LESSON
71
Name
Percent Change
of Dimensions (page 479)
We calculate the dimensions of a dilation or reduction by
finding the percent of increase or decrease.
• A dilation (size increase) or a reduction (size decrease) makes
similar figures.
Teacher Notes:
• Review Hint #47, “Scale Factor.”
• Review “Scale Factor” on page 31
in the Student Reference Guide.
• Similar figures have proportional measures (radius, side length,
or diameter).
• The ratio of similar measures is the scale factor.
The perimeters of similar figures are related by the scale factor.
The areas of similar figures are related by the scale factor squared.
The volumes of similar figures are related by the scale factor cubed.
• For percent change problems, change percents to decimals.
• The original figure is always 100%.
To find a percent increase, find the percent of the new figure and subtract 100%.
To find a percent decrease, find the percent of the new figure. Then subtract it from 100%.
Example: The towel shrunk 10% when it was washed. The area of the towel was reduced by
what percent?
The original towel is 100%.
The dimensions decrease by 10%.
100% 10% 90%
90% 0.9
(0.9)2 0.81
0.81 81%
100% 81% 19%
original decrease new
change to a decimal for scale factor
Area is scale factor squared
Change to a percent
Percent decrease (subtract from 100%)
Example: If the dimensions of a cube are increased 100%, by what percent is the volume increased?
© 2007 Harcourt Achieve Inc.
We draw a sample cube that has sides 1 inch long. A 100% percent increase means
that the new figure is 200% of the old figure, so the side length doubles. The new cube
has sides 2 inches long.
1 in.
2 in.
The cubes are similar figures and the scale factor is 2.
Saxon Math Course 3
L71-415
Adaptations Lesson 71
The volume is related by the scale factor cubed:
3
2 8
The volume of the larger cube is 8 times (800%) the volume of the smaller cube.
The smaller cube is 100%, so the volume increased by
800% 100% 700%
Practice Set (page 482)
a. There are two concentric circles on the playground. The diameter of the larger circle is 40% greater
than the diameter of the smaller circle. The area of the larger circle is what percent greater than the
area of the smaller circle?
smaller circle 100%
larger circle 100% 40% 140%
Change 140% to a decimal. This is the scale factor.
The area is related by the scale factor squared.
2
(scale factor) Change that number back to a percent:
percent greater %
% 100% b. Becky reduced the size of the image on the computer screen by 40%. By what percent was the area
of the image reduced?
original image 100%
new image 100% 40% %
Change this percent to a decimal:
The area is related by the scale factor squared.
2
(scale factor) percent reduction 100% %
% y
c. Square ABCD has vertices at A(4, 4), B(4, 4), C(4, 4), and
D(4, 4). If it is dilated by 150%, then by what percent would the
perimeter increase? By what percent would the area increase?
D
A
x
150% increase is scale factor 1.5. Multiply each coordinate by 1.5
to draw square ABCD. For instance A(4, 4) 1.5 A(6, 6).
C
B
The perimeter is related by the scale factor.
scale factor 150%
percent increase in perimeter Saxon Math Course 3
% 100% L71-416
Adaptations Lesson 71
© 2007 Harcourt Achieve Inc.
Change that number back to a percent:
Practice Set (continued) (page 482)
The area is related by the scale factor squared.
scale factor 150% 1.5
2
(scale factor) Change that number back to a percent:
percent increase in area %
% 100% d. Suppose the dimensions of the larger cube in the example were increased by 100%.
What would be the edge length of the expanded cube?
100% increase is a doubling.
The volume of the expanded cube would be what percent of the 2 inch cube?
original increase 100% 100% 200%
Change 200% to a decimal:
The volume is related by the scale factor cubed.
3
(scale factor) Change that number back to a percent:
The volume of the expanded cube is
%
% of the volume of the 2-inch cube.
The problem asked for the percent, not the percent increase.
Written Practice
1.
Ratio
(page 483)
2.
Actual count
Pencils
p
Did not watch
Total
© 2007 Harcourt Achieve Inc.
Actual count
Watched
Pens
3.
Percent
Total
Percent
Original
Actual count
s
P
1
3
2
6
5
15
100
Change(+)
New
4.
d
100
P
__
s
s side length P perimeter
Is this direct variation?
What is the constant?
2470
What type of polygon is this?
equilateral
50 150
Use work area.
Saxon Math Course 3
L71-417
Adaptations Lesson 71
(continued) (page 483)
Written Practice
6. y 2x 2
5.
y mx b
7
y
5
5
6
5
4
3
2
1
y
x
x
3
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
y
x
1 2 3 4 5 6
7.
45°
This is not direct variation because the
10
45°
10
line
.
Use work area.
8. a. decimal
Use 3.14 for π.
Area of circle
Area of square
106% b. fraction
a.
106% c.
1.06
21
b.
c.
9. number cube
P(3 or more) 10. dimensions increased by 10%
new original increase
100% % %
change to a decimal :
2
(Scale factor) Change to a percent :
percent increase Saxon Math Course 3
L71-418
% 100% Adaptations Lesson 71
© 2007 Harcourt Achieve Inc.
Area is scale factor squared
(continued) (page 484)
Written Practice
11. 7 x 5
12.
143
x
5
4
3
2
1
0
1
2
3
4
5
z y
Use a dot.
x
mj z m
14. ____
sec
13. Put the numbers in order.
1.1, ,
a.
,
,
,
min
50 sec
Cancel.
1.0
b. mean:
mode:
1.5
2.0
median:
range:
c.
Use work area.
16. ^ ABC 100%
15. A(2, 2), B(2, 2), C(0, 2)
1
scale factor __
3
1
What percent is __?
3
Find ^ ABC with scale factor 3.
© 2007 Harcourt Achieve Inc.
m
____
100 m ______
_______
1.9
,
to
A(6, 6) B(
,
) C(
,
)
Use work area.
Saxon Math Course 3
L71-419
Adaptations Lesson 71
Written Practice
(continued) (page 484)
15x2y 1
17. _______ 5xy
5
2
4
18. __ __ __ 5
3
6
19. 3 (4) (5) 1.2 0.24
20. ___________ 0.3
2
11
1
21. __ __x ___
3
12
4
15
3
22. __ ___
x
4
x
23. 0.02x 0.3 1.1
24. 6x 12 84
x
25.
See the top of page 485.
Total members 60
4 members did not rent
1, 2, 3, or 4 movies
x
© 2007 Harcourt Achieve Inc.
x
Saxon Math Course 3
L71-420
Adaptations Lesson 71
LESSON
72
Name
Multiple Unit
Multipliers (page 486)
Sometimes we use more than one unit multiplier to convert
measures and rates.
Teacher Note:
• Review “Multiple Unit Multipliers”
on page 23 in the Student
Reference Guide.
