Download 61 • Using Letters to Identify Geometric Figures

LESSON
Name
61
page 387
• Using Letters to Identify
Geometric Figures
New Concept
• To name a polygon using letters at its vertices:
1. Choose any vertex as the starting point.
2. Move around the perimeter in either direction, naming
each vertex in order.
3. Stop after all vertices have been recorded.
Naming Lines, Segments, and Rays
Figure
A
Name
Abbreviation
line AB or line BA
AB or BA
segment AB or segment BA
AB or BA
ray AB (must name endpoint
first)
AB
B
A
B
A
B
• Name an angle using the letter of its vertex. If there is a
chance for confusion, use three letters with the vertex as
the middle letter.
Example
Look at the figure below.
© 2008 Saxon
B
A
C
D
E
∠ADC (angle ADC) is inside the figure. ∠CDE (angle CDE) is
outside the figure. Both have D at their vertex.
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Adaptations Lesson 61
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Lesson Practice
___
a. Which segment is parallel to JK ?
___
J
K
M
L
___
b. If JK is 10___
cm long and if JM is half the
length of JK, then what is the perimeter of the rectangle?
Use words to show how each of these symbols is read and draw an example of each
figure.
___
c. BC
d. CD
s
r
e. PQ
l
Refer to the figure below to answer problems f–i.
B
A
M
C
D
f. Angle AMD is an obtuse angle. Using three letters, what is another way to name
© 2008 Saxon
this angle?
g. Which angle appears to be a right angle?
h. Which ray appears to be perpendicular (forms a right angle) to MD?
i. Name one angle that appears to be acute.
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Adaptations Lesson 61
10/31/07 1:59:07 PM
page 391
Written Practice
1. 1 ft =
in.
×
(
) +
=
2. _1_ absent
6
See “Fraction-Decimal-Percent Equivalents” on page 19 of the Student Reference Guide.
_1_
6
=
percent
fraction not absent
6
__
6
–
4. (7 × 1000) + (4 × 10)
1959
1790
3.
+
5. 56
23
×
6. Which of these fractions does not
1?
equal __
2
6
A ___
12
12
B ___
24
© 2008 Saxon
_____
2)1
Saxon Math Intermediate 5
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=
2
_____
2)2
399
48
D ___
98
24
C ___
48
4
_____
2)4
8
_____
2)9
8
Adaptations Lesson 61
10/31/07 1:59:09 PM
page 391
Written Practice, continued
7. factors of 12: 1,
,
,
,
, 12
factors of 16: 1,
,
,
, 16
,
3
10. 1 − __ =
4
3 + ___
4 =
2 + ___
1 + ___
12. ___
10 10 10 10
–
4263
q
1784
q=
Saxon Math Intermediate 5
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octagon 12 in.
,
3 − 1 __
2=
11. 3 __
3
3
1=
1 − __
5
14.
Add all sides.
3 + 4 __
1=
13. 5 __
4
4
15.
+
$19.34
m
$50.00
16.
58
39
24
16
52
+ 11
© 2008 Saxon
9. Rename the 1.
8. Perimeter
m=
400
Adaptations Lesson 61
10/31/07 1:59:11 PM
Written Practice, continued
17.
389
× 470
page 392
_____ =
18. 5445
9
19. Write the quotient with
a fraction.
25
___ =
6
20. long division
22. (800 − 300) × 20 =
21. long division
894 ÷ 40 =
943 ÷ 30 =
1
1 = ___
24. __
23.
20
2
2
3
1 = 20
__
___
2
0
4
Use work area.
© 2008 Saxon
25. Start counting with December.
15 months after November?
26. Find ST.
Label the figure.
R
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401
S
?
T
Adaptations Lesson 61
10/31/07 1:59:13 PM
page 392
Written Practice, continued
27. Which angle in this figure on
28. Oregon
page 392 appears to be a right angle?
1859
West Virginia (Oregon + 4)
+
Arizona (West Virginia + 49)
+
=
=
Use work area.
29. 65 guests are to be seated at 3 tables. What is a reasonable estimate of the
number of guests per table? Explain.
Using compatible
, 65 is close to
, which
is a factor of 3.
66 ÷ 3 =
is a reasonable estimate for the number of
per table.
Use work area.
30. a. How many months did he practice more than 20 days?
c. mode
most
d. median
middle
e. range
span
© 2008 Saxon
b. How many months did he practice between 15 and 20 days?
