Grade 6 Workbook — Chapter 4: Fractions, Decimals, and Percents

SOL 6.NS.1 · Companion to Textbook Chapter 4

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 4 · Fractions, Decimals, and Percents

Standard 6.NS.1

In this chapter you will:

• Find the percent shown by a model, including percents above 100% and below 1%
• Change decimals to percents and percents to decimals
• Change fractions and mixed numbers to percents, and back
• Move between all three forms
• Compare and order up to four positive numbers, and justify your answer

Words to know: percent · hundred grid · benchmark percent · simplest form · rational number · repeating decimal

Calculator note: every part of 6.NS.1 is assessed without a calculator. Do all of this chapter by hand.

Number limits for this chapter: decimals through thousandths · fraction denominators of 12 or less, or factors of 100 (2, 4, 5, 10, 20, 25, 50, 100) · no more than four numbers compared at a time · all numbers positive

PAGE 2 — Percent means per hundred

4.1 Percent as Parts per Hundred

FIGURE: fig1-hundred-grid-35.png (full width) [10 by 10 grid, 35 squares shaded]

Fill in the blanks.

The word percent means per ____________.

One small square of a hundred grid is ______%.

A whole hundred grid is ______%.

$$35\% = \frac{\phantom{00}}{100} = \underline{\phantom{0.00}}$$

Write the percent shaded.

Percent unshaded. If $35\%$ of a grid is shaded, what percent is unshaded? ______

PAGE 3 — Models that are not divided into 100

Scaling Up to Hundredths

FIGURE: fig3-twenty-five-parts.png (left half) [square in 25 equal parts, 9 shaded]

Scale each comparison up to hundredths, then write the percent.

Estimate with benchmarks.

FIGURE: fig2-percent-benchmarks-line.png (full width) [0 to 1 number line with 0%, 25%, 50%, 75%, 100% above and 0, 1/4, 1/2, 3/4, 1 below]

A bar shaded a little past halfway is about ______%.

A bar shaded just short of halfway is about ______%.

A bar shaded a little past three quarters is about ______%.

Challenge. In a hundred grid, exactly half of one small square is shaded. What percent is shaded? ______

PAGE 4 — Exit ticket 4.1

Exit Ticket · Lesson 4.1

Name: ________________________ Date: ____________

1. A hundred grid has 41 squares shaded. What percent is shaded? ______

2. A square divided into 25 equal parts has 6 parts shaded. What percent is shaded? ______

3. A bar is shaded to a point just short of halfway. Estimate the percent shaded. ______

4. Explain what $100\%$ tells you about a whole.

PAGE 5 — Decimals and percents

4.2 Decimals and Percents

FIGURE: fig4-decimal-percent-shift.png (full width) [place-value chart showing the two-place shift for 0.37 and 0.008]

Decimal to percent: multiply by 100. The point moves 2 places RIGHT. Percent to decimal: divide by 100. The point moves 2 places LEFT.

Decimal to percent.

Percent to decimal.

Check yourself. A percent less than $100\%$ becomes a decimal ____________ than 1. A percent greater than $100\%$ becomes a decimal ____________ than 1.

PAGE 6 — Watch the placeholder zero

Error Hunt · Decimals and Percents

Three of these are FALSE. Mark each, then write the correction.

Apply it. A phone battery reads $0.85$ of full charge. Write it as a percent. ______

A sales tax rate is listed as $0.06$. Write it as a percent. ______

Explain. Why does $8\%$ need a placeholder zero when you write it as a decimal?

PAGE 7 — Exit ticket 4.2

Exit Ticket · Lesson 4.2

Name: ________________________ Date: ____________

1. Write $0.62$ as a percent. ______

2. Write $7\%$ as a decimal. ______

3. Write $0.035$ as a percent. ______

4. Explain why changing a decimal to a percent moves the decimal point two places to the right.

PAGE 8 — Fractions and percents

4.3 Fractions and Percents

FIGURE: fig5-hundred-grid-three-fifths.png (right half) [hundred grid in five bands of two columns, three bands shaded, 60 squares]

Strategy 1: build an equivalent fraction with denominator 100. Works for 2, 4, 5, 10, 20, 25, 50, 100. Strategy 2: divide the numerator by the denominator, then change the decimal to a percent.