• To convert units of area, use two unit multipliers. The units will
cancel.
2
2
Example: Convert 855 ft to yd .
1 yd
Use the unit multiplier ____ twice.
3 ft
1
yd
1
yd
2
2
855 2
855 ft · ____ · ____ ____ yd 95 yd
9
3 ft 2 3 ft
ft and ft cancel ft .
• To convert units of volume, use three unit multipliers. The units will cancel.
3
3
Example: Convert 216 ft to yd .
1 yd
Use the unit multiplier ____ three times.
3 ft
1
yd
1
yd
1 yd
3
3
216 3
216 ft · ____ · ____ · ____ ____ yd 8yd
27
3 ft
3 ft 3 3 ft
ft and ft and ft cancel ft .
• To convert both units in a rate, use two unit multipliers.
• The units will cancel and leave only the correct units in the answer.
Example: Convert 440 yards per minute to miles per hour.
Both units are changing: yards to miles and minutes to hours.
440 yd
60 min
2640 mi
1 mi
mi
_______
· _______ · ________ ________ 15 ___
1 min
1 hr
1760 yd
176 hr
hr
© 2007 Harcourt Achieve Inc.
Cancel matching zeros.
• Cancel numbers and units as you go.
Saxon Math Course 3
L72-421
Adaptations Lesson 72
Practice Set (page 488)
a. Look at problems b–h. Decide if you will use 2 or 3 unit multipliers for each problem.
Write the letter of each problem in the appropriate blanks.
Two unit multipliers for area or changing both units in a rate.
Three unit multipliers for volume.
2 unit multipliers:
,
3 unit multipliers:
,
,
,
,
Use multiple unit multipliers to perform each conversion.
b. 9 sq. ft to sq. in.
2
12 in. 12 in.
9 ft · _____ · _____ 1 ft
1 ft
in.
2
c. 9 sq. ft to sq. yd
yd
yd
2
9 ft · ______ · ______ ft
ft
3
d. 1 m to cm
3
3
3
100 cm 100 cm 100 cm
1 m · _______ · _______ · _______ 10 cm
1m
1m
1m
3
e. 1,000,000 mm to cm
3
3
cm
cm
cm
1,000,000 mm · _______ · _______ · _______ mm
mm
mm
f. 12 dollars per hour to cents per minute
100 cents
12 dollars _______
1 hr
_________
·
· _________ 1 hr
60 min
1 dollar
cents/min
g. 10 yards per second to feet per minute
10 yd
sec
ft
______
· ________ · _______ 1 sec
min
ft/min
yd
h. 1 gallon per day to quarts per hour
1 gal
______
· _____ · _____ qt/hr
© 2007 Harcourt Achieve Inc.
1 day
Saxon Math Course 3
L72-422
Adaptations Lesson 72
(page 488)
Written Practice
1.
Ratio
Actual count
Fish
2.
f
No Bands
Total
Total
Original
Actual count
100
t
Bands
Ducks
3.
Percent
Percent
Actual count
100
b
4.
y
__
x
x
y
6
22
15
165
18
176
22
___
Change (+)
New
11
___
3
6
165
____
15
176
____
18
The r
is not constant
so this
yd
mi
6. ___ to ____
min
hr
5.
smaller
_______
1 hr
7
8
yd
hr
21 mi
______
· ________ · _______ larger
12
a
© 2007 Harcourt Achieve Inc.
direct variation.
min
mi
6
b
a.
b.
Saxon Math Course 3
L72-423
Adaptations Lesson 72
(continued) (page 489)
Written Practice
yd
ft
7. ____ to ____
sec
min
y
1x
8. y __
2
6
5
4
3
2
1
yd
90 ft
min
______
· _______ · ______ sec
1 min
ft
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
x
1 2 3 4 5 6
This is direct variation because the graph is
a
that goes through the
o
.
Use work area.
9. area
10. a. decimal
1
33 __ % 3
13
12
b. fraction
1
33 __ % 3
a.
b.
c.
11.
a. U HHH , HHT , HTH , HTT ,
z
85
y x
,
,
, TTT V
b. P ( 2 or more H ) mj x c. If the coin is flipped four times instead,
does P ( 2 or more H ) increase
or decrease?
mj y mj z Saxon Math Course 3
Use work area.
L72-424
Adaptations Lesson 72
© 2007 Harcourt Achieve Inc.
12. Coin flipped 3 times
(continued) (page 489)
Written Practice
13.
$85.97
14. standard form
shift
2.5 105 8 a 2 b1c
16. ________
6 a b 2c
15. Factor:
a.
7x2 35x 14 b.
3x 15 a.
b.
3
1
17. __ __ 2
4
18. x y x 3 2 19. 0.12 (0.6)(0.02) 2 2
1
20. 2 __ t __
3
3
© 2007 Harcourt Achieve Inc.
( )
t
Saxon Math Course 3
L72-425
Adaptations Lesson 72
Written Practice
(continued) (page 490)
6
x
22. __ __
9
6
21. 0.9x 1.3 0.5
x
23. 2(x 7) 4 24
x
24. x 5 3
–5
–4
–3
x
–2
–1
0
1
2
3
4
5
x
25. neither
Round to the nearest whole number.
© 2007 Harcourt Achieve Inc.
% of 680.
Saxon Math Course 3
L72-426
Adaptations Lesson 72
LESSON
73
Formulas for Sequences
Name
(page 491)
A sequence is an ordered set of numbers, called terms, that follows a rule.
• Every term in a sequence has a position and a value.
The position, n, is the term’s place in the sequence, such as 1st, 2nd, or 3rd.
The value, a, of a term is the number.
• A formula for a sequence uses the variables n and an to describe the sequence.
• If the formula is known, we can substitute a term’s position into the formula to find the value
of that term.
n
Example: The formula an 2 describes the sequence {2, 4, 8, 16, …}.
Find the tenth term in this sequence.
Substitute 10 for n and solve with a calculator.
10
a10 2 1024
• If the formula or rule is not known, find a pattern in the terms.
Example: What is the rule for this sequence?
{1, 2, 2, 1, 3, 0, 4, …}
The pattern subtracts 3 and then adds 4.
3 4 3 4 3 4 3 4
1, 2, 2, 1, 3, 0, 4, 1, 5
Practice Set (page 493)
a. What is the 7th term in this sequence?
1, 4, 9, 16, …
Look at the circled numbers in the “Multiplication Table” on page 3 of the Student Reference Guide.
Now find the 7 th term.
b. The following sequence has the rule an 5n 2. Find the tenth term.
3, 8, 13, 18, …
© 2007 Harcourt Achieve Inc.
a10 5(10) 2 c. Circle the formula that generates the terms of the following sequence.
