P.O.D. Wrap Up. Independent and Dependent Variables

Transcription

1 Wrap Up Independent and Dependent Variables P.O.D. 1. Simplify this math sentence: (x+2)+(2x-5) 2. Graph the following: x Simplify the following: a) 4(x + 7) b) 3(4 + 9) c) x(4 + 9) Tuesday, March 6th, 2018 Learning Target I can define the relationship between two variables by identifying the independent and dependent variables in real world situations

2 March 6th, 2018 Learning Target: I can define the relationship between two variables by identifying the independent and dependent variables in real world situations. Success: 1.) Identify the independent variable 2.) Identify the dependent variable 3.) Use two variables to represent real world situations

3 Independent and Dependent Variables What do you know about independent and dependent variables? What does it mean to be independent? What does it mean to be dependent? Individual Think Time (20 sec) Table Talk (2min)

4 Mini Lesson (5min) Independent Variable A variable that determines the value of the other variable. They are things that do not depend on something else. Examples: Time Dependent Variable A variable whose value is determined by another variable. They are things that change when something else happens. Examples: Money earned

5 Work Time 1: (3min) State which phrase is the independent variable and which is the dependent variable. Be ready to explain your reason using the definitions. ALSO use the phrase depends on The amount of strawberries you pick The amount of money Jarred makes in a fundraiser The number of people attending the potluck The number of jars you will be able to fill with jam The number of cookies Jarred bakes The number of pizzas purchased The time that the band is allowed to play The number of songs performed

6 Catch: (3min) Look at another way to write the dependent and independent variable written below. The amount of money Jarred makes in a fundraiser The number of cookies Jarred bakes _M_ depends on _N_. What does each variable stand for? Which one is the dependent variable? Which one is the independent variable?

7 Independent and Dependent Variable Another Example

8 Work Time 2: (7min) Look at each scenario and determine the independent variable and the dependent variable. Use the letter given to represent each variable. Work with your team and have good math conversations! Ask questions Explain your thinking Agree/Disagree respectfully Write your work in your notebook.

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11 Independent - Temperature Outside Dependent -Ice Cream Sales Graph Ice Cream Sales Temperature Outside Note that the number of ice cream purchased in Colorado is dependent on the temperature outside. As the temperature goes up the number of ice cream sales increases. My friend, John, works at Sweet Action in Denver. He noticed that for every degree outside, they sell 5 ice creams cones. Look at the table below. Temp. Sales 1 $5 2 $10 7 $35 T We can write this as an equation using two variables: T = Temperature outside S = Ice cream sales S = x T

12 Variable: Time Variable: Age Graph Age Time Discussion Questions: 1.) Which variable is the independent variable? 2.) Which variable is the dependent variable? 3.) What does the graph show about age and time? 4.) Create a table to show the relationship between age and time if every 12 months you are 1 year older. Time 12 months 24 months 36 months 60 months Age 1 year 5.) For every month, what fraction of a year older are you? 6.) For any number of months N, write an expression for how old you are? 7.) Write and equation using variables A for age and N for time.

13 Exit Ticket (3min) DEPENDENT VS. INDEPENDENT Decide in each scenarios which variables are independent and which are dependent? a.) The number of assignments you turned in b.) How much money you earn c.) Who scores more points d.) How much air conditioning you use 1)Your math grade 2)The hours you work 3)Result of a football game 4)Temperature e.) Number of cookies 5)Total calories and fat

14 March 8th, 2018 Learning Target: I can analyze the relationship between independent and dependent variables by using tables and graphs. Success: 1.) Identify the independent variable 2.) Identify the dependent variable 3.) Use a table and graph to show the relationship between variables

15 Back in Business In my t-shirt business, for every shirt I sell, I make $5.00. What is an independent and dependent variable in this scenario? depends on How can you compare the two variables mathematically? # of Shirts (N) $ made (M) $5 $10... How much money is made for 3, 4, 5, 6 t-shirts? How much money is made for 100 t-shirts? How can you write an expression for any number of t-shirts (N)?