Build to hundredths.

$$\frac{3}{5} = \frac{\phantom{00}}{100} = \underline{\phantom{000}}\% \qquad \frac{7}{20} = \frac{\phantom{00}}{100} = \underline{\phantom{000}}\%$$

$$\frac{3}{25} = \frac{\phantom{00}}{100} = \underline{\phantom{000}}\% \qquad \frac{7}{50} = \frac{\phantom{00}}{100} = \underline{\phantom{000}}\%$$

Divide instead.

Repeating cases. Fill in the exact percents.

$$\frac{1}{3} = \underline{\phantom{0000}}\% \qquad \frac{2}{3} = \underline{\phantom{0000}}\% \qquad \frac{1}{6} = \underline{\phantom{0000}}\% \qquad \frac{5}{6} = \underline{\phantom{0000}}\%$$

PAGE 9 — Percent to fraction

From Percent Back to Fraction

Write each percent over 100, then simplify.

Memory table. Fill in every blank.

Apply it. Malik made 12 of his 16 free throws. Fraction in simplest form: ______ Percent: ______

PAGE 10 — Exit ticket 4.3

Exit Ticket · Lesson 4.3

Name: ________________________ Date: ____________

1. Write $\tfrac{3}{4}$ as a percent. ______

2. Write $60\%$ as a fraction in simplest form. ______

3. Write $\tfrac{7}{8}$ as a percent. ______

4. Describe two different ways to change $\tfrac{3}{20}$ into a percent. Show that both give the same answer.

PAGE 11 — All three forms

4.4 Converting Among All Three Forms

FIGURE: fig6-triple-number-line.png (full width) [three aligned number lines from 0 to 1 labeled with fractions, decimals, and percents]

When you are unsure, go through the DECIMAL. It connects to both other forms.

Complete every row. Fractions in simplest form.

PAGE 12 — Choosing a form

Which Form, and Why?

Match each job to the best form. Write F, D, or P.

Rounding a repeating decimal.

$$\frac{5}{12} = 0.41\overline{6} \approx \underline{\phantom{00000}} \qquad \frac{5}{12} = \underline{\phantom{0000}}\%$$

$$\frac{1}{6} \approx \underline{\phantom{00000}} \qquad \frac{1}{6} = \underline{\phantom{0000}}\%$$

Apply it. A survey reports that $0.375$ of a class walks to school.

Percent: ______ Fraction in simplest form: ______

Explain. Which form would you put in a headline, and why?

PAGE 13 — Exit ticket 4.4

Exit Ticket · Lesson 4.4

Name: ________________________ Date: ____________

Give the two missing forms. Fractions in simplest form.

1. $0.65$ → percent ______ fraction ______

2. $\tfrac{3}{5}$ → decimal ______ percent ______

3. $4\%$ → decimal ______ fraction ______

4. Explain the steps to get from a fraction to a percent when the denominator is 8.

PAGE 14 — Comparing with a common form

4.5 Comparing and Ordering

Convert all the numbers to ONE form first. Then compare.

FIGURE: fig7-ordering-number-line.png (full width) [0 to 1 number line with 2/5, 0.45, 48%, 1/2 plotted and labeled]

Complete the conversion table, then order.

Least to greatest: _______________________________________________

Fill in $<$, $>$, or $=$.

PAGE 15 — Ordering practice

Order and Justify

Order from LEAST to GREATEST.

1. $0.8$, $\tfrac{3}{4}$, $78\%$, $\tfrac{7}{8}$

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2. $0.3$, $\tfrac{1}{4}$, $35\%$

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3. $1\tfrac{1}{4}$, $120\%$, $1.3$

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Order from GREATEST to LEAST.

4. $\tfrac{1}{2}$, $0.55$, $45\%$, $\tfrac{3}{5}$

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Benchmarks.

5. Which is closer to $\tfrac{1}{2}$: $0.45$ or $0.6$? ______ Distances: ______ and ______

6. Which is closest to $1$: $0.89$, $\tfrac{11}{12}$, or $95\%$? ______

Justify. Write a full justification for problem 1: name your strategy, show the common form, then state the order.

PAGE 16 — Exit ticket 4.5

Exit Ticket · Lesson 4.5

Name: ________________________ Date: ____________

1. Which is greater, $\tfrac{3}{8}$ or $0.4$? ______

2. Order least to greatest: $0.6$, $\tfrac{5}{8}$, $58\%$

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3. Which is closer to $\tfrac{1}{2}$: $\tfrac{4}{9}$ or $0.6$? ______

4. Name the strategy you would use to compare $\tfrac{7}{12}$ and $0.6$, explain why, and give the answer.

PAGE 17 — Past 100% and below 1%

4.6 Percents Above 100% and Below 1%

FIGURE: fig8-grids-145-percent.png (full width) [one fully shaded hundred grid labeled 100% beside a grid with 45 squares shaded labeled 45%, braced as 145%]

Complete the table.

