1-2 Data Collections Mathematics, especially algebra, is used to describe and interpret how quantities are related. In this lesson, we will explore how one quantity affects another and how their relationship is reflected in the graphs and tables that represent them. Miles and Intersections How long is your trip from home to school (estimate to the nearest half mile)? How many intersections do you pass through on your way to school? Distance (miles) Number of Intersections 5 15 4 20 7 10 10 7 7 4 10 3 4 5 3 2 Distance (miles) Number of Intersections 1) Create a scatterplot of the data above. Make sure to label your axis. 2) Based on the table and the scatterplot, do you see a pattern to this data? There should be no strong pattern 3) How does the number of intersections change as the distance from school increases? There should be no strong pattern, or points may be clustered fairly tight. The pattern may be slightly linear or increasing. 4) If I live 7 miles from the school, can you predict how many intersections I will pass through? Why or why not? No, the distance traveled cannot be used to reliable predict the number of intersections. Although there is no pattern to the data and it cannot be used to make predictions, the distance and the number of intersections are related because you can still write the data as ordered pairs. (distance, number of intersections) When any two sets of data can be written in ordered pairs, that comparison of data is called a relation. Burning Calories When you engage in physical activity, you burn kilocalories (kcal). Below is a table of the number of kilocalories burned per minute by a 110 pound person for different activities. # of kcal burned per Activity minute by 110 lb Basketball Card Playing Dancing Football Jumping Rope Playing the Piano Painting Walking person 6.9 1.25 3.75 6.6 8.1 2 1.7 4 1) Imagine you are going to work out after school. You have had extra snacks during the day. Does the number of minutes you need to exercise depend on the number of kilocalories you want to work off? Why or why not? Yes, the longer I exercise, the more kilocalories I burn. 2) Use proportions to calculate the number of minutes it would take to burn off 50 kilocalories while playing basketball? What shortcut could be used to calculate the number of minutes it takes to burn off a given number of kilocalories? 𝑘𝑖𝑙𝑜𝑐𝑎𝑙𝑜𝑟𝑖𝑒𝑠 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 6.9 50 = 1 𝑥 6.9𝑥 = 50 Shortcut would be to divide the number 𝑥 = 7.25 𝑚𝑖𝑛 of kilocalories burned per minute from table. 3) Choose one activity from the table. Record the name of your activity. Calculate the number minutes it would take to burn the given number of kilocalories to the nearest tenth of a minute. Energy Burned (kcal) 100 200 300 400 500 Activity: Basketball (min) 14.5 29 43.5 58 72.5 4) Create a scatterplot. Make sure to label your axis. 5) Based on the table and scatterplot, is there a pattern to this data? The points are in a straight line, the scatterplot is increasing, as the number of kilocalories increases, the number of minutes increases 6) If I wanted to burn 800 kcal, how many minutes would I have to dance in order to do this? 213.3 minutes 7) How does the number of minutes change as the number of kilocalories increases? The number of minutes increases as the number of kilocalories increases. 8) How are the data collections, Miles and Intersections and Burning Calories, similar and different? Similarities Both have a relationship with 2 quantities. Both have scales Differences Could predict in Burning Calories and couldn't in Miles and Intersections Pattern in Burning Calories and not in Miles and Intersections Burning Calories makes a straight line.