Ratio and Proportional Reasoning. ISBE Math Content Specialist Dana Cartier and Heather Brown

Transcription

1 Ratio and Proportional Reasoning ISBE Math Content Specialist Dana Cartier and Heather Brown

2 Objectives To experience exemplar tasks that integrates both ratios and proportions content and practice standards. To gain deeper understanding of available resources

3 Describe an educational topic that requires the use of ratios and proportional reasoning.

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6 Define these in your own words Ratio Rate Unit rate Proportional relationship Proportion

7 Changes throughout the grades Students prior understanding of and skill with multiplication, division, and fractions contribute to their study of ratios, proportional relationships and unit rates. How are Ratios and Proportional Reasoning addressed in the different grades?

8 4 th Grade Nita raised $45 for the PTA, which was 3 times as much money as Sandra raised. How much money did Sandra raise? What are different ways to solve it? What are the common mistakes?

9 4 th Grade Nita raised $45 for the PTA, which was 3 times as much money as Sandra raised. How much money did Sandra raise? Content contained is licensed under a Creative Commons Attribution- ShareAlike 3.0 Unported License

10 Changes throughout the grades Multiplicative comparison in fourth grade lays the groundwork for ratios and proportions in middle school.

11 How many different ways can you solve this? A mixture of concrete is made up of sand and cement in a ratio of 5 : 3. How many cubic feet of each are needed to make 160 cubic feet of concrete mix? Content contained is licensed under a Creative Commons Attribution- ShareAlike 3.0 Unported License

12 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Joey is fast at What texting. follow-up He was timed and he can text at a rate of 38 letters in 10 seconds. questions could Complete the table for Joey s texting rate. you ask?

13 On your own Solve the problem. Consider other ways to solve the problem. What are some misconceptions that may arise?

14 6 th Grade Jim and Jesse each had the same amount of money. Jim spent $58 to fill the car up with gas for a roadtrip. Jesse spent $37 buying snacks for the trip. Afterward, the ratio of Jim s money to Jesse s money is 1:4. How much money did each have at first? Content contained is licensed under a Creative Commons

15 6 th Grade Jim and Jesse each had the same amount of money. Jim spent $58 to fill the car up with gas for a road-trip. Jesse spent $37 buying snacks for the trip. Afterward, the ratio of Jim s money to Jesse s money is 1:4. How much money did each have at first? Content contained is licensed under a Creative Commons Attribution- ShareAlike 3.0 Unported License

16 Analyze the Lesson

17 Tape Diagrams Best used when two quantities have the same units. They can be used to solve problems and also to highlight the multiplicative relationship between the quantities

18 Yellow and blue paint were mixed in a ratio of 5 to 3 to make green paint. After 14 liters of blue paint were added, the amount of yellow and blue paint in the mixture was equal. How much green paint was in the mixture at first? Content contained is licensed under a Creative Commons Attribution- ShareAlike 3.0 Unported License

19 In a pair of complementary angles, the measurement of the larger angle is three times that of the smaller angle. Find the measures of the two angles. larger smaller

20 Grade 6 PARCC End of Year Assessment

21 Double number line diagrams Best used when the quantities have different units (otherwise the two diagrams will use different length units to represent the same amount.) Help make visible that there are many, even infinitely many, pairs in the same ratio, including those with rational number entries.

22 6 th Grade $ boxes

23 Lauren bikes miles in hour. What is her rate of speed in miles per hour? 7 th Grade $ boxes 1 1/3 1/5 2 2/ /3 6 2/3 2/5 3/5 4/5 1

24 6th to 7 th grade changes Whole number pairs transition to rational number entries (simple to complex fractions) Coordinate plane plotting points to writing equations Given proportional relationships to deciding if a relationship is proportional from context, table or graph (unit rate triangle = slope triangle)

25 On your own Solve the problem. Consider other ways to solve the problem. What are some misconceptions that may arise?

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27 If 75% of the budget is $1200, what is the full budget? =

28 Grade 7 PARCC Performance Based Assessment

29 Grocery Story A sign says 15 ounces of cereal for $3. Is cereal price proportional to the weight? Student A says Yes, because I can buy 30 ounces for $6, 45 ounces for $9, etc. Student B says No, because I don t know how much 1 ounce, or 5 ounces, costs.

30 7 th Grade Connections What topics are covered in 7.G and 7.SP? Write a problem that relates one of these domains to 7.RP

31 7 th RP to 8 th F Two problem comparison Linear functions still have constant rate of change but can include different y-intercepts Proportional relationships are linear functions that have a positive rate of change and take 0 to 0.

32 Discuss your definitions Ratio Rate Unit rate Proportional relationship Proportion

33 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License dcartier@illinoiscsi.org hedi0201@me.com