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Saxon Math Intermediate 5 133 Adaptations Lesson 21
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2121 Teacher Notes:
• Introduce Hint #18 “Word Problem Cues, Part 2.”
• Review Hint #10 “Word Problem Cues, Part 1.”
• Review “Word Problem Keywords” on page 6 in the Student Reference Guide.
• Review reference chart “Word Problem Keywords.”
• Word Problems About Equal Groups
New ConceptNew Concept
• Formula for equal groups problems:
number in each group× number of groups total
Example
There are 4 classes of fifth graders with 30 students in each class. How many students are in the 4 classes?
30 students in each class× 4 classes 120 students in all 4 classes
4 30
?
Example
5 pens cost $2. How much would 10 pens cost?
1. Name the two things the problem is about. pens
____ $
2. Fill in what you know. pens
____ $ 5 __
2
3. Fill in what you are looking for. pens
____ $ 5 __
2 = 10 ___
?
4. Draw a loop around the numbers thatare diagonally opposite. The loop never
pens ____
$ 5 __
2 = 10 ___
?
includes the question mark.
5. Multiply the numbers inside the loop. 10 × 2 = 20Divide by the outside number. 20 ÷ 5 = $4
page 132
Math Language
Solve equal groups problems by using the loop method.
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Write an equation and find the answer.
a. On the shelf were 4 cartons of eggs. There were 12 eggs in each carton. How many eggs were in all four cartons?
4 12
t 12 eggs in each carton× 4 cartons eggs in all 4 cartons
12 × = t
t =
b. Thirty desks are arranged in 6 equal rows. How many desks are in each row?
6 n
30 desks in each row× rows 30 desks in all 6 rows
6n = missing factor divide
n =
c. Twenty-one books are stacked in piles with 7 books in each pile. How many piles are there?
7 g
25 7 books in each pile× g piles books in all 7 piles
7g = missing factor divide
g =
d. If 56 zebras were separated into 7 equal herds, then how many zebras would be in each herd?
7 n
56
zebras in each herd× 7 herds 56 zebras in all 7 herds
7g = missing factor divide
g =
e. Write an “equal groups” word problem for this equation.
6 0.75
tThen answer the question in your word problem.
6 × $0.75 = t t =
Pat bought pens for each.
did she spend? Pat spent $ .
Lesson Practice
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Saxon Math Intermediate 5 135 Adaptations Lesson 21
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1. p students on each team 8p =
8 p
56
× teams
students in all
missing factor divide
p =
Use work area.
2. 32 ounces bottle
bowl t left
8 t
32
32 − = t
t = Use work area.
3. $487 earnedm more
cost
487 m
800
$487 + m =
m =
Use work area.
4. Draw an oblique line. Lines have arrows.
Use work area.
5.
6 7
42
) ____
) ____
× ×
Use work area.
Written PracticeWritten Practice page 136
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Written Practice,Written Practice, continued continued
Saxon Math Intermediate 5 136 Adaptations Lesson 21
6. 8 ) ____
7 2
8 ?
72
7. 6n = 42
6 n
42
n =
8. 9 ) ____
3 6
9 ?
36
9. 6n = 48
6 n
48
n =
10. 56 ÷ 7 =
7 ?
56
11. 70 ___ 10
=
10 ?
70
12. 24 ÷ 4 30 ÷ 6
13. Carry on your fingers.
367
× 8
14. $5.04× 7
two decimal places in answer
15. Write the “carry” number.
837
× 9
16. 6 × 8 × 10 = 17. 7 × 20 × 4 = 18. $40.00
– $00.00
19. r − 4568 = 6318
4568 6318
r
r =
page 136
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Saxon Math Intermediate 5 137 Adaptations Lesson 21
20. 5003 − w = 876
876 w
5003
w =
21. 268+ m
687268 m
687
m =
22. sets of ten
$9.65$2.43
+ $1.45
24. number in each group missing factor divide
× number of groups
b
) ____
123
Twelve divided by is , so there are
items in each group.
25. …, 50, 60, 70, 80, 90, , ,
, …
26. Say the greater number (dividend) first.
10 ___ 2 words:
Use work area.
27. What number is the dividend?
60 ÷ 10 = 6
28. number in each group × number of groups
There were books in all 5
boxes.
Use work area.
23. 38296
+ 182
page 137
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Written Practice,Written Practice, continued continued
Saxon Math Intermediate 5 138 Adaptations Lesson 21
29. Use fraction-decimal-percent pieces for help.
1 __ 2 = .
1 __ 2 =
Use work area.
30. See page 138.
a. island with greatest area: greatest
+ least island with least area:
b. islands with areas that have a difference of 250 square miles:
and
– 100 250 sq. mi
c. islands with combined areas equal to Attu’s area:
, , and
116134
+ 350
Use work area.
page 137
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Saxon Math Intermediate 5 139 Adaptations Lesson 22
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2222 Teacher Notes:
• Refer students to “Tests for Divisibility” on page 20 in the Student Reference Guide.
• Review “Division” on page 8 in the Student Reference Guide.
• For additional practice, students may complete Targeted Practice 22.
• Division With and Without Remainders
New ConceptNew Concept
• Division and multiplication are inverse operations.
Example
5 ) ____
1 6
Think: 5 times what is close to, but not more than, 16?
5 × 3 = 15
16 – 15 = 1 Subtract using Mental Math. 3 R15 )
____ 1 6
The remainder is 1.
• Multiply to check division.
3 × 5 = 15 Multiply the quotient times the divisor.
+ 1 ____ 16 Add the remainder.
• Divisibility tests tell whether division answers have remainders.
TESTS FOR DIVISIBILITY
A number is divisible by … 2 if the last digit is even.
