A focused Grade 7 learning session for Rewriting Expressions to Solve Problems using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving rewriting expressions to solve problems.
Rewriting Expressions to Solve Problems is part of Grade 7 Expressions. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of rewriting expressions to solve problems using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Rewriting Expressions to Solve Problems, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving rewriting expressions to solve problems.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Which expression is equivalent to \(0.95p\)?
Answer B: \(p-0.05p\)
The decimal \(0.95\) means keeping \(95\%\) of the price (removing \(5\%\)). This is the same as \(p-0.05p=(1-0.05)p=0.95p\). Both forms show a \(5\%\) discount: one expanded (subtract the discount), one simplified (multiply by the remaining scale factor).
A shirt costs \($60\). With a \(15\%\) discount, which expression represents the final price?
Answer B: \(0.85 \times 60\)
A \(15\%\) discount removes \(15\%\) from the original price. You pay the remaining \(100\%-15\%=85\%\). The multiplier \(0.85\) scales the price by this remaining percent: \(0.85 \times 60=51\).
Which expression is equivalent to \(1.08m\)?
Answer A: \(m+0.08m\)
\(m+0.08m=(1+0.08)m=1.08m\). An \(8\%\) tax adds \(8\%\) to the original price.
A book costs \($25\). With sales tax of \(6\%\), what is the total cost?
Answer C: \(25 \times 1.06\)
With a \(6\%\) tax, you pay \(100\%+6\%=106\%\) of the original price: \(25 \times 1.06\).
Use the distributive property to simplify \(3(x+5)-2x\).
Answer A: \(3x+15-2x=x+15\)
Distribute: \(3(x+5)-2x=3x+15-2x\). Combine like terms: \(3x-2x+15=x+15\).
Which expression is equivalent to \(2(4y-1)+3y\)?
Answer A: \(8y-2+3y=11y-2\)
Distribute \(2\): \(2(4y)-2(1)+3y=8y-2+3y\). Combine: \(8y+3y-2=11y-2\).
A pair of jeans costs \($80\). After a \(20\%\) discount, express the final price in factored form.
Answer A: \(80(1-0.2)\)
A \(20\%\) discount means you keep \(100\%-20\%=80\%\) of the price. The factored form \(80(1-0.2)\) emphasizes the scale factor \((1-0.2)\), which equals \(0.8\). This form reveals the structure of the discount.
Simplify: \(5(2a+3)-(a+6)\).
Answer A: \(10a+15-a-6=9a+9\)
Distribute: \(5(2a)+5(3)-(a+6)=10a+15-a-6\). Combine: \((10a-a)+(15-6)=9a+9\).
Which of the following shows that \(0.9p=p-0.1p\)?
Answer A: Factoring: \(p-0.1p=p(1-0.1)=0.9p\)
Factoring out \(p\) from \(p-0.1p\) gives \(p(1-0.1)=p(0.9)=0.9p\). This is the key rewriting.
A skateboard costs \(c\) dollars. After a \(25\%\) discount, the price is \(0.75c\). Use distribution to write this as \((1-?)c\).
Answer A: \((1-0.25)c\)
A \(25\%\) discount removes \(25\%\), so we keep \(1-0.25=0.75\) of the original price.
Simplify: \(4(x-2)+3(x+1)\).
Answer B: \(7x-5\) (simplified form)
Distribute the 4 and 3 to each term in the parentheses: \(4x-8+3x+3\). Then combine like terms: \((4x+3x)+(-8+3)=7x-5\). The simplified form shows the final equivalent expression.