Use work area.
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Adaptations Lesson 61
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LESSON
Name
62
Teacher Notes:
page 394
• Review Hint #29 “Estimating or
Rounding.”
• Estimating Arithmetic
Answers with Rounded and
Compatible Numbers
• Review “Estimate” on page 8 in the
Student Reference Guide.
• For additional practice, students
may complete Targeted Practice 62.
New Concept
• An estimated answer is not an exact answer, but it is close.
• Estimate to see if your calculated answers are reasonable.
• Estimation can use rounded numbers to make the math
easier.
Example
29
30
$08.95
$ 9
× 21
× 20
$07.23
$ 7
600
$11.42
$11
+ $06.89
+$ 7
$34
Lesson Practice
Estimate each answer by rounding or using compatible numbers before doing the
arithmetic.
© 2008 Saxon
a. 68
39
70
+ 40
110
40
× 020
×
25
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+
f. 29
−
Offset.
Saxon Math Intermediate 5
c. 585
312
e. 94
d. 38
19
b. 41
23
312
×
Offset.
403
Adaptations Lesson 62
10/31/07 2:00:51 PM
Lesson Practice, continued
_____
) 123
h. 29
g. 685
59
−
391
Cancel matching zeros.
_____
i. 703
) 123
j. 31
96
−
497
k. Estimate the sum of:
l. Estimate the perimeter:
$12.95
$ 7.03
$ 8.49
57
41
× 2=
57 mm
41 mm
Written Practice
page 397
cups per dozen
1.
6
made
0020
left over
eaten
© 2008 Saxon
made
centuries ____
1 = __
?
2. _________
years
100 0
A century is
Saxon Math Intermediate 5
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years, and 100 ×
404
= 1000.
Adaptations Lesson 62
10/31/07 2:00:57 PM
Written Practice, continued
4. Shade 3_1.
3. average
4
7
7
2
page 397
Name the fraction and
percent not shaded.
_____
) 123
5. Estimate the product.
3
7. 1− __ =
8
6. Rename the 1.
1 =
1− ___
10
39
41
3=
4 − 2 __
8. 4 __
4
4
11. 8 = 7 __
6
10 − ___
1 =
10. 6 ___
10 10
1 + 1 __
2=
9. 3 __
3
3
12. Estimate the sum.
© 2008 Saxon
586
317
numerator =
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Adaptations Lesson 62
10/31/07 2:01:01 PM
Written Practice, continued
13.
89,786
26,428
57,814
+ 91,875
14.
page 397
$35,042
− $17,651
16. 5y = 4735
15.
428
× 396
17. 8 × 43 × 602 =
602
× 43
×
8
y=
18. Write the quotient with
a fraction.
19. long division
967 ÷ 60 =
20. long division
875 ÷ 40 =
15 =
___
8
0
1 > ___
b. __
2
10
© 2008 Saxon
0
1 = ___
21. a. __
2
10
a.
0
1 < ___
c. __
2
10
b.
c.
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Adaptations Lesson 62
10/31/07 2:01:03 PM
page 398
Written Practice, continued
22. $100 − ($24 + $43.89 + $8.67 + $0.98) =
23. Perimeter
even
24.
Add all sides.
×
5
product
Last digit?
mm 10
20
30
When the numbers 0, 2, 4, 6, or
A 15 mm
B 40 mm
C 60 mm
D 100 mm
8 are multiplied by
,
product ends in
the
.
25. A flight leaves in the morning at the time shown.
If it takes 3 hours and 20 minutes, what time will the plane land?
time now:
11
10
20 minutes later:
12 1
2
9
3
4
8
© 2008 Saxon
3 hours later:
26. a. all possible outcomes:
7
,
6
5
,
1
2
b. probability of stopping on sector 3 with one spin:
3
c. probability of stopping on sector 1 with one spin:
Use work area.
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Adaptations Lesson 62
10/31/07 2:01:04 PM
Written Practice, continued
page 398
27. Which angle in this figure appears to be an obtuse angle?
X
Y
W
Z
M
28. Estimate the perimeter.
126 in.
32 in.
126
×2=
032
×2=
+
=
Use work area.
29. half of 25
30. New York City
12:00 p.m.
Chicago (New York City – 1 hour)
© 2008 Saxon
Los Angeles (Chicago – 2 hours)
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Adaptations Lesson 62
10/31/07 2:01:06 PM
LESSON
Name
63
Teacher Note:
page 400
• For additional practice, students
may complete Targeted Practice 63.