5 if the last digit is 0 or 5.
10 if the last digit is 0.
page 139
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Saxon Math Intermediate 5 140 Adaptations Lesson 22
Divide. Write each answer with a remainder.
a. R5 )
____ 2 3 b.
R6 )
____ 5 0 c. 37 ÷ 8
R ) ____
d. R4 )
____ 2 3 e.
R7 )
____ 5 0 f. 40 ÷ 6
R ) ____
g. R10 )
____ 4 2 h.
R9 )
____ 5 0 i. 34 ÷ 9
R ) ____
j. Circle the division problem below that has a remainder. Use divisibility tests. Do not divide.
10 ) ____
6 0 5 ) ____
4 4 2 ) ____
1 8
k. Which of the numbers below can be divided by 2 without a remainder?
25 30 35
Written PracticeWritten Practice page 142
1. Draw two horizontal lines. Lines have arrows.
Use work area.
2. number of groups × number in each group 8g =
bags
gifts in each bag
gifts in all
missing factor divide
8 g
32
g =
Use work area.
Lesson Practice
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Saxon Math Intermediate 5 141 Adaptations Lesson 22
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3. 26 miles total 9 miles ran m still to run
9 m
26
26 − = m
m =
Use work area.
4. Is 1000 a reasonable estimate for 384 + 618?
, because 384 is about and 618 is about
, which add up to a s of 1000.
Use work area.
5. Subtract using
Mental Math.
56 ÷ 10 =
6. 20 ÷ 3 = 7.
R7 )
____ 3 0
8. 3 × 7 × 10 =
9. Commutative Property of
Multiplication
2 × 3 × 4 × 5 =
10. Write the “carry” number.
$394
× 8
11. Carry on your fingers.
678
× 4
page 143
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Written Practice,Written Practice, continued continued
12. Write the “carry” number.
$6.49
× 9
two decimal places in answer
13. 63 ___ 7 =
7 ?
63
14. 56 ___ 8 =
8 ?
56 15. 42 ___
6 =
6 ?
42
16. Carry on your fingers.
$4.08
× 7
two decimal places in answer
17. 3645× 6
18. 3904× 4
19. Property of Zero for
Multiplication
8 × 0 = 4n
= 4n
= n
n =
20. top missing Add.
c
– 462548
462 548
c
c =
21. $36.15
– $ .62
page 143
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Saxon Math Intermediate 5 143 Adaptations Lesson 22
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22. 963+ a6000
963 a
6000
a =
23. Say the greater number (dividend) first.
4 ) ____
1 2
words:
Use work area.
24. odd× 2
product
2 ) ___
Is there a remainder?
, because when you multiply a number by 2, the product
is e . An even number divided by 2 does
have a remainder.
Use work area.
25. 50, 40, 30, 20, 10, , , , …
page 143
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Saxon Math Intermediate 5 144 Adaptations Lesson 22
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Written Practice,Written Practice, continued continued
26.
27. 46,208 46,028 28. How many fourths equal one half? Use fraction-decimal-percent pieces for help.
29. Use fraction-decimal-percent pieces for help.
a. 1 __ 4
= .
b. 1 __ 4
= %
Use work area.
30. chairs in last row = remainder
10 ) ____
7 5
page 144
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Saxon Math Intermediate 5 145 Adaptations Lesson 23
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2323 Teacher Note:
• Introduce Hint #20 “Comparing Fractions.”
• Recognizing Halves
New ConceptNew Concept
• Many fractions equal one half.
12
24
36
48
510
• The numerator of each fraction is half the denominator.
2 __ 4 Two is half of four. 4 __
8 Four is half of eight.
3__6 Three is half of six. 5___
10 Five is half of ten.
• To compare fractions:
1. Cross multiply.
2. Compare the numbers on top.
Example
2 __ 3 > 4 __
9
18 12
Lesson Practice
a. Think of a counting number. Double it. Then write a fraction equal to 1 _ 2 using your number and its double.
counting number doubled fraction
page 145
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Lesson Practice, continued
b. Which of these fractions does not equal 1 _ 2 ?
A 7___14
B 8___15
C 9___18
D 21___42
c. Compare: 5 __ 8 5 ___
12
d. Compare: 12 ___ 24
6 ___ 12
Written PracticeWritten Practice page 147
1. $5.00 gave $ . cost m get back
3.48 m
5.00
$5.00 − = m
m =
Use work area.
2. $1.45 veggie wrap $ . fruit salad t together
1.45 0.95
t
$1.45 + = t
t =
Rounding $1.45 to and $0.95 to gives a sum of
, which is close to .
Use work area.
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Saxon Math Intermediate 5 147 Adaptations Lesson 23
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3. Multiply the loop.
weeks days
1 __ 7 = d __
d
7 52
d
7 × = d
d =
Use work area.
4. Multiply the loop.
3 d
24
Divide by the outside number.
kids $
24 ___ 24
= 1 __ d
× d = 24
d =
To find the missing
f , divide 24
by .
Use work area.
5. a. 1 _ 2 of 20 ounces
b. 1 _ 4 of 20 ounces
a.
b.
6. Cross multiply.
3 ___ 10
3 __ 6
7. Subtract using Mental Math.
40 ÷ 6 =
8. R3 )
____ 2 0 9. 60 = n × 10
10 n
60
) ____
n =
page 147
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Saxon Math Intermediate 5 148 Adaptations Lesson 23
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Written Practice,Written Practice, continued continued
10. Carry on your fingers.
$3.08
× 7
two decimal places in answer
11. 2514× 3
12. Write the “carry” number.
697× 8
13. Say the greater number
(dividend) first.
7 ) ____
3 5
words:
Use work area.
