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Saxon Math Course 1 L41-161 Adaptations Lesson 41
L E S S O N
41 Name ©
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Finding a Percent of a Number (page 216)
• You already know how to change a percent to a fraction. Rewrite the percent as a fraction with a denominator of 100 and reduce.
25% = 25
____ 100
= 1 __
4 5% =
5 ____
100 =
1 ___
20 150% =
150 ____
100 = 1
1 __
2
• To change a percent to a decimal, write the number as hundredths.
25% = 0.25 5% = 0.05 150% = 1.50
• To find a percent of a number:
1. Change the percent to a fraction or decimal.
2. Then solve.
Example: What number is 75% of 20?
Change the percent to a Change the percent to a fraction; then solve. decimal; then multiply.
is
__ of
3 __
4
___
20 = 15
Practice Set (page 218)
Write each of these percents as a reduced fraction.
a. 50% = b. 10% = c. 25% =
d. 75% = e. 20% = f. 1% =
Write the following percents as decimal numbers.
g. 65% = h. 7% = i. 30% =
j. 8% = k. 60% = l. 1% =
m. What number is 10% n. Find 25% of 48. o. How much money of 350? is 8% of $15.00?
is
__ of
1 ___
10
____
350 =
p. The sales-tax rate is 9 1
__ 2
%. Estimate the tax on a $9.98 purchase. How did you get your answer? 9 1
__ 2 %
rounds to % and $9.98 rounds to $ . % equals 1 ___
10 and
1 ___
10 times $ is $ .
q. Erika sold 80% of her 30 baseball cards. How many baseball cards did she sell?
80% = is
__ of
___
___ 30
Teacher Note:• Review “Fraction Decimal
Percent” on page 13 in the Student Reference Guide.
0.750× 20
15.00
$15 0.08
is __
of
1 __
4
___ =
Saxon Math Course 1 L41-162 Adaptations Lesson 41
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1. 80% of 20
Multiply the loop.
Divide by the outside number.
80% =
is
__ of
___
___
2. 8% of $8.50 $8.50 × $8.50
An 8% sales tax means
cents per dollar. $8.50 rounds to
$ ,so the tax should be close to
× = $ .
3. perimeter 4. Convert to a f ,
and m that number by .
5. 20 – = b
$20.00 9.18
6. 16 ∙ c = 288
Multiply the loop.
Divide by the outside number.
chairs
______ rows
___ ?
__ 1
7. average
126102
141
8. area
9. least to greatest
3 __
2 , 0, –1,
2 __
3
10. prime numbers
Written Practice (page 219)
, , , 2 , , , , , , ,
Use work area.
Saxon Math Course 1 L41-163 Adaptations Lesson 41
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11. Which does NOT divide 600?Use tests for divisibility.
A 2 B 3 C 5 D 9
12. win
____ loss
___
13. diameter 14.
a. parallel to Vine
b. perpendicular to Vine
15. Which is the measure of an acute angle?See the Student Reference Guide.
A 0° B 45° C 90° D 135°
16. (2.5)2 =
2.5 2.5
17. √___
81 = 18. reduced fraction
40% =
19. decimal number
9% =
$10 $10
20. reciprocal of 2
__ 3
Written Practice (continued) (page 220)
a.
b.
Saxon Math Course 1 L41-164 Adaptations Lesson 41
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21. 7m = 3500 22. $6.25 + w = $10.00
$10.00× $16.25
23. 2
__ 3 n = 1 24. x – 37 = 76
76× 37
25. 4.0 4.0
6.25 4.00
26. 3 3
__ 4
+ 2 3
__ 4
27. 4 __
4 –
3 __
3 = 28.
5 __
6 ∙
3 __
5 =
29. is
__ of
___
___ 48
30. estimate
9% %
$32.17 $
is
__ of
___
___
Written Practice (continued) (page 220)
m =
n = x =
w =
Saxon Math Course 1 L42-165 Adaptations Lesson 42
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Renaming Fractions by Multiplying by 1 (page 221)
• To rename a fraction means to give an equivalent fraction.
• Multiply the fraction by a fraction equal to 1. The new fraction will be an equivalent fraction.
Example: Write a fraction equal to 1 _ 2 that has a denominator of 20.
1 __
2 =
? ___
20
1 __
2 ×
10 ___
10 =
10 ___
20
• You can do this easily with fraction manipulatives.
• When you do not have manipulatives, try the loop method.
Example: 2 __
3 =
___
15 (2 ∙ 15) ÷ 3 = 10
2 __
3 =
10 ___
15
Practice Set (page 223)
a. 1
__ 3
=
___ 12
b. 2
__ 3 =
___
6
c. 3 __
4 =
___
8 d.
3 __
4 =
___
12
e. Shade 2 __
3 . Shade
1 __
4 .
Name each shaded rectangle as a fraction with a denominator of 12.
00
___ 12
00
___ 12
f. Write 2
__ 3 and
1 __
4 as fractions with denominators of 12. Then add the renamed fractions.
