Download Grade 3: Step Up to Grade 4

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Grade 3: Step Up to Grade 4
Teacher’s Guide
• Teacher Notes and Answers
for Step-Up Lessons
• Practice
• Answers for Practice
• Test
• Answers for Test
Scott Foresman and enVisionMATH™
are trademarks, in the U.S. and/or other
countries, of Pearson Education, Inc.,
or its affiliates.
®
45095_SLPSHEET_FSD 1
6/6/08 3:57:25 PM
F8
45095_SLPSHEET_FSD 2
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
6/6/08 3:57:30 PM
Math Diagnosis and
Intervention System
Rounding Numbers Through
Thousands
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
F8
Teacher Notes
F8
Rounding Numbers Through Thousands
To round 34,853 to the nearest ten thousand, answer 1 to 6.
Ongoing Assessment
Materials 8 inches of yarn per pair
Ask: What does 99,249 round to when rounded
to the nearest hundred thousand? 100,000
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?
Error Intervention
30,000
3. So, what is 34,853 rounded to the nearest
If students have trouble remembering place value,
30,000
ten thousand?
then have the students make a table across the top
of their page that looks like the following:
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?
less than 5
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.
11. Keep the 7 and change the other
digits to 0s. So, 739,218 rounds to
If You Have More Time
down
10. Do you need to round up or down?
Ones
© Pearson Education, Inc.
9. Is that digit less than 5, or is it 5 or greater?
Tens
3
8. What digit is to the right of the 7?
Hundreds
7
7. Which digit is in the hundred thousands place?
Thousands
40,000
ten thousand?
Round 739,218 to the nearest hundred thousand without using
a number line. Answer 7 to 11.
Ten
Thousands
Hundred
Thousands
40,000
6. So, what is 37,421 rounded to the nearest
700,000
.
Intervention Lesson F8
71
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F8
Have 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 (continued)
Round each number to the nearest ten.
12. 94,519
94,520
537,680
13. 537,681
Round each number to the nearest hundred.
14. 968,458
968,500
58,300
15. 58,326
Round each number to the nearest thousand.
16. 318,512
319,000
21,000
17. 21,236
Round each number to the nearest ten thousand.
18. 285,431
290,000
180,000
19. 184,032
Round each number to the nearest hundred thousand.
20. 735,901
700,000
500,000
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?
200,000
Real Estate
Amount
Sale
in Dollars
Price of House
169,256
Advertising Fee
7,177
Repairs
5,873
23. What is the cost of repairs rounded to the
nearest thousand?
6,000
rounded to the nearest thousand.
Any numbers between 43,500 and 44,499
25. Reasoning Explain how to round 496,275 to the nearest ten thousand.
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.
© Pearson Education, Inc.
© Pearson Education, Inc. 3
24. Reasoning Write three numbers that would round to 44,000 when
72 Intervention Lesson F8
Intervention Lesson F8
Comparing and Ordering Numbers
Through Thousands
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Math Diagnosis and
Intervention System
Intervention Lesson
F9
Teacher Notes
F9
Comparing and Ordering Numbers
Through Thousands
Ongoing Assessment
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.
hundred
thousands
ten
thousands
thousands
hundreds
tens
ones
1
1
6
6
8
8
3
2
5
9
6
7
Error Intervention
For Exercises 2–5, write ⬍, ⬎, or ⫽.
2. Start with the left column in the chart.
100,000
ⴝ
100,000
60,000
ⴝ
60,000
8,000
ⴝ
8,000
300
⬎
200
3. Since the hundred thousands are equal,
compare the ten thousands.
4. Since the ten thousands are equal,
compare the thousands.
5. Since the thousands are equal,
compare the hundreds.
6. Since 300 ⬎ 200, compare 168,356 and 168,297.
168,356
If 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.
168,297
⬎
Henderson
7. So, which candidate received more votes?
© Pearson Education, Inc.
Ask: 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.
If You Have More Time
Have students write ordering problems for a partner
to solve.
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.
Intervention Lesson F9
73
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F9
Comparing and Ordering Numbers Through Thousands (continued)
hundred
thousands
ten
thousands
thousands
hundreds
tens
ones
3
3
3
4
1
4
6
9
8
2
3
8
1
0
6
7
4
2
9. Start on the left. Write ⬍, ⬎, or ⫽. 300,000
ⴝ
ⴝ
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?
319,304
< 8,000, compare the thousands place
11. Since 6,000 _____
of the other two numbers.
346,217
⬍
348,862
12. The numbers in order from least to greatest are:
319,304
346,217
348,862
Use ⬍ or ⬎ to compare each pair of numbers.
13. 8,112
<
8,221
14. 418,412
15. 321,159
>
312,147
16. 20,657
17. 118,111
<
118,147
18. 914,146
<
<
>
481,930
21,687
904,168
Order the numbers from least to greatest.
20. 12,984; 12,875; 11,987
21. 200; 12,945; 2,309
11,987; 12,875; 12,984
22. 321,984; 345,879; 323,490
200; 2,309; 12,945
321,984; 323,490; 345,879
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
Intervention Lesson F9
© Pearson Education, Inc.
820; 7,980; 8,200
© Pearson Education, Inc. 3
19. 8,200; 820; 7,980
Math Diagnosis and
Intervention System
Intervention Lesson
Place Value Through Millions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F10
Teacher Notes
F10
Place Value Through Millions
1. Write 462,397,158 in the place-value chart below.
Ongoing Assessment
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
Ones
Ten
Millions
Thousands
Hundred
Millions
Millions
4
6
2
3
9
7
1
5
8
Ask: 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.
2. Complete the table to find the value of each digit in 462,397,158.
Digit
Place
Error Intervention
Value
4
hundred millions
400,000,000
6
60,000,000
2,000,000
millions
300,000
hundred thousands
90,000
ten thousands
7,000
thousands
100
hundreds
50
tens
8
ones
If students are having trouble remembering the
number of zeros each value has,
ten millions
2
3
9
7
1
5
8
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.
© Pearson Education, Inc.
3. Use the table above to help you write 462,397,158 in expanded form.
400,000,000 ⫹
90,000 ⫹
60,000,000
7,000
2,000,000
⫹
⫹ 100 ⫹
50
8
⫹
300,000
⫹
⫹
.
If You Have More Time
4. Write the short word form of 462,397,158.
462 million, 397
Have students look up the population of the United
States and write the number in standard form,
expanded form, and word form.
thousand, 158
Four hundred sixty-two million,
three hundred ninety-seven thousand, one hundred fifty-eight
5. Write 462,397,158 in word form.
Intervention Lesson F10
75
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F10
Place Value Through Millions (continued)
Write the value of the underlined digit.
6. 4,562,398
7. 15,347,025
60,000
8. 37,814,956
5,000,000
9. 526,878,953
10. 782,354,065
500,000,000
4,000
11. 918,403,760
60
10,000,000
Write each number in word form and in short word form.
12. 2,160,500
Two million, one hundred sixty thousand,
five hundred; 2 million, 160 thousand,
5 hundred
13. 91,207,040
14. 510,200,450
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
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 number
sentence 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?
500,000
© Pearson Education, Inc.
© Pearson Education, Inc. 3
900,000,000 ⴙ 80,000,000 ⴙ 8,000,000 ⴙ 600,000
10
76 Intervention Lesson F10
Intervention Lesson F10
Math Diagnosis and
Intervention System
Rounding Numbers Through Millions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
F11
Teacher Notes
F11
Rounding Numbers Through Millions
Round 4,307,891 to the nearest million by answering 1 to 5.
1. What digit is in the millions place?
4
Ongoing Assessment
2. What digit is to the right of the 4?
3
Ask: What is the smallest number that will
round to 1,000,000 when rounded to the nearest
million? 950,000
3. Is the digit to the right of 4 less than 5,
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.
Down
4. Do you need to round up or down?
5. Keep the 4 and change the other digits to 0s. What
is 4,307,891 rounded to the nearest million?
Error Intervention
4,000,000
then have the students make a place value chart
across the top of their page.
Round 6,570,928 to the nearest hundred thousand by
answering 6 to 11.
6. Which digit is in the hundred thousands place?
5
7. What digit is to the right of the 5?
7
8. Is the digit to the right of 5 less than 5,
If students do not know the place values,
5 or greater
or is it 5 or greater?
then use F10: Place Value Through Millions.
Up
9. Do you need to round up or down?
10. Change the 5 to the next highest digit and change
© Pearson Education, Inc.
If students are having trouble identifying the place
values for rounding,
the other digits to 0s. What is 6,570,928 rounded
to the nearest hundred thousand?
6,600,000
11. What is 6,570,928 rounded to the nearest thousand?
6,571,000
Intervention Lesson F11
If You Have More Time
Have students round 5,830,957 to the nearest
ten, hundred, thousand, ten thousand, hundred
thousand, and million. Repeat with 9,999,999.
77
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F11
Rounding Numbers Through Millions (continued)
Round 1,581,267 to each place.
12. ten
1,581,270
14. thousand
1,581,000
16. hundred thousand
1,600,000
13. hundred
1,581,300
1,580,000
15. ten thousand
17. million
2,000,000
Round each number to the nearest ten.
18. 3,194,764
3,194,760
19. 8,967,001
8,967,000
Round each number to the nearest hundred.
20. 1,265,906
1,265,900
21. 6,906,294
6,906,300
Round each number to the nearest thousand.
22. 8,070,126
8,070,000
23. 9,264,431
9,264,000
Round each number to the nearest ten thousand.
24. 7,514,637
7,510,000
25. 2,437,894
2,440,000
Round each number to the nearest hundred thousand.
26. 1,395,384
1,400,000
27. 3,992,460
4,000,000
5,000,000
29. 5,022,121
5,000,000
30. 2,439,019
2,000,000
31. 8,888,888
9,000,000
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?
3,500,000
78 Intervention Lesson F11
Intervention Lesson F11
© Pearson Education, Inc.
28. 4,578,952
© Pearson Education, Inc. 3
Round each number to the nearest million.
Math Diagnosis and
Intervention System
Intervention Lesson
Patterns and Equations
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F29
Teacher Notes
F29
Patterns and Equations
1. Complete the table at the right.
2. What expression describes the cost
with delivery for a food order costing
c dollars?
