Download - SM H5 AD L081 FF - Weebly
L E S S O N
Name
Saxon Math Intermediate 5 529 Adaptations Lesson 81
© 2
008
Sax
on
8181 Teacher Notes:
• Introduce Hint #50 “Reducing Fractions (Manipulatives and Shortcuts).”
• Review “Tests for Divisibility” on page 20 and “Fraction Families Equivalent Fractions” on page 18 in the Student Reference Guide.
• Reducing Fractions, Part 1
New ConceptNew Concept
• To find equivalent fractions, multiply by a fraction name for 1.
1 __ 2 × 3 __
3 = 3 __
6
• To reduce fractions, divide by a fraction name for 1.
3 __ 6 ÷ 3 __
3 = 1 __
2 (3 ÷ 3 = 1)/
(6 ÷ 3 = 2)
• If both terms cannot be divided by the same number, the fraction cannot be reduced.
2 _ 5 cannot be reduced.
Lesson Practice
a. Reduce 8 __ 12 by dividing 8 __ 12 by 4 _ 4 . 8 ___ 12
÷ 4 __ 4 = 8 ÷ 4 _______
12 ÷ 4 = ___
b. Which of these fractions cannot be reduced? (Circle one.)
A 2 __ 8 B 3 __
8 C 4 __
8 D 6 __
8
page 526
SM_H5_AD_L081_FF.indd 529SM_H5_AD_L081_FF.indd 529 11/2/07 3:37:26 PM11/2/07 3:37:26 PM
Saxon Math Intermediate 5 530 Adaptations Lesson 81
© 2
008
Sax
on
Lesson Practice, continued
Add, subtract, or multiply as indicated. Remember to reduce the answers.
c. 3 __ 8
− 1 __ 8 = ___ ÷ ___ = __ d. 3 ___
10 + 3 ___
10 = ___ ÷ ___ = __
e. 2 __ 3
× 1 __ 2 = ___ ÷ ___ = ___ f. ___
30 ÷ ___ =
Rewrite each mixed number with a reduced fraction. (Keep the whole number. Reduce the fraction.)
g. 1 3 __ 9 h. 2 6 __
9 i. 2 5 ___
10
Find each sum or difference. Remember to reduce the answers.
j. 1 1 __ 4 + 2 1 __
4 = k. 1 1 __
8 + 5 5 __
8 = l. 5 5 ___
12 − 1 1 ___
12 =
Written PracticeWritten Practice page 530
1. highest
lowest
more
2. average 3. 1 ft = in.
( × ) + =
4. .
.
SM_H5_AD_L081_FF.indd 530SM_H5_AD_L081_FF.indd 530 11/2/07 3:37:29 PM11/2/07 3:37:29 PM
Saxon Math Intermediate 5 531 Adaptations Lesson 81
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
12. 3.4
+ .
13. 6.25
− .
14. Draw 32.
Use work area.
5. 2 __ 3 × ___ = ___
12
1 __ 4 × ___ = + ___ 12
Use work area.
6. prime numbers
,
7. 10 ___ 12
÷ 2 __ 2 =
8.
mm 10 20
1 __ 2 of length = width 9. a. 1 __
4 of 24 24 members
__ members
__ members
__ members
__ members
14
b. 1 __ 2 of answer to a.
c. 3 ___ 24
=
b.
a.
c.
10. rectangle in problem 8
Area = length × width
11. Q R S
?
page 530
SM_H5_AD_L081_FF.indd 531SM_H5_AD_L081_FF.indd 531 11/2/07 3:37:31 PM11/2/07 3:37:31 PM
Saxon Math Intermediate 5 532 Adaptations Lesson 81
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
15. 6 )
______________ $8 7 . 0 0
16.
R40 )
____________ 2 4 3 8
18. $10 − ($5.80 + 28¢) = 19. 5 3 __ 5 + 4 − 1 3 __
5 =
Convert.
21. 4 __ 3
× 1 __ 2 =
Reduce.
24. a. $ . collected from each
× customers
total
22. 10 ___ 7
× 7 ___ 10
=
Convert.
23. See page 532.
A translation B rotation
C reflection D slide
20. Reduce.
3 __ 6 ÷ 3 __
3 =
17. Divide 5280 by 9. Write the answer as a mixed number with a reduced fraction.
page 531
b. total
paid to company
profit
a.
b.
SM_H5_AD_L081_FF.indd 532SM_H5_AD_L081_FF.indd 532 11/2/07 3:37:34 PM11/2/07 3:37:34 PM
Saxon Math Intermediate 5 533 Adaptations Lesson 81
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
25. number cube rolled once
a. probability of an even number =
b. different event with same probability: Probability of an number.
Use work area.
26.
0–3
7654321
Number of Books
Books Read Last Year N
umbe
r of
Stu
dent
s
4–7 8–11 12–15 16–19
a. How many students read 12 books or more?
b. How many students read 15 books or fewer?
b.a.
27. All s are r , but some r
are not s .
A SR B S
R C
RS
D R S
page 532
SM_H5_AD_L081_FF.indd 533SM_H5_AD_L081_FF.indd 533 11/2/07 3:37:35 PM11/2/07 3:37:35 PM
Saxon Math Intermediate 5 534 Adaptations Lesson 81
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
28. fraction: 15% =
Reduce: ___ ÷ 5 __
5 = ___
29. 1 __ 2 × 1 __
2 1 __
2
Use work area.
30. See page 533.
283
261
I used c numbers that were multiples of 25.
+ + + =
Use work area.
page 533
SM_H5_AD_L081_FF.indd 534SM_H5_AD_L081_FF.indd 534 11/2/07 3:37:37 PM11/2/07 3:37:37 PM
L E S S O N
Name
Saxon Math Intermediate 5 535 Adaptations Lesson 82
© 2
008
Sax
on
8282 Teacher Notes:
• Introduce Hint #51 “Finding the Greatest Common Factor.”
• Review “Factors” on page 8 in the Student Reference Guide.
• For additional practice, students may complete Targeted Practice 82.
• Greatest Common Factor (GCF)
New ConceptNew Concept
• To find the greatest common factor (GCF):
1. List the factors of the smaller number in order.2. Starting with the largest factor, cross out any factor
that does not divide evenly into the larger number.3. Circle the first number that divides evenly into the
larger number. This is the GCF.
Example
Find the greatest common factor (GCF) of 8 and 20.
1. List the factors of 8. 1, 2, 4, 8
2. Eight does not divide evenly into 20.
Cross 8 out. 1, 2, 4, 8
3. Four divides evenly into 20.
Circle 4 and stop. 1, 2, 4 , 8
Four is the greatest common factor of 8 and 20.
Lesson PracticeFind the greatest common factor (GCF) of each pair of numbers:
a. 6 and 9
factors of 6: 1, 2, 3, 6
b. 6 and 12
factors of 6: , , ,
page 534
SM_H5_AD_L082_FF.indd 535SM_H5_AD_L082_FF.indd 535 11/2/07 3:40:26 PM11/2/07 3:40:26 PM
Saxon Math Intermediate 5 536 Adaptations Lesson 82
© 2
008
Sax
on
Lesson Practice, continued
c. 15 and 100
factors of 15: , , ,
d. 6 and 10
factors of 6: , , ,
e. 12 and 15 f. 7 and 10
, , , , , ,
Reduce each fraction by dividing the terms of the fraction by their GCF. (See problems a, b, and c.)
g. 6 __ 9 ÷ ___ = h. 6 ___
12 ÷ ___ = i. 15 ____
100 ÷ ___ =
Written PracticeWritten Practice page 536
1. 8 a.m. to 2 p.m. = hours
hours _______ dollars
0 ______ 34.50
= 1 __ ?