2
__ 3
=
___ 12
1 __
4 =
___
12
___
12 +
___
12 =
g. Describe how the rectangles you shaded in exercise e can help you add the fractions in f.
The shaded rectangles show the number of t in 2
__ 3
and 1
__ 4
. So I can count the
total number of t shaded fo find the s of the fractions.
h. Write 1
__ 6 as a fraction with 12 as the denominator. Subtract the renamed fraction from
5 ___
12 .
Reduce the subtraction answer.
1 __
6 =
___
12
5 ___
12
–
___ 12
=
Saxon Math Course 1 L42-166 Adaptations Lesson 42
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1. Answer with a mixed number.
1 __
2
2 __
3
___ 6
+
___ 6 =
2. two hundred billion
3. area
120 rounds to and times 40
is . This is close to my answer.
4. 40% of 30
40% =
is
__ of
___
___
5. 1 __
2 =
___
8 6.
1 __
2 =
___
10
7. 4.324.32
4.32
8. 6.300 4.030
9. (0.15)2 = 10. reciprocal of 6
__ 7
Written Practice (page 223)
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11. 12,345.8967.89
12. LCM of 3, 4, and 6
13. 5 3 __
5
+ 4 4 __
5
14. √___
36 – 4 2
__ 3
=
– 4 2__ 3
15. 8 __
3 ×
1 __
2 = 16.
6 __
5 ×
___ =
17. 1 1 _ 4
– 1 __
4
18. 10
___ 10
– 5
__ 5
=
19. 1 __
3 =
___
6
___
9
___
12 20. prime numbers
Written Practice (continued) (page 223)
, Use work area.
Saxon Math Course 1 L42-168 Adaptations Lesson 42
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21. estimate the average
12,643 9,870
14,261
Round the scores to , , and .
A the scores to get ; then
d by to find the average.
22. estimateCancel the matching zeros.
8176 41
Round 8176 to and 41 to . Then
d .
23. is
__ of
___
___
25. perimeter 26. area
27. fact family
r – d = s r – = s + = d + =
28. Divisor is .
Dividend is .
Quotient is .
29. 2 1
__ 2 hours after 11:45 p.m.
time now
Count hours.
Count minutes.
30. a. How many 5 __
6 s are in 1?
b. How many 5
__ 6
s are in 3?
Written Practice (continued) (page 224)
Regular
Fact Family
DiscountSale
Use work area.
_____
24. 3
__ 4 =
___
8
7 __
8
+ 7 __
8 Now subtract.
Use work area.
Use work area.
a.
b.
Saxon Math Course 1 L43-169 Adaptations Lesson 43
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Equivalent Division Problems Finding Unknowns in Fraction and Decimal Problems (page 225)
• If you multiply or divide the dividend and the divisor by the same number, the quotient does not change. You make an equivalent division problem.
• Short division is much easier than long division. With two-digit division problems, try to cut the numbers in half; then you have an easy short division problem.
Example: Make an equivalent division problem; then divide.
16 ) ______
1200 8 ) ______
6 0 40
Divide both numbers by 2. 7 5
• Finding unknowns with fractions and decimals is exactly the same as with whole numbers. See “Missing Numbers” in the Student Reference Guide.
Practice Set (page 228)
a. 5 1 __
3
(× 3) (× 3)
÷ =
b. Half of:
266 14
c. 5.d– d
3.2
5.0+ 3.2
d = d. f
– 1
__ 5
4 __
5
4 __
5
– 1
__ 5
f =
e. m
+ 1 1 __
5
40
4 4 __
5
– 1 1 __
5
m = f. 3 __
8 w = 1 w =
_____
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1. total cost
$120 $120
$120.00 $120.00
2. 150 – = d
150 128
3. 19.73 old record19.32 new record
4. 2
__ 3
=
___ 6
5. 1
__ 2 =
___
6 6.
2 __
3 n = 1
7. 6 – w = 1 4 __
5
6 3
__ 8
+ 1 4
__ 5
8. m – 4 1
__ 4 = 6
3 __
4
6 3 __
4
+ 4 1 __
4
9. c – 2.45 = 3
3.45+ 2.45
10. 12 – d = 1.43
12.43+ 11.43
Written Practice (page 229)
w = m =
c = d =
n =
Saxon Math Course 1 L43-171 Adaptations Lesson 43
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11. 5 __
8 ×
1 __
5 = 12.
3 __
4 ×
___ =
13. 3 7
__ 8
– 1 3 __
8
14. NOT primeSee the Student Reference Guide.
A 23 B 33 C 43
15. 2 __
2
2 __
2 ×
2 __
2 16. 12-yard loss
17. nine and twelve hundredths 18. 67, 4 92,384
19. 0.37 × 102
shift 0.3700 0
20. (0.6 × 0.4) × 0.2 =
Written Practice (continued) (page 229)
.
