Converting within the Metric System

Transcription

1 Converting within the Metric System Team members: Donna Massey and Julie Schlabaugh I. Lesson Plan (designed for teacher) Lesson Title: Convert with Metric! Lesson Summary: This lesson will allow students to explore the pattern of converting larger metric units to smaller metric units. Key words: metric, convert, powers of 10 Background knowledge: 1. Students should know that the basic unit of length in the metric system is the meter. 2. Students should be able to define meter (m), decimeter (dm), centimeter (cm), and millimeter (mm). 3. Students should know, in order from greatest to least m, dm, cm, mm. 4. Students should be familiar with powers of 10. Lesson Goal: The goal of this activity is to recognize and use the pattern for converting large units to small units of measurement within the metric system. II. Investigation: Jimmy is competing in a unique triathlon at his school. The events include the shot put, the rope climb, and the long jump. Jimmy was to record his results on a scorecard, then turn it in to the official scorer. Unfortunately, Jimmy lost his scorecard so he wrote down his results on a scrap piece of paper. Shot put: Rope climb: Long jump: Jimmy was told by the official scorer to transfer his results to the following scorecard: Name Shot Put: dm Rope Climb: cm Long Jump: mm What does Jimmy need to do with his results? Given that there are 10 decimeters in 1 meter, how many dm = 3 m? Given that there are 100 centimeters in 1 meter, how many cm = 3 m? Given that there are 1000 millimeters in 1 meter, how many mm = 3 m?

2 Please fill in Jimmy s scorecard. As Jimmy was turning in his scorecard he noticed a pattern with his results. Do you see the pattern? Explain. Therefore, to change from a larger unit to a smaller unit, you need to (multiply/divide). Now try the following examples: 15 m = dm 8 m = cm 6 m = mm Let s extend the pattern. Given that 10 cm = 1 dm, how many cm = 150 dm? Given that 10 mm = 1 cm, how many cm = 800 cm? Given that 100 mm = 1 dm, how many mm = 150 dm? See if you can complete the chart. 15 m = dm = cm = mm 8 m = cm = mm 6 m = mm Therefore, to change from a larger unit to a smaller unit, you need to multiply by powers of. Try the following: 26 m = dm 13dm = cm 315 dm = cm 125 cm = mm 18 cm = mm 203 m = dm

3 Challenge: 6 m = cm 7.5 m = dm 27 m = mm 65.3 dm = cm 14 dm = mm 2.36 cm = mm What happens to the decimal point when you change from a larger unit to a smaller unit in the metric system? III. Solution (designed for teacher) m dm cm mm 1. Measurements are in order from greatest to least, top to bottom. 2. Each step represents a power of ten. 3. To complete conversions: move 1 step on the chart, move decimal point 1 time move 2 step on the chart, move decimal point 2 time move 3 step on the chart, move decimal point 3 time 4. If you move to the right (multiplication, converting larger to smaller units), move the decimal point to the right. 5. For future lessons, if you move to the left (division, converting to larger units), move decimal point to the left. 6. The chart can be extended to cover all metric units of length (km, hm, dam, m, dm, cm, mm). The pattern stays the same. 7. This chart can also be used for metric units of mass (g) and capacity (L). II. Investigation: Jimmy is competing in a unique triathlon at his school. The events include the shot put, the rope climb, and the long jump. Jimmy was to record his results on a scorecard, then turn it in to the official scorer. Unfortunately, Jimmy lost his scorecard so he wrote down his results on a scrap piece of paper.

4 Shot put: Rope climb: Long jump: Jimmy was told by the official scorer to transfer his results to the following scorecard: Name Shot Put: 30 dm Rope Climb: 300 cm Long Jump: 3000 mm What does Jimmy need to do with his results? Convert his (m) measurements to other metric units. Given that there are 10 decimeters in 1 meter, how many dm = 3 m? 30 Given that there are 100 centimeters in 1 meter, how many cm = 3 m? Given that there are 1000 millimeters in 1 meter, how many mm = 3 m? 3000 Did you multiply or divide? Multiply By what? 1000 Please fill in Jimmy s scorecard. As Jimmy was turning in his scorecard he noticed a pattern with his results. Do you see the pattern? Explain. Changing m to dm 3x10, decimal moved 1 time m to cm 3x100, decimal moved 2 times m to mm 3x 1000, decimal moved 3 times Therefore, to change from a larger unit to a smaller unit, you need to multiply_ (multiply/divide). Now try the following examples: 15 m = 150dm 8 m = 800 cm 6 m = 6000mm Let s extend the pattern. Given that 10 cm = 1 dm, how many cm = 150 dm? 1500 Given that 10 mm = 1 cm, how many cm = 800 cm? _8000

5 Given that 100 mm = 1 dm, how many mm = 150 dm? 15,000 0 See if you can complete the chart. 15 m = _150 dm = _1500 cm = _15000 mm 8 m = 80 cm = _800 mm 6 m = _6000 mm Therefore, to change from a larger unit to a smaller unit, you need to multiply by powers of 10. Try the following: 26 m = 260dm 13dm = 130cm 315 dm = 3150cm 125 cm = 1250mm 18 cm = 180mm 203 m = 2030dm Challenge: 6 m = 600cm 7.5 m = _75 dm 27 m = 27,000mm 65.3 dm = 653cm 14 dm = 1400mm 2.36 cm = 23.6mm What happens to the decimal point when you change from a larger unit to a smaller unit in the metric system? The decimal point moves to the right. The number of steps on the chart is equal to the number of times to move the decimal point.