0, 3, 8, 15, …
A an n 1
B an 2n 1
C an n2 1
d. Substitute 1, 2, 3, and 4 for n to find the first four terms in the sequence with the formula
an n2 2n 1.
a1 a2 Saxon Math Course 3
a3 a4 L73-427
Adaptations Lesson 73
Practice Set (continued) (page 494)
e. Write another formula that generates the same first four terms as the sequence in problem d.
an (
)2
Compare the terms in the sequence in problem d to the terms of the sequence in problem a.
n ( n 1)
f. Triangular numbers are found with the formula an _________
2
Find the 20th triangular number.
20(20 1)
a20 ___________ 2
Written Practice
(page 494)
1. new original increase 100% % 2.
%
Percent
Actual count
100
t
Volunteered
Change to a decimal.
Did not
Area is the square of the scale factor.
2
(scale factor) 3.
Change to a percent.
% 100% Percent
Original
Actual count
4.
100
Change (–)
New
n
W
D
4
20
7
35
9
45
D
___
Is this direct variation?
W
constant 6 10
5. average of bases: ________ 2
yd
ft
6. ____ to ____
sec
sec
6 yd
_____
______ 3 sec
Saxon Math Course 3
L73-428
Adaptations Lesson 73
© 2007 Harcourt Achieve Inc.
increase Total
(continued) (page 494)
Written Practice
mi
ft
7. ____ to ___
min
hr
8. y x 5
y
6
5
4
3
2
1
440 ft _________
0000 min _________
00000 mi
______
1 min
0000 hr
00000 ft
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
x
1 2 3 4 5 6
Use work area.
9. Each triangle has the same area.
10. a. decimal
_______
12 )1.0000
5
6
6
b. percent
a.
5
1
c. ___
12
1
___
b.
10
c.
11. Factor:
12. perimeter and area
A bh
a. 4x2 12x 4 Opposite sides have equal length.
b. 2x 16 5 in.
4 in.
8 in.
© 2007 Harcourt Achieve Inc.
a.
b.
___
14. √39 is between which whole numbers?
13. perimeter and area
2 cm
32 3 cm
15 cm
Saxon Math Course 3
L73-429
42 52 A 3 and 4
B 4 and 5
C 5 and 6
D 6 and 7
62 72 Adaptations Lesson 73
Written Practice
(continued) (page 495)
24 m 4 b 1
16. _________
18 m 3 b 3
15. $4 is always charged.
$0.85 charges per pound.
2
1
1
18. __
__ x __
3
6
2
17. (3)1 (2)2 40 x
6
4
20. __ __
3
x
1 __
1
4 x ___
19. __
5
10
2
x
3 x 12
21. __
4
x
22. 0.09x 0.9 2.7
x
23. 3(2x 1) 45
x
24. an 2n 3
a20 a20 x
25. It cost $
for admission to the Carnival and $
proportional if there was no cost for
for each ride. The graph would be
.
Use work area.
Saxon Math Course 3
L73-430
Adaptations Lesson 73
© 2007 Harcourt Achieve Inc.
Find the 20th term.
LESSON
74
Name
Simplifying Square
Roots (page 496)
A perfect square is a number that is the product of a
number times itself.
• The first few perfect squares are shown circled on the
“Multiplication Table” in the Student Reference Guide on
page 3.
• Because perfect squares have two identical factors, their
square roots are easy to find.
__
__ __
√4 √2 √2 2
4 2 2
___
__ __
81 9 9 √81 √9 √9 9
Teacher Notes:
• Introduce Hint #54, “Simplifying
Square Roots Using Prime
Factorization.”
• Refer students to “Using Prime
Factorization to Find Square
Roots” on page 24 in the Student
Reference Guide.
• Review “Multiplication Table” on
page 3 and “Laws of Exponents”
on page 19 in the Student
Reference Guide.
• The product property of square roots states that square
roots can be factored and multiplied.
___
__ __
__
√12 √4 √3 2√3
___
__ __
__
√18 √9 √2 3√2
• Use the multiplication table to look for perfect squares that divide evenly into the factors of square
roots. The perfect squares can be factored out as whole numbers and the square root is simplified.
____
Example: Simplify √600
100 is a perfect square and factor of 600.
____
____ __
__
√600 √100 √6 10√6
___
Example: Simplify √72
Look for perfect squares on the “Multiplication Table.”
___
__ ___
√72 √4 √18
___
__
factor out √ 4
__
2√18
rewrite ( √4 2 )
___
__ __
2√18 2√9 √2
__
__
2 3√ 2 6√2
__
factor out √ 9
__
rewrite ( √9 3 )
© 2007 Harcourt Achieve Inc.
• If a problem asks for an exact answer, give the simplified square root.
• If a problem asks for an approximate answer, simplify the square root and
then use a calculator to multiply by one of these approximations:
Saxon Math Course 3
L74-431
Approximate Values
of Square Roots
Square
Root
Approximate
Value
22
1.41
23
1.73
25
2.24
210
3.16
Adaptations Lesson 74
Practice Set (page 499)
Simplify. One of the square roots below cannot be simplified.
___
__ __
___
__
a. √20 √4 √5 __ __
___
b. √24 √4 √6 √5
___
e. √125 ___
h. √90 d. √30 g. √50 __ __
c. √27 √9 √3 ____
f. √48 ___
___
i. √1000 _____
j. Use a calculator and the numbers in the table of square root approximations to calculate to the
nearest tenth the values of the square roots in problems g, h, and i.
___
g. √50 ___
h. √90 _____
i. √1000 k. Jenny folded a 10-inch square piece of paper in half diagonally, making a triangle. What is the length
of the longest side of the triangle? Give an exact answer and an approximate answer:
approximate:
exact:
It is a 45-45-90 triangle.
c
10 in.
10 in.
l. Which square root in problems a–i could not be simplified? Why?
Written Practice
1.
players
basketballs
_____
s
.
(page 500)
_____
2.
Percent
Original
Change (+)
Actual Count
100
n
New
Saxon Math Course 3
L74-432
Adaptations Lesson 74
© 2007 Harcourt Achieve Inc.
because none of the factors are p
Written Practice
(continued) (page 500)
3.
Actual Count
Percent
Original
4.
100
Change ( – )
New
n
x
y
0
0
1
3.1
2
6.2
3
9.3
y
__
x
Is this direct
variation?
Constant:
smaller 6. _______
larger
5.
b
9
6
10
Area is related by (scale factor) 2.
a
12
a
b
7. Factor perfect squares.
_____
___
___ __
8. √18 √00 √2 ___ ____
© 2007 Harcourt Achieve Inc.
