LESSON
44
• Measuring Lengths
with a Ruler
Power Up
facts
mental
math
Power Up F
a. Time: How many minutes is 5 hours?
b. Time: What time is 33 minutes after 6:27 a.m.?
7:00 a.m.
c. Money: Which bill has a value of 25% of a $20 bill?
d. Number Sense:
e. Number Sense:
3
4
3
4
+
−
1
4
1
4
$5 bill
1
2
4
or 12
f. Geometry: The sides of a triangle are 3 cm, 4 cm, and 5 cm
long. What is the distance around the triangle? 12 cm
g. Measurement: 17 yards is how many feet? (Think: 17 × 3.)
51 ft
h. Calculation: 2 × 25, − 1, ÷ 7, + 1, ÷ 2, × 5, + 1, ÷ 3
problem
solving
7
Choose an appropriate problem-solving strategy to solve
this problem. Ms. Gordy wants to arrange the 24 classroom
desks in equal-length rows. Each row must contain at least
4 desks but not more than 8 desks. How many different
arrangements of desks can she make? Describe the possible
arrangements. three arrangements; 6 rows of 4 desks, 4 rows of 6 desks,
and 3 rows of 8 desks
New Concept
Reading Math
A centimeter is
about the width of
the fingernail on
your index finger.
You might have a ruler at your desk that has both a centimeter
scale and an inch scale. We will practice using both scales in
this lesson to measure length. Length is the measure of the
distance between two points. On the next page we show a
centimeter scale and a millimeter scale. The words centimeter
and millimeter are abbreviated “cm” and “mm,” respectively.
Lesson 44
275
MM CM The centimeter scale is divided into segments 1 centimeter long
and may be further divided into millimeters (mm). Notice that
10 millimeters equals 1 centimeter. The arrow is 4 centimeters
long. It is also 40 millimeters long.
Example 1
The distance across a nickel is about 2 centimeters. Two
centimeters is how many millimeters?
We remember that 1 centimeter equals 10 millimeters, so
2 centimeters equals 20 millimeters.
What is the length, in millimeters, of ten nickels placed
end to end?
Analyze
Example 2
What is the length of the rectangle below?
MM There are tick marks on the scale to mark each millimeter.
Notice that the tick marks for every fifth and tenth millimeter are
lengthened to make the scale easier to read. We see that the
rectangle’s length is 20 millimeters plus 5 more millimeters, which
is 25 mm.
Centimeters and millimeters are units of length in the
International System of Units, which is sometimes called the
metric system. The basic unit of length in the metric system is a
meter. You might have a meterstick in your classroom. When you
1
take a big step, you move about one meter. A centimeter is 100
1
of a meter. Units in the metric
of a meter, and a millimeter is 1000
system are related by the number 10.
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Saxon Math Intermediate 5
Inches, feet, yards, and miles are not units in the metric system.
These units of length are part of the U.S. Customary System.
Units in the U.S. Customary System are not related by the number
10. Instead, 12 inches equals a foot, 3 feet equals a yard, and
5280 feet (or 1760 yards) equals a mile. Inches usually are not
divided into tenths; rather, they are divided into halves, fourths,
eighths, sixteenths, and so on. When we abbreviate the word inch
or inches, we make sure to include a period in our abbreviation.
We abbreviate inch or inches like this: in. Here we show an inch
scale divided into eighths:
Math Language
INCH
1
-inch
4
A
segment
is also called a
quarter inch. How
many quarter
inches are equal
to 1 inch? 4
Below we show a magnified portion of an inch ruler. We see that
2
of an inch equals 14 of an inch, 48 of an inch equals 12 of an inch,
8
and 6 of an inch equals 34 of an inch.
8
1
1
3
4
2
4
1 2 3 4 5 6 7
8 8 8 8 8 8 8
1
Example 3
How many inches long is this arrow?
INCH
The marks on the ruler divide each inch into eight smaller
segments. Each small segment is one eighth of an inch long.
Measuring the arrow, we see that its length is 2 full inches plus
4 small segments, or 2 48 inches. However, there are other ways to
4
name the fraction 8. We see that the mark at the end of the arrow
is exactly halfway between 2 and 3. That mark is the two-and-one1
1
half-inch mark, so the length of the arrow is 2 2 inches, or 2 2 in.
Notice on the ruler that the half-inch marks are slightly longer than
the quarter-inch marks and the eighth-inch marks.
How many 212-inch segments are equal to 10 inches?
2 12
+ 2 12
=
Explain how you know.
Analyze
5 in. + 5 in. = 10 in.
Lesson 44
277
Example 4
3
A Mangrove Skipper butterfly can have a wingspan of 2 4 inches.
3
Is 2 4 inches closer to 2 inches or to 3 inches?
3
Since 34 is more than 12 , we know that 2 4 inches is closer to 3 inches.
What types of items would you measure using:
Conclude
student work.
a. inches?
Lesson Practice
b. centimeters?
See
c. millimeters?