• Subtracting a Fraction
from a Whole Number
Greater Than 1
New Concept
• To subtract a fraction from a whole number greater than 1:
1. Line the number up vertically.
2. Borrow 1 from the whole number and rename the 1 as
a fraction.
3. Subtract.
Example
1
4 − __
3
2
4 __
2
−
3
4
2
1
__
2
1
__
2
2
2
3
Lesson Practice
Subtract. Borrow from the whole number and rename.
3
4
4 __
a.
4
1
__
© 2008 Saxon
−
d.
2
Saxon Math Intermediate 5
e.
c.
3
__
4
−
4
−
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b. 0 3 0
40
1
− 2 __
4
f.
4
−
6
−
409
Adaptations Lesson 63
10/31/07 2:02:22 PM
Lesson Practice, continued
g. At noon there were 3 pies. By 1:00 p.m., 14_3 of the pies had been served.
Shade the circles below to show how much pie was served. Then tell how much
pie remains.
pies remain.
page 402
Written Practice
1.
7 cm
34 cm
00000
+ m00000
100 cm
7 cm
2. Borrow and rename.
6 0 in.
34 cm
1 in.
− 1 __
2
?
100 cm
3.
hamburgers per pound
pounds
18
19
24
23
_____
) 000
6. factors of 14:
398
1,
487
Cross out the numbers
that are not factors
of 21.
,
, 14
© 2008 Saxon
5. Estimate the sum.
4. average
,
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Adaptations Lesson 63
11/8/07 11:29:29 AM
page 402
Written Practice, continued
7. The distance around is called the
A radius
8.
+
B diameter
,
,
,
10.
60
11.
80
3
− 3 __
4
1
− 2 __
2
1
__
3
−
2
__
9
1
− __
9
© 2008 Saxon
D area
0
70
8
__
9
13.
411
3
5 __
2
3 __
4
1
+ 1 __
4
+ 0
Saxon Math Intermediate 5
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C circumference
,
9. Borrow and rename.
12.
.
4
−
0
Adaptations Lesson 63
10/31/07 2:02:26 PM
page 403
Written Practice, continued
14.
43,716
− 19,537
15.
$6.87
×
794
16.
$14.72
_______
8
=
17. Write the
quotient with a
fraction.
20
___
9
18. long division
_________
20 ) 9 5 1
=
19. Cancel matching zeros.
R
______
50 ) 2 5 6 0
R
_____
2560
_____
5)
50
R
Add the zero back to the remainder.
21. Cancel matching zeros.
22.
(400 + 400) ÷ 40 =
8
__
8
23. 8_3 were not in the library.
Name the fraction and the percent that
were in the library.
SM_H5_AD_L063_FF.indd 412
−
%
See “Fraction-Decimal-Percent-Equivalents”
on page 19 of the Student Reference Guide.
Saxon Math Intermediate 5
4736
2849
351
+ 78
412
© 2008 Saxon
20. 50 × (400 + 400) =
Adaptations Lesson 63
10/31/07 2:02:27 PM
page 403
Written Practice, continued
24. least to greatest
5
___
10
1
__
2
5
__
8
1
__
2
5
___
12
1
__
2
25. What is the perimeter of this
equilateral triangle?
mm 10
,
26.
20
30
,
Animal
Average Weight (in pounds)
Horse
100
100
Chimpanzee
100
100
100
100
Saltwater
Crocodile
Gorilla
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
Key:
100
100
= 100 pounds
a. least to greatest
,
b. 150w = 450
,
missing factor
,
Divide.
w=
c. 2000 pounds = 1 ton
© 2008 Saxon
two animals that together weigh about 1 ton:
,
Use work area.
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Adaptations Lesson 63
10/31/07 2:02:28 PM
Written Practice, continued
27.
polar bear
page 404
28. type of angle formed by hands
arctic gull
11
10
12 1
2
9
3
4
8
7
6
5
29. Explain the best way to estimate 350 ÷ 4.
Since 4 is a factor of 36, it is also a factor of
to 350. Using
c
,
numbers, 360 ÷ 4 =
which is close
.
Use work area.
39
© 2008 Saxon
30.
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Adaptations Lesson 63
10/31/07 2:02:30 PM
LESSON
Name
64
Teacher Note:
page 405
• Review “Place Value” on page 13
in the Student Reference Guide.