√2500 √25 √100 ___
___ __
9. √75 √00 √3 Saxon Math Course 3
36 x 3 y 1
10. ________
24 x 2 y 2
L74-433
Adaptations Lesson 74
Written Practice
(continued) (page 500)
12. y 3x 1
11. in.3 to ft3
000ft ______
000ft ______
000ft 86,400 in.3 ______
000in. 000in. 000in.
Is ( 2,5 ) a solution?
y
6
5
4
3
2
1
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
x
1 2 3 4 5 6
Use work area.
14. a. decimal
13. Find the 12th term.
an n( n 1 )
________
15 ) 4. 0 0 0
a12 b. percent
c.
of the
athletes had
played in the
finals.
a.
b.
a12 c.
2 (area of circle)
16. __
6
15. Factor:
a. 6x2 30x 18 b. 2x3 2x Use 3 for π.
A 108 in.2
B 36 in.2
C 12 in.2
D 4 in.2
a.
b.
Saxon Math Course 3
L74-434
Adaptations Lesson 74
© 2007 Harcourt Achieve Inc.
12 in.
Written Practice
(continued) (page 501)
17. new original increase 100% %
Change to a decimal:
18. perimeter and area
A bh
Area is related by scale factor squared.
( scale factor )2 15 cm
12 cm
Change to a percent:
increase 20 cm
% 100% 3
2
11
20. __
__x ___
3
12
8
19. a. A bh
13 m
13 m
12 m
13 m
13 m
b. See page 18 in the Student Reference Guide.
a.
5
x
21. __
___
12
9
© 2007 Harcourt Achieve Inc.
x
b. r
4 m 8
22. __
3
x
23. 0.07 0.003x 0.1
m
24. 4x x 7 5
x
Saxon Math Course 3
x
L74-435
Adaptations Lesson 74
Written Practice
(page 500)
25. Label the front, top, and right-side views.
© 2007 Harcourt Achieve Inc.
Use work area.
Saxon Math Course 3
L74-436
Adaptations Lesson 74
LESSON
75
Area of a Trapezoid (page 502)
Name
b1
A trapezoid is a quadrilateral with one pair of parallel sides.
The parallel sides are called the bases, b1 and b2.
h
The perpendicular distance between the bases is the height, h.
b2
• To find the area of a trapezoid, multiply the average of the bases by the height.
1
A __ (b1 + b2 ) h
2
Example: Find the area of this trapezoid.
8 ft
12 ft
The bases are 24 ft and 8 ft. The height is 12.
32 12
1
1
A __ (b1 b2 ) h __ (24 8)(12) _______ 192 ft 2
2
2
2
24 ft
Practice Set (page 504)
Find the area of each trapezoid.
1
A __(b1 b2)h
2
3 in.
10 cm
10 cm
a.
8 cm
b.
16 cm
4 in.
7 in.
© 2007 Harcourt Achieve Inc.
1
A __(10 16)(8) 2
8 ft
c.
6 ft
1.6 m
d.
1.4 m
2 ft
Saxon Math Course 3
1.2 m
L75-437
Adaptations Lesson 75
Practice Set (continued) (page 504)
e. The shingles on the south side of Tamika’s roof need to be replaced. The shingles she wants come
in bundles that cover 33_13 square feet. Tamika calculates the area of the section of roof and then
determines the number of bundles she needs. She wants to buy two extra bundles to allow for
cutting and waste.
20 ft
15 ft
What is the area of the section of roof?
40 ft
How many bundles of shingles should Tamika buy?
1
33__
3
100
____
3
3
____ 100
(page 505)
1.
Actual
Count
Ratio
2.
Percent
Recommend
Original
Do not
Change (+)
Total
3.
t
Percent
Actual
Count
Actual
Count
100
c
New
4. y varies directly with x.
find a and b.
© 2007 Harcourt Achieve Inc.
Written Practice
Red Cheeks
Without
Total
100
t
x
2
8
10
a
y
6
24
b
45
a
b
Saxon Math Course 3
L75-438
Adaptations Lesson 75
Written Practice
(continued) (page 505)
1
(b1 b2 ) h
5. A __
6. A bh
2
11 in.
14 m
10 m
8m
10 m
26 m
9 in.
7 in.
9 in.
p
t
11 in.
7. See page 29 in the Student Reference Guide.
8. 0.04 0.02x 0.5
x
3
10. __ r 33
4
17
7
9. __ x 1 ___
3
3
r
x
28
4
12. __ ___
56
x
© 2007 Harcourt Achieve Inc.
11. 7x 1 x 19
x
2.8
4
13. __ ___
5.6
x
x
14. Factor
perfect squares.
___
√45 x
Saxon Math Course 3
L75-439
Adaptations Lesson 75
Written Practice
(continued) (page 505)
___
15. √50 16. a. percent
8
___
11
b. decimal
_______
11 ) 8.0000
a.
c. rounded to
thousandths
b.
c.
17. Area is related by scale factor squared.
.
18. What percent?
42
___
(scale factor)2 60
Change to a percent.
% 100% ft
mi
19. ___ to ____
sec
hr
%
2
20. y __ x 3
3
y
6
5
4
3
2
1
000hr
000min
000ft
15 mi _______
______
_______ ______ 1 hr
000min
000sec
000mi
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
x
1 2 3 4 5 6
Is (9,3) a solution?
Use work area.
Saxon Math Course 3
L75-440
Adaptations Lesson 75
© 2007 Harcourt Achieve Inc.
increase Written Practice
21. a. a (continued) (page 506)
b b. The triangles are s
because
6
6
a
corresponding
4
are congruent.
b
3
c. by sides:
d. scale factor:
Use work area.
23. Find the 20th term.
22. Convert the dimensions to feet.
9 in.
24 in. ft
12 in. ft
9 in. an 3(n 1)
12 in.
24 in.
a20 ft
volume lwh
V
surface area
Add the area of each side.
a20 SA 24. Label the length of
the sides of this net.
25. The relationship
____ m
direct variation because
____ m
____ m
the l
does not i
____ m
1.3 m
the origin.
© 2007 Harcourt Achieve Inc.
____ m
Use work area.
Saxon Math Course 3
L75-441
Use work area.
Adaptations Lesson 75
© 2007 Harcourt Achieve Inc.
LESSON
76
Name
Volumes of Prisms
and Cylinders (page 507)
The volume of a solid is the space occupied by the solid.
• Prisms and cylinders are geometric solids with two bases and
lateral sides.
Teacher Note:
• Review “Geometric Solids” on page
30 in the Student Reference Guide.
The bases are parallel and congruent.
The height of a prism or cylinder is the perpendicular distance between the two bases.
• The volume of a prism or cylinder is equal to the area of one base times the height:
area of base height volume
units2 units units3
Example: Find the volume of this triangular prism.
