Variables and Patterns

1. Variables and Patterns Introducing Algebra

2. Investigation 1 Variables, Tables, and Coordinate Graphs

3. 1.1 Preparing for a Bike Tour What do you know about bicycle tours?

4. 1.1 Preparing for a Bike Tour 1. How far do you think you could ride in a day? How do you think the speed of your ride would change during the course of the day? What conditions would affect the speed and distance you could ride?

5. 1.1 Preparing for a Bike Tour

7. Variables and Patterns 1.2 Making Graphs

8. Math Dictionary Variable – a quantity that changes EXAMPLE: Time and the number of jumping jacks were the variables in our experiment

9. Math Dictionary Coordinate graph – displays data; shows the relationship between two variables A coordinate graph relates the dependent variable (y-axis) and the independent variable (x-axis)

10. Coordinate Graph

11. Math Dictionary Dependent variable – one of the two variables in a relationship; its value depends on the other variable Independent variable – one of the two variables in a relationship; its value determines the value of the other variable

12. Example The cost of a long-distance phone call (dependent variable) DEPENDS on how long you talk (independent variable).

13. Math Dictionary

14. Math Dictionary

15. Math Dictionary Scale – A labeling plan used on each of the axes on the coordinate grid (decide on the least and greatest values and how to space the scale marks) Coordinate pair – an ordered pair of numbers used to locate a point on a coordinate grid (x,y)

16. KWL Chart What do you already KNOW about the coordinate graph? What do you WANT to know about the coordinate graph? What did you LEARN about the coordinate graph?

17. Notes: Making Graphs

18. Problem 1.2 Complete A-C on page 9

19. Day 1: Atlantic City to Lewes

20. Google Maps

21. Problem 1.3 Interpreting Graphs Learning Partners: Complete A and B Summary: What are some possible reasons for the changes in the riders’ speed and distance traveled?

22. Day 2: Lewes to Chincoteague Island

23. Map of Lewes to Chincoteague Island - Google Maps

24. Pony Swim

25. 1.4 Reading Data from Graphs Complete Problem 1.4 A-F with your Learning Partner (page 13)

26. Venn Diagram

27. Day 3: Chincoteague Island to Norfolk

28. Google Maps

29. 1.5 Finding Average Speed Make a graph of the distance traveled on day 3. Answer questions A-E.

30. Summary for Investigation 1 The problems in this investigation asked you to think about variables and the patterns relating the values of variables. You made tables and graphs to show how different variables are related. The following questions will help you summarize what you have learned.

31. Question 1: Describe the steps you would take in making a graph to show the relationship between two related variables.

32. Question 2: How do you decide which variable should be on the x-axis and which should be on the y-axis?

33. Question 3: What are the advantages and disadvantages of representing a relationship between variables in a table?

34. Question 4: What are the advantages and disadvantages of representing a relationship between variables in a graph?

35. Question 5: What are the advantages and disadvantages of describing a relationship between variables in a written report?

36. Congratulations! You have completed investigation one!