Grade 6 Workbook — Chapter 8: Ratios

SOL 6.PFA.1 · Companion to Textbook Chapter 8

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/.

PAGE 1 — Chapter opener

Chapter 8 · Ratios

Standard 6.PFA.1

In this chapter you will:

• Write a ratio for a relationship between two quantities
• Use all three notations: $\frac{a}{b}$, $a:b$, and $a$ to $b$
• Tell part-to-part, part-to-whole, and whole-to-whole comparisons apart
• Build tables of equivalent ratios from a ratio and from a story
• Write a situation in words for a ratio given in symbols

Words to know: ratio · terms · part to part · part to whole · whole to whole · equivalent ratios · ratio table

A ratio compares by "for every," not by "how many more."

PAGE 2 — What a ratio is

8.1 What a Ratio Is

FIGURE: fig8-1-ratio-counters.png (full width) [Two labeled rows of counters: top row "Apples" with 4 red circles, bottom row "Oranges" with 7 orange circles, caption band reading "4 apples for every 7 oranges".]

Fill in the blanks.

A ratio compares two quantities by ______________, not by subtraction.

The ________ quantity named in the question is written first.

Swapping the order of a ratio ____________ what the ratio says.

Write each ratio in word form.

PAGE 3 — Order matters

Order Matters

A tray holds 5 muffins and 8 rolls.

Ratio of muffins to rolls: ______________

Ratio of rolls to muffins: ______________

Explain. Jamal says $3$ to $8$ and $8$ to $3$ are the same because they use the same numbers. Why is he wrong?

Apply it. A juice recipe uses 5 cups of water for every 2 cups of concentrate. A cook uses 5 cups of concentrate and 2 cups of water.

What went wrong? _______________________________________________

How will the drink taste? _______________________________________________

PAGE 4 — Exit ticket 8.1

Exit Ticket · Lesson 8.1

Name: ________________________ Date: ____________

1. A box has 9 markers and 12 crayons. Ratio of markers to crayons: ______

2. Ratio of crayons to markers: ______

3. A runner covers 8 laps in 20 minutes. Ratio of laps to minutes: ______

4. Why does the order of the two numbers in a ratio matter?

PAGE 5 — Three notations

8.2 Three Ways to Write a Ratio

FIGURE: fig8-2-three-notations.png (full width) [Three side-by-side panels showing the same ratio as the fraction three-fifths, as 3 : 5, and as "3 to 5", with a bracket beneath labeled "Three ways to write the same ratio: quarters to dimes".]

Complete the table.

Rewrite in the two other notations.

$6:7$ → ______________ and ______________

$\frac{11}{4}$ → ______________ and ______________

15 to 8 → ______________ and ______________

PAGE 6 — Read fraction form carefully

Careful with Fraction Form

A bag has 5 blue tiles and 7 yellow tiles. $\frac{5}{7}$ compares blue to ____________. $\frac{5}{12}$ compares blue to ____________.

A backpack has 3 pens and 8 pencils. Write in colon form.

Pens to pencils: ______ Pencils to pens: ______ Pens to all writing tools: ______

Think. Nia sees $\frac{2}{9}$ describing almonds to cashews and says, "Almonds are two-ninths of the mix." Why is that wrong?

What fraction of the mix is almonds? ______

PAGE 7 — Exit ticket 8.2

Exit Ticket · Lesson 8.2

Name: ________________________ Date: ____________

1. Write 6 forks to 5 spoons three ways: ______ ______ ______

2. Rewrite $\frac{10}{3}$ in colon form: ______

3. A tray has 4 tarts and 6 cookies. Ratio of tarts to all baked goods in fraction form: ______

4. Why do $\frac{4}{6}$ and $\frac{4}{10}$ describe different comparisons for that tray?

PAGE 8 — Three kinds of comparison

8.3 Part, Whole, and Both

FIGURE: fig8-3-part-whole-bar.png (full width) [A 24-square bar model split into 10 blue squares labeled "Walk" and 14 green squares labeled "Ride", with a bracket labeled "Whole class (24)" and a second 30-square gray bar labeled "Another class (30)" for the whole-to-whole comparison.]

Complete the table for the class of 24 (10 walk, 14 ride).

Fill in. To find the whole when you are only given the parts, you ____________ the parts.

PAGE 9 — Sorting comparisons

Sort the Comparisons

Label each: PART TO PART, PART TO WHOLE, or WHOLE TO WHOLE.

Work it out. A pizza has 8 slices; 3 are pepperoni and the rest are cheese.

Pepperoni to cheese: ______ Pepperoni to all slices: ______

Work it out. In a survey, the ratio of students choosing soccer to all students surveyed is $11:29$.

Students who did not choose soccer: ______

Explain. In a club the ratio of sixth graders to seventh graders is $5:4$. Ellie says sixth graders to all members is also $5:4$. What is her error, and what is the correct ratio?

PAGE 10 — Exit ticket 8.3

Exit Ticket · Lesson 8.3

Name: ________________________ Date: ____________

1. A drawer has 7 blue socks and 5 gray socks. Blue to gray: ______

2. Gray socks to all socks: ______

3. Classify: "18 books on my shelf compared to 24 books on yours." ______________

4. In your own words, what is the difference between part to part and part to whole?

PAGE 11 — Equivalent ratios

8.4 Equivalent Ratios

FIGURE: fig8-4-ratio-table-scaling.png (full width) [A two-row ratio table, lemon juice 2, 4, 6, 8, 10 over water 3, 6, 9, 12, 15, with "+2" arrows across the top row, "+3" arrows across the bottom row, and one large "x 5" arrow from the first column to the last.]

To make an equivalent ratio, multiply or divide both terms by the same number. Never add.

Write three ratios equivalent to each.