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21. perimeter 80 ft
each side
area
22. Answer with a reduced mix number.
100
23. a. Answer with a mixed number.
100
____ 16
(÷ 4)(÷ 4)
100
____ 16
=
b. 4 1 __
2
1 __
2
(× 2) (× 2)
÷
24. LCM of 4, 6, and 8
25. Complete the sequence of 1 ___
16 s.
Remember to reduce fractions.
... 1 __
4 ,
5 ___
16 , 3
__ 8
,
7 ___
16 , , ,
4 __ 16 6 __ 16 __ 16 __ 16
26. Measure to the nearest eighth of an inch.
27. What mixed number? 28. 1 __
2
___
10
1
__ 5
+
___ 10
29. 40% = of 20 seats
is
__ of
___
___
30. acute, right, or obtuse
a. angle A
b. angle B
c. angle C
d. angle D
Written Practice (continued) (page 229)
=
Use work area.
a.
b.
, ,
Saxon Math Course 1 L44-173 Adaptations Lesson 44
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Simplifying Decimal Numbers
Comparing Decimal Numbers (page 231)
• Zeros at the end of a decimal number do not change the value of the number.
0.3 = 0.300 = 0.3000
• To simplify decimal numbers:
Get rid of the extra zeros in front and back.
Keep the zero in front of the decimal.
Do not remove a zero that has value.
Examples:
02.0100 = 2.01
0.4200 = 0.42
• To compare decimal numbers:
1. Rewrite the numbers vertically and line up the decimal points.
2. Compare the greatest place value first (start on the left).
Example: 0.3 0.209 0.3 0.3 > 0.209 0.209
Practice Set (page 233)
Write these numbers in simplified form:
a. 0.0500 . b. 50.00
c. 1.250 . d. 4.000
Compare these decimal numbers:
e. 0.2 0.15 0.20.15
f. 12.5 1.25 12.501.25
g. 0.012 0.12 0.0120.120
h. 0.31 0.039 0.3100.039
i. 0.4 0.40 0.400.40
j. Write these numbers in order from least to greatest. 0.12, 0.125, 0.015, 0.2
, , ,
least greatest
Teacher Notes:• Review Hint #43, “Tenths and
Hundredths.”
• Overhead base-ten blocks available in the Adaptations Manipulative Kit may be used to show that tenths are greater than hundredths.
0.120.1250.0150.2
Saxon Math Course 1 L44-174 Adaptations Lesson 44
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Written Practice (page 233)
1. Multiples: Think times table.
( ) + ( ) =
third multiple third multiple
of 4 of 5
2. mi
___ ft
1 _____
5280
___
?
3. 29,035 Mt. Everest14,495 Mt. Whitney
4. Mt. Everest 5 miles in feet
5. 5 1 __
3 – w = 4
5 1 __
3 + 40
6. m – 6 4 __
5 = 1
3 __
5
6 4 __
5
+ 1 3 __
5
7. 6.74 + 0.285 + f = 11.025
6.740× 0.285
11.025× 11.025
8. 0.4 – d = 0.33
0.40× 0.33
9. 67 3
__ 4
1 1 __
4
with shoes 10. 8 1
__ 2
1
__ 2
(× 2) (× 2)
÷ =
w = m =
f = d =
Saxon Math Course 1 L44-175 Adaptations Lesson 44
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Written Practice (continued) (page 233)
11. thirty-two thousandths 12. is
__ of
___
___
13. a. 0.25 0.125
b. 25% 12.5%
14. standard notation
(6 × 100) + (4 × 1)
15. Multiply by 10: shift decimal point right
Divide by 10: shift decimal point left
10% equals the fraction . Find
of $36 by d $36 by .
shift $36.00
16. a. How many 5 __
8 s are in 1?
b. How many 5
__ 8
s are in 3?
17. LCM of 2, 3, 4, and 6. 18. (1 ∙ 3)2 =
19. 3 __
4 =
? ___
12 20.
2 __
3 =
? ___
12
0.250.125
.
a.
b.
a.
b.
Saxon Math Course 1 L44-176 Adaptations Lesson 44
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21. average
263742
43
22. nearest thousand
364,857
23. boys
_____ girls
___ = 24. a. factors of 100
b. prime numbers
25. fraction and decimal numbers
9%
26. 3 __
4
___
12
2 __
3 +
___
12
27. Nearly half of the r is shaded.
Since 1 _ 2 is equivalent to %, the shaded
part of the r is close to but
l than %.
29. closest to 1
A 0.1 B 0.8 C 1.1 D 1.2
30. What mixed number?
28. 10:30 a.m. to 2:15 p.m.
10:30 a.m. to =
to 2:15 p.m. =
Written Practice (continued) (page 234)
a.
b.
.
Saxon Math Course 1 L45-177 Adaptations Lesson 45
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Dividing a Decimal Numberby Whole Number (page 235)
• Decimal numbers divided by a whole number:
Put the first number inside the division box.
Put the second number in front of the box.
Put the decimal straight up on the answer line.
