Resources/Ratios practice: unit rates and proportional reasoning
Grades 6-7•Printable worksheet + answer key•CC0 license

Ratios practice: unit rates and proportional reasoning

A printable lesson focused on understanding and scaling ratios.

Students practice writing ratios, finding unit rates, and deciding if relationships are proportional.

Print-ready worksheet with answer key and quick teaching tips.

Grades 6-70 problems10 minAnswer key included
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Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This free ratios worksheet for grades 6-7 targets unit rates and proportional reasoning skills.

Lesson plan snapshot

15-20 min
  • Warm-up (3 min): read and write ratios from quick prompts.
  • Model (5 min): solve the worked example together.
  • Guided practice (5 min): complete problems 1-3 as a group.
  • Independent practice (7 min): finish the remaining problems.

Materials: ratio table, pencil

Learning targets

  • Write ratios in multiple forms (a:b, a to b, a/b).
  • Find unit rates from tables and word problems.
  • Identify proportional relationships.

Step-by-step approach

  1. 1Write the ratio in the correct order (what to what?).
  2. 2Create a ratio table to scale by the same factor.
  3. 3Find unit rate by dividing both quantities by the same number.
  4. 4Check if the ratio stays constant across pairs.

Common mistakes

Mistake

Swapping the order of the ratio.

Try instead

Label each quantity and keep the order consistent.

Mistake

Treating ratios as part-to-whole by default.

Try instead

Clarify whether the ratio compares part-to-part or part-to-whole.

Mistake

Using inconsistent scaling factors.

Try instead

Multiply or divide both parts by the same number.

Worked example

Guided
A car travels 150 miles in 3 hours. What is the unit rate?
  1. Unit rate means per 1 hour.
  2. Divide both numbers by 3: 150 ÷ 3 = 50.
  3. The unit rate is 50 miles per hour.
Answer: 50 miles per hour

Related resources

Percents

Percent conversions and percent-of problems.

View resource

Percent change

Find percent increase and decrease.

View resource

Word problems

Multi-step ratio and rate scenarios.

View resource

Practice problems

16 problems • 24 min

Printable worksheet
  1. 1
    Write the ratio of red to blue if there are 8 red and 3 blue.
  2. 2
    Scale the ratio 6:3 by a factor of 5.
  3. 3
    Find the unit rate: 60 points in 4 games.
  4. 4
    Write the ratio of blue to total tiles if 9 are blue and 7 are red.
  5. 5
    Write the ratio of red to blue if there are 7 red and 5 blue.
  6. 6
    Write the ratio of blue to total tiles if 4 are blue and 7 are red.
  7. 7
    If 6 notebooks cost 1.5 dollars, what is the unit price per notebook?
  8. 8
    Find the unit rate: 16 pages in 4 minutes.
  9. 9
    Scale the ratio 2:5 by a factor of 4.
  10. 10
    Write the ratio of red to blue if there are 5 red and 3 blue.
  11. 11
    If 8 notebooks cost 2 dollars, what is the unit price per notebook?
  12. 12
    Find the unit rate: 27 miles in 3 hours.
  13. 13
    Scale the ratio 6:8 by a factor of 3.
  14. 14
    Write the ratio of red to blue if there are 2 red and 10 blue.
  15. 15
    Write the ratio of blue to total tiles if 3 are blue and 3 are red.
  16. 16
    Scale the ratio 4:6 by a factor of 3.

Answer key

16 answers
  1. 11) 8:3
  2. 22) 30:15
  3. 33) 15 points per game
  4. 44) 9:16
  5. 55) 7:5
  6. 66) 4:11
  7. 77) 0.25 dollars
  8. 88) 4 pages per minute
  9. 99) 8:20
  10. 1010) 5:3
  11. 1111) 0.25 dollars
  12. 1212) 9 miles per hour
  13. 1313) 18:24
  14. 1414) 1:5
  15. 1515) 1:2
  16. 1616) 12:18

Teacher tips

  • THave students label units in every ratio table.
  • TUse real-world comparisons (recipes, speed, cost) to build meaning.
  • TAsk students to justify whether a relationship is proportional.

Parent tips

  • PCompare sports stats (points per game) to practice unit rates.
  • PKeep the order consistent: say the ratio out loud.
  • PUse shopping examples to compare cost per item.

Open license

You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).