Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Different forms of the same expression can tell different stories. The expression p + 0.15p says 'take the price and add 15% of it', while its simplified form 1.15p says 'multiply the price by 1.15'. Both give the same number, but the second form reveals that a 15% increase is a single scaling, which makes it far quicker to apply to many prices or to undo later.
Seventh graders practice choosing and interpreting forms like these. A discount of 30% can be written p - 0.3p or 0.7p, the second showing that the buyer pays 70%. The perimeter 2L + 2W can be written 2(L + W), which says 'go once along a length and a width, then double it'. Students explain what each form shows about the quantities, and they use whichever form makes the question easiest to answer. This is less about mechanical simplifying, which belongs to 7.EE.A.1, and more about reading structure in context.
The 1 in 1.25 represents the original amount, so 1.25x is the original plus 25%. Splitting 1.25x back into x + 0.25x makes this clear.
A 30% discount depends on the price, so it is p - 0.3p, not p - 30. Testing a $10 item (30% off should be $7) exposes the mistake.
Students may wonder why 2(L + W) matters when 2L + 2W is fine. Asking them to compute perimeters of several rectangles quickly shows that adding first and doubling once saves steps.
Sales tax is 15% on a price p. Write the total cost in two ways, explain what each form shows, and find the total for a $40 item.
Answer: Total cost is p + 0.15p = 1.15p, so a $40 item costs $46 in all.
Pair every symbolic rewrite with a sentence starter: 'This form shows that...'. Students who must explain both forms in words understand why multipliers work and become far more flexible with percent problems in 7.RP.A.3.
Assessment items often show two expressions for the same context and ask what one form reveals, or ask students to select all the expressions that represent a given discount. Including fractions such as x - (1/4)x = (3/4)x keeps students from tying the idea only to decimals.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: A) 0.7p
p - 0.3p = 0.7p. The buyer pays 70% of the original price.
Answer: 1.08n
n is 1n, so 1n + 0.08n = 1.08n. The total is 108% of n, an 8% increase.
Answer: C) 2(L + W)
Factoring the 2 out of 2L + 2W gives 2(L + W): find L + W once, then double it.
Answer: B) An increase of 25%
1.25x = x + 0.25x. The extra 0.25x is 25% of the original, so it is a 25% increase.
Answer: 102 (also accepted: $102)
0.85 × 120 = 102, so the sale price is $102. The form 0.85p shows a 15% discount.
Answer: D) x - (1/4)x = (3/4)x
Removing 1/4 of x leaves 3/4 of x, so x - (1/4)x = (3/4)x.
A full lesson with slides, activities and an exit ticket on rewriting expressions to understand a problem, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 7.EE.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn rewriting expressions to understand a problem into a quiz students answer online that marks itself, with a class summary for you.
Build a test →7.EE.A.1 is about the skill of producing equivalent expressions. 7.EE.A.2 is about understanding what each form tells you about the situation and using that insight to solve problems.
It shows that increasing by 5% is the same as multiplying by 1.05, which turns many percent problems into a single multiplication.