Cost of Food
Order
c
Cost with
Delivery
d
$8.50
$10.50
$9.25
$11.25
$10.47
$12.47
c2
3. Set d equal to the expression to get an
equation representing the relationship
between the cost of the food order c
and the cost with delivery d.
$10.98
$12.98
$12.06
$14.06
$16.52
4. Use the equation to find d, when c ⫽ $14.52.
5. Complete the table at the right.
6. Write an equation representing the
relationship between the number
of pretzels p and the total cost c.
If students have trouble writing an expression for
the pattern in the table,
Number of
Pretzels
p
Total
Cost
c
2
$11.00
c 5.5p
7. Use the equation to find c, when p ⫽ 4.
$22.00
then use F26: Expressions with Addition and
Subtraction or F27: Expressions with Multiplication
and Division.
3
$16.50
5
$27.50
6
$33.00
7
$38.50
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
Points (p)
3
2
6
3
9
4
12
If You Have More Time
Have students think of a real-world situation which
can be represented by an equation, write the
equation, and create a table.
8. A field goal in football is worth 3 points. Complete the table below
© Pearson Education, Inc.
Ask: 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 Intervention
c2
d⫽
Ongoing Assessment
5
18
9. Write an equation to represent the relationship between
p 3f
the number of field goals f and points p.
Intervention Lesson F29
113
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F29
Patterns and Equations (continued)
Write an equation to represent the relationship between x and y in each
table. Then use the equation to complete the table.
10.
11.
y
x
y
x
y
2
8
12
2
4
32
3
9
18
3
5
40
8
14
24
4
7
56
14
20
30
64
27
42
5
7
8
21
10
80
yx6
13.
yx6
14.
15.
x
y
x
y
x
y
1
2
4.8
50
10
14
5
3
7.2
40
8
22
13
4
9.6
35
7
26
17
6
14.4
25
5
30
21
7
16.8
15
3
y 2.4x
yx5
x
2
2.5
3.2
3.8
4.7
y
9.8
10.3
11
11.6
12.5
© Pearson Education, Inc.
© Pearson Education, Inc. 3
y 8x
10
yx9
16.
12.
x
y x 7.8
17. Reasoning If a rule is c ⫽ p ⫹ 5, what is c when p ⫽ 20?
25
114 Intervention Lesson F29
Intervention Lesson F29
Math Diagnosis and
Intervention System
Intervention Lesson
Estimating Sums
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G7
Teacher Notes
G7
Estimating Sums
When Joseppi added 43 and 28, he got a sum of 71. To check
that this answer is reasonable, use estimation.
Ongoing Assessment
1. Round each addend to the nearest ten.
43 rounded to the nearest ten is
40
.
28 rounded to the nearest ten is
30
.
2. Add the rounded numbers.
Error Intervention
70
40 30 If students are having trouble with rounding the
addends correctly,
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.
then use F2: Rounding to Nearest Ten and
Hundred.
3. Round each addend to the nearest hundred.
187 rounded to the nearest hundred is
200
If You Have More Time
.
© Pearson Education, Inc.
Ask: When estimating 124 ⴙ 138, which would
give a closer estimate, rounding to the nearest
ten or to the nearest hundred? Rounding to the
nearest ten.
242 rounded to the nearest hundred is
200
.
Have students work with a partner to list ten
different sums which are about 300 when estimated
by rounding each addend to the nearest hundred.
4. Add the rounded numbers.
200 200 400
Since 429 is close to 400, the answer is reasonable.
Intervention Lesson G7
91
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G7
Estimating Sums (continued)
Estimate by rounding to the nearest ten.
5. 71 36
6. 24 81
110
9. 68 27
7. 43 91
100
10. 19 93
100
8. 54 66
130
11. 89 75
110
120
12. 54 33
170
80
Estimate by rounding to the nearest hundred.
13.
367
14.
791
506
15.
141
_
632
_
249
_
500
1,400
700
17. 940 190
1,100
20. 369 481
900
18. 675 460
16.
1,400
19. 531 776
1,200
21. 151 260
458
891
_
1,300
22. 705 936
500
1,600
23. Reasoning Jaimee was a member of the school chorus
24. Luis sold 328 sport bottles and Jorge sold 411. About
how many total sport bottles did the two boys sell?
130
700
to 46 so that the sum is 70 when both numbers are
rounded to the nearest ten? Explain.
24; Since 46 rounds to 50, and 20 ⴙ 50 ⴝ 70,
you need the largest number that rounds to 20,
which is 24.
92 Intervention Lesson G7
Intervention Lesson G7
© Pearson Education, Inc.
25. Reasoning What is the largest number that can be added
© Pearson Education, Inc. 3
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?
Math Diagnosis and
Intervention System
Intervention Lesson
Dividing with Objects
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G42
Teacher Notes
G42
Dividing with Objects
Materials 7 counters and 3 half sheets of paper for each
student or pair
Ongoing Assessment
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.
Ask: 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.
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 put
yes
another counter on each sheet of paper?
Error Intervention
4. Put another counter on each piece of paper.
If students have trouble completing problems using
counters or drawings,
5. Are there enough counters to put
© Pearson Education, Inc.
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.
no
another counter on each sheet of paper?
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.
If You Have More Time
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.
Intervention Lesson G42
161
Have partners find all the division sentences that
can be written if 8 is the dividend and the divisor is
1 to 8.
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G42
Dividing with Objects (continued)
Use counters or draw a picture to find each quotient and
remainder.
9. 8 3 10. 17 3 5 R2
11. 14 3 4 R2
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
34. 26 5 5 R1
35. 34 6 5 R4
37. 21 6 3 R3
38. 3 2 2 R1
36. 14 5 2 R4
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.
© Pearson Education, Inc.
12. 11 4 33. 9 4 © Pearson Education, Inc. 3
2 R2
She should read 8–9 pages each day; she will
read 9 pages on 2 days and 8 pages on 1 day.
162 Intervention Lesson G42
Intervention Lesson G42
Math Diagnosis and
Intervention System
Intervention Lesson
Factoring Numbers
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G59
Teacher Notes
G59
Factoring Numbers
Materials color tiles or counters, 24 for each student
Ongoing Assessment
The arrays below show all of the factors of 12.
Ask: What is the only even prime number? 2
1 ⫻ 12
Error Intervention
If students do not find all of the factors of a number,
2⫻6
3⫻4
The order factors are listed may vary.
1. What are all the factors of 12?
1
,
2
,
3
4
,
4⫻3
6
,
,
6⫻2
12
2. Create all the possible arrays you can with 17 color tiles.
1
3. What are the factors of 17?
,
12 ⫻ 1
17
Numbers which have only 2 possible arrays and exactly 2 factors
are prime numbers.
4. Is 17 a prime number?
5. Is 12 a prime number?
If You Have More Time
yes
Have 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.
no
© Pearson Education, Inc.
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
The order factors are listed may vary.
8. What are all the factors of 24?
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.
1, 2, 3, 6, 8, 12, 24
9. Is 24 a prime number or a composite number?
composite
Answers: Exercise 22 from page 196
Intervention Lesson G59
195
18 ⫻ 1 ⫽ 18
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G59
Factoring Numbers (continued)
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
composite
16. 13
17. 26
1, 13;
1, 2, 13, 26;
prime
composite
19. 55
20. 70
6 ⫻ 3 ⫽ 18 2 ⫻ 9 ⫽ 18
18. 40
3 ⫻ 6 ⫽ 18
1, 2, 4, 5, 8,
10, 20, 40;
composite
1 ⫻ 18 ⫽ 18
21. 83
1, 5, 11, 55;
1, 2, 5, 7, 10,
1, 83;
composite
14, 35, 70;
composite
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.
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.
196 Intervention Lesson G59
Intervention Lesson G59
© Pearson Education, Inc.
23. Reasoning Lee says 53 is a prime number because it is an
9 ⫻ 2 ⫽ 18
© Pearson Education, Inc. 3
See answers on page 59.
Mental Math: Multiplying by
Multiples of 10
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Math Diagnosis and
Intervention System
Intervention Lesson
G66
Teacher Notes
G66
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?
Ongoing Assessment
Find 20 ⫻ 6 and 2,000 ⫻ 6 by filling in the blanks.
1. 20 ⫻ 6 ⫽ (10 ⫻ 2) ⫻ 6
2
⫽ 10 ⫻ (
2. 2,000 ⫻ 6 ⫽ (1,000 ⫻ 2) ⫻ 6
⫻ 6)
⫽ 1,000 ⫻ (
12
⫽ 10 ⫻
120
⫽
2
12,000
⫽
120
books
12,000
books
3. How many books are in 20 boxes?
4. How many books are in 2,000 boxes?
⫻ 6)
12
⫽ 1,000 ⫻
Error Intervention
If students are making mistakes with multiplication
facts,
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?
then use some of the intervention lessons on basic
multiplication facts, G25 to G32.
Find 50 ⫻ 40 and 500 ⫻ 40 by filling in the blanks.
5. 50 ⫻ 40 ⫽ (5 ⫻
10
)⫻
(4 ⫻
10
)
4
⫽5⫻
© Pearson Education, Inc.
⫽ 20 ⫻
⫽
100
6. 500 ⫻ 40 ⫽ (5 ⫻
10
(4 ⫻
⫻ 10 ⫻ 10
⫽5⫻
100
4
⫽ 20 ⫻
2,000
8. How many books are in 500 boxes?
⫻ 100 ⫻ 10
1,000
2,000
books
20,000
books
7. How many books are in 50 boxes?
)⫻
)
Intervention Lesson G66
If You Have More Time
Have students write and solve a word problem that
involves multiplying multiples of ten.
20,000
⫽
Ask: 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.
209
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G66
Mental Math: Multiplying by Multiples of 10 (continued)
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 ⫽
1,200
14. 50 ⫻ 400 ⫽
20,000
17. 600 ⫻ 30 ⫽
18,000
20. 70 ⫻ 500 ⫽
35,000
23. 800 ⫻ 80 ⫽
64,000
12. 10 ⫻ 600 ⫽
6,000
15. 700 ⫻ 30 ⫽
21,000
18. 40 ⫻ 90 ⫽
3,600
21. 30 ⫻ 800 ⫽
24,000
24. 30 ⫻ 600 ⫽
18,000
13. 70 ⫻ 20 ⫽
1,400
16. 40 ⫻ 800 ⫽
32,000
19. 90 ⫻ 500 ⫽
45,000
22. 200 ⫻ 70 ⫽
14,000
25. 40 ⫻ 300 ⫽
12,000
a school fundraiser. If each of them collects
400 pennies, how many have they collected
all together?