I used c numbers to check my answer. $34.50 is close
to .
÷ 6 = which is close to .
SM_H5_AD_L082_FF.indd 536SM_H5_AD_L082_FF.indd 536 11/2/07 3:40:28 PM11/2/07 3:40:28 PM
Saxon Math Intermediate 5 537 Adaptations Lesson 82
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
2. Estimate the product.
396
507
3. …, 3452, 3552, 3652, ,…
4. The height of most cars is about:
A 4 to 5 feet B 8 to 10 feet
C 40 to 50 feet D 20 to 25 feet Measure yourself compared to a car.
5. .
.
6. octagon sides
each side = 12 in.
perimeter = in.
7. not prime
A 11 B 21
C 31 D 41
8. a. List the factors of the smaller number (20):
, , , , ,
Cross out those that are not factors of the larger number (30).
The biggest factor is the GCF. Circle it.
b. Divide both by the GCF. 20 ___ 30
÷ ___ = a.
b.
page 536
SM_H5_AD_L082_FF.indd 537SM_H5_AD_L082_FF.indd 537 11/2/07 3:40:30 PM11/2/07 3:40:30 PM
Saxon Math Intermediate 5 538 Adaptations Lesson 82
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
9. 3 __ 4
of a foot
is of
__ = ? ___ 12
10. See page 537.
blue to gray
A translation B rotation
C reflection D flip
11. a. 1 __ 3 of 12 12
13
23
b. 2 __ 3 of 12
is of
__ = ? ___ 12
a.
b.
12. Reduce:
6 ___ 12
=
Divide both by the GCF.
13. 23 32
Use work area.
14. 5 __ 7 + 3 __
7 =
Convert.
15. 4 __ 4 − 2 __
2 =
Convert.
16. 2 __ 3 × ___ = 6 __
9
17. 976.5470.4436.7
+ 98.6
18. $40.00− $32.85
19. $8.47× 70
page 536
SM_H5_AD_L082_FF.indd 538SM_H5_AD_L082_FF.indd 538 11/2/07 3:40:32 PM11/2/07 3:40:32 PM
Saxon Math Intermediate 5 539 Adaptations Lesson 82
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
20. R6 )
_______________ 4 3, 7 1 5
21. 2640 _____ 30
= 22. 367× 418
23. 3 1 __ 4 + 3 1 __
4 =
Simplify.
24. $18.64 ÷ 4 =
25. Find the probability that with one spin the spinner will not stop on A. Write the answer as a reduced fraction.
A
A
B
C
D
E
E
F
27. fraction: 22% =
Reduce: ÷ ___ =
26. All r are p , but
some p are not r .
A R P
B R P
C R
P
D
RP
page 537
SM_H5_AD_L082_FF.indd 539SM_H5_AD_L082_FF.indd 539 11/2/07 3:40:34 PM11/2/07 3:40:34 PM
Saxon Math Intermediate 5 540 Adaptations Lesson 82
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
28. a. Soledad
Garret
needs
b. ft in.
1 __ 0 = 5 __ ?
Which child is exactly 5 feet tall?
c. average d. range e. median
Use work area.
29. Mt. Blackburn
Mt. McKinley (Mt. Blackburn + 1198)
Mt. Foraker (Mt. McKinley – 890)
Use work area.
30. 1976 I used c numbers.
1957 – =
Use work area.
Soledad
Hei
ght
(in in
ches
)
68
66
64
62
60
58
James
Heights of the Children
Garret
page 538
SM_H5_AD_L082_FF.indd 540SM_H5_AD_L082_FF.indd 540 11/8/07 12:31:32 PM11/8/07 12:31:32 PM
Name
Saxon Math Intermediate 5 541 Adaptations Lesson 83
© 2
008
Sax
on
Teacher Notes:
• Introduce Hint #52 “Faces on a Cube” and Hint #53 “Geometric Solids (Manipulatives).”
• Refer students to “Geometric Solids” on page 17 in the Student Reference Guide.
• Use geometric solids to illustrate concepts in this lesson.
• Properties of Geometric Solids
New ConceptNew Concept
Geometric Solids
Shape Name
Cube
Pyramid
Rectangular prism
Cylinder
Sphere
Cone
• The flat surfaces of solids are called faces.
• Two faces meet at an edge.
• Three edges meet at a vertex.
edgeface
vertex
Example
AB C
D
E
FG
H
___ AB and
___ CD Parallel Segments remain the
same distance apart.___
CD and ___
CE Perpendicular Segments intersect at right angles.___
AG and ___
EH Skew Segments on different faces do not intersect.
page 539
Math Language
A plane figure is a flat shape.
8383L E S S O N
Math Language
Geometric solids are 3-dimensional shapes. They take up space.
SM_H5_AD_L083_FF.indd 541SM_H5_AD_L083_FF.indd 541 11/2/07 3:44:18 PM11/2/07 3:44:18 PM
Saxon Math Intermediate 5 542 Adaptations Lesson 83
© 2
008
Sax
on
Name the geometric shape of each of these real-world objects.
a. brick b. soup can
c. ice cream cone d. shoebox
Use geometric solids for help.
e. The pyramid has how many triangular faces?
f. How many rectangular faces? g. Edges?
h. Vertices?
Use the rectangular solid to answer problems i–k.
i. Name a pair of parallel line segments.
j. Perpendicular line segments: K
H I
JN
OL
M
k. Pair of skew line segments:
l. Which figure has faces that are perpendicular to its base?
A B C D
m. Which figure has six congruent faces?
A B C D
Lesson Practice
SM_H5_AD_L083_FF.indd 542SM_H5_AD_L083_FF.indd 542 11/2/07 3:44:21 PM11/2/07 3:44:21 PM
Saxon Math Intermediate 5 543 Adaptations Lesson 83
© 2
008
Sax
on
1. time Alycia left:
Count hours forward.
Count 1 _ 2 hour forward.
2. Subtract the largest value coins first.
47¢
− 25¢ 1 quarter dimes?
nickels?
pennies?
3. twenty-three million, two hundred eighty-seven thousand, four hundred twenty
digits: , ,
Use work area.
5. prime numbers
, , ,
6. a. List the factors of the smaller number (4).
, ,
Cross out those that are not factors of the larger number (8). The biggest factor is the GCF. Circle it.
b. Divide both by the GCF. 4 __ 8 ÷ __ =
Use work area.
Written PracticeWritten Practicepage 543
4. a. 1 __ 3 of 24
b. 2 __ 3 of 24
2413
23 is __
of 00 ___
00 = ? ___
24
a.
b.
SM_H5_AD_L083_FF.indd 543SM_H5_AD_L083_FF.indd 543 11/2/07 3:44:24 PM11/2/07 3:44:24 PM
Saxon Math Intermediate 5 544 Adaptations Lesson 83
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
7. a. Shape?
b. How many faces?
a. b.
8. Shape of the earth?
A circle B cylinder
C sphere D plane
9. 1 7 ___ 10
decimal number
.
10. distance across a circle
A center B circumference
C radius D diameter
11. 3.62
+ .
12. 3.704
– .
