# Measuring Lengths with a Ruler

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1 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 6:7 a.m.? 7:00 a.m. c. Money: Which bill has a value of 5% of a \$0 bill? \$5 bill d. Number Sense: e. Number Sense: or f. Geometry: The sides of a triangle are 3 cm, 4 cm, and 5 cm long. What is the distance around the triangle? cm g. Measurement: 7 yards is how many feet? ( Think: 7 3.) 5 ft h. Calculation: 5,, 7, +,, 5, +, 3 7 problem solving Choose an appropriate problem-solving strategy to solve this problem. Ms. Gordy wants to arrange the 4 classroom desks in equal-length rows. Each row must contain at least 4 desks but not more than 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 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 75

2 Example The centimeter scale is divided into segments centimeter long and may be further divided into millimeters (mm). Notice that 0 millimeters equals centimeter. The arrow is 4 centimeters long. It is also 40 millimeters long. The distance across a nickel is about centimeters. Two centimeters is how many millimeters? We remember that centimeter equals 0 millimeters, so centimeters equals 0 millimeters. Analyze What is the length, in millimeters, of ten nickels placed end to end? Example What is the length of the rectangle below? 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 0 millimeters plus 5 more millimeters, which is 5 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 take a big step, you move about one meter. A centimeter is 00 of a meter, and a millimeter is 000 of a meter. Units in the metric system are related by the number Saxon Math Intermediate 5

3 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 0. Instead, inches equals a foot, 3 feet equals a yard, and 50 feet (or 760 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 A 4 -inch segment is also called a quarter inch. How many quarter inches are equal to inch? 4 Below we show a magnified portion of an inch ruler. We see that of an inch equals 4 of an inch, 4 of an inch equals of an inch, and 6 of an inch equals 3 of an inch Example 3 How many inches long is this arrow? 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 full inches plus 4 small segments, or 4 inches. However, there are other ways to name the fraction 4. We see that the mark at the end of the arrow is exactly halfway between and 3. That mark is the two-and-onehalf-inch mark, so the length of the arrow is inches, or in. Notice on the ruler that the half-inch marks are slightly longer than the quarter-inch marks and the eighth-inch marks. Analyze How many -inch segments are equal to 0 inches? Explain how you know. + = 5 in. + 5 in. = 0 in. Lesson 44 77

4 Example 4 A Mangrove Skipper butterfly can have a wingspan of 3 4 inches. Is 3 4 inches closer to inches or to 3 inches? Since 3 4 is more than, we know that 3 4 inches is closer to 3 inches. Conclude What types of items would you measure using: See student work. a. inches? b. centimeters? c. millimeters? Lesson Practice Use a centimeter ruler to measure each segment in centimeters and in millimeters: a. 3 cm; 30 mm b. 6 cm; 60 mm c. 9 cm; 90 mm d. Estimate Measure the length of your math book to the nearest centimeter. cm e. One centimeter is how many millimeters? 0 millimeters f. How many millimeters is 5 centimeters? 50 millimeters g. Write the abbreviations for centimeter and millimeter. cm, mm h. How many millimeters long is the nail? 5 mm mm i. How many centimeters long is the arrow? 3 cm Connect For problems j o, name the mark on the ruler to which each arrow is pointing. j. in. k. 4 in. l. 7 in. m. 3 in. n. 3 in. o in. Use an inch ruler to measure each segment to the nearest eighth of an inch: p. 3 4 in. q. in. r. 5 in. 7 Saxon Math Intermediate 5

5 s. Estimate Is 6 inches closer to 6 inches or 7 inches? 6 in. t. Round 5 7 inches to the nearest inch. 6 in. Written Practice Distributed and Integrated *. (3, 3) Represent Draw a quadrilateral that has four right angles. Sample:. (3) In her pocket Sh Marah has 3 pennies, nickels, a dime, 3 quarters, and a half dollar. How much money is in Sh Marah pocket? \$.4 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 = 3; 46 children 4. (44) Blanca is in third grade. The index finger of Blanca s left hand is 6 centimeters long. What is that length in millimeters? 6 0 = m; 60 mm 5. (35) South Dakota became our 40th state in 9. Vermont became our 4th state in 79. How many years before South Dakota became a state did Vermont become a state? 9 79 = y; 9 years 6. (40) Three friends want to share five oranges equally. How many oranges should each friend receive? 3 oranges * 7. (3) Connect What mixed number names point Z on this number line? 3 5. (4) (4) Lesson 44 79

6 4. (44) What is the length of this rectangle? 6 mm 5. (6) ,77 6. (9) (4) 904 (000 66) 770. (9) , (, 9) , (6) 5 n = (6) R 4 *. (Inv. 3, 37) Represent Draw a circle. Shade all but one third of it. What percent of the circle is shaded? ; 66 3 % * 3. (33) Multiple Choice When we count by tens, we find that the number 56 is closest to which of the following numbers? C A 40 B 50 C 60 D (35) The principal of an elementary school has scheduled a fire drill for 30 minutes after the time shown on the clock. What time is the fire drill scheduled for? 0:4 a.m. 5. (5) List Write the common factors of 50 and 00.,, 5, 0, 5, (Inv. ) One foot is inches. One fourth of a foot is how many inches? 3 inches 7. (33) *. (, 4) Estimate 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 dollars, and 3 dollars + 3 dollars = 7 dollars. Multiple Choice Which of these numbers is divisible by 3 and by 5? B A 305 B 35 C 35 D Saxon Math Intermediate 5

7 9. (4) 30. (7) The recipe called for cup of vegetable oil for one batch of corn bread. 3 How much vegetable oil is needed to bake two batches of corn bread? 3 cup The thermometer shows the low temperature for a winter day in International Falls, Minnesota. The high temperature that day was 3 warmer. What was the high temperature that day? F Early Finishers Real-World Connection Two pieces of wood are 0 cm long when placed end to end. One piece is cm longer than the other. How many millimeters long is each piece of wood? 400 mm; 60 mm Lesson 44

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