12,000
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?
pennies
© Pearson Education, Inc.
© Pearson Education, Inc. 3
26. A class of 30 students is collecting pennies for
No, one of the zeros is from 6 ⴛ 5 which is 30.
210 Intervention Lesson G66
Intervention Lesson G66
Math Diagnosis and
Intervention System
Intervention Lesson
Estimating Products
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G67
Teacher Notes
G67
Estimating Products
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.
Ongoing Assessment
Ask: Why is it preferable to round 591 to the
nearest hundred rather than the nearest ten?
It is easier to multiply 600 than 590.
Estimate 21 ⫻ 33 and compare the answer to 600.
Round each factor to get numbers you can multiply mentally.
20
1. What is 21 rounded to the nearest ten?
30
2. What is 33 rounded to the nearest ten?
Error Intervention
600
20 ⫻ 30 ⫽
3. Multiply the rounded numbers.
If students have problems rounding numbers,
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
yes
7. Will the goal be reached?
then use F2: Rounding to Nearest Ten and Hundred
and F4: Numbers Halfway Between and Rounding.
If You Have More Time
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.
Have students name situations when an estimate
if sufficient and situations when an exact answer is
needed.
Estimate 18 ⫻ 590 and compare the answer with 12,000.
© Pearson Education, Inc.
Round each factor to get numbers you can multiply mentally.
20
8. What is 18 rounded to the nearest ten?
600
9. What is 590 rounded to the nearest hundred?
10. Multiply the rounded numbers.
20 ⫻ 600 ⫽
12,000
The answer is the same as the number needed to meet the goal.
Intervention Lesson G67
211
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G67
Estimating Products (continued)
up
11. 18 was rounded to 20. Was it rounded up or down?
up
590 was rounded to 600. Was it rounded up or down?
less
12. Is 18 ⫻ 590 more or less than 20 ⫻ 600?
no
13. Will the goal be reached?
Round each factor so that you can estimate the product mentally.
14. 71 ⫻ 382
15. 27 ⫻ 62
70 ⴛ 400
30 ⴛ 60
28,000
1,800
17. 58 ⫻ 176
18. 831 ⫻ 42
60 ⴛ 200
800 ⴛ 40
12,000
32,000
20. 87 ⫻ 67
21. 373 ⫻ 95
16. 45 ⫻ 317
50 ⴛ 300
15,000
19. 16 ⫻ 768
20 ⴛ 800
16,000
22. 57 ⫻ 722
90 ⴛ 70
400 ⴛ 100
60 ⴛ 700
6,300
40,000
42,000
23. Debra spends 42 minutes each day driving to
1,200 minutes
the estimate be an overestimate or an underestimate?
Explain.
It would be an underestimate because you are
rounding both factors down.
212 Intervention Lesson G67
Intervention Lesson G67
© Pearson Education, Inc.
24. Reasoning If 64 ⫻ 82 is estimated to be 60 ⫻ 80, would
© Pearson Education, Inc. 3
work. About how many minutes does she spend
driving to work each month?
Math Diagnosis and
Intervention System
Intervention Lesson
Equal Parts of a Whole
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H1
Teacher Notes
H1
Equal Parts of a Whole
Materials rectangular sheets of paper, 3 for each student;
Ongoing Assessment
crayons or markers
fold
1. Fold a sheet of paper so the two shorter edges
Ask: 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
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?
4. How many equal parts are there?
yes
Number of
Name of
Equal Parts Equal Parts
2
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?
© Pearson Education, Inc.
9. How many equal parts are there?
yes
2
halves
3
thirds
4
fourths
5
fifths
6
sixths
8
eighths
If You Have More Time
tenths
12
twelfths
New
fold
10. What is the name for the parts you colored?
If children have trouble understanding the concept
of equal parts,
then use A35: Equal parts.
10
4
Error Intervention
Old
fold
Have students fold other rectangular sheets of
paper and circular pieces of paper to find and name
other equal parts.
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.
Intervention Lesson H1
85
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H1
Equal Parts of a Whole (continued)
Tell if each shows parts that are equal or parts that are not equal.
If the parts are equal, name them.
equal
12.
13.
not equal
fourths
14.
equal
15.
thirds
16.
equal
equal
eighths
17.
not equal
19.
equal
twelfths
18.
not equal
fifths
20.
equal
21.
not equal
23.
not equal
halves
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
© Pearson Education, Inc.
© Pearson Education, Inc. 3
22.
86 Intervention Lesson H1
Intervention Lesson H1
Math Diagnosis and
Intervention System
Intervention Lesson
Parts of a Region
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H2
Teacher Notes
H2
Parts of a Region
Materials crayons or markers
Ongoing Assessment
__
1. In the circle at the right, color 2 of the equal
Ask: Janet said she ate 4 of an orange. Explain
parts blue and 4 of the equal parts red.
4
Write fractions to name the parts by answering 2 to 6.
2. How many total equal parts
does the circle have?
3. How many of the equal parts
of the circle are blue?
6
why Janet could have said she ate the whole
2
orange. Sample answer: The orange would be cut
4. What fraction of the circle is blue?
in 4 pieces and she ate 4 pieces, so she ate the
2 ⫽ _____________________________
number of equal parts that are blue
(numerator)
____
⫽ ____________
(denominator)
total number of equal parts
6
whole thing.
Two sixths of the circle is blue.
4
5. How many of the equal parts of the circle are red?
Error Intervention
6. What fraction of the circle is red?
If children have trouble writing fractions for parts of
a region,
4 ⫽ ____________________________
number of equal parts that are red
(numerator)
____
⫽ ____________
(denominator)
total number of equal parts
6
Four sixths of the circle is red.
then use A36: Understanding Fractions to Fourths
and A38: Writing Fractions for Part of a Region.
© Pearson Education, Inc.
3
by answering 7 to 9.
Show the fraction __
8
3
7. Color __ of the rectangle at the right.
8
8. How many equal parts does
If You Have More Time
8
the rectangle have?
9. How many parts did you
color?
3
Intervention Lesson H2
87
Have 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.
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H2
Parts of a Region (continued)
Write the fraction for the shaded part of each region.
10.
11.
12.
_2_
_1_
3
13.
14.
5
15.
_1_
_2_
2
16.
_4_
4
_2_
5
8
17.
18.
_1_
_3_
_5_
5
3
8
Color to show each fraction.
5
20. __
6
7
21. ___
10
each of the parts in half. What fraction of the parts does
1
the __
represent now? Check
3
students’ drawings.
23. Ben divided a pie into 8 equal pieces and ate 3 of them.
How much of the pie remains?
88 Intervention Lesson H2
Intervention Lesson H2
_2_
6
_5_
8
© Pearson Education, Inc.
1
22. Math Reasoning Draw a picture to show __. Then divide
3
© Pearson Education, Inc. 3
3
19. __
4
Math Diagnosis and
Intervention System
Intervention Lesson
Parts of a Set
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H3
Teacher Notes
H3
Parts of a Set
Materials two-color counters, 20 for each pair; crayons or markers
Ongoing Assessment
1. Show 4 red counters and 6 yellow counters.
2
2
2
2
9
9
9
9
9
3 of a group of
Ask: What does it mean that ___
9
12
marbles are green? There are 3 green marbles out
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
of a total of 12 marbles.
4. What fraction of the group of counters is red?
Error Intervention
4 ⫽ __________________________
number of counters that are red
(numerator)
____
⫽ ____________
10
total number of counters
If children have difficulty describing parts of a set,
(denominator)
Four tenths of the group of counters is red
5. How many of the counters are yellow?
then use A37: Fractions of a Set and A39: Writing
Fractions for Part of a Set.
6
6. What fraction of the counters are yellow?
6 ⫽ _____________________________
number of counters that are yellow
(numerator)
____
⫽ ____________
10
total number of counters
If You Have More Time
(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.
Have students look around the classroom and
© Pearson Education, Inc.
5
Show a group of counters with __
red by answering 7 to 9.
6
7. How many counters do you need in all?
6
name different fractions they see. For example: ___
6
8. How many of the counters need to be red?
18
5
2 of the
of the students have their math book out; __
Check that students color 5 circles red.
9. Show the counters and color below to match.
5
5 of the boys have on
computers are turned off; __
9
Intervention Lesson H3
89
shorts.
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H3
Parts of a Set (continued)
Write the fraction for the shaded parts of each set.
10.
11.
_2_
_1_
3
12.
2
13.
_3_
_4_
5
4
14.
15.
_2_
_4_
5
6
Draw a set of shapes and shade them to show each fraction.
5
16. __
9
6
17. ___
10
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 ; Students should draw 12 marbles with 5 blue.
12
© Pearson Education, Inc.
© Pearson Education, Inc. 3
Check students’ drawings.
90 Intervention Lesson H3
Intervention Lesson H3
Math Diagnosis and
Intervention System
Intervention Lesson
Equivalent Fractions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H14
Teacher Notes
H14
Equivalent Fractions
Materials crayons or markers
Ongoing Assessment
1
2
1
1. Show __ by coloring 2 of the __ strips.
3
3
1
__
1
__
3
1
2. Color as many __ strips as it takes
6
2
to cover the same region as the __
.
3
1
How many __
strips did you color?
6
1
__
3
1
__
1
__
6
6
1
__
3
1
__
6
6
1
__
6
1
__
6
4
2
__
____
3
6
Error Intervention
2
You can use multiplication to find a fraction equivalent to __
. To do this,
3
multiply the numerator and the denominator by the same number.
If students do not understand how two fractions
can be equivalent,
2
4. What number is the denominator
2
of __
multiplied by to get 6?
3
4
2
__
____
3
6
2
2
then use H7: Using Models to Find Equivalent
Fractions.
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.
3
© Pearson Education, Inc.