13. 162 + √___
16
+
14. $6.25
15. 6w = $14.58
w =
16. 1 __ 3 × __ = 00 ___
12
3 __ 4 × __ = 00 ___
12
=
Convert.
Use work area.
17. Reduce.
6 __ 8 =
Divide both by the
GCF.
18. Write the numerator as your answer.
3 __ 4 × __ = 00 ___
12
page 543
SM_H5_AD_L083_FF.indd 544SM_H5_AD_L083_FF.indd 544 11/2/07 3:44:25 PM11/2/07 3:44:25 PM
Saxon Math Intermediate 5 545 Adaptations Lesson 83
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
19. 4 1 __ 6
+ 2 1 __ 6
=
Reduce.
20. 3 3 __ 4
+ 1 1 __ 4
=
Convert.
21. 5
− 1 1 __ 4
=
22. 0.1 0.01
0.1
0.01
Use work area.
23. 3 × 1 __ 2 =
1 __ 2 + 1 __
2 + 1 __
2
Convert.
24. Age
Adults $10.00
$8.50
$6.50
Age 9–12
Under 9
Price a. $4.50 Madison (12)
$ . Douglas (8)
$ . Mom
+ $ . Dad
b. $6.50
before 5 p.m.
after 5 p.m.
before 5 p.m.
saved
b.a.
25. Which “takes up space?”
A B C D
page 544
SM_H5_AD_L083_FF.indd 545SM_H5_AD_L083_FF.indd 545 11/2/07 3:44:28 PM11/2/07 3:44:28 PM
Saxon Math Intermediate 5 546 Adaptations Lesson 83
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
26. Estimate the area.
14 ft 2 in.
10 ft 3 in.
14 ft 2 in. ft
10 ft 3 in. ft
27. a. Which expense consumes about one third of the budget?
b. About what fraction of the budget does food consume?
Entertainment
Rent
Food
Car
Utilities
b.a.
28. perimeter
2.4 cm
Rhombus
29. Which transformation?
A translation B rotation
C reflection D flip
30. See page 545.
a. range of the temperatures
b. September October warmer or cooler?
c. November October warmer or cooler? Use work area.
page 545
SM_H5_AD_L083_FF.indd 546SM_H5_AD_L083_FF.indd 546 11/2/07 3:44:30 PM11/2/07 3:44:30 PM
L E S S O N
Name
Saxon Math Intermediate 5 547 Adaptations Lesson 84
© 2
008
Sax
on
8484 Teacher Notes:
• Review Hint #37 “Average.”
• Refer students to “Statistics” on page 20 in the Student Reference Guide.
• Review “Average” on page 9 in the Student Reference Guide.
• Mean, Median, Mode,and Range
New ConceptNew Concept
Statistics
Median: the middle number of a set of numbers arranged in order
Median middle
1, 3, 4, 4 , 5, 6, 6median = 4
Mode: the number that appears the most often in a set of numbers
Mode most
3, 5, 8, 2, 5, 7, 6, 1mode = 5
Range: the difference between the least and the greatest numbers in a set of numbers
Range span
3, 5, 8, 2, 5, 7, 7, 6, 1
8 – 1 = 7range = 7
Lesson PracticePut the numbers into numerical order first.
a. 3, 7, 9, 9, 4 Mean: Median:
3, , , , 9 Mode: Range:
b. 16, 2, 5, 7, 11, 13 Mean: Median:
, , , , , Mode: Range:
page 546
SM_H5_AD_L084_FF.indd 547SM_H5_AD_L084_FF.indd 547 11/2/07 3:48:13 PM11/2/07 3:48:13 PM
Saxon Math Intermediate 5 548 Adaptations Lesson 84
© 2
008
Sax
on
c. 3, 10, 2, 10, 10, 1, 3, 10
, , , , , , ,
Mean: Median: Mode: Range:
d. Name Andrei Raj Althea Mary Bedros Ann Yolanda
Age 13 10 10 11 11 10 11
, , , , , ,
Mean: Median: Mode: Range:
Written PracticeWritten Practicepage 549
1.
3 ) _____________
$2 4 5 7
2. Shade 1 __ 3 .
% shaded
Use work area.
3. one kilogram = grams 4. Estimate the product.
732
480
Lesson Practice, continued
SM_H5_AD_L084_FF.indd 548SM_H5_AD_L084_FF.indd 548 11/2/07 3:48:15 PM11/2/07 3:48:15 PM
Saxon Math Intermediate 5 549 Adaptations Lesson 84
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
5. At which of these times do the hands of a clock form an acute angle?
A 3:00 B 6:15 C 9:00 D 12:10
3
121110
9
87 6 5
4
21
3
121110
9
87 6 5
4
21
3
121110
9
87 6 5
4
21
3
121110
9
87 6 5
4
21
6. least to greatest 0.1
0.1, 0.01, 1.0, 1.01 0.01
1.0
1.01
, , ,
8. a. 1 __ 4 of 80 = 80
14
34
b. 3 __ 4 of 80 =
is __ of
80 ___ 80
= ? ___ 80
b.a.
9. 1 __ 2 × __ = 3 __ 6 10. Reduce.
4 __ 6 =
Divide both by the GCF.
7. a. List the factors of the smaller number (8).
Cross out those that are not factors of the larger number (12).
The biggest factor is the GCF. Circle it.
b. Divide both by the GCF. 8 ___ 12
÷ __ =
b.a.
page 549
SM_H5_AD_L084_FF.indd 549SM_H5_AD_L084_FF.indd 549 11/2/07 3:48:17 PM11/2/07 3:48:17 PM
Saxon Math Intermediate 5 550 Adaptations Lesson 84
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
14.
R30 )
_________ 6 7 2
15. 5 × 68¢ = 16. $3.40 ÷ 5 = 17. 10 − 3 1 __ 3 =
20. In rectangle MNOP, which segment is parallel to
–––– MN ?
A ––––
MP B –––
PO C –––
NO D ––––
MO
M N
P O
21. Which appears to be a right angle?
O
A
BC
D
A ∠AOB B ∠BOC
C ∠BOD D ∠AOD
18. 3 __ 4
× 5 __ 4 = 19. Opposite faces are p .
Adjacent faces are p .
Use work area.
11. Mixed number and decimal
.
12. 9.9
0.0
0.0
+ .0
13. $10.00
– $ .
page 550
SM_H5_AD_L084_FF.indd 550SM_H5_AD_L084_FF.indd 550 11/2/07 3:48:19 PM11/2/07 3:48:19 PM
Saxon Math Intermediate 5 551 Adaptations Lesson 84
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
22. a. $3.10 eggs
$0.00 juice
$0.00 juice
+ $0.00 cereal
Milk . . . . . . . Milk . . . . . . . Milk . . . . . . . Milk . . . . . . . Apple juice . . Apple juice . . Eggs . . . . . . Cereal . . . . .
TOTAL
1.941.941.941.941.381.383.103.98
17.60 b. average (mean)
c. median
d. mode
e. range
a. e.c. d.b.
23. Draw the next figure in the pattern, and then
count the dots.
Use work area.
24. perimeter in inches
34
1411
25. fraction: 90% =
Reduce: ÷ __ =
decimal: .
.