6 cm
8 cm
12 cm
10 cm
The base is a right triangle, with perpendicular sides of 6 cm and 8 cm.
area of base = _12 (6 8) 24 cm2
The height is 12 cm.
V = area of base height 24 cm2 12 cm 288 cm3
Example: A cylindrical soup can has a diameter of 2 in. and a height of 3 in. Find the volume of the
soup can. Leave as .
2 in
© 2007 Harcourt Achieve Inc.
3 in
2 in. 1 in.
The base is a circle with a diameter of 2 in., so its radius is __
2
area of base r 2 (1)2 The height is 3 in.
V area of base height in.2 3 in. 3 in.3
Saxon Math Course 3
L76-443
Adaptations Lesson 76
Practice Set (page 511)
a. A pup-tent has the dimensions shown. Label the diagram of the triangular base. Then find the volume
of the tent.
5 ft
____ ft
7ft
6 ft
____ ft
area of base V area of base height b. A cylindrical backyard pool 3 feet high and 20 feet in diameter holds how many cubic feet of water
when full? Use 3.14 for and round the answer to the nearest ten cubic feet.
3 ft
20 ft
area of base V area of base height c. The walls of a garage are 8 feet high and the peak of the gable roof is 12 feet high. The floor of the
garage is a 20 foot square. Find the volume of the garage.
Add the volume of a rectangular prism and a triangular prism.
8 ft
8 ft
____ ft
20 ft
12 ft
ft
20
20 ft
20 ft
rectangular prism
triangular prism
area of base area of base V V © 2007 Harcourt Achieve Inc.
20 ft
20 ft
___cm
total volume d. A cylindrical candle that is 15 cm high has a diameter of 8 cm. Label the figure and
___cm
find the volume. Leave as .
Saxon Math Course 3
L76-444
Adaptations Lesson 76
Practice Set (continued) (page 511)
e. Brenda is putting cubical boxes that are 6 inches on edge into a larger cubical box with inside
dimensions that are 12 inches on edge. How many of the smaller boxes will fit in the larger box?
How many times larger is the volume of the larger box?
V (length of edge)3
Volume of smaller cube Volume of larger cube (page 511)
Written Practice
1.
Percent
Original
Actual
Count
2.
Sheep
100
Goats
Change (+)
New
Total
n
3.
Percent
Trombones
Actual
Count
x
4.
Hours
Pay
3
27
4
36
5
45
6
54
Not trombones
Total
Actual
Count
s
Ratio
p
__
The relationship is
h
d
variation with a
100
constant of
. The
pay rate is
dollars per
.
© 2007 Harcourt Achieve Inc.
Use work area.
5. V area of base height
12 m
20 m
6. Find the volume in terms of . Round to the nearest unit
(use 3.14 for ).
V area of base height
7m
5m
10 m
Saxon Math Course 3
L76-445
Adaptations Lesson 76
Written Practice
(continued) (page 512)
7. yd3 to ft3
8. similar triangles
00 ft
00 ft
00 ft
1 yd3 ______ ______ ______ 00 yd 00 yd 00 yd
a
8
4
5
b
5
b
a
10. a. See page 18 in the
9. a. A = bh
Student Reference Guide.
b. See page 18 in the Student Reference Guide.
1
b. A __
(b2 b2 )h
10 cm
2
c. perimeter
10 cm
8 cm
10 cm
6 in.
10 cm
___ in.
8 in.
12 in.
a.
b. r
a.
c.
12. Volume smaller .
Volume larger .
000
Volume smaller
______________
____ Volume larger
%
000
c. The
are the same but the
order is different.
2 ft
1 ft
1 ft
1 ft
2 ft
2 ft
Use work area.
Saxon Math Course 3
L76-446
Adaptations Lesson 76
© 2007 Harcourt Achieve Inc.
11. Use a calculator.
1
a. __ 7
2
b. __ 7
b.
Written Practice
(continued) (page 513)
13. an 7(2n)
14. Factor:
a. 2x2 2x 2 a1 7(21) b. 5x2 10x a2 a.
a3 ,
15. Write the equation for the line.
,
b.
16. (3)(2) (1)2 y
6
5
4
3
2
1
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
x
1 2 3 4 5 6
17. Factor perfect squares.
___
√27 y
© 2007 Harcourt Achieve Inc.
___
18. √32 12m3
19. _______
18xm2
4.5
x
20. ___ __
7
6.3
34
2
4
21. __x __ ___
7
21
3
x
x
Saxon Math Course 3
L76-447
Adaptations Lesson 76
Written Practice
(continued) (page 513)
0.42
x
22. __ _____
0.14
4
23. 0.03 0.011x 0.36
x
m
24. __ 2.2
5
x
25. A (
,
A (
)
,
)
Move down
units and left
units.
y
m
D
A
D
C
A
B
x
C
B
© 2007 Harcourt Achieve Inc.
Use work area.
Saxon Math Course 3
L76-448
Adaptations Lesson 76
LESSON
77
Name
Inequalities with Negative
Coefficients (page 514)
Inequalities use the comparison symbols ⬍, ⬎, ⱕ, and ⱖ.
6 ⬎ 5
Six is greater than 5.
• Multiply both sides by ⫺1 and something happens.
(⫺1)(6) ⬎ (⫺1)(5)
⫺6 ⬎ ⫺5
Negative six is greater than negative five.
This is wrong!
• When multiplying or dividing an inequality by a negative number, reverse the comparison symbol.
6 ⬎ 5
(⫺1)(6) ⬍ (⫺1)(5)
⫺6 ⬍ ⫺5
Negative six is less than negative five.
• Solving inequalities is just like solving equations: Isolate the variable.
• If the variable has a negative sign (⫺x), reverse the symbol.
Example: Solve and graph: ⫺3x ⫺ 10 ⬎ 8
⫺3x ⫺ 10 ⬎ 8
Given inequality
⫺3x ⬎ 18
Added 10 to both sides
x ⬍ ⫺6
Divided both sides by ⫺3 and reversed the symbol
–6
0
Use a circle because x cannot equal ⫺6.
© 2007 Harcourt Achieve Inc.
Practice Set (page 517)
Solve and graph each inequality. When you divide by a negative number, reverse the symbol.
a. ⫺5x ⫺ 6 ⬍ ⫺1
⫺5
⫺4
⫺3
⫺2
⫺1
0
1
2
3
4
5
⫺5
⫺4
⫺3
⫺2
⫺1
0
1
2
3
4
5
⫺5x ⬍
x ⬎
b. 7x ⫹ 2 ⱕ 8x ⫹ 4
⫺x ⱕ
x ⱖ
Saxon Math Course 3
L77-449
Adaptations Lesson 77
Practice Set (continued) (page 517)
c. ⫺5x ⫹ 25 ⬎ 5(x ⫺ 5)
⫺5x ⫹ 25 ⬎ 5x ⫺ 25
⫺5
⫺4
⫺3
⫺2
⫺1
0
1
2
3
4
5
⫺5
⫺4
⫺3
⫺2
⫺1
0
1
2
3
4
5
⫺10x ⬎
x ⬍
d. ⫺2x ⫹ 3 ⱖ ⫺(x ⫺ 7)
⫺2x ⫹ 3 ⱖ ⫺x ⫹ 7
⫺x ⱖ
x ⱕ
1.