3
If You Have More Time
4
7.
6
2
__
____
3
Have students create and number a cube 2, 2, 3, 3,
4
1
__
____
9
2
4
8
6 , ___
6 , ___
6 , ___
6,
1 , __
2 , __
4 , ___
6, and 6. Label 8 index cards: __
9
1
8. Show ___ by coloring 9 of the ___ strips.
12
12
1
9. Color as many __ strips as it takes
4
9
to cover the same region as ___
.
12
1 strips did you color?
How many __
4
7
form. 3 and 7 have only 1 as a common factor.
4
2
1
3. So, __ is equivalent to four __ strips.
3
6
6.
__
Ask: Explain how you can tell 3 is in simplest
2 3 6 18 24 10 12
1
1
__
1
__
4
4
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1
___
12 12 12 12 12 12 12
1
__
1
__
4
4
1 ___
1 ___
1 ___
1 ___
1
___
12 12 12 12 12
3
Intervention Lesson H14
111
3 . Shuffle the index cards. One student rolls the
and __
4
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
Math Diagnosis and
Intervention System
Intervention Lesson
Name
by the number rolled. Have students check each
H14
others’ work. Sometimes either operation can be
Equivalent Fractions (continued)
done, sometimes only one can be used.
3
9
9
1
10. So, ___ is equivalent to three __ strips. ___ ____
4
4
12
12
9
You can use division to find a fraction equivalent to ___
. To do this,
12
divide the numerator and the denominator by the same number.
3
11. What number is the denominator of
9
___
divided by to get 4? 3
12
3
9
___
____
12
3
4
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.
2
13.
14.
10
2
5
2
10
___
____
4
8
___
____
15
5
5
3
If the numerator and denominator cannot be divided by anything
else, then the fraction is in simplest form.
yes
5
15. Is ___ in simplest form?
12
6
16. Is __ in simplest form?
8
no
4
8 ____
18. ___
5
10
1
19. _2_ ____
4
8
14
7 ____
20. ___
20
10
3
6 ____
21. ___
7
14
16
8 ____
22. ___
22
11
Write each fraction in simplest form.
23. _6_
8
_3_
4
8
24. ___
12
_2_
3
7
25. ___
35
_1_
5
16
26. ___
24
_2_
3
4
27. Reasoning Explain why __ is not in simplest form.
6
Sample answer: 4 and 6 have a common factor of 2.
112 Intervention Lesson H14
Intervention Lesson H14
© Pearson Education, Inc.
3
17. _1_ ____
15
5
© Pearson Education, Inc. 3
Find each equivalent fraction.
Math Diagnosis and
Intervention System
Intervention Lesson
Mixed Numbers
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H18
Teacher Notes
H18
Mixed Numbers
Materials fraction strips
Ongoing Assessment
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
1
4__
3
8
__
2. Circle the number that is an improper fraction.
3
__
3
2__
9
__
4
3
Ask: What is 15 written as a mixed number? 3__
5
Error Intervention
4
7
as a mixed number by answering 3 to 6.
Write the improper fraction __
3
1
3. Show seven __ fraction strips.
3
4. Use fraction strips. How many
1 strips can you make with
2
1
seven __
strips?
3
1
5. How many __ strips do you
3
21
__
7
6. Write __ as a mixed
3
1
have left over?
3
number.
7
Write __
as a mixed number without fraction strips by answering 7 to 9.
3
7. Divide 7 by 3 at the right.
© Pearson Education, Inc.
Quotient
2
1
Remainder
3
Divisor
6
1
1
strips are left over.
The remainder 1 tells how many __
3
2_1_
3
Intervention Lesson H18
119
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Mixed Numbers (continued)
__
5
strips. How many
_1_ strips does it
5
_?
take to equal 2_1
5
fractions strips.
12. Use fraction
H18
24
14
10. Since 14 5 2 R4, what is ___ as a mixed number?
5
1_
_
Write 2 5 as an improper fraction by answering 11 to 13.
1
11. Show 2__ with
5
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,
If You Have More Time
Notice, the quotient 2 tells how many one strips you can make.
7
9. Write __ as a mixed number.
3
If students have difficulty dividing when converting
from an improper fraction to a mixed number,
then, have the students write the word DoWN
on their paper to remind them of the correct
procedure: (D W) N.
2 R1
3 7
8. Fill in the missing numbers below.
4
4
5
Have 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.
__
11
11
1
5
13. What improper fraction equals 2__?
5
1_
_
Write 2 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
1
16. What improper fraction equals 2__?
5
_ strips equal 2 wholes. The 1 tells
Notice, 2 5 tells how many _1
5
1_
_
how many additional 5 strips there are.
3
17. Since 6 4 3 27, what is 6__ as an improper fraction?
4
Change each improper fraction to a mixed number or a whole
number and change each mixed number to an improper fraction.
2
18. 3__
7
23
__
7
19. _7_
3
__
21
3
20. _7_
2
__
31
2
1
21. 1___
10
11
__
__
11
5
11
5
__
27
4
© Pearson Education, Inc.
© Pearson Education, Inc. 3
15. Write the 11 you found above over the denominator, 5.
__
11
10
120 Intervention Lesson H18
Intervention Lesson H18
Math Diagnosis and
Intervention System
Congruent Figures and Motions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
I8
Teacher Notes
I8
Congruent Figures and Motions
Materials construction paper, markers, and scissors
Ongoing Assessment
Follow 1–10.
1. Cut a scalene triangle out of construction paper.
Slide
2. Place your cut-out triangle on the bottom left side of
another piece of contruction paper. Trace the triangle
with a marker.
Ask: Why are all squares not congruent?
Congruent figures must have the same size and
shape. Squares can be different sizes.
3. Slide your cut-out triangle to the upper right of the
same paper and trace the triangle again.
Error Intervention
4. Look at the two triangles that you just traced. Are the
yes
two triangles the same size and shape?
If students have trouble understanding congruency,
When a figure is moved up, down, left, or right, the motion is
called a slide, or translation.
then use D54: Same Size, Same Shape.
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
If students have trouble differentiating between
slides, flips, and turns,
Flip
shown at the right. Place your cut-out triangle on the left
side of the dashed line. Trace the triangle with a marker.
then use D55: Ways to Move Shapes.
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
© Pearson Education, Inc.
If students understand congruency, but have
trouble deciding if two figures are congruent,
yes
two triangles congruent?
When a figure is picked up and flipped over, the motion is called
a flip, or reflection.
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.
Turn
8. On a new sheet of paper, draw a point in the middle of
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.
Intervention Lesson I8
105
Have 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.
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I8
Congruent Figures and Motions (continued)
10. Look at the two triangles you just traced. Are the two
yes
triangles congruent?
If You Have More Time
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.
slide
14.
13.
flip
turn
15.
turn
16.
flip
slide
For Exercises 17 and 18, use the figures to the right.
by a slide, a flip, or a turn?
18. Are Figures 1 and 3 related
by a slide, a flip, or a turn?
slide
flip
© Pearson Education, Inc.
If so, what motion could be used to show it?
Yes; one is a turn of the other.
Intervention Lesson I8
;^\jgZ'
;^\jgZ(
19. Reasoning Are the polygons at the right congruent?
106 Intervention Lesson I8
;^\jgZ&
© Pearson Education, Inc. 3
17. Are Figures 1 and 2 related
Math Diagnosis and
Intervention System
Intervention Lesson
Solids and Nets
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I10
Teacher Notes
I10
Solids and Nets
Materials tape, scissors, copy of nets
face: flat surface
of a solid
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
1.
Ongoing Assessment
vertex: point where
3 or more edges meet
(plural; vertices)
Ask: What solid best represents a can of corn?
cylinder
edge: line segment
where 2 faces meet
Faces
Edges
Vertices Shapes of Faces
Pyramid
1 square
5
8
Error Intervention
If students have trouble identifying solids,
5
then use I1: Solid Figures.
4 triangles
2. Rectangular Pyramid
5
3.
© Pearson Education, Inc.
4.
5.
8
5
1 rectangle,
4 triangles
Cube
6
12
8
6 squares
6
12
8
6
rectangles
5
9
6
2 triangles,
3 rectangles
Rectangular Prism
Triangular Prism
Intervention Lesson I10
If You Have More Time
In 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 yesor-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.
109
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I10
Solids and Nets (continued)
What solid will each net form?
6.
7.
cylinder
8.
cube
9.
rectangular prism
10.
11.
cone
square pyramid
12. Reasoning Is the figure a net for a cube? Explain.
© Pearson Education, Inc.
© Pearson Education, Inc. 3
triangular prism
No; the net only has five faces and a cube
has six faces.
110 Intervention Lesson I10
Intervention Lesson I10
Math Diagnosis and
Intervention System
Intervention Lesson
Views of Solid Figures
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I11
Teacher Notes
I11
Views of Solid Figures
Materials 6 blocks or small cubes from place-value blocks for
Ongoing Assessment
each pair or group, crayons or markers
Top View
Stack blocks to model the solid shown at the
right. Assume that there are only 6 cubes in
the solid so that none are hidden.
Side View
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.
Front View
1. How many cubes can you see when you look straight
3
down at the solid?
Error Intervention
2. Color in squares on the grid to indicate
If students have trouble seeing the views using
blocks or small cubes,
the blocks seen from the top view.
The front view is the image seen when
looking straight at the cubes.
then use larger boxes to illustrate the solids in front
of the class.
Draw the front view of the solid above
by answering 3 and 4.
3. How many cubes can you see when you look straight
6
at the solid?
If You Have More Time
4. Color in squares on the grid to indicate
the blocks seen from the front view.
Have 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.
© Pearson Education, Inc.
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?
Ask: 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.
3
6. Color in squares on the grid to indicate
the blocks seen from the side view.
Intervention Lesson I11
111
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I11
Views of Solid Figures (continued)
Draw the front, right, and top views of each solid figure. There
are no hidden cubes.
7.
8.
Side
9.
Top
10.
Front
Side
Top
11.
Top
Top
Top
Front
Front
Front
Side
Side
Side
Exercise 11, what views would change? What view would
not change?
The front and side views would change
but the top view would not.
112 Intervention Lesson I11
Intervention Lesson I11
© Pearson Education, Inc.