26. See page 2 in the Student Reference Guide.
212ºF water boils
____________ water freezes
page 551
SM_H5_AD_L084_FF.indd 551SM_H5_AD_L084_FF.indd 551 11/2/07 3:48:21 PM11/2/07 3:48:21 PM
Saxon Math Intermediate 5 552 Adaptations Lesson 84
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
27. It takes the moon about 29 1 _ 2 days to complete one cycle. Estimate the number of
cycles the moon completes in 365 days. Explain.
I used c numbers.
365 is about and 29 1 _ 2 is about .
÷ =
Use work area.
28. Draw a translation of the triangle shifted down 2 units.
x
y54321
1 2 3 4 50Use work area.
29. See page 552. Write the names of the lakes on the graph.
800
700
600
500
400
300
200
Dep
th (i
n fe
et)
Maximum Depth of Lakes
Use work area.
30. area 16 feet
12 feet
page 551
SM_H5_AD_L084_FF.indd 552SM_H5_AD_L084_FF.indd 552 11/2/07 3:48:22 PM11/2/07 3:48:22 PM
L E S S O N
Name
Saxon Math Intermediate 5 553 Adaptations Lesson 85
© 2
008
Sax
on
8585 Teacher Notes:
• Introduce Hint #54 “Measuring Liquids and Capacities of Containers.”
• Refer students to “Liquids” on page 1 in the Student Reference Guide.
• Review “Equivalence Table for Units” on page 1 in the Student Reference Guide.
• Display reference chart “Liquids.”
• Units of Capacity
New ConceptNew Concept
• Capacity is the amount of liquid a container can hold.
Equivalency Table for Units of Liquid Measure
U.S. Customary System Metric System
16 oz 1 pt2 pt 1 qt4 qt 1 gal
1000 mL 1 L
A liter is about 2 ounces more than a quart.
Lesson Practice
a. One fourth of a dollar is a quarter. What is one fourth of a gallon?
b. How many pints equal 1 gallon?
c. How many milliliters equal 2 liters? L ______ mL
1 __ 0 = 22 ____
??
d. A cup is one half of a pint. A cup is how many ounces?
page 553
SM_H5_AD_L085_FF.indd 553SM_H5_AD_L085_FF.indd 553 11/2/07 3:51:00 PM11/2/07 3:51:00 PM
Saxon Math Intermediate 5 554 Adaptations Lesson 85
© 2
008
Sax
on
Written PracticeWritten Practice page 555
1. Shade all but 2 __ 5 .
___ 5 = percent
2. prime number 4
1
0
A prime number can’t end in an even number.
3. length in centimeters and in millimeters
1 2 3cm
mm 10 20 30
.
4. 1 minute = seconds
heartbeats ____________________ seconds
20 ___ 15
= ? __ 0
5. perpendicular to –––
AB
A –––
BC B –––
CD C –––
DA D –––
DC
BC
D
A
6. a. List the factors of the smaller number (6).
Cross out those that are not factors of the larger number (9).
Circle the GCF.
b. Divide both by the GCF.
6 __ 9 ÷ ___ =
b.a.
SM_H5_AD_L085_FF.indd 554SM_H5_AD_L085_FF.indd 554 11/2/07 3:51:02 PM11/2/07 3:51:02 PM
Saxon Math Intermediate 5 555 Adaptations Lesson 85
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
7. a. 1 __ 5 of 60 60
15
25
b. 2 __ 5 of 60
is ____ of
0 __ 0
= ?? ______ 6060
b.a.
8. Find –––
AC . Label the figure.
CBA
?
9. least to greatest 0.1
0.
0.01
1.0
0.1, 0, 0.01, 1.0
, , ,
10. qt
____ pt
1 __ 0 = 4 __
?
11. L ______ mL
1 __ 0 = 33 ____
?? 12. Divide 100 by 6.
Write the answer as a mixed number.
Reduce.
page 556
SM_H5_AD_L085_FF.indd 555SM_H5_AD_L085_FF.indd 555 11/2/07 3:51:04 PM11/2/07 3:51:04 PM
Saxon Math Intermediate 5 556 Adaptations Lesson 85
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
13. $17.56
$ .
+ $ .
14. 4.324
– .
15. 396× 405
16. $1.25
17.
R9 )
____________ 3 6 0 5
18. $2.50 ÷ 10 = 19. Reduce.
15 ___ 20
=
Divide both by the GCF.
20. 3 − 2 2 __ 3 − 1 = 21. 3 __
5 × __ = 0000 ___
10
1 __ 2 × __ = 0000 ___
10
= Convert.
Use work area.
page 556
SM_H5_AD_L085_FF.indd 556SM_H5_AD_L085_FF.indd 556 11/2/07 3:51:05 PM11/2/07 3:51:05 PM
Saxon Math Intermediate 5 557 Adaptations Lesson 85
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
22. 0000 .
0000 .
23. Count the 1 _ 4 s.
24. a. 1 ft = in.
Genaro (5 × ) + in.
Roberta (Genaro − 4 in.) in.
b. Stan (Roberta + 6 in.) in.
b. ft in.a. ft in.
25. Double the previous number.
4, , , , …
26. The probability of “heads” is what fraction?
of 50 =
27. 90, 85, 80, 90, 95, 90, 100 Put the numbers in order.
, , , , , ,
a. range
b. The mode is because it is the score that occurs often.
c. The median is because it is the score.
a. b. Use work area. c. Use work area.
page 557
SM_H5_AD_L085_FF.indd 557SM_H5_AD_L085_FF.indd 557 11/2/07 3:51:06 PM11/2/07 3:51:06 PM
Saxon Math Intermediate 5 558 Adaptations Lesson 85
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
28. Maya
Justin (Maya + 3)
Coretta (Justin + 2)
Use work area.
29.
, , , , , . . .
a. Draw the next term of the sequence.
b. Which transformation describes the change from term to term in this sequence?
A translation B rotation C reflection D flip
a. Use work area. b.
30. 154
147
page 558
SM_H5_AD_L085_FF.indd 558SM_H5_AD_L085_FF.indd 558 11/2/07 3:51:07 PM11/2/07 3:51:07 PM
L E S S O N
Name
Saxon Math Intermediate 5 559 Adaptations Lesson 86
© 2
008
Sax
on
8686
• Multiplying Fractions and Whole Numbers
New ConceptNew Concept
• To multiply a fraction and a whole number:
1. Convert the whole number to a fraction. (Write the whole number over 1.)
2. Multiply the fractions.3. Simplify the answer.
Example
What number is 2 __ 3 of 4?
2 __ 3 of 4
2 __ 3 × 4 __ 1 = 8 __ 3 = 2 2 __
3
Lesson PracticeMultiply. Simplify answers when possible. Reverse the order of factors to check your answer.
a. 1 __ 3 × 4 b. 3 __
5 × 2 c. 2 __
3 × 2 d. What number is 1 __
5 of 4?
1 __ 3 × 00 ___ 00 = 3 __ 5 × 00 ___ 00 = 2 __
3 × 00 ___ 00 = 1 __
5 × 00 ___ 00 =
e. What number is 1 __ 6 of 5? f. What number is 2 __
3 of 5?
1 __ 6 × 00 ___ 00 = 2 __
3 × 00 ___ 00 =
page 559
Teacher Note:
• For addtional practice, students may complete Targeted Practice 86.
SM_H5_AD_L086_FF.indd 559SM_H5_AD_L086_FF.indd 559 11/2/07 3:57:50 PM11/2/07 3:57:50 PM
Saxon Math Intermediate 5 560 Adaptations Lesson 86
© 2
008
Sax
on
Lesson Practice, continued
g. Shade to show 1 _ 3 of 4.