Ratio
Broken
(page 517)
2.
Actual
Count
b
Percent
Original
Working
Change
Total
Total
3. 8% ⫹ 20% ⫽ 28%
100
t
5. 50¢ ⫹ 3¢ per minute
a.
$ 8.40
9.20
Actual
Count
min
¢
0
50
5
65
⫻ 1.28
¢
____
min
10
20
4.
y
__
This
direct variation with
x
y
2
3
4
6
a constant of
In 10 min, she
6
9
travels
x
.
b. y =
x ⫹
c. This
direct variation because the
miles.
Use work area.
Saxon Math Course 3
L77-450
are not constant.
Use work area.
Adaptations Lesson 77
© 2007 Harcourt Achieve Inc.
Written Practice
Written Practice
(continued) (page 517)
6. 5 out of 8 are made.
b. P (miss) ⫽
a. P (made) ⫽
P (made) ⫻ 360° ⫽
P (miss) ⫻ 360° ⫽
°
°
Use work area.
0.22
4
9. __ ⫽ _____
x
0.55
7. ⫺x ⫹ 15 ⬎ 0
5
10
15
Use a circle.
x⬍
8. ⫺2x ⱖ 2
⫺5
⫺4
⫺3
⫺2
⫺1
0
1
2
3
4
5
Use a dot.
xⱕ
3
11
2
10. __ ⫺ __ x ⫽ ___
3
12
4
7
12. __ x ⫽ 49
8
11. 12 ⫽ 16 ⫺ 4x
x⫽
x⫽
13. new ⫽ original ⫹ increase
100% ⫹
x⫽
% ⫽
x⫽
14. an ⫽ n 2 ⫺ n
%
a10 ⫽
Change to a decimal.
© 2007 Harcourt Achieve Inc.
Area is related by scale factor squared.
(scale factor)2 ⫽
Change to a percent.
increase ⫽
% ⫺ 100% ⫽
a10 ⫽
Saxon Math Course 3
L77-451
Adaptations Lesson 77
Written Practice
(continued) (page 518)
16. Name the shape and find its area.
15. Name the shape and find its area.
1
A = __ ( b1 + b2 ) h
2
A = bh
5m
8m
5m
5m
4m
4m
5m
8m
8m
p
t
7x ⫺3 y 3 z 3
=
18. _________
14 x 4 y 3 z 2
17. Factor perfect squares.
___
√54 ⫽
19. Use the “Multiplication Table” on page 3 in the
Student Reference Guide.
ft
in.
20. ________ to ____
sec
min
sec _______
10 in. ________
ft
______
⭈
⭈
=
___
a. √90
2 sec
min
in.
___
b. √80
___
Saxon Math Course 3
a. between
and
b. between
and
c. between
and
© 2007 Harcourt Achieve Inc.
c. √70
L77-452
Adaptations Lesson 77
(continued) (page 518)
Written Practice
1
21. y ⫽ ⫺__ x ⫹ 2
2
22. V ⫽ area of base ⫻ height
Is (2,1) a solution?
Leave ␲ as ␲.
y
7 cm
6
5
4
3
2
1
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
4 cm
x
1 2 3 4 5 6
Use work area.
23. V ⫽ area of base ⫻ height
24. a. decimal
b. percent
______
4
___
⫽
11 ) 4.000
11
10 mm
4 mm
5 mm
a.
b.
25. a.
+
strawberries
bananas
b. Round blueberries to a whole percent.
© 2007 Harcourt Achieve Inc.
% of 30 ⫽
c. Fraction not grapes
a.
b.
c.
Saxon Math Course 3
L77-453
Adaptations Lesson 77
© 2007 Harcourt Achieve Inc.
LESSON
78
Name
Products of Square
Roots (page 519)
Teacher Note:
• Review “Laws of Exponents” on
page 19 in the Student Reference
Guide.
We can multiply square roots to simplify expressions.
• The product rule of square roots means that square roots
can be factored:
___
__ __
___
__ __
√ab √a √b
__
√18 √9 √2 3√2
• This rule also means that square roots can be multiplied.
• Try to factor perfect squares before multiplying:
__
___
Example: Simplify: √3 √12
__
___
__
__
√3 √12
Given
___
√ 3 2√ 3
__
__ __
__
√12 √4 √3 2√3
__
2√ 3 √ 3
Commutative Property
23
√3 √3 3
6
Simplified
__
__
• Sometimes we cannot factor out perfect squares before multiplying,
but we can factor perfect squares after multiplying.
__
___
Example: Simplify: 3√6 √15
__
___
3√6 √15
Given
___
__
3√90
___
___
√6 √15 √90
___
___
3 3√ 10
__
___
√90 √9 √10
___
9√10
Simplified
© 2007 Harcourt Achieve Inc.
Practice Set (page 522)
Simplify.
Factor perfect squares after multiplying.
__ ___
___
___ __
a. √2 √14 √ 28
___
__ __
√28 √4 √7 __ __
c. 3√5 √ 5 Saxon Math Course 3
___
b. √15 √3 √45
__
√7
___
√45 __
__
d. 5√ 3 2√3 L78-455
Adaptations Lesson 78
Practice Set (continued) (page 522)
e. The square has vertices at (5, 4), (1, 5), (0, 1), and (4, 0). Find the length of a
side of the square. Then find the area of the square.
y
Pythagorean Theorem
s2 12 42 1 16 s units
A s2 s
x
units2
f. The rectangle has vertices at (0, 5), (3, 1), (1, 3), and (4, 3). Find the
length and width of the rectangle. Then find the area of the rectangle.
l 2 62 32 w2 (
)2 (
l units
A lw )2 w
x
l
w y
units
units 2
g. Describe two ways to find the area of the shaded square.
1. The length of each side of the shaded square is
cm.
cm2.
The area is
1 cm
2. The length of each side of the large square is 1 cm 2 cm
1 cm
cm. The area of the large square is
cm2.
The area of one triangle is
cm2. Subtract four times
the area of one triangle from the area of the large square:
cm2 cm2 Written Practice
(page 522)
1. larger 100% % 2 cm
2 cm
1 cm
2 cm
cm2
1 cm
% change to a decimal
© 2007 Harcourt Achieve Inc.
