Let’s play “Name T hat Car !”

1. Let’s play “Name That Car!”

2. What car is this?

3. And this?

4. How about this one?

5. Which one of these weighs the least? Which one weighs the most?

6. Which one of these gets the best gas mileage? Which one gets the worst?

7. How about these 2009 Chevy vehicles?

8. Welcome to Grade 6, Lesson 6: Scatter Plots

9. Learning Targets and Success Criteria We are learning to… • Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, and to describe patterns such as positive or negative association, and linear association (8.SP.A.1). • Recognize linear relationships in scatter plots, and informally predict an outcome based on the observed pattern of scattered points (8.SP.A.2). • Look for and make use of structure by identifying a pattern or structure in scatter plots. (MP.7).

10. Learning Targets and Success Criteria We will be successful when we can: • Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, and to describe patterns such as positive or negative association, and linear association Construct and interpret a relative frequency table given a two-way frequency table. • Recognize linear relationships in scatter plots, and informally predict an outcome based on the observed pattern of scattered points. • Look for and make use of structure by identifying a pattern or structure in scatter plots. • Explain why association does NOT imply causation.

11. What does “bivariate” mean? “Bi” = Two “Variate” = Variables Up until now we’ve only used “univariate” data.

12. Is there an apparent relationship between the two given variables? Which one would you use as the explanatory variable? Age of a tree and its trunk diameter Rainfall amount and corn yield Car weight and fuel efficiency

13. We will look for a relationship between the “weight of a vehicle” and the “fuel efficiency(mpg)” of a variety of 2009 Chevy cars using ordered pairs of data graphed on a coordinate plane. This method is called a scatter plot. Why do you think the graph of bivariate data is called a “scatter plot?” The “scattered” points will be displayed by using the x-axis for the weight of the car, and the y-axis for the fuel efficiency of the car. Plot the ordered pairs (x,y) by using the (weight, mpg) for each vehicle!

14. You will find this bivariate data set on page 41 in your student book.

15. On page 42 the first ordered pair is graphed for you. Please graph the remaining 12 points of the scatter plot and answer questions #1-3 on those pages. You have about 10 minutes to do this with your table.

16. This is what your first scatter plot should look like.

17. Using the observed pattern on your scatter plot, raise your hand when your group thinks they can predict what the fuel efficiency would be for a 5,000 pound car. Be ready to explain your answer and tell why this observed relationship might be important to someone?

18. You have 10 minutes to work on exercises #4-8 and discuss the responses at your table. Then we will discuss your responses with the big group. Big group discussion of questions #4 - 8.

19. Your graph for exercise #6 should look similar to this, depending upon your choice for horizontal and vertical scale.

20. Please examine the scatterplot on page 45. Is there a pattern that indicates a relationship between the dependent variable and the independent variable? Is it reasonable to conclude that shoe size “causes” high reading scores? Can you think of a different explanation for why you might see a pattern like this?

21. Lesson Summary

22. Learning Targets and Success CriteriaReview of our learning intentions and success criteria. Did we learn to… • Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, and to describe patterns such as positive or negative association, and linear association (8.SP.A.1). • Recognize linear relationships in scatter plots, and informally predict an outcome based on the observed pattern of scattered points (8.SP.A.2). • Look for and make use of structure by identifying a pattern or structure in scatter plots. (MP.7).

23. Learning Targets and Success CriteriaReview of our learning intentions and success criteria. We will be successful when we can: • Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, and to describe patterns such as positive or negative association, and linear association Construct and interpret a relative frequency table given a two-way frequency table. • Recognize linear relationships in scatter plots, and informally predict an outcome based on the observed pattern of scattered points. • Look for and make use of structure by identifying a pattern or structure in scatter plots. • Explain why association does NOT imply causation.

24. Grade 8, Lesson 6 Mathematical Practices CCSSM MP.7 engageny MP.7 MP.7 Look for and make use of structure Students identify pattern or structure in scatter plots. They fit lines to data displayed in a scatter plot and determine the equations of lines based on points or the slope and initial value. MP.7 Look for and make use of structure Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well remembered 7x5 + 7x3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.