1. Draw two horizontal parallel segments.
Make the lower segment longer.
Connect the ends.
Use work area.
2. Estimate the difference.
6970
3047
3. The sum of six and four is ten. 4. LmL
1 __ = 2 __ ?
Written PracticeWritten Practicepage 561
5. fraction, decimal, and percent shaded
.
6. a. 1 __ 3 of 120
b. 2 __ 3 of 120
is of
___ = ? ____ 120
12013
23
a.
b.
SM_H5_AD_L086_FF.indd 560SM_H5_AD_L086_FF.indd 560 11/2/07 3:58:00 PM11/2/07 3:58:00 PM
Saxon Math Intermediate 5 561 Adaptations Lesson 86
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
7. Which segment names a diameter of this circle?
A ___
RS B –––
RT
C –––
OS D –––
OT
R
S
TO
8. least to greatest Compare each to 1 _ 2 .
9 ___ 18
, 8 __ 7 , 7 ___ 16
, 6 __ 6 , 5 __ 8
, , , ,
9.
2 3 4
10. 2 __ 3 × 00 ___ 00 =
Convert.
11. 3 __ 4 of ___ =
Convert.
12. 3 − 2 3 __ 5 − 1 1 __
5 =
13. 4.7
.
+ .
14. 301.4− 143.5
page 562
SM_H5_AD_L086_FF.indd 561SM_H5_AD_L086_FF.indd 561 11/2/07 3:58:02 PM11/2/07 3:58:02 PM
Saxon Math Intermediate 5 562 Adaptations Lesson 86
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
15. 4760× 890
17. Cancel matching final zeros.
40 ) ____________
3 4 8 0
18. $42.36 ÷ 6 = 19. 222 =
20. a. List the factors of the smaller number (60).
Cross out those that are not factors of the larger number (100).
Circle the GCF.
b. Divide both by the GCF.
60 ____ 100
÷ __ =
a.
b.
21. 3 __ 4 = ___ 12
2 __ 3 = ___ 12
Use work area.
22. Count the 3 _ 4 s.
page 563
16. 4 )
_________ 3 4 8
SM_H5_AD_L086_FF.indd 562SM_H5_AD_L086_FF.indd 562 11/2/07 3:58:04 PM11/2/07 3:58:04 PM
Saxon Math Intermediate 5 563 Adaptations Lesson 86
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
23. a. Shape?
b. How many vertices?
a.
b.
24. a. 12 goal
Steven
more
Number of Books Read
Class Book Club
Willis
Stu
den
t StevenYuko KentBeth
0 4 8 12 b. books pages 1 ____
180 = ___
?
c. median
a. b. c.
25. What is the probability of rolling a number under 5? Reduce.
1 2
3
26. 1 quart = 1 __ 4 gallon
1 quart = percent of a gallon
page 563
SM_H5_AD_L086_FF.indd 563SM_H5_AD_L086_FF.indd 563 11/2/07 3:58:05 PM11/2/07 3:58:05 PM
Saxon Math Intermediate 5 564 Adaptations Lesson 86
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
27. 1 quart 1 liter
See page 1 in the Student Reference Guide.
Use work area.
28. 1 1 __ 2 morning
+ 2 1 __ 2 evening
one day
Use work area.
29.
, , , ...
a. Draw the next term.
b. Which transformation describes the change from term to term?
A translation B rotation C reflection D slide
a. Use work area.
b.
30. A 10° change on the Celsius scale is an 18° change on the Fahrenheit scale.
212
685032
F
100
2030405060708090
100
C
Label the blank tick marks.
Use work area.
page 564
SM_H5_AD_L086_FF.indd 564SM_H5_AD_L086_FF.indd 564 11/2/07 3:58:06 PM11/2/07 3:58:06 PM
L E S S O N
Name
Saxon Math Intermediate 5 565 Adaptations Lesson 87
© 2
008
Sax
on
8787
• Using Manipulativesand Sketches to DivideFractions
New ConceptNew Concept
• When dividing fractions, you can:
Use fraction manipulatives. Make sketches.
Lesson Practice
a. How many one sixths are in one half?
b. How many one twelfths are in one third?
Find each quotient. Try answering the problems mentally.
c. 2 __ 3 ÷ 2 __
3 = d. 1 ÷ 1 __
4 =
How many fourths are in one?
e. 2 __ 3 ÷ 1 __
3 = f. 1 ÷ 1 __
2 =
How many thirds are in two thirds?
page 565
SM_H5_AD_L087_FF.indd 565SM_H5_AD_L087_FF.indd 565 11/2/07 4:01:31 PM11/2/07 4:01:31 PM
Written PracticeWritten Practice page 568
1. 10 ft
a. perimeter
b. Area = length × width
a. b.
2. In which of these numbers does the
1 mean 1 __ 10 ?
A 12.34 B 21.43
C 34.12 D 43.21
3. least to greatest Find the least and greatest numbers. Then
compare the other two.
1, 0, 1 __ 2 , 0.3
1 _ 2 = 0.5
, , ,
4. qt
oz 1 ___ 32
= __ ?
5. a. A quarter is what fraction of a dollar?
b. one dollar = quarters
c. quarters
dollars
__ = ? __ 3
a. b. c.
Saxon Math Intermediate 5 566 Adaptations Lesson 87
© 2
008
Sax
on
6. fraction, decimal, and percent shaded
.
SM_H5_AD_L087_FF.indd 566SM_H5_AD_L087_FF.indd 566 11/2/07 4:01:33 PM11/2/07 4:01:33 PM
7. If a = 3, then 2a + 5 equals which of the following?
A 10 B 11 C 16 D 28
8. Find BC.
1 __ 4 of 84 mm is mm.
BA C?
9. 1 __ 2 = ___
6
1 __ 3 = ___
6
Use work area.
Saxon Math Intermediate 5 567 Adaptations Lesson 87
© 2
008
Sax
onWritten Practice,Written Practice, continued continued page 569
11. 3 __ 5 of 4 12. 1 __
2 ÷ 1 ___
12 =
How many 1 __ 12 s are in 1 _ 2 ?
Use fraction manipulatives.
13. 3 7 __ 8 − 1 1 __
8 =
Reduce.
10. a. List the factors of the smaller number (20).
, , , , ,
Cross out those that are not factors of the larger number (50). Circle the GCF.
b. Divide both by the GCF.
20 ___ 50
÷ __ =
a. b.
SM_H5_AD_L087_FF.indd 567SM_H5_AD_L087_FF.indd 567 11/2/07 4:01:34 PM11/2/07 4:01:34 PM
Saxon Math Intermediate 5 568 Adaptations Lesson 87
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
14. Cancel matching zeros.
2250 ÷ 50 =
15. 5 )
_________ 2 2 5
16. 5365428
3997659
7073+ 342
17. 4 )
__________ $8 . 2 0
18. 202 − √____
100
20
−
19. $12.750× 80
20. Divide 100 by 8.
Write the answer as a mixed number.
Reduce.
21. How many 1 _ 8 s are in 1 _ 4 ?
Use fraction manipulatives.