12. Reasoning If a cube is added to the top of the solid in
© Pearson Education, Inc. 3
Front
Math Diagnosis and
Intervention System
Intervention Lesson
Congruent Figures
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I13
Teacher Notes
I13
Congruent Figures
Materials tracing paper and scissors
Ongoing Assessment
Two figures that have exactly the same size and shape are congruent.
Ask: 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.
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
Error Intervention
Figure B
Figure C
2. Place the cutout on top of Figure B.
no
Is Figure B the same size as Figure A?
then have students trace one figure and move the
tracing over the other figure.
no
3. Is Figure B congruent to Figure A?
4. Place the cutout on top of Figure C.
no
Is Figure C the same shape as Figure A?
no
5. Is Figure C congruent to Figure A?
6. Place the cutout on top of Figure D.
© Pearson Education, Inc.
If students have trouble identifying shapes that are
the same size,
Figure D
If You Have More Time
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
Have student work in pairs to find congruent
objects in the classroom.
9. Circle the figure that is congruent to the figure at the right.
Intervention Lesson I13
115
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I13
Congruent Figures (continued)
Tell if the two figures are congruent. Write Yes or No.
10.
11.
yes
13.
12.
no
14.
yes
16.
yes
15.
no
17.
yes
no
18.
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
© Pearson Education, Inc. 3
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.
© Pearson Education, Inc.
into 2 pairs of congruent triangles.
116 Intervention Lesson I13
Intervention Lesson I13
Math Diagnosis and
Intervention System
Intervention Lesson
More Perimeter
Teacher Notes
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I45
I45
More Perimeter
Jonah’s pool is a rectangle. The pool is 15 feet long and 10 feet wide.
What is the perimeter of the pool?
Ongoing Assessment
Find the perimeter of the pool by answering 1 to 3.
1. Write in the missing measurements on the pool
15 ft
shown at the right.
10
10 ft ⫹
15
ft ⫹ 15 ft ⫹
10
10 ft
2. Add the lengths of the sides.
50
50 ft
ft ⫽
3. What is the perimeter of the pool?
15
ft
ft
ft
Ask: Why is the formula for the perimeter of
a square P ⴝ 4s? Because all of the sides of a
square are equal, you can just multiply one side by
4 instead of adding each side.
Find a formula for the perimeter of a rectangle by answering 4 to 10.
3 in.
Rectangle A
Rectangle
B
8 in.
Error Intervention
4 ft
If students do not know the properties of
rectangles,
5 ft
4. Write the side lengths of the rectangle.
8
8⫹3⫹
⫹3⫽
22
3
⫽
)⫽
22
6
⫽
22
in.
© Pearson Education, Inc.
16 ⫹
4
5⫹5⫹
in.
6. Rewrite the number sentence.
3
4
⫹
⫽
18
ft
⫽
18
ft
8. Rearrange the numbers.
22
2(8) ⫹ 2 (
5
5⫹4⫹
5. Rearrange the numbers.
8⫹8⫹3⫹
7. Write the side lengths of the rectangle.
in.
4
⫹
9. Rewrite the number sentence.
in.
2(5) ⫹ 2(
4
)⫽
18
10
⫽
18
ft
8⫹
ft
Length
Width
A
8
2(
B
5
3
4
Perimeter
Any
ᐉ
w
2ᐉ ⫹ 2
8
) ⫹ 2(3)
2(5) ⫹ 2(4)
If You Have More Time
w
Intervention Lesson I45
179
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I45
More Perimeter (continued)
The formula for the perimeter of a rectangle is P ⫽ 2ᐉ ⫹ 2w
11. Reasoning Use the formula to find the perimeter of Jonah’s pool.
P⫽
2ᐉ
⫹
P⫽2(
15 ) ⫹ 2( 10 ) ⫽ 30
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.
10. Complete the table.
Rectangle
then use I7: Quadrilaterals.
Have 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.
2w
⫹
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
⫹
5
5
⫹
⫹
5
⫽
14. What could you multiply to find
the perimeter of the square?
20
5 cm
4ⴛ5
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. ᐉ ⫽ 9 mm, w ⫽ 12 mm
17. ᐉ ⫽ 13 in., w ⫽ 14 in.
42 mm
54 in.
18. ᐉ ⫽ 2 ft, w ⫽ 15 ft
19. ᐉ ⫽ 17 cm, w ⫽ 25 cm
34 ft
84 cm
21. s ⫽ 10 in.
8 yd
22. s ⫽ 31 km
40 in.
124 km
23. s ⫽ 11 m
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.
180 Intervention Lesson I45
Intervention Lesson I45
© Pearson Education, Inc.
20. s ⫽ 2 yd
© Pearson Education, Inc. 3
Find the perimeter of the square with the given side.
Name
Practice
F8
Rounding Numbers Through
Thousands
Round each number to the nearest ten.
1. 326
2. 825
3. 162
4. 97
Round each number to the nearest hundred.
5. 1,427
6. 8,136
7. 1,308
8. 3,656
Round each number to the nearest thousand.
9. 18,366
10. 408,614
11. 29,430
12. 63,239
Round each number to the nearest ten thousand.
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
© Pearson Education, Inc. 3
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?
Practice F8
Name
Practice
F9
Comparing and Ordering
Numbers Through Thousands
Use the chart for help if you need to.
hundred
thousands
ten
thousands
thousands
Compare. Write ⬎ or ⬍ for each
1. 54,376
3. 9,635
hundreds
tens
ones
.
45,763
9,536
2. 6,789
9,876
4. 4,125
3,225
Order the numbers from least to greatest.
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
© Pearson Education, Inc. 3
9. Tell how you could use a number line to determine which of
two numbers is greater.
Practice F9
Name
Practice
F10
Place Value Through Millions
Write 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
© Pearson Education, Inc. 3
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.
Practice F10
Name
Practice
F11
Rounding Numbers Through
Millions
Round each number to the nearest thousand.
1. 6,326
2. 2,825
3. 2,162
4. 4,097
Round each number to the nearest ten thousand.
5. 31,427
6. 68,136
7. 76,308
8. 93,656
Round each number to the nearest hundred thousand.
9. 618,366
10. 409,614
11. 229,930
12. 563,239
Round each number to the nearest million.
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
18. What is 681,542 rounded to the nearest hundred thousand?
A 600,000
B 680,000
C 700,000
D 780,000
ten
hundred
thousand
ten thousand
hundred thousand
million
Practice F11
© Pearson Education, Inc. 3
19. Round 2,672,358 to each place value?
Name
Practice
F29
Patterns and Equations
For 1 through 6, complete each table. Find each rule.
1.
x
y
81
63
45
27
9
7
5
?
2.
Rule:
5.
x
y
6
8
10
12
42
56
70
?
3.
Rule:
2
22
x
y
4
44
x
y
36
42
48
54
6
7
8
?
4.
Rule:
6
66
8
?
6.
x
y
10
15
20
25
30
45
60
?
Rule:
x
y
9
3
12
4
15
5
18
?
Rule:
Rule:
7. Lucas recorded the growth of a plant. How tall will the plant
be on Day 5?
Day
Height in inches
1
6
2
12
3
18
4
24
5
?
8. Danielle made a table of the rental fees at a video store.
What is the rule?
x
y
A y ⫽ 3x
1
$3
2
$6
C y⫽x⫹3
3
$9
4
$12
B y ⫽ 6x
D y ⫽ 4x
© Pearson Education, Inc. 3
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?
Practice F29
Name
Practice
G7
Estimating Sums
Estimate 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
Estimate by rounding to the nearest hundred.
9.
478
252
_
10.
680
743
_
11.
617
358
_
12.
569
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?
© Pearson Education, Inc. 3
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.
Practice G7
Name
Practice
G42
Dividing with Objects
Divide. 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
© Pearson Education, Inc. 3
18. Pencils are sold in packages of 5. Explain why you need
6 packages in order to have enough for 27 students.
Practice G42
Name
Practice
G59
Factoring Numbers
In 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
14. 1,212
15. 57
16. 17
13. 3,235
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?
A 1, 3, 7, 9
C 0, 2, 4, 5, 6, 8
B 1, 3, 5, 9
D 1, 3, 7
Practice G59
© Pearson Education, Inc. 3
18. Every prime number larger than 10 has a digit in the ones
place that is included in which set of numbers below?
Name
Practice
G66
Mental Math: Multiplying by
Multiples of 10
Multiply. 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?
16. How many pounds can Truck A haul in 70 trips?
© Pearson Education, Inc. 3
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.
Practice G66
Name
Practice
G67
Estimating Products
Round 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
© Pearson Education, Inc. 3
19. A wind farm generates 330 kilowatts of electricity each day.
About how many kilowatts does the wind farm produce in a
week? Explain.
Practice G67
Name
Practice
H1
Equal Parts of a Whole
Tell if each shows equal or unequal parts.
If the parts are equal, name them.
1.
2.
3.
4.
7.
8.
Name the equal parts of the whole.
5.
6.
Use the grid to draw a region showing the number of equal
parts named.
9. tenths
10. sixths
© Pearson Education, Inc. 3
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
Practice H1
Name
Practice
H2
Parts of a Region
Write a fraction for the part of the region below that is shaded.
1.
2.
Shade in the models to show each fraction.
3.
7
4. __
10
ᎏ2ᎏ
4
5. What fraction of the pizza is cheese?
cheese
green
peppers
6. What fraction of the pizza is mushroom?
mushrooms
7. Number Sense Is ᎏ41ᎏ of 12 greater than ᎏ14ᎏ of 8? Explain your
answer.
8. A set has 12 squares. Which is the number of squares in ᎏ13ᎏ of
the set?
A 3
B 4
C 6
D 9
Region A
Practice H2
Region B
© Pearson Education, Inc. 3
9. Explain why ᎏ12ᎏ of Region A is not larger than ᎏ12ᎏ of Region B.
Name
Practice
H3
Parts of a Set
9 shaded.
1. Draw a group of squares with ___
10
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.
© Pearson Education, Inc. 3
Draw a model and shade it in to show each fraction.
8
10. ___
12
15
11. ___
20
Practice H3
Name
Practice
H14
Equivalent Fractions
To find an equivalent fraction by
multiplying, use this example.