2 cm
Area is related by scale factor squared
(scale factor)2 increase Saxon Math Course 3
change to a percent.
% 100% L78-456
Adaptations Lesson 78
Written Practice
2.
(continued) (page 522)
Percent Actual Count
Last Year
3. 12% of 4000
100
Change
This Year
4. direct variation
boxes _____ _____
apples
___ __
5. Factor
perfect squares.
__ __
√8 √6 __ ___
7. √6 √ 12 8m 4 b 3
8. ________
4 m 2 b 1
8
0.32
9. _____ __
m
0.56
© 2007 Harcourt Achieve Inc.
6. √21 √3 m
Saxon Math Course 3
L78-457
Adaptations Lesson 78
Written Practice
10. 0.5 0.02x 0.1
(continued) (page 522)
6
1
1
11. __ __ x __
7
7
2
x
2
12. __ m 6
3
x
m
5
13. Name the shape and find its area.
1
A __ (b1 b2 )h
2
4
4
10
5
14. Name the shape and find its area.
A bh
10
5
4
5
___
15. a. √60
___
b. √50
___
c. √40
Saxon Math Course 3
L78-458
a. between
and
b. between
and
c. between
and
Adaptations Lesson 78
© 2007 Harcourt Achieve Inc.
10
(continued) (page 523)
Written Practice
1
17. y __ x 5
2
¢
$
16. __ to ____
min
hr
Is (10, 0) a solution?
¢
$15 ________
hr ______
____
min
1 hr
y
$
6
5
4
3
2
1
x
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
18. Label the triangles and make a proportion.
1 2 3 4 5 6
x
5 ft
___ ft
___ ft
Use work area.
19. V area of base height
20. V area of base height
leave as .
10 cm
10 2 cm
6 in.
20 in.
20 cm
10 cm
21. proportion
22. number cube and spinner
© 2007 Harcourt Achieve Inc.
Multiply the probabilities.
P (even cube) P (even spinner) percent:
decimal:
.
_______
) 00000
Use work area.
Saxon Math Course 3
L78-459
Adaptations Lesson 78
Written Practice
(continued) (page 523)
23. 4(x 1) 0
5
10
15
x
24. 2(3 x) 2
5
4
3
2
1
0
1
2
3
4
5
x
25. Build the figure out of cubes for help.
a.
© 2007 Harcourt Achieve Inc.
b.
Saxon Math Course 3
L78-460
Adaptations Lesson 78
LESSON
79
Transforming Formulas (page 525)
Name
Formulas are equations that use variables instead of numbers.
• Sometimes we will want to solve a formula for one of the variables.
• Formulas can be solved in the same way as equations:
Isolate the variable you are solving for.
Do the same thing to both sides.
• After solving a formula, substitute numbers for the variables and solve.
Example: The formula for the area of a rectangle is A lw, where A is the area, l is the length,
and w is the width. Solve the formula for l.
A lw
Given formula
A ___
lw
__
Divided both sides by w
w
w
A
__
l w
l
Symmetric Property
w
Use the formula to find the length of a rectangle with area 42 and width 3.
A
Transformed formula
l __
w
42
l ___
3
Substituted 42 for A and 3 for w
l 14
Simplified
Practice Set (page 528)
© 2007 Harcourt Achieve Inc.
a. The formula for the area of a rectangle is A = lw. Solve the formula for w. Then describe the meaning
of the transformed formula.
A lw
w The width of a rectangle is the
divided by the
.
b. Solve the formula P a b c for a.
P a b c
a Saxon Math Course 3
L79-461
Adaptations Lesson 79
Practice Set (continued) (page 528)
c. The Pythagorean Theorem is a2 b2 c2. Solve the formula for c.
a2 b2 c2
c d. The formula for the perimeter of a rectangle is P 2l 2w. Solve the formula for l.
P 2l 2w
l Use the formula to find the length of a rectangular field with a perimeter of 620 feet and a width of 140 feet.
l (page 528)
Written Practice
1.
Percent
Original
100
Change
c
2.
Actual
Count
Actual
Count
Percent
Responded
Did not respond
New
Total
3. Percent greater
new 100% Change to a decimal.
d
100
4. Solve for r.
% %
C 2r
Area is related by scale factor squared.
( scale factor )2 increase © 2007 Harcourt Achieve Inc.
Change to a percent:
% 100% r
Saxon Math Course 3
L79-462
Adaptations Lesson 79
Written Practice
(continued) (page 528)
6. a. percent
5. R1, R2, and B
a. U R1R1 , R1R2 , R1B ,
,
,
,
,
,
BB V
5 __
9
b. decimal
________
9 ) 5. 0 0 0
b. P( BB ) 5 closer to __
1 or __
2?
c. Is __
9
2
3
Change all to decimals.
b.
Use work area.
8. 0.03x 0.1 0.7
7. Name the shape and find its area.
1
A __ ( b1 b2 )
2
7m
4m
13 m
x
1 __
1
2x __
9. __
2
6
3
10. Distribute first.
© 2007 Harcourt Achieve Inc.
3( x 2 ) x 6
x
x
11. 2x 3 x 5
12. Factor perfect squares.
___
__
√30 √3 x
Saxon Math Course 3
L79-463
Adaptations Lesson 79
Written Practice
__
(continued) (page 529)
__
13. √8 √5 14. (2)(3) (2) (3) 32 r 2 m 3
15. ________
16 r 2 m 1
16. Name the shape and find its area.
A bh
13 ft
8 ft
8 ft
5 ft
13 ft
¢
$
17. ____ to __
hr
min
1x
18. y __
3
50¢
000$
000min _____
______
_______
1 min
000hr
000¢
Is (15, 3)
a solution?
y
6
5
4
3
2
1
x
1 2 3 4 5 6
© 2007 Harcourt Achieve Inc.
–6 –5 –4 –3 –2 –1 0
–1
–2
–3
–4
–5
–6
Use work area.
Saxon Math Course 3
L79-464
Adaptations Lesson 79
(continued) (page 529)
Written Practice
19.
4
4+2=_____
4+2+2=_____
x
y
10
x
20. V area of base height
y
21. Round to the nearest unit.
ft3 to yd3
10 ft
000yd ______
000yd ______
000yd
000ft ______
______
3
1 ft
000
000ft
000ft
000ft
Use 3.14 for .
22. V area of base height
23. Earth _____ _____
Moon
© 2007 Harcourt Achieve Inc.
6 cm 10 cm
12 cm
1 cm
Saxon Math Course 3
L79-465
Adaptations Lesson 79
Written Practice
(continued) (page529)
24. Collect like terms.
2x 2 x 6
5
4
3
2
1
0
1
2
3
4
5
x
25. a. Turn your textbook 90° clockwise.
b. Z is the center of r
, so its coordinates do not change.