16 Mini Lesson: Table to Graph (4min) # of Shirts (N) $ made (M) $5 $10 $15 $20 $25 $30... $1000 What would the graph of this look like? Independent: (x-axis) Dependent: (y-axis)

17 Work Time 1: (2min ITT) (3min work together) Identify the independent and dependent variables in the tables. Then, match each table with the correct graph. Note: The scales for the x and y axis may go by a number other than 1. Table A Temp # of Ice Cream Graph A Table B Demand for T-Shirts Price $5 $7 $8 $9 $12 Graph C Table C Age Height Graph B

18 Work Time 2: (7min Group work) For each problem, identify the the dependent and independent variable, show the relationship on a table and graph, and then answer the question. 1.) During the first game of a season, a team scored 10 points. Over the course of the season, the team improved by 5 points per game. T stands for the total points improved and G stands for the number of games played. a. depends on Dependent Variable Independent Variable b. Fill in the table below showing the improvement for each additional game. Total points (T) 10 Games (G) c. Graph the situation on the coordinate plane to the right. d. What does the graph show you about the two variables?

19 Work Time 2: (7min Group work) 2.) When I opened the last box of Kleenex for class use, I noticed that the box says there are 124 Kleenex in it. Each class period I counted and on average 8 Kleenex were used. C stands for the number of periods and R stands for how many Kleenex remain in the box. a. depends on Dependent Variable Independent Variable b. Fill in the table below showing how many Kleenex remain after each period. Remaining Kleenex (R) Number of Periods (C) c. Graph the situation on the coordinate plane to the right. d. What does the graph show you about the two variables?

20 Make your own Business data table. On a piece of graph paper and using your T-shirt where you wrote how much you are selling your shirt for create a table representing how much money you would make after selling N number of shirts. # of Shirts $ You made $ $ $ $ $ $ $ Now using your data identify the independent and dependent variables. Then using these variables create a graph using your data. Which one is the X variable? Which one is the Y-variable? Graph your points. Y axis= $ made So each coordinate point is (x,y) =, (# of shirts, $ made) X axis= # of shirts

21 Reflection (3min) Jack is selling lemonade for a fundraiser. For every increase in 1 degree, Jack sells 5 more lemonades. 1.) What is the independent and dependent variables? 2.) Show the relationship in a table if he sells 0 lemonades when it is 0 degrees Celsius. Temperature Number of Hot Chocolate sold 0 3.) Graph the scenario.

22 Independent and Dependent Variables P.O.D. (3 min) For each scenario: identify the independent and dependent variable. Use sentence phrase in each scenario. depends on 1.) Jack makes $10 dollars every hour that he baby sits. 2.) Table: 3.) Graph: Temp # of Ice Cream March 9th, 2018 Learning Target I can analyze the relationship between independent and dependent variables by creating equations. Height Age

23 PAT Time Preferred Activity Time Everyone Needs: ( Pencils down) Individual Think Time

24 March 9th, 2018 Learning Target: I can analyze the relationship between independent and dependent variables by using equations. Success: 1.) Identify the independent variable 2.) Identify the dependent variable 3.) Use a table and graph to create an equation to represent the relationships

25 Mini Lesson: Creating an Equation (5 min) # Instagram Followers (F) # of Likes (L) What is the independent variable? What is the dependent variable? Is there a pattern that we can identify? Could we create a rule that allowed us to find out how many likes we would get with F instagram followers?

26 Work Time- Stations- Each 8 min Work through the stations with your table to identify the independent and dependent variables. The goal for each station is to use your independent and dependent variables to create equations to represent each scenario. Please record your information for each station on your station paper.

27 Reflection (3min) Jack is selling lemonade for a fundraiser. For every increase in 1 degree, Jack sells 5 more lemonades. 1.) What is the independent and dependent variables? 2.) Show the relationship in a table if he sells 0 lemonades when it is 0 degrees Celsius. Temperature Number of Hot Chocolate sold 0 3.) Graph the scenario.