Teaching Faster and Faster!

Transcription

1 Teaching Faster and Faster! Skills: Solving problems with data in decimal form and in a double-line graph Students solve problems based on Olympic event data given in a table and in a line graph. Tasks Tier 1 Below Level Tier 2 On Level Tier 3 Above Level Compare, order, and compute with decimals. X X X Calculate and analyze measures of central tendency. X X X Generate, record, and display game data. X X X Use metric measures of length. X X X Summarize results using mathematical language. X X X Analyze data to find patterns and make predictions. X X Make a line graph. Getting Started See the tips below for introducing the lesson. Make copies of the student data sheet (page ) and the appropriate leveled activity sheet for each group of learners (pages 45 47). Access prior knowledge by discussing the Olympics Games and the measurements used to decide the time, distance, weight, or score involved in winning events. Tier 1 Tier 2 Tier 3 Use the Data: Explain that the table and graph show the same data. Review each. Point out that m stands for men and w stands for women. Guide students to notice that times were measured in tenths of a second until 1968, when officials recorded times to the hundredths of a second. Review range as the difference between the fastest and slowest winning times. Play a Game: Help students set up their lane. If time permits, let each player make more flicks. Write About It: Discuss the questions to help students focus their thinking. Then have students summarize the discussion in writing, using mathematical language. Use the Data: Discuss how the table and graph show the same data. Note that s stands for Ask: What change do you notice about times from 1968 on? Discuss the effect of improved technology on greater accuracy in measuring time in the events. Review range and mean, as well as how to round decimals to the nearest tenth. Play a Game: Assist students in recording as they play. If time permits, let each player make more flicks. Write About It: Have students write their summaries using mathematical language. Invite volunteers to take 50 flicks, analyze the results, and share the findings. Extension: Ask students to use online sources to determine whether winning times in other Olympic events have improved over time. X Use the Data: Discuss student answers. Ask why 20-year rather than 10-year, intervals were used in the graph and table. [Olympics have been held every four years except in 1938 and 1958.] Play a Game: Have team members work cooperatively to measure, play the game, record the data, as well as make their line graphs. Assist with creating keys and lines on the graph, as needed. Write About It: Help students focus on how to use a line graph to make predictions. Extension: Ask students to conduct online research about other Olympic events and their record times. Have them compare the results to those of the 100-meter dash and share their findings. 43

2 Faster and Faster! Data Sheet Skills: Solving problems with data in decimal form and in a double-line graph The first Olympic Games were held in Greece nearly 3,000 years ago. It was just one race! Poets read their works aloud. There were horse races and political meetings. This event grew into a big festival. More races and sports were added. It went on for about 200 years. Then the ancient Olympic Games stopped. The modern Olympics first took place in They were held in Greece, just like the first ancient Games. There have been Olympic Games every four years since then. The Winter Olympic Games were added, beginning in 1924 and also take place every four years. The Summer Olympics now hosts more than 10,000 athletes from over 200 countries who compete in at least 300 events. Today s technology lets millions of fans follow the events from almost anywhere in the world. Female athletes first competed at the 1928 Games. They had three running races: the 100-meter, the 800- meter, and the 400- meter relay. Women also competed in the high jump and threw the discus. The table and graph show winning times for the 100-meter dash in 1928 and every 20 years thereafter. Winning Times in 100-Meter Dash Winning Olympic Times in the 100-Meter Dash Year Men s Times 10.8s 10.3s 9.95s 9.92s 9.69s Women s Times 12.2s 11.9s 11.08s 10.54s 10.78s Year Key Men Women

3 Faster and Faster! Activity Sheet Use the Data Complete the sentences. 1. The graph compares winning times for men and women in the dash. 2. The winning men s time in 1928 was 3. The fastest women s time in 1948 was 4. The fastest winning time was The slowest was 5. In 1988, the women s winning time was seconds slower than the men s winning time. 6. The range of men s winning times is The range of women s winning times is Play a Game Athletes usually get better with practice. Will you get better with practice at the Checker Flick? Find out! Player 1 Make a team of four students. Player 2 Use chalk or tape and a meter stick. Make a Player 3 lane that is 2 meters long and 50 centimeters wide. Mark a Start line on one end of the lane. Mark the Finish line at the other end. Player 4 Place a checker just behind the Start line. Use your finger and thumb to flick it down the lane. Aim to get as close to the Finish line as you can. Record how close you got, in centimeters. Each team member flicks the checker 5 times. Record how close each flick is to the Finish line. On separate paper, set up a table like the one shown. Record the results. 1 st Flick 2 nd Flick 3 rd Flick 4 th Flick 5 th Flick Write About It Study the team results. Answer these questions on the back of this page: A. Who had the closest flick? How close was it? B. What was the worst flick? How far away was it? C. What patterns, if any, do you see? Explain. 45

