New Unit: Comparing and Scaling Math CC7/8 – Be Prepared New Unit: Comparing and Scaling In your journal: New Tab: CS New Unit: Comparing and Scaling (CS) Ratios, Rates, Percents, Proportions Title: CS 1.1-1.3 Scaling Up Recipes Date: 11/6/2018 New Seats! On Desk: In your planner: HW: CS p. 22 #10-12, 42

Tasks for Today New Unit – Comparing & Scaling (CS) Ratios, Rates, Percents & Proportions Summarize Lesson 1.1 & 1.2 Do Lesson 1.3 A-D Begin HW?

Quick Overview…

Quick Overview…

Quick Overview…

Which mix will make juice that is the most “orangey”? Mariah and Arvin made orange juice for the school camping trip. They made the juice by mixing water and orange juice concentrate. To find the mix that would taste best, they tested some mixes. Which mix will make juice that is the most “orangey”? Which mix will make juice that is the least “orangey”? Explain your thinking.

2 parts out 5 parts total 3/5 C. 1 2÷5 = 40% 2/5 C. 3 5/14 C. 9/14 C. 5÷14 = 36% 1/3 C. 2/3 C. 4 1÷3 = 33% 3/8 C. 5/8 C. 2 3÷8 = 38% 5 cups total 14 cups total 3 cups total 8 cups total

Quick Overview… Isabelle compared the parts: 5 C. concentrate to 9 C. water PART to PART ratio Doug compared the parts: 5 C. concentrate to 14 C. total PART to WHOLE ratio

Max thinks that Mix A and Mix C are the same. Max says, “They are both the most ‘orangey’ since the difference between the number of cups of water and the number of cups of concentrate is 1.” Is Max’s thinking correct? Explain. 2/5 = 40% Max’s thinking is incorrect. He subtracted the numerator from the denominator. Use PART-to-WHOLE you see that 2/5 is more orangey than 1/3 1/3 = 33.3%

24 batches 24 x 2 C. = 48 C. 24 x 3 C. = 72 C. 9 batches *Hint: Mix D: Each 8‑cup batch serves 16 people a half cup = 15 batches. Mix A: Each 5‑cup batch serves 10 people a half cup = 24 batches. Mix B: Each 14‑cup batch serves 28 people a half cup = 9 batches. Mix C: Each 3‑cup batch serves 6 people a half cup = 40 batches. For Mix B, 43 and 77 are closer approximations. Why can’t you make exactly 120 cups with whole numbers by scaling up this recipe?

CS p. 12

part-to-part part part part-to-whole part whole 5:9 5/9 5 to 9

These are called: scaling ratios 3 5 8 10 4 6 2 4 12 9 18 10 15 25 3 36 54 30 9 These are called: scaling ratios

Part-to-whole Ratio 1 : 4 Scale up 12 : 48 48 oz. pitcher A. A typical can of o.j. concentrate holds 12 fluid oz. The standard recipe is: How large of a pitcher will you need to hold the juice made from a typical can? (Show or explain your answer) Part-to-whole Ratio 1 : 4 Scale up 12 : 48 48 oz. pitcher Double check: 1 can concentrate = 12 oz. 3 cans water = 36 oz. Total = 48 oz.

Part-to-whole Ratio 1 : 5 ⅓ Scale up 12 : 64 oz. 64 oz. pitcher A typical can of lemonade concentrate holds 12 fluid oz. The standard recipe is: How large of a pitcher will you need to hold the lemonade made from a typical can? (Show or explain your answer) Part-to-whole Ratio 1 : 5 ⅓ Scale up 12 : 64 oz. 64 oz. pitcher Double check: 1 can concentrate = 12 oz. 4⅓ cans water = 52oz. Total = 64 oz.

Part-to-whole Ratio 1 : 5 ⅓ Scale up 12 : 64 oz.

1 : 4 (Part-to-whole) Scale up 16 : 64 64 oz. container 1 Gallon = 128 oz. 1 : 3 (part to part) 1 : 4 (part to whole) x : 128 (scale factor of 32) 32 : 128 She needs 2 (16 oz.) cans!

Ounces (oz.) of concentrate 1 : 3 (part to part) 1 : 4 (part to whole) x : 128 (scale factor of 32) 32 : 128 She needs 2 (16 oz.) cans! cans of concentrate Ounces (oz.) of concentrate she needs Total juice made in one recipe, in cans Ounces (oz.) of juice she wants to make There are a number of ways. One way is to think about these ratios as equivalent fractions. The denominator of the left fraction is multiplied by 32 to get the denominator of the right fraction. So, x=32×1=32 Remember that these ratios are equivalent fractions.

15 1 80 5⅓ 15 oz. of lemonade concentrate 1 : 4 ⅓ (part to part) 1 : 5⅓ (part to whole) scale factor of 15 ratio - 15 oz : 80 oz He needs a pitcher large enough to hold 80 oz. 5⅓ 15 1 80 Ounces of concentrate that he has to use. Cans of concentrate. Total juice made in one recipe, in cans Total ounces of juice he can make.

What other ratios and equivalent fractions can you find for August’s problem? 5⅓ 15 1 80 15 1 80 15 1 80 53.33 15 10 80 5⅓ 1.5 1 8.0 15 1 80