RATIOS AND PROPORTIONS. Lesson 2.2

Transcription

1 RATIOS AND PROPORTIONS Lesson 2.2

2 DO NOW

3 TEACHING POINT Mathematicians will be able to determine proportionality using a graph and rate table

4 STANDARD 7.RP.2a Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationships e.g., by testing equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin

5 VOCAB

6 RATE TABLE Isaiah sold candy bars to help raise money for his scouting troop. The table shows the amount of candy he sold to the money he received. x Candy Bars Sold y Money Received ($)

7 LETS GRAPH What is the origin and where is it located? Why are we going to focus on quadrant 1?. What should we label the x-axis and y-axis? How do we plot the first ratio pair? When we are plotting a point, where do we count from? What should we label the x-axis and y-axis?

8 FILL IN THE GRAPH Fill in the graph What observations can you make about the arrangement of points? Do we extend the line in both directions? Explain why or why not. Would all proportional relationships pass through the origin? What can you infer about graphs of two quantities that are proportional to each other?

9 FILL IN GRAPH

10 WHAT IF THE RATE TABLE SAID x Candy Bars Sold y Money Received ($)

11 SOMETHING TO THINK ABOUT Does the ratio table represent quantities that are proportional to each other? What can you predict about the graph of this ratio table?

12 PLOT POINTS ON GRAPH

13 PLOT THE POINTS x y

14 How are the graphs of the data in examples 1 and 3 similar? How are they different? What do you know about the ratios before you graph them? What can you predict about the graph of this ratio table? Was your prediction correct? What are the similarities of the graphs of two quantities that are proportional to each other and graphs of two quantities that are not shared?

15 DETERMINE PROPORTIONALITY BY A GRAPH Must be a straight line Must go through the origin (0,0)

16 In Words Proportional Relationship Example: Ms. O drives 70 miles per hour Mr. Chavez earns $350 every week for playing guitar

17 In Words Non Proportional Example Example: Ms. O buys 5 bags of chips during the week and 2 bags during the weekend Mr. Chavez spent $25 week during the first week of the summer and $100 every week after.

18 TURN AND TALK What is similar and what is different between a proportional word description and a non-proportional word description

19 RATE TABLE Proportional Example Non-Proportional Example X Y X Y

20 TURN AND TALK - 2 MINS What is similar and what is different between a proportional rate table and a nonproportional rate table

21 GRAPH Proportional Graph Non-Proportional Graph

22 Turn and Talk 2 Mins What is similar and what is different between a proportional graph and a non-proportional graph

23 PROPORTIONAL EQUATION

24 Turn and Talk 2 mins What is similar and what is different between a proportional equation and a nonproportional equation

25 Function bowl 15 Mins The teams competing represent the proportional league and the non proportional league 10 players (5 for each team) You will determine if they are on the proportionality team or non-proportionality team Next you will justify their placement

26 BOWL DIAGRAM Proportionality Team Player Justification Non - Proportionality Team Player Justification

27 CREATE your Own 10 Mins In this part of the activity you will create three different players on each team. These players must be represented in different forms (graphs, equations, table, description)

28 Facilitator Make sure that the task is clear to everyone, that the group is working together towards the agreed goals, and that everyone is participating and has their ideas heard. Recorder Record strategies and methods as well as solutions, and be ready to share the group s mathematical journey Resource Manager Make sure everyone has a useful task to work on, and that they have the tools and information they need to complete the task. Understanding Coordinator Make sure that calculations are checked and mathematical reasoning is justified. Make sure the

29 GROUP PROJECT -30 MINUTES 5 Groups Each Group gets a problem Fold Paper into Fours Names: Date Calss Write Problem Rate Table: Graph: Explanation

30 Names: Date Class Problem: COPY PROBLEM IN ItS ENTIRETY Graph: Draw Graph - Axis Labeled - Title of Graph Rate Table: CREATE RATE TABLE USING SLIPS IN RATIO FORMS TO HELP Explanation : Is the two quantities proportional

31 ANSWER QUESTIONS FOR EACH POSTER Was the poster done accurately and correctly? If yes, explain how you know. If not, explain what needs to be corrected. How is this problem similar or dissimilar to yours? Write 1 question or comment regarding the groups poster.

32 GALLERY WALK (2 MINS/POSTER) Each group will walk to each poster and jot down notes about the ratios Then they will answer the following questions: Which graphs in the art gallery walk represented proportional relationships and which did not? List the group number. Proportional Relationship Non-proportional Relationship 2. What are the characteristics of the graphs that represent proportional relationships? 3. For the graphs representing proportional relationships, what does (0,0) mean in the context of the given situation?

33 WORKSHEET HOMEWORK