14. 4 × 3 × 10 = 15. 12 × 2 × 10 =
16. bottom missing Subtract.
4035– s
3587
3587 s
4035
s =
17. top missing Add.
m– 1056
5694
1056 5694
m
m =
18. $70.00– $ 7.53
page 147
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19. $5.00
$ .00
$ .00
+ $ .
20. $6.25 + $0.85 + $4.00 + d = $20.00
$6.25
$ .
$ .
$20.00
$ .
d =
21.
7 9
63
× × ) ____
) ____
Use work area.
22. greatest to least
48, 16, 52
, ,
23. Draw two vertical lines side by side. Lines have arrows.
Use work area.
24. 212,500
words:
Use work area.
25.
7 9
16
+ + – –
Use work area.
page 148
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Saxon Math Intermediate 5 150 Adaptations Lesson 23
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Written Practice,Written Practice, continued continued
26. Which fraction below does not equal 1 _ 2 ?
A 10 ___ 20
B 20 ___ 40
C 40 ___ 80
D 80 ___ 40
27. Use fraction-decimal-percent pieces for help.
3 __ 4 = .
28. value of nine quarters
9 × =
29.
3 12
p
There were customers in the diner. Each customer ordered
pancakes. In all, how many were ordered?
30. 8, 16, 24, 32, , , , , ,
page 148
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Saxon Math Intermediate 5 151 Adaptations Lesson 24
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2424 Teacher Notes:
• Review “Properties of Operations” on page 22 in the Student Reference Guide.
• For additional practice, students may complete Targeted Practice 24.
page 149
Math Language
There are four operations of arithmetic:
addition
subtraction
multiplication
division
• Parentheses and the Associative Property
New ConceptNew Concept
• Parentheses separate a problem into parts.
• Always work the part inside the parentheses first:
2 × (3 + 4) (2 × 3) + 4
2 × 7 6 + 4
14 10
• Associate Property of Addition: Any way we group the addends, the answer is the same.
(4 + 5) + 6 = 4 + (5 + 6)
• Associative Property of Multiplication: Any way we group the factors, the answer is the same.
(2 × 3) × 4
2 × (3 × 4)
• The Associate Property does not work for subtraction or division.
>
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a. 6 – (4 – 2) = b. (6 – 4) – 2 = c. (8 ÷ 4) ÷ 2 =
d. 8 ÷ (4 ÷ 2) = e. 12 ÷ (4 – 1) = f. (12 ÷ 4) – 1 =
g. Name the four operations of arithmetic: , ,
,
h. (8 ÷ 4) ÷ 2 8 ÷ (4 ÷ 2) Does the Associative Property apply?
i. (8 – 4) – 2 8 – (4 – 2) Does the Associative Property apply?
j. (8 × 4) × 2 8 × (4 × 2) Does the Associative Property apply?
Lesson Practice
Written PracticeWritten Practice page 151
1. one half of a dollar $0.50
one fourth of a dollar $ .
2. number in each group × number of
groups
25 × = t
25 4
t
t =
Use work area.
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Saxon Math Intermediate 5 153 Adaptations Lesson 24
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3. carton
– e removed 9 remained
9 e
12
– e = 9
e = Use work area.
4. 956 seats s not occupied
occupied
498 s
956
956 – s = . I subtracted from
to get .
s = Use work area.
5.
5 10
50
× × ) _____
) _____
Use work area.
6. parentheses first
3 × (4 + 5) (3 × 4) + 5
3 × + 5
page 151
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Written Practice,Written Practice, continued continued
7. 30 – (20 + 10) =
30 – =
8. (30 – 20) + 10 =
+ 10 =
9. Associative Property of Multiplication
4 × (6 × 5) (4 × 6) × 5
4 × × 5
10. Subtract using Mental Math.
60 ÷ 7 =
11. 50 ÷ 6 = 12. R10 )
____ 4 4
13. Carry on your fingers.
$50.36 × 4
two decimal places in answer
14. 7408 × 4
page 151
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Saxon Math Intermediate 5 155 Adaptations Lesson 24
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15. Write the “carry” number.
4637 × 9
16. w– $09.62
$14.08
9.62 14.08
w
w =
17. 4730– j
2712
2712 j
4730
j =
18. $30.00– $00.56
19. $3.54
$ .
$ .
20. $20.00
– $
21.
9 5
14
+ + – –
Use work area.
22. hundreds
256
23. $35 + $35 + $35 + $35 =
× =
page 152
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Written Practice,Written Practice, continued continued
24. 10th term
3, 6, 9, 12, 15, …
25. Which is divisible by 5?
A 23 B 25 C 27 D 29
28. parentheses first
(8 + 4) + 2 8 + (4 + 2)
+ 2 8 +
29. a. half of 14
b. 1 __ 2 = 0 ___
14
a.
b.
26. Draw two vertical lines. Lines have arrows.
Use work area.
27.
7 8
56
× × ) _____
) _____
Use work area.
30. woke up 65°F
high temperature 83°F
Which equation shows the number of degrees the temperature increased?
A 65 + d = 83 B 83 + 65 = d
C d + 83 = 65 D 83 + d = 65
page 152
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Saxon Math Intermediate 5 157 Adaptations Lesson 25
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• Listing the Factors of Whole Numbers
New ConceptNew Concept
• To list the factors of whole numbers:
1. Always start with 1.
2. Always end with the number given.
3. Find all the other whole numbers that divide evenly into the given number.
Ask: Will 2 divide evenly?
Will 3 divide evenly? (etc.)