• Using Money to Model
Decimal Numbers
New Concept
• Money helps us understand decimal place value:
Place-Value Chart
Whole Numbers
Decimals
Place Name
hundreds
tens
ones
tenths
hundredths
Place Value
100
10
1
1
10
1
100
$100 bills
$10 bills
$1 bills
dimes
pennies
Place
Money Value
of Place
Example
ones
tenths
hundredths
$6 .
2
5
six
two
five
dollars
dimes
pennies
Lesson Practice
© 2008 Saxon
Name the place value of the 5 in each of these numbers.
a. $25.60
b. $54.32
c. $12.75
d. $21.50
e. What combination of dollars, dimes, and pennies makes $3.84 using the fewest
bills and coins possible?
dollars
Saxon Math Intermediate 5
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dimes
415
pennies
Adaptations Lesson 64
10/31/07 2:03:49 PM
Lesson Practice, continued
f. Is $12.63 closer to $12.60 or to $12.70?
g. Is $6.08 closer to $6.00 or to $6.10?
h. $1.49
$00000
× 000003
,
$1.49 can be rounded to
×3=
so
e
.
page 409
Written Practice
1.
is a reasonable
,
+
,
2. 00$30.63
00$17.85
3.
×
© 2008 Saxon
total
empty
filled
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Adaptations Lesson 64
10/31/07 2:03:51 PM
Written Practice, continued
4. missing factor
page 409
5. Estimate the product.
Divide.
68
_____
)
6h =
52
3 up
6. ___
10
Name the fraction and the percent down.
7. Numbers written in dollars
and cents (such as $54.63)
have how many decimal
places?
10
00___
10
%
8. What combination of dollars, dimes,
and pennies makes $3.25 using the
fewest bills and coins possible?
9. Is $4.82 closer to $4.80 or $4.90?
dollars
dimes
pennies
Use work area.
© 2008 Saxon
10. Divide 25 by 8.
11. factors of 20:
Write the quotient with a fraction.
1,
,
,
,
, 20
Cross out the numbers that are not factors of 30.
,
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417
,
,
Adaptations Lesson 64
10/31/07 2:03:52 PM
page 409
Written Practice, continued
13. 360 − a = 153
12. What time is 12_1 hours before noon?
1 hour before noon:
_1
2
hour before that:
a=
14. 5m = 875
3
5 − z = __
16. __
5
3
15. Rename the 1.
3+f=1
__
5
17. $30.48 ÷ 6 =
z=
f=
18.
20. Property of Zero for Multiplication
____________
60 ) 1
5
8
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6
19.
$4.34
$0.26
$5.58
$9.47
$6.23
+ $0.65
21. Borrow and rename.
5×4×3×2×1×0=
Saxon Math Intermediate 5
R
70
2
– 3 __
3
418
© 2008 Saxon
m=
Adaptations Lesson 64
10/31/07 2:03:54 PM
page 410
Written Practice, continued
22.
1
1__
3
2
__
+ 2
3
23. Borrow and rename.
24. perimeter
PQ = 12 mm
4
3
− 3 __
4
P
T
Q
S
25. Find the remainder.
a.
_____
3 )1
R
0
b.
R
26. What is the perimeter of this
equilateral triangle?
_________
3 )1
0
R
0
inch
1
2
a.
b.
27. What is the probability that the letter selected will be one of the letters that follows
Q in the alphabet?
© 2008 Saxon
T C B F M R J
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Adaptations Lesson 64
10/31/07 2:03:55 PM
page 411
Written Practice, continued
28. Display the below data in a line graph.
April Day in Hershey, PA
Time
Temperature
(°F)
60
12:00 a.m.
43
58
3:00 a.m.
46
6:00 a.m.
45
9:00 a.m.
48
12:00 p.m.
58
56
Temperature (ºF)
54
52
50
48
46
44
42
12:00 3:00 6:00 9:00 12:00
a.m. a.m. a.m. a.m. p.m.
Time
Use work area.
29. Wednesday
59º
Tuesday (Wednesday – 7º)
Monday (Tuesday + 12º)
Use work area.
30. The hockey coach purchased six hockey pucks for $3.49 each. Explain how
addition can be used to make a reasonable estimate of the total cost.
,
and $3.50 + $3.50 is
the cost of two pucks is about
+
+
.
,
the cost of six pucks is
,
or
Since
© 2008 Saxon
$3.49 is about
.