To find the equivalent fraction by
dividing, use this example.
⫻2
⫼5
10 ⫽ ____
___
2 ⫽ ____
__
3
15
6
⫻2
⫼5
3
Find the equivalent fraction.
1 ⫽ ____
1. __
6
2. ___
⫽ ____
6
3. __
⫽ ____
6
4. ___
⫽ ____
8
5. ___
⫽ ____
9 ⫽ ____
6. ___
6
10
18
10
14
20
5
8
4
11
7
22
Write each fraction in simplest form.
5
8. ___
9
7. ___
12
5
9. ___
10
24
10. ___
25
36
Multiply or divide to find an equivalent fraction.
6
12. ___
11
11. ___
22
5
14. ___
9
13. ___
36
10
35
7
15. ___
12
16. At the air show, _13 of the airplanes were gliders. Which fraction
is not an equivalent fraction for _13?
5
A ___
15
7
B ___
21
6
C ___
24
9
D ___
27
© Pearson Education, Inc. 3
17. In Missy’s sports-cards collection, _57 of the cards are baseball.
12
are baseball. Frank says they have
In Frank’s collection, __
36
the same fraction of baseball cards. Is he correct?
Practice H14
Name
Practice
H18
Mixed Numbers
Write _52 as a mixed number without using fraction strips.
1. Divide 5 by 2 at the right.
2 5
2. Fill in the missing numbers below.
Quotient
Remainder
Divisor
3. Write _52 as a mixed number.
Write each improper fraction as a mixed number.
12
4. ___
7
5. __
9
6. __
9
7. __
29
8. ___
34
9. ___
7
4
7
3
13
8
10. Write 2_45 as an improper fraction.
Whole Number Denominator Numerator __________________________________________
Denominator
4
2
10 ____________________________________________
_______
© Pearson Education, Inc. 3
Change each mixed number to an improper fraction.
4
11. 2__
7
12. 8__
6
13. 3__
1
14. 7__
3
15. 4__
1
16. 5__
5
8
9
7
7
4
Practice H18
Name
Practice
Congruent Figures and Motions
I8
Congruent 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.
Flip
Slide
Turn
Write slide, flip, or turn for each diagram.
7.
8.
10.
11.
12.
© Pearson Education, Inc. 3
6.
Practice I8
Name
Practice
I10
Solids and Nets
For 1 and 2, predict what shape each net will make.
2.
1.
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
© Pearson Education, Inc. 3
7. Draw a net for a triangular pyramid. Explain
how you know your diagram is correct.
Practice I10
Name
Practice
I11
Views of Solid Figures
Draw the front, right, and top views of each solid figure.
2.
1.
Front
Side
Top
3.
Front
Front
Side
Top
Front
Side
Top
4.
Side
Top
Side
Top
5.
© Pearson Education, Inc. 3
Front
Practice I11
Name
Practice
I13
Congruent Figures
Congruent 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.
8. Divide this shape into
2 congruent shapes.
9. Divide this shape into
3 congruent shapes.
10. Divide this shape into
8 congruent shapes.
© Pearson Education, Inc. 3
7. Divide this shape into
4 congruent shapes.
Practice I13
Name
Practice
I45
Perimeter
Look at Rectangle A and Rectangle B. Complete the table.
Rectangle A
3 in.
Rectangle
B
9 in.
4 ft
6 ft
Rectangle
Length
Width
Perimeter
A
B
So, Any
w
2 ⫹ 2w
Find the perimeter of these rectangles.
1. ⫽ 9
w⫽2
2. ⫽ 6
3. ⫽ 11
w ⫽ 12
4. ⫽ 10
w⫽7
w⫽5
Find the perimeter of the square with the given side.
5. s ⫽ 4
6. s ⫽ 2
7. s ⫽ 9
8. s ⫽ 6
9. s ⫽ 20
10. s ⫽ 5
12. s ⫽ 10
© Pearson Education, Inc. 3
11. s ⫽ 8
Practice I45
Answers for Practice
F8, F9, F10, F11
Name
Name
Practice
F8
Rounding Numbers Through
Thousands
330
2. 825
Use the chart for help if you need to.
3. 162
4. 97
160
830
F9
Comparing and Ordering
Numbers Through Thousands
Round each number to the nearest ten.
1. 326
Practice
hundred
thousands
100
ten
thousands
thousands
hundreds
tens
ones
Round each number to the nearest hundred.
5. 1,427
1,400
6. 8,136
7. 1,308
8,100
8. 3,656
1,300
1. 54,376
3. 9,635
Round each number to the nearest thousand.
9. 18,366
18,000
10. 408,614
409,000
11. 29,430
29,000
12. 63,239
10,000
14. 70,274
70,000
15. 33,625
30,000
B 680,000
C 700,000
2. 6,789
4. 4,125
< 9,876
> 3,225
5. 959,211 936,211 958,211
958,211
936,211
6. 456,318 408,405 459,751
16. 17,164
456,318
408,405
20,000
7. Write three numbers that are greater
than 43,000 and less than 44,000.
17. What is 681,542 rounded to the nearest hundred thousand?
A 600,000
> 45,763
> 9,536
Order the numbers from least to greatest.
63,000
Round each number to the nearest ten thousand.
13. 12,108
.
Compare. Write ⬎ or ⬍ for each
3,700
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?
959,211
459,751
Answers will vary.
8. Which number has the greatest value?
A 86,543,712
Round to the nearest 10.
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.
© Pearson Education, Inc. 3
© Pearson Education, Inc. 3
Answers will vary.
Practice F8
F8
6/30/08 12:01:54 PM
Name
F10
1. 300,000,000 ⫹ 70,000,000 ⫹ 2,000,000 ⫹ 500,000 ⫹ 10,000 ⫹ 2,000 ⫹ 800 ⫹ 5
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
2. 4,600,028
Four hundred eighty-eight
million, four hundred twenty-three
thousand, forty-six; forty
Number Sense Write the number that is
one hundred million more than 15,146,481. 115,146,481
6,000
2. 2,825
3. 2,162
3,000
2,000
4,000
30,000
6. 68,136
7. 76,308
70,000
80,000
8. 93,656
90,000
Round each number to the nearest hundred thousand.
10. 409,614
400,000
11. 229,930
200,000
12. 563,239
600,000
Round each number to the nearest million.
13. 12,108,219
14. 7,570,274
15. 9,333,625
16. 4,307,164
12,000,000 8,000,000 9,000,000 4,000,000
Thirty-three million, eight hundred
seventy-one thousand, six hundred
forty-eight
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
18. What is 681,542 rounded to the nearest hundred thousand?
86. Which is the expanded form for 43,287,005?
A 600,000
A 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹ 8,000 ⫹ 700 ⫹ 5
B 680,000
C 700,000
19. Round 2,672,358 to each place value?
B 40,000,000 ⫹ 3,000,000 ⫹ 200,000 ⫹ 80,000 ⫹ 7,000 ⫹ 5
2,672,360
2,672,000
hundred thousand 2,700,000
C 400,000,000 ⫹ 30,000,000 ⫹ 2,000,000 ⫹ 8,000 ⫹ 500
ten
D 4,000,000 ⫹ 30,000 ⫹ 2,000 ⫹ 800 ⫹ 70 ⫹ 5
thousand
7. In the number 463,211,889, which digit has the greatest value? Explain.
Practice F10
6/30/08 12:01:57 PM
D 780,000
2,672,400
2,670,000
million 3,000,000
hundred
ten thousand
4; it is in the hundred millions place.
F10
4. 4,097
Round each number to the nearest ten thousand.
600,000
5. The population of a state was estimated to be 33,871,648.
Write the word form.
© Pearson Education, Inc. 3
1. 6,326
9. 618,366
3. 488,423,046
45095_Practice_F8-I45.indd F10
F11
Round each number to the nearest thousand.
5. 31,427
Write the word form and tell the value of the underlined digit for each number.
© Pearson Education, Inc. 3
Practice
Rounding Numbers Through
Millions
Write the number in standard form and in word form.
4.
6/30/08 12:01:56 PM
Name
Practice
Place Value Through Millions
F9
45095_Practice_F8-I45.indd F9
© Pearson Education, Inc. 3
45095_Practice_F8-I45.indd F8
Practice F9
Practice F11
45095_Practice_F8-I45.indd F11
F11
6/30/08 12:01:59 PM
Answers: F8, F9, F10, F11
Answers for Practice
F29, G7, G42, G59
Name
Name
Practice
F29
Patterns and Equations
9
7
5
?
xⴜ9
Rule:
5.
2
22
x
y
Rule:
3
y
6
8
10
12
42
56
70
?
7x
Rule:
4
44
3.
x
Estimate by rounding to the nearest ten.
6
66
8
?
84
x
y
36
42
48
54
6
7
8
?
9
xⴜ6
Rule:
11x
9
3
x
y
6.
88
4.
Rule:
x
y
10
15
20
25
30
45
60
?
12
4
75
1
6
2
12
18
?
A y 3x
2
$6
3
$9
4
24
5
?
B y 6x
F29
G42
© Pearson Education, Inc. 3
Dividing with Objects
3 R3
5. 27 8
9 R1
9. 19 2
9
6. 27 3
4 R2
10. 30 7
2 R3
3 R2
5 R3
11. 17 3
14. 19 pennies into 5 rows
15. 17 balloons into 7 rows
8 R3
1 R7
12. 16 9
18. 605 825
1,400
1,300
500
1,400
G7
45095_Practice_F8-I45.indd G7
6/30/08 12:02:02 PM
Practice
2. 43
G59
3. 572
1, 43
prime
6. 87
9. 88
1, 2, 4, 4. 63
11, 13, 22, 26, 1, 3, 7, 9,
44, 52, 143,
21, 63
286, 572
composite
composite
7. 3
1, 3, 29, 87
composite
10. 19
8. 27
1, 3
11. 69
1, 19
1, 3, 23, 69
22, 44, 88
composite
prime
composite
3235
composite
14. 1,212
1, 3, 9, 27
prime
1, 2, 4, 8, 11,
13. 3,235
15. 57
composite
12. 79
1, 79
prime
16. 17
1, 2, 4, 6, 12,
1, 3, 19, 57
101, 202, 303,
composite
606, 1212
composite
1, 17
prime
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?