22. Count the 2 _ 3 s.
23. a. Marysville to Red Bluff
Marysville to Sacramento
more than
Red Bluff
Chico
Marysville
Sacramento
41
49
40
b. Sacramento to Chico
halfway to Marysville
still to go a. b.
page 569
SM_H5_AD_L087_FF.indd 568SM_H5_AD_L087_FF.indd 568 11/2/07 4:01:36 PM11/2/07 4:01:36 PM
Saxon Math Intermediate 5 569 Adaptations Lesson 87
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
24. eggs5 2 10
cereal
a. How many students ate cereal for breakfast?
b. How many students ate eggs for breakfast?
c. How many students ate both cereal and eggs for breakfast?
d. Altogether, how many students ate eggs or cereal or both?
e. How many of the 20 students ate neither eggs nor cereal for
breakfast? Use work area.
25. 57˚ highest
lowest
8˚ greater
26. started eight hours before midnight
started
5:32 drove
stopped
page 570
SM_H5_AD_L087_FF.indd 569SM_H5_AD_L087_FF.indd 569 11/2/07 4:01:37 PM11/2/07 4:01:37 PM
Saxon Math Intermediate 5 570 Adaptations Lesson 87
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
27. studied
1 3 __ 4 read
total
28. 3 1 __ 4 dozen made
− dozen eaten
dozen left
29. Use compatible numbers.
186
184
Use work area.
30. Use the data on page 571 to make a line graph.
0
2
4
6
8
10
12
Tem
per
atur
e
Time
6:00 am 9:00 am noon 3:00 pm 6:00 pm
Mt. Wilson Temperatures
Use work area.
page 570
SM_H5_AD_L087_FF.indd 570SM_H5_AD_L087_FF.indd 570 11/2/07 4:01:38 PM11/2/07 4:01:38 PM
L E S S O N
Saxon Math Intermediate 5 571 Adaptations Lesson 88
© 2
008
Sax
on
• Transformations
New ConceptNew Concept
Transformations
Name Movement
Translationsliding a figure in one direction without turning the figure
Reflectionreflecting a figure as in a mirror or “flipping” a figure over a certain line
Rotation turning a figure about a certain point
x
y
translationx
y
reflection x
y
rotation
• Rotations can be described by their direction and by their degree.
clockwise same direction as clock hands
counterclockwise opposite direction as clock hands
full turn 360º
half turn 180º
quarter turn 90º
turn clockwise14 turn counterclockwise1
4
8888 page 572
Name
SM_H5_AD_L088_FF.indd 571SM_H5_AD_L088_FF.indd 571 11/2/07 4:07:38 PM11/2/07 4:07:38 PM
Saxon Math Intermediate 5 572 Adaptations Lesson 88
© 2
008
Sax
on
ActivityActivity page 574
Describing Transformations
• This activity is optional.
Lesson Practice a. Sketch an uppercase letter R after a b. Sketch an uppercase letter R after a reflection in its vertical segment. 180º counterclockwise rotation.
Name the transformations that could be used to position triangle A on triangle B.
c. y
x
A B
d. y
x
AB
r r
e.
AB
x
y f. y
x
A
B
r , r ,
t r ,
t
New Concept,New Concept, continued continued
SM_H5_AD_L088_FF.indd 572SM_H5_AD_L088_FF.indd 572 11/2/07 4:07:43 PM11/2/07 4:07:43 PM
Saxon Math Intermediate 5 573 Adaptations Lesson 88
© 2
008
Sax
on
Written PracticeWritten Practice page 577
1. Lilah lives 1 _ 4 mile from school. How far does she travel each day going to school
and back?
Home School
mi14
2. According to this calendar, what is the date of the first Friday in April 2070?
MARCH 2070
310172431
S
29
162330
18
152229
7142128
6132027
5121926
4111825
FTWTMS
,
3. .
– .
.
4. a. one dollar = dimes
b. dimes ______ dollars
1 __ 1 = ? __ 5
a.
b.
5. 2 __ 3 of 150
is __ of
1 __ 1 = ? ____ 150
6. gallon
quart
quart
quart
quart12 gallon
SM_H5_AD_L088_FF.indd 573SM_H5_AD_L088_FF.indd 573 11/2/07 4:07:46 PM11/2/07 4:07:46 PM
Saxon Math Intermediate 5 574 Adaptations Lesson 88
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
7. Which part of a bicycle wheel is most like a radius?
hub
rim
spoke
tire
A rim
B spoke
C hub
D tire
8. 5 __ 6
1 __ 3 = 0 __
6
= Reduce. Use work area.
9.
a. fraction shaded Reduce.
b. percent shaded
b.
a.
11. 3 __ 5
+ 3 __ 5 + 3 __
5 3 × 3 __ 5
Use work area.
10. Find ST.
R TS ?
1 _ 3 of 84 mm is mm.
12. In this drawing, which angle appears to be obtuse?
A
BC
D A ∠ABC B ∠ABD
C ∠BDC D ∠DAB
page 577
SM_H5_AD_L088_FF.indd 574SM_H5_AD_L088_FF.indd 574 11/2/07 4:07:47 PM11/2/07 4:07:47 PM
Saxon Math Intermediate 5 575 Adaptations Lesson 88
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
13. 1 __ 8 × 3 =
Convert.
14. 3 __ 8 ÷ 1 __ 8 =
How many 1 _ 8 s are in 3 _ 8 ?
Use fraction pieces.
16. 1 __ 4 + 1 __ 4 =
Reduce.
17. 7 __ 8 – 1 __
8 =
Reduce.
18. 5 – 1 3 ___ 10
=
19. $6.57
$8.43
+ $ .
20. 421.05
– 421.05
21. 302 =
15. a. How many 1 _ 4 s are in 1?
b. 1 __ 6 × ___ =
Reduce.
a.
b.
22. School Schedule
Subject Time
Reading 8:00–8:50
Math 8:50–9:40
Recess 9:40–10:10
Language 10:10–10:50
Science 10:50–11:30
Lunch 11:30–12:30
a. reading
language
total
b. lunch ends:
Count hours forward.
Counts minutes forward.
a. b.
page 578
SM_H5_AD_L088_FF.indd 575SM_H5_AD_L088_FF.indd 575 11/2/07 4:07:49 PM11/2/07 4:07:49 PM
Saxon Math Intermediate 5 576 Adaptations Lesson 88
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
23. 6070× 340
24. 9 )
__________ $7 . 6 5
25. area 30 ft.
30 ft.
26. 1 __ 2
, 1, 1 1 __ 2 , 2, 2 1 __
2 , 3, ,
, , …
Use work area.
28. a. See page 16 in the Student Reference Guide.
P T
A P T
B
TP
C
PT
D
b. ; No p is a t , and no
t is a p .Use work area.
29. area of shaded portion
1 in.
1 in.
in.12
in.34
27. probability of black
W W W
B B B B BBBBBB
R R
Reduce.
page 579
30. anniversary 1983
first flight (anniversary − 200)
bicycle invented (first flight + 56)
SM_H5_AD_L088_FF.indd 576SM_H5_AD_L088_FF.indd 576 11/2/07 4:07:51 PM11/2/07 4:07:51 PM
L E S S O N
Name
Saxon Math Intermediate 5 577 Adaptations Lesson 89
© 2
008
Sax
on
8989 Teacher Note:
• Use geosolids to introduce this concept.
• Analyzing Prisms
New ConceptNew Concept
• A prism is a three-dimensional solid with two congruent bases.
Triangular prism6 vertices9 edges
Rectangular prism8 vertices12 edges
Trapezoidal prism8 vertices12 edges
Pentagonal prism10 vertices15 edges
Hexagonal prism12 vertices18 edges
Octagonal prism16 vertices24 edges
Lesson PracticeName each type of prism in a–c.
a. b. c.
d. Look at the prism in problem a.