4. List the numbers in order.
Example
Factors of 20:
end withstart with
divide evenly into 20
1, 2, 4, 5, 10, 20
ActivityActivity
page 155
Grouping by Factors
Illustrate the factors of 12 by circling equal groups of dots and labeling each group.
groups of 1
groups of 2
2525 Teacher Notes:
• Introduce Hint #21 “Factors of Whole Numbers.”
• Refer students to “Factors” on page 8 in the Student Reference Guide.
• Review “Multiplication Table” on page 5 in the Student Reference Guide.
page 154
Math Language
The factors of a number are all the whole numbers that can divide it without leaving a remainder.
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Saxon Math Intermediate 5 158 Adaptations Lesson 25
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groups of 3
groups of 4
groups of 6
groups of 12
Lesson PracticeList the factors of each number:
a. 4 1 , , 4 b. 3 1 ,
c. 6 1 , , , d. 5 ,
e. 8 , , , f. 11 ,
g. 9 , ,
h. 12 , , , , ,
i. 1 j. 14 , , ,
k. 2 , l. 15 , , ,
m. Two is not a factor of which of these numbers?
A 236 B 632 C 362 D 263
n. Five is not a factor of which of these numbers?
A 105 B 150 C 510 D 501
o. Which of these numbers is not a factor of 40?
A 2 B 5 C 6 D 10
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1. number in each group × number of groups
9 × = t
t =
Use work area.
2. $10.00 paid
$ . cost m got back
6.75 m
10
$10 − = m
m =
My answer is r because $6.75 + = $10.
Use work area.
3. Multiply the loop.
cartons $
1 __ = 4 __ c
4 × = c
c =
Use work area.
4. factors of 13:
,
Written PracticeWritten Practice page 157
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Written Practice,Written Practice, continued continued
5. factors of 10:
1 , , 10
factors of 30:
1 , , , ,
, , , 30
, , ,
6. parentheses first
4 (6 10)
(4 6) 10
4 × × 10
7. Which property of multiplication is illustrated in problem 6?
Property
8. parentheses first
6 × (7 + 8) =
9. (6 × 7) + 8 = 10.
10 12
120 ) _____
) _____
× ×
Use work area.
11. 9n 54
9 n
54
n =
12. Subtract using Mental Math.
55 ÷ 8 =
13. Carry on your fingers.
1234× 5
page 157
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14. two decimal places in answer
$5.67× 8
Use work area.
15. 987× 6
16. w − $13.55 = $5
13.55 5
w
w =
17. 2001 − r = 1002
r 1002
2001
r =
18. 4387
+
19. 3715
+
20. $6.75 + $8 + $1.36 + p = $20
$6.75
$ .
$ .
$20.00
$ .
p =
21. 1 _ 2 of a dollar $0.50
1 _ 4 of a dollar $ .
1 __ 10 of a dollar $ .
22. 894,201
words:
Use work area.
page 157
23. Which number is the divisor?
7
6 ) ____
4 2
24. 10th term
5, 10, 15, 20,…
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Written Practice,Written Practice, continued continued
25. whole number
× 2
Answer odd or even?
26. Two is not a factor of which of these numbers?
See “Tests for Divisibility” on page 20 of the
Student Reference Guide.
A 456 B 465 C 654 D 564
27. Which property of addition is illustrated below?
(6 + 7) + 8 = 6 + (7 + 8)
Property
28.
× × =
29. Use fraction-decimal-percent pieces for help.
1 ___ 10
= .
30. Number of Yards 1 2 3 4
Number of Feet 3 6 9 12
a. To find the number of feet, m the number of yards
times .
b. 20
feet = 20 yards
Use work area.
page 158
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Saxon Math Intermediate 5 163 Adaptations Lesson 26
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2626
• Division Algorithm
New ConceptNew Concept
• Use short division when divisors are one-digit.
• After multiplying and subtracting, any number “left over”goes in front of the next digit.
• Place a digit above each digit.
• Use zero as a placeholder.
• Any final number “left over” becomes the remainder(must be less than the divisor).
Example
234 ÷ 5 =
0 4 6 R 45 )
______ 2 3 34
• Factor missing Divide.
5n = 365 n = 365 ÷ 5
n = 73 0 7 35 )
______ 3 6 15
5 n
365
page 159
Teacher Notes:
• Introduce Hint #22 “ShortDivision.”
• Review “Division” on page 8 in the Student Reference Guide.
• For additional practice, students may complete Targeted Practice 26.
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Saxon Math Intermediate 5 164 Adaptations Lesson 26
Divide, using short division with one-digit divisors.
a. $4 )
__________ $5 . 5 6 b.
0 R9 )
_________ 3 7 5 c.
$3 )
__________ $4 . 6 5 d. 5 )
_________ 6 4 5
e. $0
7 ) __________
$3 . 6 4 f. 0 R7 )
_________ 3 6 5 g.
0 R10 )
_________ 5 4 6 h.
$4 )
__________ $4 . 5 6
i. Show how to check this division answer. 1 2 R 36 )
____ 7 5
Find each missing factor. Check each answer using a calculator.
j. 3x = 51 ) ___
k. 4y = 92 ) ___
x = y =
l. 6z = 252 ) ___
z =
I divided to find the missing f .
Lesson Practice
Written PracticeWritten Practice page 162
1. $5.00 paid
$ . cost m get back
2.98 m
5.00
$5 – $ = m
m = $
Use work area.
2. number in each group × number of groups
3 12
t
3 × = t
t = Use work area.
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Saxon Math Intermediate 5 165 Adaptations Lesson 26
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3. s before 3 new after
3 s
28
s + 3 =
s =
I subtracted 3 from
and got .
Use work area.
4. a. smallest
even
b. half of that
c. 1 __ 2 =
a.
b.
c.