Use work area.
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Adaptations Lesson 64
10/31/07 2:03:56 PM
LESSON
Name
65
Teacher Notes:
page 412
• Review Hint #32 “Reading Metric
Rulers.”
• Review “Equivalence Table for
Units” on page 1 in the Student
Reference Guide.
• Decimal Parts of a Meter
New Concept
• Meters can be divided into smaller units:
Math Language
decimeters (tenths)
• The meter is
the basic unit
of length in the
metric system.
centimeters (hundredths)
millimeters (thousandths)
1 meter
10 decimeters
100 centimeters
1000 millimeters
cm 10
20
30
40
50
60
70
80
90
• The fractional parts of a meter can represent a decimal
number.
ó10
meter
ó10
ó10
decimeter centimeter
millimeter
© 2008 Saxon
Example
How many millimeters equal 4 decimeters?
4 dm = 40 cm
40 cm = 400 mm
Eduardo was 1 meter plus 35 centimeters tall. What was his
height in meters?
1 m + 35 cm = 1 m + 3 dm + 5 cm = 1.35 m
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Adaptations Lesson 65
10/31/07 2:06:43 PM
New Concept, continued
Activity 1
page 414
Decimal Parts of Meter
• This activity is optional.
Activity 2
page 415
Measuring with a Meterstick
• Use your textbook to complete this activity.
Lesson Practice
a. Which of these is the most reasonable measurement for the length of an
automobile? (Circle one.)
A 4.5 meters
B 4.5 decimeters
C 4.5 centimeters
D 4.5 millimeters
b. Alonso is 1 meter plus 43 centimeters tall.
Use a decimal number to write Alonso’s height in meters.
© 2008 Saxon
c. A ruler is about 30 centimeters long.
About how many decimeters long is a ruler?
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Adaptations Lesson 65
10/31/07 2:06:46 PM
page 415
Written Practice
1. Draw a quadrilateral with one pair of
horizontal segments and one pair of
vertical segments.
2. number in each group × number of groups
total players
____
8)
Use work area.
3. perimeter
100 yards
40 yards
4.
_1
4
of a yard
36 in.
1
4
____ in.
___
) 36
1
__
4
=
____ in.
____ in.
percent
____ in.
5. Count on a clock the minutes from 7:45 to 8:30.
6. Estimate the sum.
© 2008 Saxon
672
830
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423
Adaptations Lesson 65
10/31/07 2:06:48 PM
page 416
Written Practice, continued
7. a. fraction shaded
b. fraction not shaded
r
c. My answers are
+
because
=
a.
10
__
, or 1 whole.
10
b.
c.
8. height of refrigerator
9. half a meter =
1 m + 32 cm =
8
1,
__
2
11. How many factors?
2
__
1,
__
2
3
,
12. Write the quotient as a
mixed number.
5
___
1
__
10
2
,
factors of 10:
,
13. greatest
3
4
5
15 =
___
4
© 2008 Saxon
4
3
__
decimeters
m
10. least to greatest
4,
__
Use work area.
odd
Saxon Math Intermediate 5
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424
Adaptations Lesson 65
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page 416
Written Practice, continued
500
14.
15.
36,195
17,436
+ 42,374
16.
41,026
− 39,543
more than
17.
608
× 479
18. 2637 ÷ 4 =
19. Cancel matching zeros.
_____________
40 ) $3
20. Cancel matching zeros.
3 + 5 __
5 =
21. 3 __
8
8
3360
_____
22. Borrow and rename.
8
24. 6 × 42 × 20 =
25. $20 − ($5.63 + $12) =
© 2008 Saxon
4
0
3 =
5 − 3 __
20
3 −3=
23. 3 __
3 . 6
Saxon Math Intermediate 5
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Written Practice, continued
page 417
27. By which of these numbers is 1080
divisible?
26. Use the Distributive Property.
2 2_1 dozen = 2 dozen +
_1
2
dozen
2, 3, 5, 6, 9, 10
Check all the numbers. See “Tests for
Divisibility” on page 20 in the Student Reference
Guide.
How many eggs?
+
2
28. probability
1
2
3
4
a. even number
b. less than 4
c. less than 5
a.
b.
c.
29.
degrees cooler
J’Ron
60 minutes
© 2008 Saxon
30.
Adolfo (J’Ron ÷ 2)
Shaun (Adolfo ÷ 2)
Saxon Math Intermediate 5
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