Use zero as a placeholder.
Put a digit above each digit.
Use short division.
Add zeros to the dividend and keep dividing until thereis no remainder.
Practice Set (page 236)
Teacher Note:• Review Hint #9, “Short Division.”
When dividing by a whole number,decimal goes straight up.
.
Example: 0.3 ÷ 4
4 ) _____
0. 3
0. 4 )
_____ 0. 3
0. 0 7 5
4 ) ________
0. 3 0 0
a. The distance from Margaret’s house to school and back is 3.6 miles. How far does Margaret live from school?
) ________
3. 6000
b. The perimeter of a square is 6.4 meters. How long is each side of the square? How can you check that your answer is reasonable?
sides
_______ meters
4
__ 0
1
__ ?
I can m my answer by .
× = 6.4.
c. 4.5
___ 3
d. 0.6 ÷ 4 e. 2 ) ______
0. 1 4
) _____
4. 5 ) ______
0. 6 0
f. 0.4 ÷ 5 g. 4 ) ________
0. 3 0 0 h. 0.012
______ 6
) ______
0. 4 0 ) ________
0. 0 1 2
i. 10 ) ______
1. 4 0 j. 0.7
___ 5
k. 0.1 ÷ 4
) ______
0. 7 0 ) ________
0. 1 0 0
Saxon Math Course 1 L45-178 Adaptations Lesson 45
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1. rule of reciprocals
5 __
3 × ? = 1
2. 1000
_____ 20
=
3. ( is __ of
00
___ 00
00
___ 00
) × 2 = 4. 3 ) _____
4. 5
5. 8 ) ______
0. 2 4 6. Add a zero.
5 ) _____
0. 8
7. LCMGo down the 2s, 4s, 6s, and 8s.
Find the first one in common.
8. √___
36 – m = 2 3 ___
10
9. g – 2 2 __
5 = 5
4 __
5
5 4
__ 5
+ 2 2
__ 5
10. m – 1.56 = 1.44
1.56+ 1.44
Written Practice (page 236)
m =
m =g =
Saxon Math Course 1 L45-179 Adaptations Lesson 45
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11. 32 – n = 5.39 12.
4 3 __
8
– 2 1
__ 8
13. 8 __
3 ∙
5 __
2 = 14. estimate
694 412
15. 0.7 × (0.6 × 0.5) = 16. 0.46× 0.17
17. 8 ∙ a = 177.6
miles
_______ gallons
177.6
______ 177.6
? __
1
18. is
__ of
00
___ 00
00
___ 00
19. 25% = is
__ of
00
___ 00
00
___ 00
25% is the fraction .
So I m
times $40.
20. 5 __
6 =
00 ___
12
– 7 ___
12
Written Practice (continued) (page 237)
n =
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21. area 36 ft2
a. each side Think square root.
b. perimeter
22. fraction and decimal numbers
27%
23. Measure length to the nearest eighth of an inch. 24. 75% =
is
__ of
00
___ 00
00
___ 00
25. 1 __
2 ×
2 __
3 =
1 __
3
1 __
3 ÷ =
2 __
3 ×
2 __
3 =
1 __
3
1 __
3 ÷ =
26. Since a little more than h the
circle is shaded, a little more than %
is shaded.
27. nine hundredths
a. fraction
b. decimal
28. 5 × 3 = 00
___ 00
1 __
3 × 3 =
29. students
___________ classrooms
? __
0
24 ___
1
30. 1
__ 2
mi = ft
yd ft
1 __
0
? __
0
Written Practice (continued) (page 237)
Use work area.
b. a.
b.
a.
Saxon Math Course 1 L46-181 Adaptations Lesson 46
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Writing Decimal Numbersin Expanded Notation
Mentally MultiplyingDecimal Numbers by 10and by 100 (page 239)
• The values of some decimal places are shown in this table:
• Write 4.025 in expanded notation this way:
(4 × 1) + ( 2 × 1 ___ 100 ) + ( 5 × 1 ____ 1000 ) The zero that acts as a placeholder is not included in expanded notation.
• To multiply by 10: Shift the decimal to the right one place.
• To multiply by 100: Shift the decimal to the right two places.
• To multiply by 1000: Shift the decimal to the right three places.
Examples: Shift right
1.234 × 100 = 123.4 7.8 × 100 = 780
Practice Set (page 241)
Write these numbers in expanded notation:
a. 2.05 ( × ) + ( × ) b. 20.5 ( × ) + ( × )
c. 0.205 ( × ) + ( × )
Write these numbers in decimal form:
d. (7 × 10) + ( 8 × 1 ___
10 ) e. ( 6 ×
1 ___
10 ) + ( 4 ×
1 ____
100 )
. .
Mentally calculate the product of each multiplication: shift
f. 0.35 × 10 = g. 0.35 × 100 =
h. 2.5 × 10 = i. 2.5 × 100 =
j. 0.125 × 10 = k. 0.125 × 100 =
Teacher Notes:• Review Hint #45, “Multiplying by
10, 100, or 1000.”