5. factors of 8: factors of 16:
1 , , , 8 1 , , , , 16
, , ,
6. short division
5 ) _________
3 7 5
7. short division
R4 )
_________ 3 6 5
8. 6m = 234
) ___
page 163
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Written Practice,Written Practice, continued continued
9. short division
$ 0 .6 )
__________ $4 . 3 2
10. short division
3 ) _________
1 2 3
11. short division
6 ) _________
5 7 6
12. Carry on your fingers.
$7.48
×
two decimal places in answer
13. Write the “carry” number.
609
×
14. Associative Property of
Multiplication
7 × 8 × 10 =
15. Property of Zero for
Multiplication
7 × 8 × 0 =
16. 9374 – m = 4938
m 4938
9374
m =
17. $10.00
$1010.00
18. l 427+ 85 2010
2010
l =
19. $12.43
$12.43
$12.43
page 163
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20. 3 × 40 3 × 4 × 10
Since 4 × 10 = , the quantities are the s .
21. 8 × 90 = 8 × 9 × n
n =
22. ) ___
) ___
8 9
72
× ×
Use work area.
23. missing factor Divide.
8s = 64 ) ___
24. 3 _ 4 of a dollar $0.75
$0.75 3 __ 10 of a dollar
25. What number is halfway between 400 and 600?
600400
26. This equation shows that 7 is a factor of 91. Which other factor of 91 is shown by this equation?
1 37 )
____ 9 1
page 163
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27. 347
28. 1 6 R 34 )
____ 7 5
Check: 4 × =
+
Correct or not?
Todd’s answer correct because
the product plus the does not equal the dividend.
Use work area.
29. Which of these numbers is not a factor of 15?
A 1 B 2 C 3 D 5
30. 3n = 24
bought three packages of .
If she had 24 in all, how many were in each pack?
missing factor Divide.
n =
Use work area.
page 164
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• Reading Scales
New ConceptNew Concept
• Number lines can be horizontal, vertical, or curved.
• They can count by any number.
• To find points on number lines, split the difference:
1. Subtract the two numbers on both sides of the pointto find the difference.
2. Count the parts between the numbers.
3. Divide the difference by the number of parts.
4. Now count by that number.
Example
200 600
400
1. Subtract two adjacent numbers: 600– 400
200
2. Count the parts between the numbers: 4
3. Divide 200 by 4: 5 04 )
_____ 2 0 0
4. Now count by 50s: 400, 450, 500, 550
page 165
Teacher Notes:
• Introduce Hint #23 “Splitting the Difference.”
• Refer students to “Temperature” on page 2 in the Student Reference Guide.
• Display reference chart “Fahrenheit and Celsius Temperature Scales,” from Intervention Masters.
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Saxon Math Intermediate 5 170 Adaptations Lesson 27
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• The number line on a thermometer is a scale for measuring temperature.
Water boils.
Celsius Scale Fahrenheit Scale
room temperature
Water freezes.
100
20
0
212
32
68
FC
Lesson Practice a. Finish labeling this number line b. On the Celsius scale, what is five temperature from 0 to 100 degrees less than the freezing using tens: point of water?
1000
c. Points A and B on this number line indicate two numbers. Write the two numbers, using a comparison symbol to show which is greater and which is less.
50 1000
A B
50– 0
5 ) ___
00
A B
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Saxon Math Intermediate 5 171 Adaptations Lesson 27
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1. 408 mi Day 1 347 mi Day 2 419 mi Day 3 t altogether
408 + + = t
t =
Use work area.
2. Multiply the loop.
ft in.
1 __ = 5 __ t
5 × = t
t =
Use work area.
3. f total
purchased7 remained 27 7
f
f – = 7
f =
Use work area.
4. Multiply the loop.
$ cups 0.15 ____ 1 = m __
× $0.15 = m
m =
Use work area.
5. 1 _ 2 of Mahmood’s age = Colvin’s age
1 _ 2 of =
6. short division
864 ÷ 5 =
7. short division
$2.72 ÷ 4 =
8. short division
608 ÷ 9 =
9. parentheses first
378 ÷ (18 ÷ 3) =
Written PracticeWritten Practice page 167
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10. Split the difference.
100
90
80
70
60
F
80– 70
5 ) ___
00
– 13
15. 3864287672
+ m5350
5350
m =
16. Finish labeling this number line from0 to 50 using tens:
500
Use work area.
12. 3874× 6
13. 9063× 8
14. Split the difference.
200 400
60
400200
) ___
page 168
11. $52.60× 7
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17. The number 78 is between which of these pairs of numbers?
A 60 and 70 B 70 and 80
C 80 and 90 D 0 and 10
18. factors of 30
1 , , , ,
, , , 30
Use work area.
19. 405
22. Subtract to find the rule.
…, 160, 170, 180, ,
, ,…
Use work area.
25. Split the difference.
40 6020 80
60 40
) ___
20. In Khadija’s class, there is one more boy than there are girls. Which could not be the number of students in Khadija’s class?
Which number does not have a
remainder when divided by 2?
A 25 B 27 C 28 D 29
21. On the Celsius scale, what temperature is ten degrees below the freezing point of water?
See “Temperature” on page 2 of
the Student Reference Guide.
23. hundreds
537
24. 327,040
words:
Use work area.
page 168
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Written Practice,Written Practice, continued continued
26. Show three ways to write “24 divided by 3.”
÷ _____ ) _____
Use work area.
27. 1 4 R 27 )
_____ 1 0 0
Check: 14 × =
+
Correct or not?
Madeline’s answer is because the p
plus the r equals the dividend.
Use work area.
28. parentheses first
12 ÷ ( 6 ÷ 2 ) (12 ÷ 6) ÷ 2
12 ÷ ÷ 2
Does the Associative Property apply
to division? Use work area.