How many perpendicular rectangular faces?
page 580
SM_H5_AD_L089_FF.indd 577SM_H5_AD_L089_FF.indd 577 11/2/07 4:13:03 PM11/2/07 4:13:03 PM
Saxon Math Intermediate 5 578 Adaptations Lesson 89
© 2
008
Sax
on
e. Look at the prism in problem b.
How many pairs of parallel faces?
f. Look at the prism in problem c.
How many edges?
g. Is this figure a prism?
, because it does not have two p
c bases.
Written PracticeWritten Practice page 582
1. Thomas Jefferson wrote the Declaration of Independence.
1776 wrote
25 later
became president
2. Greater than or less than a year?
a. $ days
__ 1 =
10,000 _______
?
b. Greater than or less than a year?
b.
a.
3. Which is divisible by both 4 and 5? Look down the 4s and 5s columns of the Multiplication Table.
A 15 B 16 C 20 D 25
Lesson Practice, continued
SM_H5_AD_L089_FF.indd 578SM_H5_AD_L089_FF.indd 578 11/2/07 4:13:05 PM11/2/07 4:13:05 PM
Saxon Math Intermediate 5 579 Adaptations Lesson 89
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
4. least to greatest 0.5
1.5 3 __ 2
1.
0.
1.1
0.5, 3 __ 2 , 1, 0, 1.1
, , , ,
5. a. one gallon = half gallons
b. half gallons
gallons
1 __ 1 = ? __
3
a.
b.
6. one million, three hundred fifty-four thousand, seven hundred sixty
, ,
7. 5 __ 6
1 __ 2 = __ 6
= Reduce.
Use work area.
8.
a. fraction shaded (Reduce.)
b. percent shaded
a.
b.
9.
a. Shape?
b. How many edges?a.
b.
page 583
SM_H5_AD_L089_FF.indd 579SM_H5_AD_L089_FF.indd 579 11/2/07 4:13:06 PM11/2/07 4:13:06 PM
Saxon Math Intermediate 5 580 Adaptations Lesson 89
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
12. 2 __ 5
+ 2 __ 5 + 2 __
5 =
Convert.
13. 1 1 __ 4 + 1 1 __
4 =
Simplify.
14. 3 5 __ 6 − 1 1 __
6 =
Simplify.
15. 42.6
.
.
+ .
16. $10 − (57¢ + $2.48) = 17. 42 × 5 × 36 =
18. $6.15 × 10 = 19. 40 )
____________ 2 7 6 0
page 583
10. length in centimeters and in millimeters
10 20 30 40mm
1 2 3 4cm
.
11. 2 __ 5 of ___ =
Convert.
SM_H5_AD_L089_FF.indd 580SM_H5_AD_L089_FF.indd 580 11/2/07 4:13:08 PM11/2/07 4:13:08 PM
Saxon Math Intermediate 5 581 Adaptations Lesson 89
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
20. 4w = 276
w =
21. 1 __ 2 ÷ 1 ___ 10 =
How many 1 __ 10 s are in 1 _ 2 ?
Use fraction pieces.
22. 1 __ 2 × 6 __
8 =
Simplify.
23. Divide 371 by 10. Write the answer with a remainder.
24. Fill in the chart starting with Monty.
Age
Monty
Noah
Jenny
Dad
a. How old is Jenny?
b. How old is Jenny’s dad?
a.
b.
25. √___
25 − √__
9
− =
26. 32 + 42
+ =
page 584
SM_H5_AD_L089_FF.indd 581SM_H5_AD_L089_FF.indd 581 11/2/07 4:13:09 PM11/2/07 4:13:09 PM
Saxon Math Intermediate 5 582 Adaptations Lesson 89
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
27. A dime is tossed and then a quarter is tossed.
List the possible outcomes.
Dime Quarter
heads tails
Use work area.
28. a. A pint is what fraction of a quart?
b. What fraction of a gallon is a quart?
c. What fraction of a gallon is a pint?
d. The answers to a–c show that one half of one fourth equals what fraction?
Use work area.
29. See page 585.
and Use work area.
30.
Act it out.
triangular faces
rectangular faces Use work area.
page 584
SM_H5_AD_L089_FF.indd 582SM_H5_AD_L089_FF.indd 582 11/2/07 4:13:11 PM11/2/07 4:13:11 PM
L E S S O N
Name
Saxon Math Intermediate 5 583 Adaptations Lesson 90
© 2
008
Sax
on
9090 Teacher Notes:
• Review Hint #50 “Reducing Fractions (Manipulatives and Shortcuts)” and Hint #51 “Finding the Greatest Common Factor.”
• Review “Factors” on page 8, “Tests for Divisibility” on page 20, and “Fraction Families Equivalent Fractions” on page 18 in the Student Reference Guide.
• For additional practice, students may complete Targeted Practice 90.
• Reducing Fractions,Part 2
New ConceptNew Concept
• To reduce a fraction to lowest terms:
1. Find the GCF of the numerator and denominator.2. Divide both by the GCF.
Example
Reduce 8 ___ 12
factors of 8: 1, 2, 4 GCF
8 ___ 12
= 8 ÷ 4 _______ 12 ÷ 4 = 2 __ 3
• To write a percent as a reduced fraction:
1. Write the percent as a fraction.2. Cancel matching zeros.3. Reduce the fraction.
Example
Write 40% as a reduced fraction.
1. 40% = 40 ____ 100
2. 40 ____ 100
= 4 ÷ 2 _______ 10 ÷ 2
= 2 __ 5
Lesson PracticeReduce each fraction to lowest terms.Find the GCF first.
a. 4 ___ 12
= b. 6 ___ 18
= c. 16 ___ 24
=
page 586
SM_H5_AD_L090_FF.indd 583SM_H5_AD_L090_FF.indd 583 11/2/07 4:19:00 PM11/2/07 4:19:00 PM
Saxon Math Intermediate 5 584 Adaptations Lesson 90
© 2
008
Sax
on
Lesson Practice, continued
d. 4 ___ 16
= e. 12 ___ 16
= f. Cancel matching zeros.
60____100
=
Solve. Reduce each answer to lowest terms.
g. 7 ___ 16
+ 1 ___ 16
=
h. 3__4
× 4__5
= i. 19 ___ 24
− 1 ___ 24
=
Write each percent as a reduced fraction.
j. 25% = k. 60% = l. 90% =
Written PracticeWritten Practice page 589
1. See page 589. 2. Convert.
1 __ 2 = 00 ___
10
3 __ 5 = 00 ___
10
3. a. one gallon = quarts
b. gal
___ qt
1 __ 0 = 6 __
?
a.
b.
4. .
. 0
SM_H5_AD_L090_FF.indd 584SM_H5_AD_L090_FF.indd 584 11/2/07 4:19:03 PM11/2/07 4:19:03 PM
Saxon Math Intermediate 5 585 Adaptations Lesson 90
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
5. decimal, reduced fraction, and percent shaded
.
6. How many vertices?
7. Which segment is parallel to –––
AB ?
x
y
D A
C B
A –––
BC B –––
CD
C –––
BD D –––
DA
8. Classify triangle BCD by angles.
x
y
D A
C B
9. What transformation would move triangle DAB to triangle BCD?
x
y
D A
C B
r
10. 5 __ 6 + 5 __
6 =
Convert and reduce.
