An item with original price p is discounted 25%. Rewrite p - 1/4p in a form that shows the fraction of the original price the customer pays.
Equivalent form: _____________
What does the new form reveal?
CCSS 7.EE.A.2 · rewrite forms to reveal meaning
Equivalent Expressions in Context Worksheets
Move beyond symbolic matching. Each problem starts with a real quantity model, asks for an equivalent form, and then asks what the new form makes easier to see—remaining groups, percent paid, fixed perimeter, or separated totals.
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Equivalent Expressions in Context
Equivalent expressions in context · Grade 7 standard · Seed 271801
1.
2.
Each of 4 teams receives x practice cards plus 2 challenge cards. Rewrite 4(x + 2) so the total number of regular and challenge cards is visible separately.
Equivalent form: _____________
What does the new form reveal?
3.
A rectangle has width x and length x + 8. Its perimeter can be written 2(x + 8) + 2x. Rewrite the expression to show the variable and fixed parts of the perimeter.
Equivalent form: _____________
What does the new form reveal?
4.
A rectangle has width x and length x + 2. Its perimeter can be written 2(x + 2) + 2x. Rewrite the expression to show the variable and fixed parts of the perimeter.
Equivalent form: _____________
What does the new form reveal?
5.
Each of 8 teams receives x practice cards plus 3 challenge cards. Rewrite 8(x + 3) so the total number of regular and challenge cards is visible separately.
Equivalent form: _____________
What does the new form reveal?
6.
A rectangle has width x and length x + 7. Its perimeter can be written 2(x + 7) + 2x. Rewrite the expression to show the variable and fixed parts of the perimeter.
Equivalent form: _____________
What does the new form reveal?
7.
An item with original price p is discounted 10%. Rewrite p - 1/10p in a form that shows the fraction of the original price the customer pays.
Equivalent form: _____________
What does the new form reveal?
8.
A rectangle has width x and length x + 6. Its perimeter can be written 2(x + 6) + 2x. Rewrite the expression to show the variable and fixed parts of the perimeter.
Equivalent form: _____________
What does the new form reveal?
9.
An item with original price p is discounted 30%. Rewrite p - 3/10p in a form that shows the fraction of the original price the customer pays.
Equivalent form: _____________
What does the new form reveal?
10.
A rectangle has width x and length x + 5. Its perimeter can be written 2(x + 5) + 2x. Rewrite the expression to show the variable and fixed parts of the perimeter.
Equivalent form: _____________
What does the new form reveal?
Construction rule: equations are built around known exact solutions, expression rewrites use exact rational arithmetic, 7.EE.3 money stays in integer cents, and inequality answer graphs are withheld until answers are revealed.
Writing equivalent expressions for a situation
Two expressions are equivalent when they give the same value for every number. In a word problem, the same quantity can often be written in more than one way, and rewriting it can make a relationship easier to see. Use the properties of operations, such as distributing and combining like terms, to move from one form to another.
Worked examples
- A rectangle has width x and length x + 4. Its perimeter is 2x + 2(x + 4) = 4x + 8, which can also be written 4(x + 2).
- A price p with 10% tax costs p + 0.10p. Combining like terms gives 1.10p, so multiplying the price by 1.10 adds the tax in one step.
- A 20% discount takes off 0.20p, so the sale price is p − 0.20p = 0.80p, which means paying 80% of the price.
Common slips
- Treating 1.10p and 0.10p as the same. 0.10p is only the tax; 1.10p is the price plus the tax.
- Checking only one value. Two expressions need to agree for every value, not just one.
- Forgetting to distribute across the whole group. 2(x + 4) is 2x + 8, not 2x + 4.
How to use this worksheet
Ask students to test an equivalent pair with two different values and explain what each form tells them about the situation. The answer key lists the equivalent form for each context.
Common Core connection
- 7.EE.A.2 · Rewrite expressions in different forms to show how quantities relate in a problem.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Teacher tip 1
Equivalent expressions can highlight different features of the same quantity without changing its value.
Teacher tip 2
A factored form often reveals equal groups or a unit structure; an expanded form often separates variable and fixed contributions.
Teacher tip 3
In percent contexts, rewriting p - dp as (1 - d)p shows the share of the original amount that remains.
Continue the 7.EE progression
Move to another Grade 7 algebra skill
Common questions
Is this just identifying equivalent expressions?
No. Students rewrite a contextual expression and interpret what the new form means.
Does this overlap with the percent generator?
The context may use percents, but the assessed skill here is algebraic rewriting and interpretation, not percent computation itself.