29. Use fraction-decimal-percent pieces for help.
3 ___ 10
= .
30. a. To find the number of centimeters, d the number of
m by .
b. ) _________
1 0 0
a. Use work area.
b.
page 169
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Saxon Math Intermediate 5 175 Adaptations Lesson 28
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2828 Teacher Notes:
• Introduce Hint #24 “Reading Clocks” and Hint #25 “Elapsed Time.”
• Refer students to “Time” on page 2 in the Student Reference Guide.
• For additional practice, students may complete Targeted Practice 28.
• Measuring Time and Elapsed Time
New ConceptNew Concept
• A half hour, or 30 minutes, later or earlier is a line directly across the clock from where the minute hand is pointing.
• Twelve hours later or earlier is the same time as now—only the a.m. or p.m. changes.
• Twenty-four hours later or earlier is exactly the same time as now, only the day before or after.
• Elapsed time is the amount of time between a starting time and an ending time.
Example
You started your homework at 4:00 p.m. and finished at 5:15 p.m. How long did it take?
4:00 p.m. 5:00 p.m. = 1 hour5:00 p.m. 5:15 p.m. = 15 minutes
1 hour and 15 minutes
Lesson Practice
a. Four centuries is how many years? number in each group × number of groups
b. According to the calendar on page 172, what is the date of the third Thursday in June 2014?
, month day year
page 171
Math Language
Use a.m. for the 12 hours before noon.
Use p.m. for the 12 hours after noon.
Midnight is 12:00 a.m.
Noon is 12:00 p.m.
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c. A leap year has how many days?
d. What is the name for 1 __ 10 of a century? 10 ) _____
e. Write the time that is 2 minutes after eight in the evening.
f. Write the time that is a quarter to nine in the morning.
g. Write the time that is 20 minutes after noon.
h. Write the time that is 30 minutes after midnight.
i. Write the time that is a quarter after nine in the morning.
j. If it is morning, what time is shown
by the clock? 3
121110
9
87 6 5
4
21
k. 2 hours later? Count forward 2 hours:
2 hours earlier? Count backward 2 hours:
l. The movie started at 3:15 p.m. and ended at 5:00 p.m. How long was the movie?
3:15 p.m. 4:15 p.m. = hours
4:15 p.m. 5:00 p.m. = minutes
hours and minutes
Lesson Practice, continued
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1. m had $600 rent
remaining 600 1267
m m − $600 = $
m = $
Use work area.
2. $1873 had
$ more t total
1873 200
t $1873 + $ = t
t = $
Use work area.
3. cards in each pile
piles
cards in all
4c = missing factor Divide.
c = ) _____
I divided by and got .
Use work area.
5. factors of 18: 1 , , , , , 18
factors of 24: 1 , , , , , , , 24
, , ,
4. 1 _ 2 of a decade years
Written PracticeWritten Practice page 174
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Written Practice,Written Practice, continued continued
8. parentheses first
528 ÷ (28 ÷ 7) =
9. 6w = 696
) ____
6 w
696
w =
11. half past noon 12. 1 _ 2 of a dollar $0.50
5 __ 10 of a dollar $0.
13.
SFTWTMS321
10987654171615141312112423222120191831302928272625
MAY 2042
May 10, 2042 is what day of the week?
14. largest 567
even
10. It is evening. What time is shown by this clock?
3
121110
9
87 6 5
4
21What time will it be in three hours?
time now:
Count forward 3 hours.
Use work area.
6. short division
543 ____ 3 =
7. short division
$6.00 _____ 8 =
page 175
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15. 43872965
+ 4943
16. $63.75
.....$ .00
17. 4010– f
563
563 f
4010
f =
18. 3408× 7
19. $3.56× 8
20. 487× 9
21. Use your student clock.
What time is 5 minutes before 9 in the morning?
22.
2 10
20
× × ) _____
) _____
Use work area.
page 175
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Written Practice,Written Practice, continued continued
23. 2 2 R 29 )
_____ 2 0 0
Check: 22 × =
+
Use work area.
24. …, 400, 500, 600, 700, ,
, , …
Use work area.
25. Split the difference. 00600040 )
____
40 6020 80
27. How many centuries equal a millennium?
100 years in a century× c centuries 1000 years in a millennium
28. How many fourths equal one whole? Use fraction-decimal-percent pieces for help.
29. a. one hour = minutes
b. half of an hour = minutes
c. 1 __ 2 =
Use work area.
30. See page 176.
A n + 29 = 50 B n = 29 + 48
C 29 + n = 48 D n + 48 = 29
26.
× =
page 176
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2929 Teacher Notes:
• Introduce Hint #26 “Multiplying by 10, 100, or 1000.”
• Review “ Multiplication Table” on page 5 in the Student Reference Guide.
• For additional practice, students may complete Targeted Practice 29.
• Multiplying by Multiplesof 10 and 100
New ConceptNew Concept
• To multiply a whole number by 10, attach a zero.
25 × 10 = 250
• To multiply a whole number by 100, attach two zeros.
25 × 100 = 2500
• When multiplying by multiples of 10, use offset multiplication:
1. Write the multiple of 10 as the bottom number.
2. Let the zero “hang out” (offset to the right).
3. Copy the zero into the answer.
4. Multiply.
zero “hangs out” Copy the zero. Multiply.
to the right
250× 30
250× 30
0
250× 30
750• When multiplying a money amount by a multiple of 10, put
two decimal places in the answer.
