Measuring in Millimeters

Transcription

1 Measuring in Millimeters Objectives To guide students as they measure lengths to the nearest millimeter; and to provide practice converting measurements between millimeters and centimeters. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Coon Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Use extended multiplication facts to convert between metric measurements. Use a scale to determine actual size. [Operations and Computation Goal 7] Measure lengths to the nearest millimeter. [Measurement and Reference Frames Goal 1] Describe the relationship among metric units of length. [Measurement and Reference Frames Goal 3] Key Activities Students examine the millimeter marks on their centimeter rulers. They measure line segments in millimeters and centimeters. Then they measure illustrations of various invertebrates in millimeters and convert their measurements to centimeters. Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. Materials Math Journal 1, pp Study Link 4 9 Math Masters, p. 429 centimeter ruler slate scissors highlighter Math Boxes 4 10 Math Journal 1, p. 104 Students practice and maintain skills through Math Box problems. Study Link 4 10 Math Masters, p. 133 Students practice and maintain skills through Study Link activities. READINESS Exploring the Need for Millimeters Math Masters, p. 134 scissors ruler Students explore the need for a metric unit of measure smaller than a centimeter. ENRICHMENT Investigating Ratios If You Hopped Like a Frog Students explore the concept of scale by comparing what humans could do if they had bodies like different animals. Measuring to the Nearest Millimeter ruler Students draw line segments and measure them to the nearest millimeter. Taking a 0-Facts Test Math Masters, pp. 413 and 414; p. 416 (optional) pen or colored pencil Students take a 0-facts test. They use a line graph to record individual and optional class scores. Advance Preparation For Part 1, make one copy of Math Masters, page 429 per four students. Cut the sections apart along the dashed lines. For the optional Enrichment activity in Part 3, obtain the book If You Hopped Like a Frog by David M. Schwartz (Scholastic Inc., 1999). Teacher s Reference Manual, Grades 4 6 pp. 217, 218 Lesson

2 Getting Started Mental Math and Reflexes Pose multiplication facts and extended facts. Suggestions: 0 6 = = = = = = 1, = = =,600 8 = = = 3, = = = 1,000 Math Message Complete Problems 1 4 on journal page 101. Study Link 4 9 Follow-Up Ask students to circle the most difficult problems. Then have students see if someone at their table can suggest a solution strategy. Ongoing Assessment: Recognizing Student Achievement Mental Math and Reflexes Use Mental Math and Reflexes to assess students automaticity with multiplication facts. Students are making adequate progress if they demonstrate automaticity with the and problems. Some students may demonstrate automaticity with the problems. 1 Teaching the Lesson Math Message Follow-Up (Math Journal 1, p. 101) WHOLE-CLASS Math Message Measuring in Millimeters On your centimeter ruler, the numbered marks are for centimeters and the little marks between the centimeter marks are for millimeters. 10 Sample answers: thickness of the wire in a paper clip; width of a pencil point; the edge of a dime 1. Look at your centimeter ruler. How many millimeters are in 1 centimeter? 2. Name something that measures about 1 millimeter. 3. Draw a line segment that is 8 centimeters long. 128 If students have difficulty naming things that measure about 1 millimeter, suggest these possibilities: the thickness of the wire in a paper clip; the width of a pencil point; or the edge of a dime. Students should conclude that both line segments they drew are the same length. Thus, 8 centimeters = 80 millimeters. In this lesson students use millimeters to measure very small invertebrates. They also practice converting millimeters to centimeters. 4. Draw a line segment that is 80 millimeters long. Measure each line segment below using both the millimeter side and the centimeter side of the / ruler. Record both measurements. A Length of AB C D 6. Length of CD 0.8 E F 7. Length of EF 8 62 B 6.2 Measuring Land Invertebrates An invertebrate is an animal that does not have a backbone. (The backbone is also called the spinal column.) Some invertebrates live on land, others in water. The most coon land invertebrates are insects. The invertebrates shown on page 102, except the earthworm, bumblebee, and mealybug, have been drawn to about actual size. The earthworm can grow to about 4 times the length shown. The bumblebee is shown about twice its actual size and the mealybug about 3 times its actual size. Math Journal 1, p Unit 4 Decimals and Their Uses