4 Faster and Faster! Activity Sheet Use the Data What was the difference in men s winning times from 1928 to 1948? In women s winning times for those same two Olympics? In what year was the difference in men s and women s winning times 1.13 seconds? 3. In what year was the difference in winning times the greatest? In what year was the difference the least? 4. What is the range of winning times for men? For women? To the nearest tenth of a second, what is the mean winning time for men for these five Olympics? For women? Which is more useful for finding statistics such as the range and mean the table or the graph? Explain. Play a Game 1 st Flick 2 nd Flick 3 rd Flick 4 th Flick 5 th Flick Athletes usually get better with practice. Will you get better with practice at the Player 1 Checker Flick? Find out! Player 2 Make a team of four students. Player 3 Use chalk or tape and a meter stick. Make Player 4 a lane that is 2 meters long and 50 centimeters wide. Mark a Start line on one end of the lane. Mark the Finish line at the other end. Place a checker just behind the Start line. Use your finger and thumb to flick it down the lane. Aim to get as close to the Finish line as you can. Record how close you got, in centimeters. Each team member flicks the checker 5 times. Record how close each flick is to the Finish line. On a separate paper, set up a table like the one shown. Record the results. Write About It On the back of this page, summarize what your table shows. Include the mean distance and the range of distances. Explain whether your results improved. How might the results differ if each player made 50 flicks? 46

5 Faster and Faster! Activity Sheet Use the Data What patterns in winning times does the table and the graph show? Write your answer on the back of this page. What change in scoring do you notice starting with the 1968 Games? 3. If you were asked to show the winning times for the years 1938, 1958, 1978, and 1998, would you be able to do this? Why or why not? 4. What is the range of men s winning times? What is the range of women s winning times? Compare the ranges. What do you notice about the rate of change? 5. Study the trend in winning times. What do you predict the winning times will be for men and for women in 2028? Explain. Play a Game Athletes usually get better with practice. Will you get better with practice at the Checker Flick? Find out! Make a team of four students. Use chalk or tape and meter stick. Make a lane that is 2 meters long and 50 centimeters wide. Mark a Start line on one end of the lane. Mark the Finish line at the other end. Place a checker just behind the Start line. Use your finger and thumb to flick it down the lane. Aim to get as close to the Finish line as you can. Record how close you got, in centimeters. Each team member flicks the checker 5 times. Record how close each flick is to the Finish line. On a separate paper, set up a table like the one shown. Record the results. Display the results in a quadruple line graph a line for each player. Use a different color for each line. Be sure to include a key. Player 1 Player 2 Player 3 Player 4 Distance in Centimeters st Flick 2 nd Flick 3 rd Flick 4 th Flick 5 th Flick Flick 1 Flick 2 Flick 3 Flick 4 Flick 5 Key Number of Flicks Player 1 Player 2 Player 3 Player 4 47

6 Answer Key Faster and Faster! Tier 1, page 45: Use Data: meter ; ; 1.66; Play a Game: Check student tables; Write About It: Answers will vary. Tier 2, page 46: Use the Data: seconds; 0.3 seconds ; seconds; 1.66 seconds seconds; 11.3 seconds 6. The table is more useful because it lists the data precisely. Play a Game: Check student tables; Write About It: Check student summaries. Tier 3, page 47: Use the Data: 1. Runners in the 100-meter dash got faster over time. Women s times came closer to men s times over the years 2. Winning times are measured to hundredths of a second instead of tenths. 3. No, it s not possible because the Summer Olympics are held every four years and there were no Games in those years seconds; 1.66 seconds; The range for the women is greater, indicating that their winning times are getting faster more quickly than the men s times are. 5. Answers will vary. Check that students justify their answers; Play a Game: Check student line graphs; Write About It: Check student summaries. 79