$5:6$ → ______ ______ ______

$7:2$ → ______ ______ ______

$2:9$ → ______ ______ ______

Fill in the blanks.

Circle the ratios equivalent to $6:8$.

$$3:4 \qquad 9:12 \qquad 8:10 \qquad 18:24 \qquad 12:14$$

PAGE 12 — Ratio tables

Ratio Tables

Complete each table.

1. Paint coverage

2. Ratio $9:4$

3. Go-kart track: 7 dollars for every 3 laps

Cost of 15 laps: ______ Laps you can buy with 28 dollars: ______

Find the error. Priya says $4:6$ and $6:8$ are equivalent because "each goes up by 2."

What is wrong? _______________________________________________

A ratio equivalent to $4:6$ with first term 6: ______

PAGE 13 — Exit ticket 8.4

Exit Ticket · Lesson 8.4

Name: ________________________ Date: ____________

1. Two ratios equivalent to $5:3$: ______ and ______

2. Fill in: $2:7 = 10:\underline{\ \ \ }$

3. A recipe uses 4 eggs for every 3 cups of milk. Complete the table.

   Eggs	4
   Milk (cups)	3

4. Why do you multiply, and not add, to make an equivalent ratio?

PAGE 14 — From symbols to a story

8.5 Writing a Situation for a Ratio

FIGURE: fig8-5-symbol-to-situation.png (full width) [A three-box flow diagram: "3 : 8" → "Choose two quantities: teachers, students" → "For every 3 teachers on the trip, there are 8 students," with a caption reading "First term goes with the first quantity named."]

A good situation does three things:

1. Names both ______________
2. Keeps the ______________
3. Uses the phrase ______________ (or something like it)

Write a situation for each ratio.

$4:3$ (part to part): _______________________________________________

$\frac{2}{5}$ (part to whole): _______________________________________________

$60:1$ (two different units): _______________________________________________

$7:2$: _______________________________________________

$\frac{5}{8}$: _______________________________________________

9 to 4: _______________________________________________

PAGE 15 — Same symbols, different stories

Same Symbols, Different Stories

For the ratio $2:9$, write two situations.

Part to part: _______________________________________________

Part to whole: _______________________________________________

How are the two situations different, even though the symbols are the same?

Rewrite each weak situation so it is clear.

"There are 8 and 3 of something." → _______________________________________________

"For every 3 students there are 10 students." → _______________________________________________

Find the error. Devin writes for $\frac{3}{7}$: "There are 3 boys and 7 children, so there are 7 girls."

What is wrong? _______________________________________________

Correct number of girls: ______

PAGE 16 — Exit ticket 8.5

Exit Ticket · Lesson 8.5

Name: ________________________ Date: ____________

1. Part-to-part situation for $6:5$: _______________________________________________

2. Part-to-whole situation for $\frac{3}{8}$: _______________________________________________

3. Situation for $45:1$ with two different units: _______________________________________________

4. Why must a written situation name both quantities?

PAGE 17 — Chapter 8 review, part 1

Chapter 8 Review

Part A · Writing ratios

1. 8 melons, 5 pineapples. Melons to pineapples: ______

2. 150 miles on 5 gallons. Miles to gallons: ______

3. Difference between comparing by subtraction and comparing with a ratio:

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Part B · Three notations

4. "11 cats to 4 dogs" three ways: ______ ______ ______

5. $\frac{9}{5}$ in colon form ______ and word form ______

6. $7:12$ in fraction form: ______

7. A bag has 5 red and 9 blue chips. $\frac{5}{9}$ compares ______________; $\frac{5}{14}$ compares ______________

Part C · Types of comparison

8. A class has 13 boys and 12 girls. Boys to girls: ______ Girls to whole class: ______ Types: ______________

9. Classify: a) 6 apples to 10 pieces of fruit in one bowl ______ b) 6 apples to 4 oranges ______ c) 10 in my bowl to 14 in yours ______

10. Green beads to all beads is $9:20$. Beads that are not green: ______

PAGE 18 — Chapter 8 review, part 2

Chapter 8 Review (continued)

Part D · Equivalent ratios and tables

11. Three ratios equivalent to $8:3$: ______ ______ ______

12. Fill in: a) $5:4 = 20:\underline{\ \ \ }$ b) $6:15 = 2:\underline{\ \ \ }$

13. Five-column ratio table for $7:2$.

    	7
    	2

14. A shop sells 4 apples for 3 dollars.

    Apples	4	8	12	16	20
    Cost (dollars)	3

    Cost of 20 apples: ______

Part E · Writing situations

15. Part-to-part situation for $9:2$: _______________________________________________

16. Part-to-whole situation for $\frac{5}{12}$: _______________________________________________

Part F · Application and reasoning

17. Trail mix: 5 cups oats to 3 cups dried cherries. Part to part: ______ Oats to whole: ______ Cherries to whole: ______

    Oats (cups)	5
    Cherries (cups)	3

18. Marco doubles 3 cups broth and 2 cups rice by using 5 and 4. Error: ______________ Correct amounts: ______________

19. Why can $\frac{2}{3}$ mean "2 out of 3 parts" in one problem and "2 compared to 3" in another? Give an example of each.

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20. Are $12:18$ and $10:15$ the same mix? Justify with equivalent ratios.

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Canva production notes

• Page size: 8.5 × 11 in, 0.75 in margins
• Type: headings 24–28 pt, body 12–14 pt, answer blanks 14 pt with 1.5 line spacing
• Ratio tables: keep all tables to a single row height per quantity so students can write inside cells; minimum cell height 0.4 in
• Figure widths: fig8-1, fig8-2, fig8-4, and fig8-5 full width; fig8-3 full width and tall enough to show both bars
• Answer blanks: keep every blank on the same line as its prompt so the Canva text box does not reflow