Use a centimeter ruler to measure each segment in centimeters
and in millimeters:
a.
3 cm; 30 mm
b.
6 cm; 60 mm
c.
d.
9 cm; 90 mm
Measure the length of your math book to the
nearest centimeter. 28 cm
Estimate
e. One centimeter is how many millimeters?
f. How many millimeters is 5 centimeters?
10 millimeters
50 millimeters
g. Write the abbreviations for “centimeter” and
“millimeter.” cm, mm
h. How many millimeters long is the nail?
mm 10
20
30
15 mm
40
i. How many centimeters long is the arrow? 3 cm
For problems j–o, name the mark on the ruler to
which each arrow is pointing.
Connect
J
K
INCH
j.
1
2
in.
L
k.
1 14
in.
M
N
l.
1 78
in.
O
m.
3
28
in.
n.
3 18
in.
o.
3 43
in.
Use an inch ruler to measure each segment to the nearest eighth
of an inch:
3 14 in.
p.
2 12 in.
q.
r.
278
Saxon Math Intermediate 5
1 58 in.
s.
Estimate
t. Round
inches to the nearest inch.
Draw a quadrilateral that has four right angles.
Represent
(31, 32)
6 in.
6 in.
Distributed and Integrated
Written Practice
* 1.
5 78
Is 6 18 inches closer to 6 inches or 7 inches?
Sample:
2. In her pocket Sh’Marah has 3 pennies, 2 nickels, a dime, 3 quarters,
and a half dollar. How much money is in Sh’Marah pocket? $1.48
(13)
For problems 3–5, write an equation and find the answer.
3. One hundred thirty-eight kindergartners climbed on three buses to
go to the zoo. If the same number of children were on each bus, how
many children were on each bus? 3b = 138; 46 children
(21)
4. Blanca is in third grade. The index finger of Blanca’s left hand is
6 centimeters long. What is that length in millimeters? 6 × 10 = m; 60 mm
(44)
5. South Dakota became our 40th state in 1889. Vermont became our
14th state in 1791. How many years before South Dakota became a
state did Vermont become a state? 1889 − 1791 = y; 98 years
(35)
6. Three friends want to share five oranges equally. How many oranges
should each friend receive? 1 23 oranges
(40)
* 7.
Connect
(38)
What mixed number names point Z on this number line?
3
25
:
1
8. 33 ⫺ 1 2 2 4
4
4
(41)
9. 4 1 ⫺ 1 4
2 2
(43)
10. 5 1 ⫺ 4 1 14
(43)
4
11. 33 1 ⫹ 33 1
(41)
3
3
12. 5 1 ⫹ 3
(43)
3
13. 8 3 ⫹ 4
(43)
8 8
8 13
66 23
8 78
Lesson 44
279
14. What is the length of this rectangle?
16 mm
(44)
MM 15. 352 + 4287 + 593 + 7684 + 9856
22,772
(6)
16. 3627 − 429
3198
(9)
343,700
20. 5n = 3175
635
19. 60 × 8 × 37
17,760
(18, 29)
(29)
(26)
(Inv. 3,
37)
7170
(24)
18. 491 × 700
* 22.
17. 9104 − (2000 − 66)
21. 2964 ÷ 10
296 R 4
(26)
Draw a circle. Shade all but one third of it. What percent
; 66 23%
of the circle is shaded?
Represent
* 23. Multiple Choice When we count by tens, we find that the number
(33)
256 is closest to which of the following numbers? C
A 240
B 250
C 260
D 300
24. The principal of an elementary school has scheduled a fire
(35)
drill for 30 minutes after the time shown on the clock. What
time is the fire drill scheduled for? 10:48 a.m.
25.
(25)
List
Write the common factors of 50 and 100.
1, 2, 5, 10, 25, 50
26. One foot is 12 inches. One fourth of a foot is how many inches? 3 inches
(Inv. 2)
27.
(33)
A shopper purchased two items at a hardware store.
The cost of each item was $3.49. Explain how to estimate the cost in
dollars of the purchase. $7; sample: $3.49 is close to $3.50, or 3 12 dollars, and
Estimate
3 12 dollars + 3 12 dollars = 7 dollars.
* 28. Multiple Choice Which of these numbers is divisible by 3 and
by 5? B
A 305
B 315
C 325
D 355
(22, 42)
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Saxon Math Intermediate 5
29. The recipe called for 13 cup of vegetable oil for one batch of corn bread.
(41)
How much vegetable oil is needed to bake two batches of corn bread?
2
3
cup
30. The thermometer shows the low temperature for a winter
(27)
day in International Falls, Minnesota. The high temperature
that day was 13° warmer. What was the high temperature
that day? 1°F
ä
Ľ£ä
ĽÓä
Early
Finishers
Real-World
Connection
Two pieces of wood are 108 cm long when placed end to end. One
piece is 28 cm longer than the other. How many millimeters long is
each piece of wood? 400 mm; 680 mm
Lesson 44
281