• Review “Multiplication and Division of Decimal Numbers by 10, 100, and 1000” on page 6 in the Student Reference Guide.
Saxon Math Course 1 L46-182 Adaptations Lesson 46
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Practice Set (continued) (page 241)
For the following statements, answer “true” or “false”:
l. If 0.04 is multiplied by 10, the product is a whole number.
m. If 0.04 is multiplied by 100, the product is a whole number.
Multiply as shown. Then complete the division.
n. 1.5
___ 0.5
× 10
___ 10
= 00
___ 00
= o. 2.5
_____ 0.05
× 100
____ 100
= 00
___ 00
=
1. Convert and reduce.
30
___ 8 =
2. 100.2 – = d
100.2× 098.6
3. Four and twenty is how many dozen? 4. decimal form
(5 × 10) + ( 6 × 1 ___
10 ) + ( 7 ×
1 _____
1000 )
5. fraction and decimal number
21%
6. reduced fraction
20% =
7. 5 ) ______
6. 3 5 8. Add zeros.
4 ) _____
0. 5
Written Practice (page 242)
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9. Add zeros.
8 ) _____
1. 0
10. x + 3 5 __
8 = 9
9 5
__ 8
× 3 5
__ 8
11. y – 16 1 __
4 = 4
3 __
4
16 1
__ 4
× 14 3 __
4
12. 1 – q = 0.235
1.000× 0.235
13. 26.9 + 12 + w = 49.25
26.9× 12.9
49.25× 49.25
14. whole area
50% = 1
__ 2
1
__ 2
of whole area?
15. ratio
dime
_______ quarter
000
____ 000
=
16. 0.25× 03.7
17. 3 __
4 =
? ___
12 18. LCM of 3, 4, and 8
Written Practice (continued) (page 242)
19. a. 1 ___
10 0.1
b. 0.1 (0.1)2
20. thousandths place
1,234.5678
x =
y = q =
w =
a.
b.
Saxon Math Course 1 L46-184 Adaptations Lesson 46
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21. estimate
3967 48
22. area
each side Think square root.
perimeter
23. 6 – 8 = ? 24. Cancel the 2 and the 4.
1 __
2 ×
4 __
5 =
25. Cancel the 3s.
( 3 __ 4 ) ( 5 __
3 ) =
26. circumference, radius, diameter
least
greatest
27. total cost
$6.95× $6.95
$6.95+ $6.95
28. Measure width to the nearest eighth of an inch.
29. a. How many 3 __
8 s are in 1?
b. How many 3
__ 8
s are in 3?
30. 1 __
2 = +
1 __
3
1
__ 3
= + 1
__ 3
Written Practice (continued) (page 243)
estimate
8% %
$6.95 $
0000
_____ 0000
Use work area.
a.
b.
Saxon Math Course 1 L47-185 Adaptations Lesson 47
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Circumference Pi (π ) (page 244)
Circumference Activity• Part One—How to measure the circumference of a circular object:
1. Cut a string the length of the diameter of the object.
2. Begin wrapping the string around the object.
3. Mark the object at the beginning and the end of the string.
4. Put the beginning of the string on the previous end mark; wrap and mark the object again.
5. Continue wrapping the string andmarking the object until you reachthe starting point.
6. From the marks you made, count how many times the string was used to wrap around the object.
Give a mixed number answer.
• Part Two—Measuring a circular object:
1. Get a circular object: can, plate, pie pan, etc.
2. Use a cloth tape measure to measure the circumference (around the object).
3. Measure the diameter.
4. Divide the circumference by the diameter. Use a calculator.
How many diameters equal a circumference?
5. If a circle has a diameter of 10 inches, estimate the circumference of the circle. inches
• The exact number of diameters in the circumference is a number between 3 and 4 called pi (π ).
• If the radius or diameter of a circle is known, the circumference can be found.
Multiply the diameter by π: C = πd
• Use 3.14 as an approximation for π: C = 3.14d
Practice Set (page 246)
a. In this lesson two formulas for the circumference of a circle are shown, C = πd and C = 2π r. Why are these two formulas equivalent?
The factors 2 and r in the second equation are equivalent to the d in the first e because
two radii equal one d . So t radii times π is equivalent to the d
times π.
Teacher Notes:• Review “Circle” on page 17 in the
Student Reference Guide.
• Students will need the following items to complete the activity: one or more circular objects (pie pan, plastic lid, trash can); string; scissors; a cloth tape measure; a calculator.
• Students may use this page rather than Activity Master 11.
Saxon Math Course 1 L47-186 Adaptations Lesson 47
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Practice Set (page 246)
Find the circumference of each of these circles. (Use 3.14 for π.) C = πd
b. c.
d. The diameter of a penny is about 3 __
4 of an inch (0.75 inch). Find the circumference of a penny.
Round your answer to two decimal places. Explain why your answer is reasonable.