$3.755× 10
$37.50
$2.4000× 200
$480.00
page 177
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Lesson Practice
Use offset multiplication.
a. 34 × 20 340 × 20
b. 50 × 48 480 × 50
c. 34 × 200
×
d. 500 × 36
×
e. 55 × 30
×
f. $1.25 × 30
×
g. 55 × 300
×
h. $1.25 × 300
×
i. 60 × 45
×
j. $2.35 × 40
×
k. 400 × 37
×
l. $1.43 × 200
×
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1. missing factor Divide.
3c =
c = ) _____
Use work area.
2. 00$841 had00$ 75 tax00 m after
75 m
841
$841 – $ = m
m = $Use work area.
3. number in each group × number of groups
10 × = t
t =
Use work area.
4. 1845
one century
5. factors of 60:
1 , , , , , ,
, , , , , 60
Use work area.
7. Associative Property of Multiplication, then
offset
37 × 6 × 10 =
8. Offset.
46× 50
Written PracticeWritten Practice page 180
6. Offset.
37× 60
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Written Practice,Written Practice, continued continued
9. Offset.
$0.73× 60
10. parentheses first, then offset
50 × (1000 − 200) =
11. 356
12. Use your student clock.
30 minutes before noon
13. 1 _ 2 of a dollar $0.50
3 _ 4 of a dollar $ .
3 __ 10 of a dollar $ .
14. Offset.
38
×
15. 944,000
words:
Use work area.
16. 46372843
+ 6464
17. 4618– 2728
18. $60.00– $07.63
page 180
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19. short division
364 ÷ 10 =
20. 7w = 364
7 w
364
) _____
w =
21. short division
7 ) _________
3 6 4
Use work area.
23. According to this calendar, what is the date of the third Sunday in May 1957?
SFTWTMS4321
1110987651817161514131225242322212019
313029282726
MAY 1957 , month date year
Use work area.
24. The number 356 is between which pair of numbers?
A 340 and 350 B 350 and 360 C 360 and 370 D 370 and 380
25. …, 600, 700, 800, , , , …
Use work area.
page 181
22. ( × 2 ) + 1 =
whole number odd or even?
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Written Practice,Written Practice, continued continued
26. a. See “Tests for Divisibility” on page 20 of the Student Reference Guide.
A 205 B 502 C 250 D 202
b. is e , so 2 is a factor, and since it ends
in 0, is a factor.Use work area.
27. 4 3 R 17 )
_____ 3 0 0
Check: 43 × =
+
correct or not?
28. parentheses first
a. 12 – (6 – 2) (12 – 6) – 2
12 – – 2
b. Does the Associative Property apply to subtraction?
Use work area.
29. Use fraction-decimal-percent pieces for help.
5 ___ 10
= .
30. a. greatest to least
, , ,
b. Two stores with a cost difference of $1.30
and
Use work area.
page 181
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3030 Teacher Notes:
• Introduce Hint #27 “Naming Fractions/Identifying Fractional Parts.”
• Review “Fraction-Decimal-Percent Equivalents” on page 19 of the Student Reference Guide.
• Review reference chart “Fraction-Decimal-Percent Equivalents.”
• Interpreting Pictures of Fractions, Decimals, and Percents
New ConceptNew Concept
• Name how many parts are shaded out of a total number of parts.
25 is not shaded.
35 is shaded.
14 is shaded.
34 is not shaded.
• Just as one cent is one hundredth of a whole dollar ($0.01), one percent is one hundredth of a whole (0.01).
of a dollar is 50¢ or $0.50.
12
of a whole is 50% or $0.50 0.5.
12
of a dollar is 25¢ or $0.25.
14
of a whole is 25% or $0.25.
14
of a dollar is 10¢ or $0.10.
110
of a whole is 10% or $0.10 0.1.
110
Lesson PracticeUse fraction-decimal-percent pieces for help.
a. What fraction of the triangle is shaded?
b. What percent of the triangle is shaded?
c. What decimal part of the triangle is shaded? .
page 183
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d. What two fractions name the shaded part of this circle?
,
e. What percent of the circle is shaded?
f. What decimal part of the circle is shaded? .
g. What fraction of this rectangle is shaded?
h. What percent of the rectangle is shaded?
i. What decimal part of the rectangle is shaded? .
Name the percent of a dollar represented by the number of coins stated and write the value as a decimal number.
Number of quarters
Percent of a dollar
Value
4 quarters j.
3 quarters k.
2 quarters l.
1 quarter m.
Number of
dimesPercent of
a dollarValue
10 dimes n.
09 dimes o.
08 dimes p.
07 dimes q.
06 dimes r.
05 dimes s.
04 dimes t.
03 dimes u.
02 dimes v.
01 dime w.
Lesson Practice, continued
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1. 100 points on a quiz
division pointss other points
36 s
100
100 − = s
s = Use work area.
2. common year0031 days January
d left
31 d
365
−31 = d
d = Use work area.
3. Multiply the loop. Divide by the outside number.
quarts
______ cups 1 __ 1 = q ___
28
q = 28
q =
Use work area.
4. Multiply the loop.
$ _______ stamps
0.45 ____ 1 = m __ m
× $0.45 = m
m =
Use work area.
5. Draw two vertical lines that stay the same distance apart.
Use work area.
Written PracticeWritten Practice page 186
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Written Practice,Written Practice, continued continued
6. factors of 25:
, ,
factors of 50:
, , , , ,
, ,
7. a. fraction shaded?
b. fraction not shaded?
a.
b.
