Free printable summer review

6th Grade Summer Math Review

A printable 6th grade summer math review with 40 problems covering rational-number operations, ratios, percent, negative numbers, equations, visual geometry, and word problems.

40 problems8 skill areasAbout 85 minutesAnswer key included
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What this review measures

Sixth grade shifts mathematics toward proportional and algebraic reasoning. This expanded packet gives each major prerequisite room to develop: fluent rational-number computation, ratio language, percent, signed numbers, equations tied to meaningful situations, and geometry supported by diagrams rather than words alone.

For parents and educators

A calculator is unnecessary for most items. If computation hides the student's reasoning, allow one only after the student writes the setup and estimates the answer.

Preview the complete review

Every question below appears in the printable packet. Students should show their work and simplify answers unless directed otherwise.

Fractions and decimals

Compute with positive rational numbers and estimate first.

  1. 1Find 5/6 - 7/18.
  2. 2Find 2 2/5 x 1 1/4.
  3. 3Find 3.78 / 0.14.
  4. 4Find 4.625 + 2.78.
  5. 5Find 3 3/4 / 5/8.
  6. 6Write the shaded amount as a fraction, decimal, and percent.

Ratios and rates

Use equivalent ratios and unit rates.

  1. 7A drink uses 3 cups of juice for 5 cups of water. How much juice is needed for 20 cups of water?
  2. 8A car travels 156 miles on 6 gallons. Find the unit rate.
  3. 9Which is the better price: 8 ounces for $2.64 or 12 ounces for $3.72?
  4. 10Complete the equivalent ratio: 7/9 = 35/n.
  5. 11A map uses 1 inch for every 24 miles. Two towns are 3.5 inches apart on the map. How far apart are they?

Percent

Connect percent to fractions, decimals, and change.

  1. 12Find 35% of 240.
  2. 1342 is what percent of 60?
  3. 14A $50 jacket is discounted 20%. What is the sale price?
  4. 15Write 0.085 as a percent.
  5. 16A restaurant bill is $36. Find a 15% tip and the total with the tip.

Negative numbers

Order and compute with signed numbers in context.

  1. 17Order from least to greatest: -3, 4, -8, 0, 2.
  2. 18Find -7 + 12 - 9.
  3. 19The temperature rises from -6 degrees to 5 degrees. What is the change?
  4. 20Find the distance between -9 and 4 on a number line.
  5. 21A submarine is at -125 feet and rises 48 feet. What is its new elevation?

Expressions and equations

Evaluate, combine terms, and solve one-step equations.

  1. 22Evaluate 3a + 2b when a = 4 and b = -1.
  2. 23Simplify 5x + 8 - 2x + 3.
  3. 24Solve x/4 - 3 = 5.
  4. 25Write an equation: seven more than twice a number is 31.
  5. 26Use the distributive property to rewrite 6(2x - 5).
  6. 27Solve 2.5n = 17.5.

Geometry

Use diagrams, coordinates, area, surface area, and volume formulas with units.

  1. 28Find the area of the triangle.base 12 cm; height 7 cm
  2. 29Find the volume of the rectangular prism.4.5 m2 m3 m
  3. 30The rectangle has area 84 square feet. Find the missing side length and its perimeter.12 ft? ftArea = 84 sq ft
  4. 31Points A and B are shown. Find the horizontal distance between them.AB
  5. 32Classify the angle, then find its complement.62 degrees
  6. 33Find the area of the trapezoid. Use A = 1/2(b1 + b2)h.bases 8 and 12; height 6
  7. 34A rectangular prism is 6 inches long, 4 inches wide, and 3 inches high. Find its surface area.6 in.3 in.4 in.

Word problems

Model proportional and algebraic situations.

  1. 35Five movie tickets cost $61.25. At that rate, how much do 8 tickets cost?
  2. 36Jordan reads 18 pages per day. After 12 days, 64 pages remain. How many pages are in the book?
  3. 37A recipe is 40% flour by mass. How much flour is in 750 grams of dough?
  4. 38A 15.75-foot ribbon is cut into 7 equal pieces. How long is each piece?

Challenge

Test a claim and reason with constraints.

  1. 39Is 25% of 80 equal to 80% of 25? Explain.
  2. 40The mean of four numbers is 18. Three numbers are 11, 17, and 23. Find the fourth.
View the complete answer key

Open-ended explanations may use different wording while showing the same reasoning.

Fractions and decimals

1. 4/9

2. 3

3. 27

4. 7.405

5. 6

6. 7/10, 0.7, and 70%

Ratios and rates

7. 12 cups

8. 26 miles per gallon

9. 12 ounces for $3.72; $0.31 per ounce versus $0.33

10. n = 45

11. 84 miles

Percent

12. 84

13. 70%

14. $40

15. 8.5%

16. $5.40 tip; $41.40 total

Negative numbers

17. -8, -3, 0, 2, 4

18. -4

19. 11 degrees

20. 13 units

21. -77 feet

Expressions and equations

22. 10

23. 3x + 11

24. x = 32

25. 2x + 7 = 31

26. 12x - 30

27. n = 7

Geometry

28. 42 square cm

29. 27 cubic m

30. 7 feet; perimeter 38 feet

31. 6 units

32. Acute; 28 degrees

33. 60 square units

34. 108 square inches

Word problems

35. $98

36. 280 pages

37. 300 grams

38. 2.25 feet

Challenge

39. Yes; both equal 20

40. 21

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