11. 5 __ 6 × 2 =
Convert and reduce.
page 589
SM_H5_AD_L090_FF.indd 585SM_H5_AD_L090_FF.indd 585 11/2/07 4:19:05 PM11/2/07 4:19:05 PM
Saxon Math Intermediate 5 586 Adaptations Lesson 90
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
12. 2 __ 5 ÷ 1 ___
10 =
How many 1 __ 10 s are in 2 _ 5 ?
Use fraction pieces.
13. 1 ___ 12
+ 7 ___ 12
=
Reduce.
14. Borrow and rename.
6 2 __ 3 − 4 − 1 __
3 =
15. 2 __ 3 × 3 __
4 =
Reduce.
16. 26.4
+ .00
17. 8.36
− .00
18. 402 = 19. √___
36 + √___
64
+
20. 480 ÷ 10 =
21. 5n = 240
n =
22. 1 ÷ 1 __ 3 =
How many 1 _ 3 s are in 1?
23. 3 __ 4 × 3 =
Convert.
page 590
SM_H5_AD_L090_FF.indd 586SM_H5_AD_L090_FF.indd 586 11/2/07 4:19:07 PM11/2/07 4:19:07 PM
Saxon Math Intermediate 5 587 Adaptations Lesson 90
© 2
008
Sax
onWritten Practice,Written Practice, continued continued
24. 3 __ 5 × __ = 60 ____
100
25.
Magazine report
TV report
Book report
Museum report
Extra Credit
35 points
50 points
75 points
100 points
a. book report 2 magazine reports TV report
points earned
b. 400 total earned
needs
a. b.
26. probability of orange
O O O O O OW W W W W
R R RB B
Reduce.
27. area = 25 in.2
a. each side
b. perimeter
a. b.
page 590
SM_H5_AD_L090_FF.indd 587SM_H5_AD_L090_FF.indd 587 11/2/07 4:19:08 PM11/2/07 4:19:08 PM
Saxon Math Intermediate 5 588 Adaptations Lesson 90
© 2
008
Sax
on
Written Practice,Written Practice, continued continued
28. , , , ...
3 sides, sides, sides, sides
This is a pattern of regular p .
The number of sides is i by .
Use work area.
29. a. factors of 16: , , , ,
b. Is the number of factors odd or even?
c. What is the median of the factors?
d. What is √___
16 ?
Use work area.
30. $24,575
$23,460
I used c numbers.
$24,575 is about .
$23,460 is about .
– =
Use work area.
page 591
SM_H5_AD_L090_FF.indd 588SM_H5_AD_L090_FF.indd 588 11/2/07 4:19:10 PM11/2/07 4:19:10 PM
Saxon Math Intermediate 5 589 Adaptations Investigation 9
Name I N V E S T I G A T I O N©
200
8 S
axon
page 592
Focus onFocus on• Performing Probability
Experiments
• A typical dot cube has six faces.
• Each time a dot cube is rolled there are 6 possible outcomes.
Each outcome is equally likely.
The probability of each outcome is 1_6 .
• The total of the possible outcomes must add up to one.
1__6
+ 1__6
+ 1__6
+ 1__6
+ 1__6
+ 1__6
= 6__6
= 1
• The probability that the upturned face will be an even number is the sum of the probabilities of rolling a 2, a 4, or a 6.
1__6
+ 1__6
+ 1__6
= 3__6
= 1__2
1. What is the probability that the upturned face is either 1 or 6?
+ =
Teacher Notes:
• Review Hint #42 “Probability and Chance.”
• Each student will need a copy of Lesson Activity 30.
99
Math Language
Probability tells how likely something is to happen. It is expressed in fractions.
SM_H5_AD_Inv009_FF.indd 589SM_H5_AD_Inv009_FF.indd 589 11/2/07 3:33:46 PM11/2/07 3:33:46 PM
Saxon Math Intermediate 5 590 Adaptations Investigation 9
© 2
008
Sax
on
I N V E S T I G A T I O N continued9
2. What is the probability that the upturned face is less than 5?
• If we rolled our dot cube 24 times, we guess that we would roll a certain number 1 _ 6 of 24 times.
24 ÷ 6 = 4 times
3. If a standard dot cube is rolled 60 times, how many times
would you guess that the upturned face will be 1?
Explain how you got your answer.
Since the outcome 1 can be expected to occur of
the time, I divided 60 by .
4. If a standard dot cube is rolled 60 times, how many times would
you guess that the upturned face will be either 1 or 6?
Explain how you got your answer.
Since one outcome can be expected to occur times
in 60 rolls, then two outcomes can be expected to
occur + , or times.
SM_H5_AD_Inv009_FF.indd 590SM_H5_AD_Inv009_FF.indd 590 11/2/07 3:33:49 PM11/2/07 3:33:49 PM
Saxon Math Intermediate 5 591 Adaptations Investigation 9
© 2
008
Sax
onI N V E S T I G A T I O N continued9
ActivityActivity 1 1 page 593
Probability Experiment 1
• Use the tallies on Lesson Activity 30 to answer problems 5 – 8.
5. Complete the “Frequency” column on Lesson Activity 30.
6. Which outcome occurred more frequently than you
would guess?
7. How many times was the upturned face even?
8. Predict what the next roll would be.
SM_H5_AD_Inv009_FF.indd 591SM_H5_AD_Inv009_FF.indd 591 11/2/07 3:33:50 PM11/2/07 3:33:50 PM
Saxon Math Intermediate 5 592 Adaptations Investigation 9
© 2
008
Sax
on
I N V E S T I G A T I O N continued9
2
1 3
• The table shows the results of 50 spins of the spinner shown above.
Outcome Tally RelativeFrequency
1
2
3
1750
2850
550
9. Since 28 __ 50 > 17
__ 50 , outcome 2 seems more likely than outcome 1.
How does the spinner show the same probabilities?
Region is larger than region .
Since 17 __ 50 > 5 __ 50 , outcome 1 seems more likely than outcome 3.
How does the spinner show the same probabilities?
Region is larger than region .
10. 28 __ 50 overestimates the true probability of stopping on 2.
Region 2 is slightly s
than 1 _ 2 ( or 25 __ 50 ) of the spinner.
SM_H5_AD_Inv009_FF.indd 592SM_H5_AD_Inv009_FF.indd 592 11/2/07 3:33:52 PM11/2/07 3:33:52 PM
Saxon Math Intermediate 5 593 Adaptations Investigation 9
© 2
008
Sax
onI N V E S T I G A T I O N continued9
ActivityActivity 2 2 page 595
Probability Experiment 2
Complete Activity 2 with a partner.
Use Lesson Activity 30 to answer problems 11–16.
11. Use the tallies to complete the “Relative Frequency” column on your table.
number of tallies _______________ 30
12. Look at your “Relative Frequency” table.
Estimate the probability that you choose a T.
13. If a letter was written once, about how many times would you expect to choose it out of 30?
30 ___ 5
14. If a letter was written twice, about how many times would
you expect to choose it out of 30?
15. If a letter was written three times, about how many
times would you expect to choose it out of 30?
16. Which of the letters do you think your partner wrote
once?
twice?
three times?
SM_H5_AD_Inv009_FF.indd 593SM_H5_AD_Inv009_FF.indd 593 11/8/07 12:35:06 PM11/8/07 12:35:06 PM