If the d were one inch, the c would be about 3.14 inches. Since the
diameter is a little than one inch, the circumference should be a little than inches.
e. Roll a penny through one rotation on a piece of paper. Mark the start and the end of the roll. How far
did the penny roll in one rotation? Measure the distance to the nearest eighth of an inch.
f. The radius of the great wheel was 14 7 __
8 ft. Circle the number that is the best rough estimate of the
wheel’s circumference. Explain how you decided on your answer.
A 15 ft B 60 ft C 90 ft D 120 ft
estimate radius ft
estimate π
2 × estimate radius = × estimate π =
g. Use the formula C = 2π r to find the circumference of a circle
with a radius of 5 inches. (Use 3.14 for π.) Shift
1. tenth positive odd number
, , , , ,
, , , ,
4. A = bh
b = 8 h = 4
5. 3 ∙ 7 ∙ 2 ∙ 5 ∙ 2 ∙ 3 ∙ 3 ∙ 5
∙ ∙ ∙ ∙ ∙ ∙ ∙ least greatest
Written Practice (page 247)
1 3 5
2. 600 × h =
mi
___ hr
600
____ 1
000
____ ?
3. roses
_______ months
2
__ 1
00
___ ?
A = Use work area.
Saxon Math Course 1 L47-187 Adaptations Lesson 47
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c.
6. s = 1
__ 2
4s =
7. expanded notation
6.25
8. fraction and decimal number
99%
9. Add zeros.
12 ) ______
0. 1 8
10. shift
10 ) ________
1 2. 3 0
11. w ÷ √___
36 = 62
12. 5y = 1.25 13. n + 5 11
___ 12
= 10
10 11
___ 12
× 5 11
___ 12
14. m – 6 2
__ 5 = 3
3 __
5
6 2
__ 5
× 3 3
__ 5
15. 8 3 __
4
+ 5 3 __
4
16. 5
__ 3
× 5
__ 4
= 17. 3
__ 4
= ? ___
20
Written Practice (continued) (page 247)
18. 3__5
= ?___20
19. average closest to which number
18201820
+ 20
A 17 B 18
C 19 D 20
( × ) + ( 1 __ 3 ×
1 __
3 ) + ( 1 __
3 ×
1 __
3 )
w =
y = n = m =
Saxon Math Course 1 L47-188 Adaptations Lesson 47
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22. shift
6.25
S the decimal point one p
to the r .
24. 90% =
is
__ of
00
___ 00
? ___
40
25. 687 Mars365 Earth
26. Venus ) ______
Mars
Drop the remainder.
27. Measure length and width.
28. perimeter
29. 2
__ 5 =
00 ___
10
Subtract and reduce.
30. The numbers 1.5 and 1.50 are e . Attaching a
z to a decimal number does not shift place
v . To multiply 1.5 by 10, we may move the
d point one place to the r , which
shifts the place v and makes the product
.
23. shift Then divide.
1.25
_____ 0.5
∙ 10 ___
10 =
000 ____
000 =
Written Practice (continued) (page 248)
20. C = πd
The c of a circle is a
little than
times the diameter. My answer is a little
than × 20.
21. Here are the factors of 20. Cross off the factors that are NOT factors of 30.
1, 2, 4, 5, 10, 20
Use work area.
, , ,
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Subtracting Mixed Numbers with Regrouping, Part 1 (page 250)
• To subtract mixed numbers with regrouping:1. Borrow 1 from the whole number and rename.
2. Combine the top fraction with the renamed 1.
3. Then subtract.
Example: 5 1 __
3
– 2 2 __
3
45
1 __
3 +
3 __
3 = 4
4 __
3
– 2 2
__ 3
2 2 __
3
Practice Set (page 251)
a. 4 1 __
3
– 1 2 __
3
34
1 __
3 +
3 __
3 = 3
4 __
3
– 1 2 __
3
b. 3 2
__ 5
– 2 3
__ 5
23
2 __
5 +
5 __
5 = 3 4 _ 3
– 2 3
__ 5
c. 5 2
__ 4
– 1 3 __
4
3 4 _ 3
– 1 3 __
4
d. 5 1
__ 8
– 2 4
__ 8
3 4 _ 3
– 2 4
__ 8
e. 7 3 ___
12
– 4 10
___ 12
3 4 _ 3
– 4 10
___ 12
f. 6 1
__ 4
– 2 3
__ 4
3 4 _ 3
– 2 3
__ 4
g. Shade the bottom row of circles to complete the model of exercise a.
4 1
__ 3
– 1 2 __
3
3 4 __
3
– 1 2 __
3
=
=
h. Complete this word problem based on exercise c.
Allan had pot pies. He ate of them at lunch.
How pot pies were left?
Saxon Math Course 1 L48-189 Adaptations Lesson 48
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c.
