Proportional Reasoning with Algebraic Structures

1. B.A.SSE.A.2. Use algebraic structures to solve problems involving proportional reasoning in real world context. Tuesday, 20181023Proportional Reasoning EQ10: How do we use algebraic structures to solve proportional reasoning problems?

2. Tuesday, 20181023 Essential Questions • EQ10: How do we use algebraic structures to solve proportional reasoning problems? Vocabulary: Agenda Bridge Math • Store your phones • Find your seat • Bellwork: ACT • Calculator • Proportional reasoning problems • Exit Ticket • Remain in seat until bell rings. Teacher Dismisses NOT the bell. It’s always a great day to be a Wolverine! No Sleeping!

3. ACT Bellwork: Tuesday, 20181023

4. A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles? ACT Question 1 Answer A. $44.44 B. $109.08 C. $118.80 D. $408.04 E. $444.40

5. What is the value of x when 2x + 3 = 3x – 4 ? ACT Question 2 Answer A. -7 B. -1/5 C. 1 D. 1/5 E. 7

6. When x = 3 and y = 5, by how much does the value of 3x2 – 2y exceed the value of 2x2 – 3y ? ACT Question 3 Answer A. 4 B. 14 C. 16 D. 20 E. 50

7. What is the greatest common factor of 42, 126, and 210 ? ACT Question 4 Answer A. 2 B. 6 C. 14 D. 21 E. 42

8. Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year? ACT Question 5 Answer A. 16 B. 17.5 C. 20.5 D. 22 E. 35

9. ACT Question KEY 1. D 2. E 3. B 4. E 5. A

11. V O C A B U L A R Y

12. Proportional Reasoning Ratios/Rates Proportions

13. What do ratios compare?

14. What is a Ratio? • A ratio is a comparison of two quantities by division. • A ratio can be represented in 3 different ways, but they all mean the same thing. • Order matters. Whatever is mentioned first in the question is what goes first in the ratio.

15. So, you might wonder…. • How does a person represent a ratio?

16. Here’s how we represent ratios. • Ratios can be represented as a fraction. Part Part Part Whole

17. Another way to represent ratios • Ratios can be represented as a rate with a colon between the two numbers. Part : Part 90:50 Part : Whole 90:140

18. Finally…. • Ratios can be written with words. For example, the fraction 2/3 can be written as… 2 to 3 (part to part) (part to whole) Or 2 out of 3 (part to whole)

19. The Exception to the Rule • The word “to” is used when comparing part to part or part to whole. • Only when expressing part to whole, can the phrase “out of” be used since this phrase refers to the whole. • Part to Part • Part to Whole or • Part out of the Whole

20. FYI • Ratios should be reduced to lowest term since they are fractions.

21. Real life example • Mark shoots baskets every night to practice for basketball. While training, he will shoot 50 baskets. He usually makes 35 of those 50 baskets. Represent this data as a ratio.

22. Mathematically Speaking… • This data can be represented as.. Baskets made 35 Baskets shot 50 35 : 50 35 to 50 35 out of 50 *Remember to reduce all fractions whenever possible

23. Once again… • Marla has 15 pants in her closet and 25 shirts to go with her pants. What is the ratio of pants to shirts in her closet?

24. Mathematically Speaking • The ratio of pants to shirts in Marla’s closet can be represented as… Pants 15 Shirts 25 Or 15:25 or 15 to 25 but not……. Remember to reduce all fractions whenever possible.

25. Exception to the Rule • We can not saythis ratio using the phrase “out of” because we are comparing part to part…Does it make sense to say, “15 shirts out of 25 pants”?

26. Remember…. • A ratio is a comparison of two quantities by division. • A ratio compares part to part or part to whole. • A ratio can be written 3 different ways… n/d n:d or “n to d” or “n out of d”

27. Now it is your turn! • Lynnie is helping her husband David, package blankets and pillows for boys and girls in shelters. He has 108 blankets and 54 pillows. Write the ratio of pillows to blankets.

28. Can you create ratios on your own? • Use the next few slides to create the ratios presented in the examples. • Be sure to write them 3 different ways. • You will turn this in for a grade.

29. Problem #1 • A recipe for pancakes requires 3 eggs and makes 12 pancakes. What is the ratio of eggs to pancakes? a) 12:3 b) 1:4 c) 3:1 d) 1:3

30. Problem #2 • Don took a test and got 15 out of 20 correct. What is the ratio of correct answers to total answers? • 1 to 2 • 20 to 15 • 4 to 3 • 3 to 4

31. Problem #3 • Arnold participated in volleyball for 8 hours and drama for 5 hours over a period of 1 week. If Arnold continues participating in these two activities at this rate, how many hours will he spend participating in each of the activities over a 9 week period? a) 45 hours of volleyball and 72 hours of drama b) 8 hours of volleyball and 5 hours of drama c) 72 hours of volleyball and 45 hours of drama d) 5 hours of volleyball and 8 hours of drama

32. Ratio Problem #4 • The ratio of terror books to funny books in a library is 7 to 3. Which combination of terror to funny books could the library have? • 21 terror to 9 funny B) 35 terror to 50 funny C) 14 terror to 9 funny D) 21 terror to 15 funny

33. Problem #5 • There were 14 boats and 42 people registered for a boat race. Which ratio accurately compares the number of people to the number of boats? A) 2:6 B) 3:1 C) 7:21 D) 14:42

34. B.A.SSE.A.2. Use algebraic structures to solve problems involving proportional reasoning in real world context. Monday, 20181022Proportional Reasoning EQ10: How do we use algebraic structures to solve proportional reasoning problems?

35. EQ9 Scientific Notation That's All Folks! Get Ready for the EXIT TICKET!!!

36. EXIT TICKET The ratio of Kate's stickers to Jenna's stickers is 7:4. Kate has 21 stickers. How many stickers does Jenna have? 12

37. 20181018 MAKE-UP 20181012 MAKE-UP