7th grade checking contextual solutions worksheets

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Students test proposed values in six quantity problems, correct them when needed and explain the result with units. The sheet mixes correct candidates with sign, offset and missed-division mistakes.

Free printable PDF worksheet, aligned to Common Core 7.EE.B.4.a.

Each print is a different sheet with its own answer key. You don't need to sign up.

The kind of problems you'll get

Define the given variable with units and write the equation. Test the proposed value. Correct it if needed and explain your answer.

  1. A 19 -meter ribbon is cut into 2 equal pieces, with 6 meters left over. How long is each piece? Let y be meters per piece (positive). Proposed value: y = −13/2.

    Answer: Let y be meters per piece (positive). 2 × y + 6 = 19 ; False; find the correct value. This quantity cannot have that value. 13/2 m. A positive length in meters per piece.

  2. Tickets cost $4.00 each. One booking fee is $4.00. The total is $28.00. How many tickets were bought? Let b count tickets: a positive whole number. Proposed value: b = 8.

    Answer: Let b count tickets: a positive whole number. 4 × b + 4 = 28 ; False; find the correct value. 6 tickets. A positive whole number of tickets.

  3. A 15/2 -meter ribbon is cut into 3 equal pieces, with 3/2 meters left over. How long is each piece? Let x be meters per piece (positive). Proposed value: x = 6.

    Answer: Let x be meters per piece (positive). 3 × x + 3/2 = 15/2 ; False; find the correct value. 2 m. A positive length in meters per piece.

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on a 7th grade sheet

Every version prints on US Letter or A4, with its answer key after the problems.

How to teach this

Ask what the variable measures before writing the equation. Have your child identify the repeated amount, the fixed amount and the total. Finish by substituting and checking whether the answer fits the context.

Watch for: The fixed fee or leftover is added once, after multiplying. A count must be a positive whole number; a length or volume may be fractional.

Common questions about 7th grade checking contextual solutions

What arithmetic is included?
Positive whole numbers and simple fractions appear in two-step equations. Counts have whole-number solutions; lengths and volumes can have half-unit solutions.
What does the answer key show?
By default, each key defines the unknown, explains the model and tests the proposed value. If the value is incorrect, the key solves the equation and checks the corrected answer. It also explains the units and whether the value fits the situation. Choose Answers only for final answers without the worked steps.
Can students use another equation or method?
Yes. Review whether their equation represents the same quantities, their steps are valid and their answer includes units. The key shows one method.

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Aligned to Common Core 7.EE.B.4.a. Reviewed by the One more sheet team. Content version 241, updated October 2026.

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