1. ( + ) ÷ 2 = 10
sum
2. shift
$ ___
gal
2.279 ______
x
? ___
10
3. 11:45 a.m. to 12:45 p.m. = hr
12:45 p.m. to 1:20 p.m. = min
4. Which number is NOT equal to the others?
A 1
__ 2 B 0.2
C 0.5 D 10
___ 20
5. least to greatest 6.
7. 0.125 8. 3 2.1 = r
9. estimate
4967 8142 6890
10. 8 ) ________
0. 1 4 4
Written Practice (page 252)
0.10.20.3
0.4
Saxon Math Course 1 L48-190 Adaptations Lesson 48
1.02 0.102 0.12 1.20 0 –1
, , , , ,
3.1 2.1
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11. Add a zero.
6 ) ____
0.9
12. Add zeros.
4 ) ____
0.9
13. shift
$0.39
14. standard form
(5 × 10) + ( 6 × 1 ___
10 ) + ( 4 ×
1 ____
100 )
15. LCM of 6 and 8 16. w – 7 7 ___
12 = 5
5 ___
12
7 7 ___
12
+ 5 5 ___
12
17. 12 – m = 5 2 __
3
12 2
__ 3
+ 5 2 __
3
18. n + 2 3
__ 4 = 5
1 __
4
5 1 __
4
+ 2 3 __
4
19. x + 3.21 = 4
4.00+ 3.21
20. 2
__ 3
of 3
__ 4
=
Written Practice (continued) (page 252)
Saxon Math Course 1 L48-191 Adaptations Lesson 48
.
w =
m = n =
x =
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21. gains of 3 yd and 5 yd
loss of 12 yd
Use a negative number.
23. length
______ width
xxx
____ xxx
=
24. ft ___
in.
1 ___
xx
4 __
?
25. 1 ft × 1 ft = 1 sq. ft
12 in. × 12 in. = sq. in.
26. d = rt
r = 60 t = 4
27. 75% =
is
__ of
xx
___ x
xxx ____
x
28. 1 __
3 = +
x ___
12
1 __
4 =
+
x ___
12
29. shift Then divide.
3.5
___ 0.7
∙ 10
___ 10
=
Written Practice (continued) (page 252)
22. C = πd
π is a little than ,
so the answer should be about
× = .
Saxon Math Course 1 L48-192 Adaptations Lesson 48
30. The server can cut one of the whole p
into 6 _ 6 . Then there will be 2 and pies on the shelf.
The server can remove 1 and pies, and there will
be 1 and pies left on the s .
d =
Use work area.
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Dividing by a Decimal Number (page 254)
• Move the decimal over, over, and up.
• Use zero as a placeholder.
• Put a digit above each digit.
• Use short division.
• Add zeros to the dividend and keep dividing until there is no remainder.
Example: 0.13 ÷ 0.4
Practice Set (page 256)
a. 1.44
_____ 1.2
What would you multiply 1.2 by to make it 12?
b. 0.12 ) ______
0.144 What would you multiply 0.12 by to make it 12?
Make each divisor a whole number; then divide.
c. 0.4 ) _____
2.24 d. 0.3 ) ___
90 e. 0.05 ) _____
2.50 f. 0.3 ) _____
120
g. 0.24 ÷ 0.8 h. 0.3 ÷ 0.03 i. 0.05 ) ____
0.4 j. 0.2 ÷ 0.4
) _____
0.24 ) _____
0.30 0 ) _____
0.20
k. Find how many nickels are in $3.25 by dividing 3.25 by 0.05.
) _____
3.25
Teacher Note:• Review “Multiplication and Division
of Decimal Numbers by 10, 100, 1000” on page 6 in the Student Reference Guide.
0 0. 3 2 50.4 )
__________ 0. 1 3 0 0
over over
up
Saxon Math Course 1 L49-193 Adaptations Lesson 49
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c.
1. ( ) – ( ) = 2. is
__ of
x00
____ 000
____
100
3. area 4. perimeter
5. a. 0.31 0.301 b. 31% 30.1%
0.31 31% 0.301 30.1%
6.
7. 0.25 8. over, over, up
0.07 ) ______
3. 5 0
9. over, over, up
0.5 ) ______
1 2 0
10. Add zeros.
8 ) ______
0. 1 4
Written Practice (page 256)
Saxon Math Course 1 L49-194 Adaptations Lesson 49
2.2 in.
2.6 in.
b. a.
0.670.00
0.00
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11. 12. n – 6 1
__ 8
= 4 3 __
8
6 1
__ 8
+ 4 3 __
8
13. 4 __
5 =
x ____
100 14. 5 – m = 1.37
5.37+ 1.37
15. m + 7 1
__ 4
= 15
15 1
__ 4
+ 7 1 __
4
16. one and twelve thousandths
17. 5 7 ___
10
+ 4 9 ___
10
18. 5 __
2 ∙
5 __
3 =
19. 40% =
is
__ of
xx
___ xx
xx
___ xx
20. xx
___ 24
a. Eight hours is what fraction?
b. sleep
c. not sleep
Written Practice (continued) (page 256)
0.012 001.5
Saxon Math Course 1 L49-195 Adaptations Lesson 49
n =
m =
m =
a.
b.
c.
x =
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21. List the factors of 12.