3 Measuring Lengths in Millimeters and Centimeters (Math Journal 1, p. 101; Math Masters, p. 429) WHOLE-CLASS Pass out the quarter-sheets of Math Masters, page 429 and have students cut out the / rulers. Then have them fold the rulers carefully along the center line. Encourage students to use a highlighter to mark and on the ruler so that the units are emphasized. Demonstrate how to use the centimeter side of the ruler by having students measure the line segment they drew in Math Message Problem 3. Instruct students to place the centimeter side of the folded ruler above the line segment with 0 aligned with the left end of the segment. Then demonstrate how to use the millimeter side of the ruler by having students measure the line segment they drew in Problem 4. Instruct students to place the millimeter side of the folded ruler under the line segment with 0 aligned with the left end of the segment. Now ask students to measure line segments AB, CD, and EF (Problems 7) using both sides of the / ruler. Record their measurements on the board: 12 = 12. ; 62 = 6.2 ; 8 = 0.8. Name A / Ruler Teaching Aid Master Math Masters, p NOTE When converting between millimeters and centimeters, tell students to think of the centimeter as the ONE, or the unit, and the millimeter as 1_ 10. Adjusting the Activity Some students may note that the measurements of each line segment on journal page 101 vary slightly. Ask students to explain why they think this might happen. Possible response: The spaces between millimeter marks are so small. A measurement is never exact it is only an approximation. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Write several millimeter/centimeter conversion problems on the board. Ask students to write their answers on their slates. Suggestions: 1 = 10 4 = = = 1 1 = = 13 4 = = = 0.8 Measuring Land Invertebrates Mayfly Dragonfly Adjusting the Activity ELL Ground beetle Lacewing Have students use their / rulers as concrete models for conversions between metric units. Pose millimeter/meter conversions to students. Water scavenger beetle Earthworm A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Threadworm Bumblebee (2 times actual size) Horsefly Mealybug (3 times actual size) Math Journal 1, p. 102 Lesson

4 4 10 Measuring Land Invertebrates continued Refer to the pictures on page 102 to answer the following questions. 1 centimeter () = 10 millimeters () 1 millimeter = 0.1 centimeter 1. Measure the following invertebrates to the nearest millimeter by finding the distance between the two guidelines. Then give the lengths in centimeters. a. mayfly About b. dragonfly About c. water scavenger beetle About d. ground beetle About e. lacewing About 0 f. horsefly About How much longer is the ground beetle than the water scavenger beetle? About 3. The bee has been drawn to twice its actual size. horsefly In reality, which is longer, the bee or the horsefly? 8 How much longer? About 4. The mealybug has been drawn to 3 times its 4 actual size. In the space at the right, draw a mealybug that is about the actual size. 4. What is the actual size of the mealybug in millimeters? 6. How did you solve Problem? Sample answer: The size of the mealybug in the picture is 12 millimeters long, which is 3 times its actual size. So I divided 12 by 3 to find its actual size 4 millimeters. 7. When straight, the threadworm in the drawing is 306 millimeters long Measuring Invertebrates in Metric Units (Math Journal 1, pp ) Links to the Future PARTNER PROBLEM SOLVING Science Link Ask students to read about measuring land invertebrates on journal page 101 and to examine the illustrations of land invertebrates on page 102. Explain how to measure the length or wingspan of the invertebrates by measuring the distance between the guidelines. Students should use their regular centimeter ruler to measure in millimeters (not the paper / ruler) and then convert the measurements to centimeters. Drawing and measuring line segments to the nearest millimeter is a Grade Goal. In Unit 8 of Fourth Grade Everyday Mathematics students use measurements to create scale drawings and use scale drawings to find area. What is its length in centimeters? 30.6 Math Journal 1, p. 103 In meters? m When students have finished journal page 103, have them look at the picture they drew for Problem 4. Ask them to use times-asmany language to compare the length of their drawing to the length of the mealybug picture on journal page 102. Sample answer: The picture is 3 times as long as my drawing. Then ask them to use a multiplication equation to represent this comparison. 4 3 = 12 2 Ongoing Learning & Practice 4 10 Math Boxes 1. Solve mentally or with a paper-and-pencil algorithm. a. 4,647 b. 2,00 + 3,228-1,398 7,87 1, Complete. a. 7 = 70 b. 1 = 10 c. 00 = m Math Boxes 4 10 (Math Journal 1, p. 104) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-8. The skill in Problem 6 previews Unit content. d. 4 = Tell whether each number sentence is or false. a = 2.2 b = c < 33 d > false e. 800 = 8 m 4. Name two properties of a regular polygon. a. The sides are the same length. b. The angles have the same measure. Sample answers. 129 Study Link 4 10 (Math Masters, p. 133) Home Connection Students convert between metric units. INDEPENDENT Without measuring, estimate the height of your chair. Then measure it. a. Estimate: About b. Measurement: About Answers vary. 6. Complete. a. Is 326 closer to 300 or 400? 300 b. Name the number halfway between 00 and Math Journal 1, p Unit 4 Decimals and Their Uses