Ms. Vernon’s
D 4
18. Every prime number larger than 10 has a digit in the ones
place that is included in which set of numbers below?
© Pearson Education, Inc. 3
5 ⴛ 5 ⴝ 25 (not enough)
Practice G42
Answers: F29, G7, G42, G59
150
members
800
magazines
Practice G7
1, 5, 647,
G42
1,400
17. 141 370
prime
18. Pencils are sold in packages of 5. Explain why you need
6 packages in order to have enough for 27 students.
45095_Practice_F8-I45.indd G42
1,000
569
780
_
16. 458 681
1, 53
17. Which is the remainder for the quotient of 79 8?
6 ⴛ 5 ⴝ 30
12.
15. 421 887
5. 53
8 rows; 2 left over
3 rows; 4 left over
2 rows; 3 left over
C 5
617
358
_
14. 764 571
composite
8. 35 4
No. The teams will not be even.
23 ⴜ 4 ⴝ 5R3
B 6
11.
1,400
1. 81
16. Ms. Nikkel wants to divide her class of 23 students into
4 equal teams. Is this reasonable? Why or why not?
A 7
680
743
_
13. 840 501
1, 3, 9, 27, 81
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
10.
In 1 through 12, find all the factors of each number. Tell whether
each number is prime or composite.
4. 29 9
7. 28 5
5 R2
478
252
_
Factoring Numbers
Divide. You may use counters or pictures to help.
3. 17 7
50
Name
Practice
5 R2
170
24; 28 rounds to 30, so the second
number must round to 20, 30 ⴙ 20 ⴝ 50
6/30/08 12:02:00 PM
Name
2. 32 6
100
120
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.
Practice F29
6 R3
110
20. Karen sold 534 magazines and Carly sold 308. About
how many total magazines did the two girls sell?
D y 4x
The y-value is 7 times greater than the
x-value.
1. 27 4
8. 33 23
1,200
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?
45095_Practice_F8-I45.indd F29
7. 88 76
110
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?
4
$12
C yx3
6. 39 64
1,300
8. Danielle made a table of the rental fees at a video store.
What is the rule?
1
$3
5. 58 47
800
30 inches
x
y
4. 53 69
9.
6
xⴜ3
3
18
3. 33 81
100
Estimate by rounding to the nearest hundred.
15
5
7. Lucas recorded the growth of a plant. How tall will the plant
be on Day 5?
Day
Height in inches
2. 34 71
100
3x
Rule:
1. 51 46
6/30/08 12:02:04 PM
A 1, 3, 7, 9
C 0, 2, 4, 5, 6, 8
B 1, 3, 5, 9
D 1, 3, 7
Practice G59
45095_Practice_F8-I45.indd G59
G59
6/30/08 12:02:06 PM
© Pearson Education, Inc. 3
81
63
45
27
2.
© Pearson Education, Inc. 3
y
© Pearson Education, Inc. 3
x
G7
Estimating Sums
For 1 through 6, complete each table. Find each rule.
1.
Practice
Answers for Practice
G66, G67, H1, H2
Name
Name
Practice
G66
Mental Math: Multiplying by
Multiples of 10
Round each factor so that you can estimate the product mentally.
Use rounding to estimate each product.
5. 3 ⫻ 600 ⫽
7. 90 ⫻ 70 ⫽
9. 50 ⫻ 800 ⫽
11. 90 ⫻ 500 ⫽
450
3,000
6 ⫻ 500 ⫽
0
0 ⫻ 600 ⫽
28,000
70 ⫻ 400 ⫽
24,000
30 ⫻ 800 ⫽
120,000
30 ⫻ 4,000 ⫽
4.
6.
8.
10.
12.
3. 54 ⫻ 76
5. 548 ⫻ 28
7. 67 ⫻ 289
13.
3,600 lb
15,000 lb
15. How many pounds can Truck B haul in 50 trips?
© Pearson Education, Inc. 3
50 ⴛ 300; 15,000 12.
80
ⴛ 600; 48,000 14.
81 ⫻ 643
72 ⫻ 285 70 ⴛ 300; 21,000 16.
A 240
B 1,600
A 6,000
D 280,000
70 ⴛ 700; 49,000
44 ⫻ 444 40 ⴛ 400; 16,000
61 ⫻ 76160 ⴛ 800; 48,000
65 ⫻ 724
C 2,400
D 24,000
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.
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.
7 ⴛ 300 ⴝ 2,100 kilowatts
Multiply 7 days in one week ⴛ 300.
(300 is incompatible to 330)
Answers will vary. Sample answer:
Multiply 3 ⴛ 9 ⴝ 27; 27 ⴛ 10 ⴝ 270
Practice G66
G66
6/30/08 12:02:07 PM
Name
H1
Equal Parts of a Whole
Practice G67
G67
45095_Practice_F8-I45.indd G67
6/30/08 12:02:09 PM
Name
Practice
Practice
H2
Parts of a Region
Tell if each shows equal or unequal parts.
If the parts are equal, name them.
Write a fraction for the part of the region below that is shaded.
1.
2.
Equal,
halves
Answers
may vary.
700 ⴛ 90; 6,300
10. 673 ⫻ 85
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?
16. How many pounds can Truck A haul in 70 trips?
1.
3,500
6,000
64,000
6,000
17. Vera has 8 boxes of paper clips. Each box has 275 paper
clips. About how many paper clips does Vera have?
14. How many pounds can Truck A haul in 9 trips?
45095_Practice_F8-I45.indd G66
8. 183 ⫻ 34
11. 54 ⫻ 347
Truck A can haul 400 lb in one trip. Truck B can haul 300 lb
in one trip.
C 28,000
6. 823 ⫻ 83
30 ⴛ 90; 2,700
15.
B 2,800
4. 121 ⫻ 62
9. 28 ⫻ 87
Answers will vary.
A 280
2. 71 ⫻ 47
Use compatible numbers to estimate each product.
13. Number Sense How many zeros are in the product of
60 ⫻ 900? Explain how you know.
3
1,200
4,000
15,000
21,000
1. 38 ⫻ 29
2. 5 ⫻ 90 ⫽
© Pearson Education, Inc. 3
3. 9 ⫻ 200 ⫽
120
1,800
1,800
6,300
40,000
45,000
G67
Estimating Products
Multiply. Use mental math.
1. 4 ⫻ 30 ⫽
Practice
3.
Unequal
2.
4.
Equal,
eighths
ᎏ4ᎏ
8
3
ᎏ4ᎏ
Equal,
fourths
Shade in the models to show each fraction.
3.
ᎏ2ᎏ
4
7
4. __
10
or
Name the equal parts of the whole.
5.
6.
7.
8.
5. What fraction of the pizza is cheese?
_3
eighths
thirds
fifths
8
sixths
6. What fraction of the pizza is mushroom?
_2
8
Use the grid to draw a region showing the number of equal
parts named.
9. tenths
cheese
green
peppers
mushrooms
Answers will vary.
7. Number Sense Is ᎏ41ᎏ of 12 greater than ᎏ14ᎏ of 8? Explain your
answer.
10. sixths
Yes. Answers will vary.
1
of 12 is 3 and ᎏ4ᎏ of 8 is 2; 3 > 2.
ᎏ1
4ᎏ
8. A set has 12 squares. Which is the number of squares in ᎏ13ᎏ of
the set?
11. Geometry How many equal parts does this figure have?
A 3
12. Which is the name of 12 equal parts of a whole?
45095_Practice_F8-I45.indd H1
halves
tenths
sixths
B 4
C 6
D 9
9. Explain why ᎏ12ᎏ of Region A is not larger than ᎏ12ᎏ of Region B.
twelfths
They each have the same
_1
region shaded for 2
Practice H1
Practice H2
_1
2
Region A
H1
6/30/08 12:02:10 PM
45095_Practice_F8-I45.indd H2
H2
Region B
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© Pearson Education, Inc. 3
4
6/30/08 12:02:12 PM
Answers: G66, G67, H1, H2
Answers for Practice
H3, H14, H18, I8
Name
Name
Practice
H3
Parts of a Set
Practice
To find an equivalent fraction by
multiplying, use this example.
10
Answers will vary.
2
3. How many should be shaded?
3
5
4
15
6
2
6
3
18
6
2. ___
____
12
8
5. ___
____
10
6
4. ___
____
10
_2
5
11
11. ___
6
12. ___
36
2
9
16
© Pearson Education, Inc. 3
15
11. ___
20
Practice H3
H3
6/30/08 12:02:14 PM
Name
H18
Mixed Numbers
35
answers given
7
15. ___
_1
12
7
20
14
__
24
6
C ___
7
B ___
21
9
D ___
24
27
Practice H14
H14
45095_Practice_F8-I45.indd H14
6/30/08 12:02:16 PM
Practice
I8
Congruent figures have the same size and shapes, although they
may face different directions.
2
Write yes or no to tell if the figures are congruent.
2 5
4
1
1.
Remainder
4.
2.
No
2. Fill in the missing numbers below.
1
2
5
14. ___
Congruent Figures and Motions
Write _52 as a mixed number without using fraction strips.
2
3
36
Name
Practice
Quotient
18
__
_2
24
10. ___
5
12
In simplest form, __
ⴝ _13 . The fraction _57
36
is already in simplest form. Since _13 ⴝ _57 ,
Frank and Missy do not have the same
fraction of baseball cards.
Draw a model and shade it in to show each fraction.
_1
22
17. In Missy’s sports-cards collection, _57 of the cards are baseball.
12
are baseball. Frank says they have
In Frank’s collection, __
36
the same fraction of baseball cards. Is he correct?
4
__
1. Divide 5 by 2 at the right.
25
18
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_7
45095_Practice_F8-I45.indd H3
5
9. ___
10
4
11
7
9
13. ___
_1
3
8
16. At the air show, _13 of the airplanes were gliders. Which fraction
is not an equivalent fraction for _13 ?
15
12
9 ____
6. ___
6
5
A ___
Answers will vary.
4
2
10
_1
22
9.
8
10. ___
3. _6_ ____
Multiply or divide to find an equivalent fraction. Sample
5
8
5
_1
5
8. ___
4
12
_2
8.