Cross off the factors that are NOT factors of 18.
1 , , , , , 12
22. average
23. 51% %
$49.78 $
24. a. How many 3
__ 4 s are in 1?
b. How many 3 __
4 s are in 4?
25.
a. halfway between 1 and 2
b. closer to 1 than 2
c. closer to 2 than 1
27. over, over, up
0.25 ) _____
3.00
28. Measure a side to the nearest eighth of an inch. Then find the perimeter.
29. C = πd
Written Practice (continued) (page 257)
26. Cancel the matching factors.
2 ∙ 3 ∙ 2 ∙ 5 ∙ 7
______________ 2 ∙ 5 ∙ 7
=
Saxon Math Course 1 L49-196 Adaptations Lesson 49
30. Answer: Yes or No
Both 10
___ 10
and 100
____ 100
are e to 1. When we multiply a number
by different f names for one, the numbers may look
d , but they are e . So 2.5
___ 0.5
and 25
___ 5
and 250
____ 50
are three e problems with the s quotient.
, , ,
1.21.3
1.7
a.
b.
a.
b.
c.
Use work area.
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Decimal Number Line (Tenths) Dividing by a Fraction (page 259)
• We can locate decimal numbers on the number line.
• On a decimal number line, each tick mark is one tenth from the next.
Example:
y = 7 4 ___
10 y = 7.4
• To divide by a fraction, use two steps:
Original problem: How many 3 _ 4 s are in 6? 6 ÷ 3
__ 4
Step 1: Find the number of 3 _ 4 s in 1. 1 ÷ 3
__ 4
= 4
__ 3
(reciprocal)
Step 2: Use the number of 3 _ 4 s in 1 to 6 × 4
__ 3
= 24
___ 3
find the number of 3 _ 4 s in 6. Then simplify the answer.
24 ___
3 = 8
Practice Set (page 261)
To which decimal number is each arrow pointing?
g. Write and solve a fraction division problem to find the number of quarters
in four dollars. Use 1 __
4 instead of 0.25 for a quarter.
Follow this pattern.
Original problem: 4 ÷ 1 __
4
Step 1: 1 ÷ =
Step 2: 4 × =
h. Write and solve a fraction division problem for this question:
Pads of writing paper were stacked 12 inches high on a shelf. The thickness
of each pad was 3 __
8 of an inch. How many pads were in a 12-inch stack?
Original problem: 12 ÷
Step 1: 1 ÷ =
Step 2: 12 × =
Saxon Math Course 1 L50-197 Adaptations Lesson 50
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Saxon Math Course 1 L50-198 Adaptations Lesson 50
1. 1 + 3 + 5 = 9 1 + 3 + 5 + 7 + 9 = 25
32 = 9 52 = 25
102 =
I found a pattern.
2. 6 ÷ 3 __
8
reciprocal of 3 __
8
6 __
1 ×
xx ___
x =
3. (3 × ) + = 4. a. 3.4 3.389 b. 0.60 0.600
3.4 0.60 3.389 0.600
5. 7.25 + 2 + w = √_____
100
7.25+ 2.25
6. 6w = 0.144
7. w + 5 ___
12 = 12 8. 6
1 __
8 – x = 1
7 __
8
6 1
__ 8
+ 1 7
__ 8
9. total cost
$20.00$020.00
$20.00$020.00
10.
Written Practice (page 262)
b. a.
w = w =
w = x =
1.00 1.00
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Saxon Math Course 1 L50-199 Adaptations Lesson 50
11. over, over, up
0.12 ) _____
7.20
12. over, over, up
0.4 ) ___
70
13. 6 ) ______
0.138 14.
15. 3 __
4 =
? ___
24 16. 4.637
85.21
17. 1 m × 1 m = 1 sq. m100 cm × 100 cm = sq. cm
18. LCM of 6 and 9
19. 6 5 __
8
+ 4 5 __
8
20. 8
__ 3
∙ 3 __
1 =
Written Practice (continued) (page 262)
3.75+ 02.4
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Saxon Math Course 1 L50-200 Adaptations Lesson 50
21. 2
__ 3 ∙
3 __
4 =
23. average
2.46.3
5.7
24. over, over, up
) _____
8.75
25. What decimal number? 26. Cancel the matching factors.
2 ∙ 3 ∙ 5 ∙ 7
__________ 2 ∙ 5
=
27. 0.375 × 100 = 28. 1
__ 3
= xx
___ 6
Subtract and reduce.
29.
a. halfway between 6 and 7
b. 6 7 ___
10
c. closest to 6
30. Which is divisible by both 2 and 5?Use tests for divisibility.
A 552 B 255 C 250 D 525
Written Practice (continued) (page 262)
22. C = πd
π is a little
than , so my
answer should be about
× = .
quarters
a.
b.
c.
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