1. 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 Scaling Up Recipes
Date: 11/6/2018
New Seats!
On Desk:
In your planner:
HW: CS p. 22 #10-12, 42

2. 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?

3. Quick Overview…

4. Quick Overview…

5. Quick Overview…

6. 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.

7. 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

8. 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

9. 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%

10. 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?

11. CS p. 12

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

13. These are called: scaling ratios 3 5 8 10 4 6 2 4 12 9 18 10 15 25 336 54 30 9
These are called:
scaling ratios

14. 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 cans water = 36 oz Total = 48 oz.

15. 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 ⅓ cans water = 52oz Total = 64 oz.

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

17. 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!

18. 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.

19. 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.

20. 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