FIGURE: fig9-one-square-partly-shaded.png (right half) [one small square of a hundred grid divided into four quadrants with one quadrant shaded]

Percents below 1% — write each as a decimal.

PAGE 18 — Sorting across the whole range

Above, Below, or Exactly One Whole?

Sort each value into the correct column: less than one whole, exactly one whole, more than one whole.

$$0.9\% \qquad 100\% \qquad 1.6 \qquad 0.09 \qquad 250\% \qquad 1 \qquad 0.002 \qquad 108\%$$

Order from least to greatest. $0.9\%$, $1\%$, $0.09$

Watch out. $0.5\%$ = ____________ as a decimal. $0.5$ = ______% as a percent.

Explain. A savings account pays $0.75\%$. Why is that less than one percent?

Explain. A town's population is now $140\%$ of its population in 2000. What does that tell you?

PAGE 19 — Exit ticket 4.6

Exit Ticket · Lesson 4.6

Name: ________________________ Date: ____________

1. Write $225\%$ as a decimal. ______

2. Write $0.7\%$ as a decimal. ______

3. Which is greater, $0.4\%$ or $0.04$? ______

4. Explain how a model can show a percent greater than $100\%$.

PAGE 20 — Chapter 4 review, part 1

Chapter 4 Review

Part A · Percent from a model

1. A hundred grid has 68 squares shaded. Percent shaded: ______

2. A rectangle in 20 equal parts has 9 shaded. Percent shaded: ______

3. A bar is shaded a little past the one-quarter mark. Estimate: ______

4. a) One full grid plus 60 squares of a second grid: ______ b) Half of one small square: ______

Part B · Decimals and percents

5. Decimal to percent: a) $0.42$ ______ b) $0.09$ ______ c) $1.6$ ______ d) $0.004$ ______

6. Percent to decimal: a) $65\%$ ______ b) $7\%$ ______ c) $210\%$ ______ d) $0.5\%$ ______

7. Is $0.08$ greater than, less than, or equal to $8\%$? ______ Justify:

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Part C · Fractions, mixed numbers, and percents

8. As a percent: a) $\tfrac{4}{5}$ ______ b) $\tfrac{7}{8}$ ______ c) $\tfrac{1}{3}$ ______ d) $\tfrac{9}{4}$ ______

9. Simplest form: a) $55\%$ ______ b) $4\%$ ______ c) $150\%$ ______

PAGE 21 — Chapter 4 review, part 2

Chapter 4 Review (continued)

Part D · All three forms

10. Complete each row. Fractions in simplest form.

11. $1\tfrac{1}{8}$ → decimal ______ percent ______

Part E · Comparing and ordering

12. Least to greatest: $0.65$, $\tfrac{5}{8}$, $63\%$, $\tfrac{2}{3}$

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    Justification: _______________________________________________

13. Greatest to least: $\tfrac{7}{10}$, $0.72$, $68\%$, $\tfrac{3}{4}$

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14. Fill in: a) $\tfrac{2}{5} \ \square \ 0.4$ b) $\tfrac{5}{6} \ \square \ 85\%$ c) $1.2 \ \square \ 115\%$

Part F · Application and reasoning

15. Quiz scores: Ana $\tfrac{17}{20}$, Ben $0.86$, Cruz $84\%$. Highest to lowest:

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16. Use a benchmark: is $\tfrac{7}{12}$ greater or less than $\tfrac{1}{2}$? ______ Why?

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17. Why is $0.7\%$ much smaller than $7\%$? Decimals: $0.7\% =$ ______ and $7\% =$ ______

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18. A sign reads "This year's sales are $125\%$ of last year's." What does that mean?

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    $125\% =$ ______ as a decimal and ______ as a mixed number.

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
• Hundred grids: print at least 2.5 in square so students can count individual cells; keep gridlines hairline so shading reads clearly
• Figure widths: number-line figures full width; single-grid figures half width so a table can sit beside them
• Blank hundred grids: pages 2, 3, and 17 benefit from an unshaded 10 by 10 grid in the margin for student work
• Answer blanks: keep every blank on the same line as its prompt so the Canva text box does not reflow
• Repeating decimals: the overbar in $0.41\overline{6}$ must survive the paste; if it does not, set that value as an image