 _ 8

D 7 _ 8

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Name Grade 3


T3

13. Find the fraction for the shaded parts

of this set.

A 3 _ 5

B 4 _ 5

C 5 _ 6

D 4 _ 7

14. Which fraction is not equivalent to 2 _ 3 ?

A 4 _ 6

B 8 __ 12

C 9 __ 12

D 10 __ 15

15. What is the mixed number for this

improper fraction? 15 __ 8

A 2 7 _ 8

B 2 1 _ 8

C 1 7 _ 8

D 1 5 _ 8

16. What motion does this shape show?

A slide

B fl ip

C turn

D motion

17. Which solid can be made from this net?

A square

B cube

C triangular prism

D rectangular prism

18. What would the top view of this solid

look like?

A B

C D

6 ft

3 ft 4 ft

3 ft3 ft 1 ft

Name Grade 3


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T4

19. Which set of fi gures is not congruent?

A

B

C

D

20. What is the perimeter of this garden?

A 12 ft

B 20 ft

C 22 ft

D 24 ft

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Answers for Test

T1, T2, T3, T4

T1 T2

T4T3Answers: T1, T2, T3, T4

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Name Grade 3


T1

1. Round 43,864 to the nearest ten

thousand.

A 40,000

B 43,000

C 43,900

D 44,000

2. Which is the expanded form of

4,321,189?

A 4,000,000 � 300,000 � 20,000 �

1,000 � 100 � 80 � 9

B 4,000,000 � 300,000 � 21,000 �

100 � 89

C 4,000,000 � 300,000 � 20,000 �

1,000 � 90 � 9

D 400,000 � 300,000 � 21,000 �

1,000 � 100 � 80 � 9

3. Which digit is in the thousands place?

128,698,473

A 1

B 2

C 6

D 8

4. Round this number to the nearest

ten million. 15,679,841

A 5,000,000

B 11,000,000

C 15,000,000

D 16,000,000

5.

If x = 35, what is the value of y?

A 30

B 27

C 25

D 23

6. Estimate by rounding to the nearest

hundred. 689 � 228

A 628

B 800

C 889

D 900

x 20 25 30 35y 12 17 22 ?

45095_T1-T4.indd T1 7/1/08 2:09:36 PM

Name Grade 3


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T2

7. Find the quotient and the remainder.

26 � 4

A 4 R 2

B 6 R 2

C 6 R 4

D 8 R 2


A 1, 6, 12

B 1, 2, 6, 12

C 1, 2, 3, 6, 12

D 1, 2, 3, 4, 6, 12

9. The comic book store packs 30 comic

books into one envelope. How many

comic books will be packed into

30 envelopes?

A 90

B 300

C 600

D 900

10. Estimate the product by rounding

each factor.

28 � 23

A 900

B 600

C 500

D 400

11. Name the equal parts of the whole.

A fifths

B fourths

C thirds

D halves

12. Write the fraction for the shaded part

of the region.

A 4 _ 5

B 5 _ 8

C 6 _ 8

D 7 _ 8

45095_T1-T4.indd T2 7/2/08 1:20:15 PM

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Name Grade 3


T3

13. Find the fraction for the shaded parts

of this set.

A 3 _ 5

B 4 _ 5

C 5 _ 6

D 4 _ 7

14. Which fraction is not equivalent to 2 _ 3 ?

A 4 _ 6

B 8 __ 12

C 9 __ 12

D 10 __ 15

15. What is the mixed number for this

improper fraction? 15 __ 8

A 2 7 _ 8

B 2 1 _ 8

C 1 7 _ 8

D 1 5 _ 8

16. What motion does this shape show?

A slide

B fl ip

C turn

D motion

17. Which solid can be made from this net?

A square

B cube

C triangular prism

D rectangular prism

18. What would the top view of this solid

look like?

A B

C D

45095_T1-T4.indd T3 7/1/08 2:09:38 PM

6 ft

3 ft 4 ft

3 ft3 ft 1 ft

Name Grade 3


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T4

19. Which set of fi gures is not congruent?

A

B

C

D

20. What is the perimeter of this garden?

A 12 ft

B 20 ft

C 22 ft

D 24 ft

45095_T1-T4.indd T4 7/1/08 2:09:39 PM

upper saddle river, new jersey grade 3: step up to grade...

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