_3
9
7. ___
7.
_6
14
20
3
Write each fraction in simplest form.
3
6.
3
5
1. _1_ ____
5.
_4
3
10 ____
___
Find the equivalent fraction.
Write the fraction for each shaded model.
4.
To find the equivalent fraction by
dividing, use this example.
_2_ ____
10
9
2. How many squares do you need to draw altogether.
H14
Equivalent Fractions
9 shaded.
1. Draw a group of squares with ___
3.
Yes
5.
No
6.
Divisor
2_12
3. Write _52 as a mixed number.
Yes
No
Yes
Slide
Flip
Turn
Write each improper fraction as a mixed number.
1_57
4
2_17
6. _9_
1_27
29
8. ___
3
2__
13
34
9. ___
4_28 ; 4_14
3
2_14
7. _9_
5. _7_
13
7
8
10. Write 2_54 as an improper fraction.
Write slide, flip, or turn for each diagram.
Whole Number Denominator Numerator __________________________________________
6.
Denominator
5
4
14
15
2
4
10 ____________________________________________
_______
5
slide
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Change each mixed number to an improper fraction.
11. 2_4_
5
14. 7_1_
8
14
__
5
57
__
8
12. 8_7_
9
15. 4_3_
7
79
__
9
31
__
7
13. 3_6_
7
16. 5_1_
4
10.
27
__
H18
Answers: H3, H14, H18, I8
8.
turn
11.
flip
12.
7
turn
21
__
4
Practice H18
45095_Practice_F8-I45.indd H18
7.
6/30/08 12:02:18 PM
slide
flip
Practice I8
45095_Practice_F8-I45.indd I8
I8
7/1/08 11:40:17 AM
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7
© Pearson Education, Inc. 3
12
4. ___
Answers for Practice
I10, I11, I13, I45
Name
Name
Practice
I10
Solids and Nets
Draw the front, right, and top views of each solid figure.
2.
1.
2.
Front
square pyramid
rectangular prism
I11
Views of Solid Figures
For 1 and 2, predict what shape each net will make.
1.
Practice
Top
Side
3.
Front
Side
Top
Front
Side
Top
4.
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
cube
triangular pyramid
cylinder
Front
Side
Top
Side
Top
6. Which solid can be made by a net that has exactly one circle in it?
A Cone
B Cylinder
C Sphere
5.
D Pyramid
7. Draw a net for a triangular pyramid. Explain
how you know your diagram is correct.
Answers will vary.
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© Pearson Education, Inc. 3
Front
Practice I10
I10
45095_Practice_F8-I45.indd I10
6/30/08 12:02:23 PM
Name
H11
45095_Practice_F8-I45.indd I11
6/30/08 12:02:25 PM
Name
Practice
I13
Congruent Figures
Practice I11
Practice
I45
Perimeter
Look at Rectangle A and Rectangle B. Complete the table.
Congruent figures have the same size and shape, although they
may face different directions.
3 in.
Rectangle A
Rectangle
B
9 in.
6 ft
Tell if the figures are congruent.
1.
2.
yes
4.
3.
no
5.
no
Rectangle
Length
Width
Perimeter
A
9
6
3
4
24
20
B
6.
no
yes
7–10: Answers will vary.
7. Divide this shape into
4 congruent shapes.
So, Any
2 ⫹ 2w
w
Find the perimeter of these rectangles.
yes
8. Divide this shape into
2 congruent shapes.
1. ⫽ 9
w⫽2
2. ⫽ 6
3. ⫽ 11
w ⫽ 12
4. ⫽ 10
P ⴝ 22
P ⴝ 46
Find the perimeter of the square with the given side.
10. Divide this shape into
8 congruent shapes.
P ⴝ 26
w⫽5
P ⴝ 30
16
6. s ⫽ 2
8
7. s ⫽ 9
36
8. s ⫽ 6
24
9. s ⫽ 20
80
10. s ⫽ 5
20
32
12. s ⫽ 10
40
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11. s ⫽ 8
Practice I13
45095_Practice_F8-I45.indd I13
w⫽7
5. s ⫽ 4
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© Pearson Education, Inc. 3
9. Divide this shape into
3 congruent shapes.
4 ft
I13
6/30/08 12:02:26 PM
Practice I45
45095_Practice_F8-I45.indd I45
I45
6/30/08 12:02:29 PM
Answers: I10, I11, I13, I45
Grade 3
Name
1.
2.
Round 43,864 to the nearest ten
thousand.
Step Up to Grade 4 Test
4.
Round this number to the nearest
ten million. 15,679,841
A 40,000
A 5,000,000
B 43,000
B 11,000,000
C 43,900
C 15,000,000
D 44,000
D 16,000,000
Which is the expanded form of
4,321,189?
5.
x
y
20
12
25
17
30
22
35
?
A 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹
1,000 ⫹ 100 ⫹ 80 ⫹ 9
If x = 35, what is the value of y?
B 4,000,000 ⫹ 300,000 ⫹ 21,000 ⫹
100 ⫹ 89
B 27
A 30
C 25
C 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹
1,000 ⫹ 90 ⫹ 9
D 23
D 400,000 ⫹ 300,000 ⫹ 21,000 ⫹
1,000 ⫹ 100 ⫹ 80 ⫹ 9
Which digit is in the thousands place?
128,698,473
6.
Estimate by rounding to the nearest
hundred. 689 ⫹ 228
A 1
A 628
B 2
B 800
C 6
C 889
D 8
D 900
© Pearson Education, Inc. 3
3.
T1
Grade 3
Name
7.
Find the quotient and the remainder.
26 ⫼ 4
A 4R2
B 6R2
C 6R4
D 8R2
Step Up to Grade 4 Test
10. Estimate the product by rounding
each factor.
28 ⫻ 23
A 900
B 600
C 500
D 400
8.
What are all the factors of 12?
11. Name the equal parts of the whole.
A 1, 6, 12
B 1, 2, 6, 12
C 1, 2, 3, 6, 12
D 1, 2, 3, 4, 6, 12
A fifths
B fourths
C thirds
D halves
9.
The comic book store packs 30 comic
books into one envelope. How many
comic books will be packed into
30 envelopes?
12. Write the fraction for the shaded part
of the region.
A 90
B 300
C 600
A _45
D 900
B _58
C _68
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D _78
T2
Grade 3
Name
13. Find the fraction for the shaded parts
of this set.
A _35
B _45
C _56
D _47
14. Which fraction is not equivalent to _23?
Step Up to Grade 4 Test
16. What motion does this shape show?
A slide
B flip
C turn
D motion
17. Which solid can be made from this net?
A _46
8
B __
12
9
C __
12
10
D __
15
A square
B cube
C triangular prism
D rectangular prism
15. What is the mixed number for this
15
improper fraction? __
8
18. What would the top view of this solid
look like?
A 2_78
B 2_18
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C 1_78
D 1_58
A
B
C
D
T3
Grade 3
Name
19. Which set of figures is not congruent?
Step Up to Grade 4 Test
20. What is the perimeter of this garden?
A
6 ft
3 ft
4 ft
3 ft
B
1 ft
3 ft
A 12 ft
B 20 ft
C 22 ft
C
D 24 ft
© Pearson Education, Inc. 3
D
T4
Answers for Test
T1, T2, T3, T4
Grade 3
Name
1.
4.
Round 43,864 to the nearest ten
thousand.
2.
7.
Round this number to the nearest
ten million. 15,679,841
A 5,000,000
A 4R2
B 43,000
B 11,000,000
B 6R2
C 43,900
C 15,000,000
C 6R4
D 16,000,000
D 8R2
5.
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
x
y
20
12
25
17
30
22
Step Up to Grade 4 Test
Find the quotient and the remainder.
26 ⫼ 4
A 40,000
D 44,000
Grade 3
Name
Step Up to Grade 4 Test
10. Estimate the product by rounding
each factor.
28 ⫻ 23
A 900
B 600
C 500
D 400
35
?
8.
11. Name the equal parts of the whole.
What are all the factors of 12?
If x = 35, what is the value of y?
A 1, 6, 12
A 30
B 1, 2, 6, 12
B 27
C 1, 2, 3, 6, 12
C 25
D 1, 2, 3, 4, 6, 12
A fifths
D 23
B fourths
D 400,000 ⫹ 300,000 ⫹ 21,000 ⫹
1,000 ⫹ 100 ⫹ 80 ⫹ 9
C thirds
D halves
3.
Which digit is in the thousands place?
128,698,473
6.
Estimate by rounding to the nearest
hundred. 689 ⫹ 228
9.
A 1
A 628
B 2
B 800
The comic book store packs 30 comic
books into one envelope. How many
comic books will be packed into
30 envelopes?
C 6
C 889
A 90
D 8
D 900
B 300
12. Write the fraction for the shaded part
of the region.
A _45
B _58
C 600
D 900
C _68
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© Pearson Education, Inc. 3
D _78
T1
T1
45095_T1-T4.indd T1
T2
7/1/08 2:09:36 PM
Grade 3
Name
7/2/08 1:20:15 PM
Grade 3
Name
Step Up to Grade 4 Test
13. Find the fraction for the shaded parts
of this set.
T2
45095_T1-T4.indd T2
16. What motion does this shape show?
Step Up to Grade 4 Test
19. Which set of figures is not congruent?
20. What is the perimeter of this garden?
A
6 ft
3 ft
4 ft
3 ft
A _35
A slide
B _45
B
A 12 ft
B flip
C _56
B 20 ft
C turn
D _47
C 22 ft
D motion
D 24 ft
C
14. Which fraction is not equivalent to _23?
1 ft
3 ft
17. Which solid can be made from this net?
A _46
8
B __
12
D
9
C __
12
10
D __
15
A square
B cube
C triangular prism
D rectangular prism
15. What is the mixed number for this
15
improper fraction? __
8
18. What would the top view of this solid
look like?
A 2_78
C 1_78
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© Pearson Education, Inc. 3
D 1_58
A
B
C
D
© Pearson Education, Inc. 3
B 2_18
T3
45095_T1-T4.indd T3
T3
T4
7/1/08 2:09:38 PM
45095_T1-T4.indd T4
T4
7/1/08 2:09:39 PM
Answers: T1, T2, T3, T4