5 3 Differentiation Options READINESS Exploring the Need for Millimeters (Math Masters, p. 134) PARTNER Name STUDY LINK Decimals and Metric Units 129 Symbols for Metric Units of Length meter (m) centimeter () decimeter (dm) millimeter () Study Link Master 1 decimeter 0 1 dm 1 m 10 dm 1 dm 0.1 m 10 centimeters m m 1 dm dm 100 millimeters m 1, m 1 dm dm To explore the need for standard units of measure, have students cut out the ruler at the bottom of Math Masters, page 134, and use it to measure the pencils in Problem 1. Discuss the need for a unit of metric measure that is smaller than a centimeter. Use your tape measure or ruler to help you fill in the answers below a. 4.2 b. 64 c. 2.6 m , a. 6. b. 26 c. 6.1 m 3. a. b. 30 c. 3 m 4. a. 80 b. 110 c. m 00. a. 43 b. 98 c. m a. 0.6 b. 4 c..2 m ENRICHMENT PARTNER Investigating Ratios 1 30 Min Literature Link To further explore the concept of scale, have students read If You Hopped Like a Frog by David M. Schwartz (Scholastic Inc., 1999). This book compares what humans could do if they had bodies like different animals. After students have read the book, have them answer the questions posed at the back of the book. Practice 7 3 and , 49, and 6 are multiples of. 8. 4, 63, and 18 are multiples of. Math Masters, p. 133 PARTNER Measuring to the Nearest Millimeter To practice measuring to the nearest millimeter, have students draw line segments, measure them to the nearest millimeter, and record the measurements in millimeters and centimeters. Partners measure each other s line segments and compare answers. Name Teaching Master Centimeters and Millimeters Taking a 0-Facts Test (Math Masters, pp. 413, 414, and 416) SMALL-GROUP See Lesson 3-4 for details regarding the administration of the 0-facts test and the recording and graphing of individual and optional class results. Cut out the ruler below. Use it to measure the pencils to the nearest centimeter. 1. a. b. Pencil A is about Pencil B is about long. long. 2. One pencil is longer than the other. Which pencil is longer? Circle your answer. Pencil A Pencil B 3. How did you figure out which pencil is longer? Sample answer: I measured both pencils. Pencil A is a little bit shorter than 12, and Pencil B is a little bit longer. 4. Marco wants to know the difference in length between the two pencils. Can you tell him? Why or why not? No. Sample answer: The ruler is not precise enough to be able to report the difference in length. I need a ruler divided into smaller units Centimeters Math Masters, p. 134 Lesson