© 2007 Harcourt Achieve Inc.
a.
Saxon Math Course 3
L79-466
Adaptations Lesson 79
LESSON
80
Adding and Subtracting
Mixed Measures
Polynomials (page 532)
A mixed measure uses two different units from the
same type of measurement.
Name
Teacher Note:
• Review “Equivalence Table for
Units” on page 1 in the Student
Reference Guide.
• To add mixed measures:
1. Line up the matching units.
2. Add like units.
3. Simplify from right to left.
Example:
27 min
15 sec
48 min
18 sec
42 min
53 sec
117 min 96 sec
Change 96 sec
to 1 min 36 sec
118 min
36 sec
Change 118 minutes
to 1 hr 58 min
1 hr 58 min
36 sec
Simplified
• To subtract mixed measures:
1. Line up matching units.
2. Subtract like units from right to left.
3. When necessary regroup units using equivalences.
Example:
12 lb
7 lb
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11
12 lb
7 lb
4 lb
Saxon Math Course 3
5 oz
12 oz
21
5 oz
12 oz
9 oz
5 ounces 12 ounces ?
Regroup 1 lb (16 oz)
Subtracted
L80-467
Adaptations Lesson 80
A term has a signed number and may have one or more variables.
• A monomial is a number, variable, or combination of numbers and variables.
2x3
5
x2y
7xyz
z
Each of the above examples is one term.
• A binomial is two terms connected by a plus or minus sign.
x 5
xy 7y
x2 4
• A trinomial is three terms connected with plus or minus signs.
x 2 7x 10
x xyz y
• All of these examples are polynomials.
A polynomial is any monomial, binomial, or trinomial.
• The degree of a polynomial is the same as the greatest exponent in the polynomial.
Examples: Name the degree of each polynomial:
4x3 x2 x 3
The greatest exponent is 3, so this is a third degree (cubic) polynomial.
x 2 2x 3
The greatest exponent is 2, so this is a second degree (quadratic) polynomial.
x y 3
The greatest exponent is 1, so this is a first degree (linear) polynomial.
• These three examples are all written with the greatest exponent on the left and the least exponent on the
right. This is called descending order.
• Polynomials should always be written in descending order.
Example: Write this polynomial in descending order:
x 2x3 2 x2
2x3 x2 x 2
• To add polynomials:
1. Line up like terms.
2. Add like terms.
Example: Add the binomials x 6 and 2x 3.
© 2007 Harcourt Achieve Inc.
x 6
2x 3
3x 3
Practice Set (page 534)
Add and simplify.
a.
3 hr
32 min
45 sec
1 hr
43 min
27 sec
hr
hr
min
min
sec
sec
Saxon Math Course 3
b.
5 lb 8 oz
simplify
L80-468
8 lb
9 oz
lb
lb
oz
oz
simplify
Adaptations Lesson 80
Practice Set (continued) (page 535)
c. Neil needs to buy molding to mount around the room, so he makes a sketch of the room recording its
length and width. What is the perimeter of the room?
12'4"
10'10"
12
12
10
10
ft
ft
ft
ft
4
4
10
10
ft
ft
in.
in.
in.
in.
in.
in. simplify
Subtract.
Regroup when necessary.
d.
3 hr 15 min 12 sec
1 hr 42 min 30 sec
hr
min
sec
e.
6 ft
4 ft
ft
2 in.
7 in.
in.
f. Tony cut a 2 ft 7_12 in. length from an 8 ft long board. What is the remaining length of the board?
8 ft
1
2 ft 7__ in.
2
ft
in.
Identify each polynomial below as a monomial, binomial, or trinomial and name its degree.
g. x 2 25
h. x 2 6 x 7
degree
i. 2 x 3 y 4
degree
degree
j. Arrange the terms in descending order.
k. Add the trinomials
x y 2 and x y 4.
x y 2
x y 4
© 2007 Harcourt Achieve Inc.
5 4x2 x3 6x
Written Practice
1. a.
(page 535)
b.
Percent Actual Count
Original
Sale
100
Change
Sale
Percent Actual Count
Change
Closeout
s
a.
Saxon Math Course 3
100
L80-469
c
b.
Adaptations Lesson 80
(continued) (page 535)
Written Practice
2.
3.
Percent Actual Count
Planted
2 red
7 green
total
Unplanted
Total
100
4. 52 72 P (red) t
92 5. Solve for r.
A r2
The triangle
a right triangle
because the side lengths do not fit the
P
theorem.
√ 000
___________
r
Use work area.
12 in.
6. V area of base height
Round to nearest ft 3
7. 7x 3 2x 33
24 in.
Use 3.14 for .
x
x
10. 3(x 2) 2(2x 1)
x
11. a.
b.
x
Saxon Math Course 3
1 yd 2 ft 7 in.
2 yd 1 ft 10 in.
yd
ft
in. simplify
2 hr 15 min
1 hr 37 min
hr
min
a.
b.
L80-470
Adaptations Lesson 80
© 2007 Harcourt Achieve Inc.
2
1
4
9. __ x __ __
5
3
3
8. 0.003x 0.2 0.01
Written Practice
(continued) (page 536)
13. Factor perfect squares.
12. a. monomial, binomial or trinomial?
3x 2
_____
√1000 b. 3x 2
x 1
a.
b.
___ ___
__ ___
14. √40 √10 15. √3 √ 24 12 x 3 y 4
16. _______
3 x 4 y 3
1 (b b ) h
17. A __
2
2 1
4 miles
4 miles
6 miles
19. 2x 1 x 2
18. area
10 ft
© 2007 Harcourt Achieve Inc.
5
10 ft
8.2 ft
4
3
2
1
0
1
2
3
4
5
10 ft
x
10 ft
$
$
20. ___2 to __2
ft
yd
yd
yd
$27
_____
_______ _______ 2
1 yd
Saxon Math Course 3
L80-471
ft
ft
Adaptations Lesson 80
(continued) (page 537)
Written Practice
Y
21. y 2x 6
Is (3, 0) a solution?
n n n n n n n n n n
n
n
n
n
n
n
n
n
22. Find a first.
X
Use work area.
23. volume:
V area of base height
10
c
a
Label the sides of this net of the prism.
3
4
a
b
in.
b
in.
in.
c
24. a. decimal
in.
______
9 ) 2. 0 0
b. percent
2
__
9
in.
10 in.
a.
8 in.
6 in.
b.
25. a. total in 16-21 age group
classical
country
pop
+ R&B
Use work area.
a.
b.
b. difference in classical
c. total in R&B
Saxon Math Course 3
c.
L80-472
Adaptations Lesson 80
© 2007 Harcourt Achieve Inc.
10 in.