9. quarter to 8 in the morning 10. top missing Add.
w
− $19.46$28.93
19.46 28.93
w
w =
11. 3010− 1342
12. 28547591
+ 26
13. 7640× 30
14. $9.080× 60
8. denominator
2 __ 3
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15. short division
6 ) __________
$7 . 4 4
16. 362 ÷ 10 = 17. short division
R4 )
_________ 8 9 8
18. $42.37
$00.00
$00.00
+ $00.00
20. Commutative Property of
Multiplication, then offset
6 × 30 × 12 =
23. Which of these numbers is between 360 and 370?
A 356 B 367
C 373 D 381
24. …, 250, 260, 270, 280, ,
, , …
19. parentheses first
(48 × 6) − 9 =
21. Don’t count February.
February 1 September 1
22. 605
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Written Practice,Written Practice, continued continued
25. Split the difference.
40
30
C
40˚c
30˚c
) _____
27. two quarters
a. decimal part of a dollar:
.
b. percent of a dollar:
Use work area.
28. 100 ÷ 7 = 14 R 2
Check: 14 × =
+
correct or not?
29. 100 ÷ 4 100 ÷ 5
The more parts a number is divided into, the s the parts
will be, so 100 ÷ 5 is than 100 ÷ 4.
30. 2n = 20
At snacktime, each child in the class ate pieces of fruit. If 20
pieces of were eaten altogether, how many children
were in the ? n =
26. 1803
one decade
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page 189
Focus onFocus on• Fraction: Thirds, Fifths,
and Eighths
• To find a fraction of a number, divide by the denominator (bottom number).
1 _ 3 of a number Divide by 3.
1 _ 5 of a number Divide by 5.
1 __ 10 of a number Divide by 10.
Example
1 _ 3 of 24 83 )
____ 2 4
The survey has 120 questions.
1 _ 3 of 120 were true/false.
1 _ 5 of 120 were fill-in-the-blank.
1 _ 8 of 120 were short answer.
The rest of the 120 were multiple choice.
Stephanie answered 1 _ 2 of 120 in the first hour.
1. How many questions did Stephanie answer in 2 ) ________
1 2 0
the first hour?
Teacher Notes:
• Review Hint #15 “Fraction Manipulatives,” Hint #16 “Fraction of a Group, Part 1,” and Hint #17 “Percent.”
• Review “Fraction-Decimal-Percent Equivalents” on page 19 of the Student Reference Guide.
33Name
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I N V E S T I G A T I O N continued
2. How many questions were true/false? ) _____
1 2 0
3. How many questions were fill-in-the-blank? 5 ) ____
21
4. How many questions were short answer? ) ____
21
5. How many questions were multiple choice?
true/false 120 questions
fill-in-the-blank total
short answer multiple choice
total
6. Did the multiple-choice questions make up more than or less
than 1 _ 3 of the questions on the survey?
multiple choice 1 __ 3
7. Together, did the true/false and fill-in-the-blank questions make up more than or less than half of the survey?
true/false total half of 120
fill-in-the-blank
total
3
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8. Together, did the true/false and short-answer questions make up more than or less than half of the survey?
true/false total half of 120
short-answer
total
ActivityActivity page 190
Using Fraction Manipulatives
Use fraction pieces.
9. How many eighths equal one half?
10. How many tenths equal one fifth?
11. How many eighths equal a fourth?
12. Is two fifths more or less than one half?
13. Two fifths of a whole is what decimal part of a whole?
14. Three fifths of a whole is what decimal part of a whole?
15. Four eighths of a whole is what decimal part of a whole?
16. Can you make a half using only thirds?
17. Can you make a half using only fifths?
3
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I N V E S T I G A T I O N continued
18. If you had fraction pieces for sevenths, could you make a half using only sevenths? Why or why not?
, because the denominator is an number.
Half of an number is not a whole number of
fraction pieces.
19. Sarah has one half, one quarter, and one eighth. How much
more does she need to have a whole?
20. What single fraction piece equals 2 _ 8 ?
21. If you had a half made from eighths, could you take away three eighths? Why or why not?
because 1 _ 2 is the same as 4 _ 8 , and 3 _ 8 is
than 4 _ 8 .
22. What fraction is 1 _ 2 of 1 _ 2 ?
23. What fraction is 1 _ 2 of 1 _ 4 ?
24. What fraction is 1 _ 2 of 1 _ 5 ?
25. What fraction is 1 _ 2 of 1 _ 3 ?
Use fraction pieces to illustrate these addition and subtractions. Write a complete equation for each.
26. 1 __ 5 + 2 __ 5 1 _ 5 + 2 _ 5 = 00 __
00
3
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27. 3 __ 8 + 5 __
8 3 _ 8 + 00 __
00 = 00 __
00
28. 2 __ 3 − 1 __
3 2 _ 3 − 00 __
00 = 00 __
00
29. 5 __ 8 − 2 __
8 5 _ 8 − 00 __
00 = 00 __
00
Compare. Use fraction pieces for help.
30. 1 __ 8 + 1 __ 5 1 __
2
31. 1 __ 8 + 1 __
8 1 __
2
32. 1 __ 3 + 1 __
3 1 __
2
33. 1 __ 3 + 1 __
3 + 1 __ 5 + 1 __ 8 1
34. Arrange in order from least to greatest:
1 __ 2 , 1 __
8 , 1 __
5 , 1 __
3 , 1 ___
10 , 1 __
4
First compare 1 _ 2 with 1 __ 10 .
, , , , ,
least greatest
35. Arrange in order from least to greatest.
0.3, 0.125, 0.10, 0.50, 0.25, 0.20
, , ,
, ,
3
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I N V E S T I G A T I O N continued
Refer to your manipulatives or “Fraction-Decimal-Percent Equivalents” on page 19 of the Student Reference Guide.
36. One third of a whole is what percent of a whole?
37. Three fifths of a whole is what percent of a whole?
38. Four eighths of a whole is what percent of a whole?
Compare.
39. 2 __ 3 50% 40. 2 __
5 50%
3
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