A focused Grade 7 learning session for Solving Equations with the Distributive Property using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving solving equations with the distributive property.
Solving Equations with the Distributive Property is part of Grade 7 Equations and Inequalities. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of solving equations with the distributive property 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 Solving Equations with the Distributive Property, 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 solving equations with the distributive property.
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.
Solve for \(x\): \(3(x+4)=27\)
Answer A: \(x=5\)
Distribute: \(3x+12=27\). Subtract \(12\): \(3x=15\). Divide by \(3\): \(x=5\). (Distractor D: forgetting to distribute gives \(x+4=27 \Rightarrow x=23\).)
Solve for \(x\): \(5(x-2)=35\)
Answer C: \(x=9\)
Distribute: \(5x-10=35\). Add \(10\): \(5x=45\). Divide by \(5\): \(x=9\). (Distractor A: solving \(x-2=5\) instead; Distractor D: arithmetic error when isolating \(x\).)
Solve for \(x\): \(2(x+6)=20\)
Answer B: \(x=4\)
Distribute: \(2x+12=20\). Subtract \(12\): \(2x=8\). Divide by \(2\): \(x=4\). (Distractor A: dividing only the right side; Distractor C: forgetting to divide by 2; Distractor D: arithmetic error in final step.)
Solve for \(x\): \(4(x-3)=12\)
Answer C: \(x=6\)
Distribute: \(4x-12=12\). Add \(12\): \(4x=24\). Divide by \(4\): \(x=6\).
Solve for \(x\): \(6(x+2)=30\)
Answer B: \(x=3\)
Distribute: \(6x+12=30\). Subtract \(12\): \(6x=18\). Divide by \(6\): \(x=3\).
Solve for \(x\): \(2(x-5)=14\)
Answer B: \(x=12\)
Distribute: \(2x-10=14\). Add \(10\): \(2x=24\). Divide by \(2\): \(x=12\).
Solve for \(x\): \(7(x+1)=49\)
Answer B: \(x=6\)
Distribute: \(7x+7=49\). Subtract \(7\): \(7x=42\). Divide by \(7\): \(x=6\).
Solve for \(x\): \(-2(x+3)=10\)
Answer A: \(x=-8\)
Distribute: \(-2x-6=10\). Add \(6\): \(-2x=16\). Divide by \(-2\): \(x=-8\).
Solve for \(x\): \(-3(x-2)=15\)
Answer A: \(x=-3\)
Distribute: \(-3x+6=15\). Subtract \(6\): \(-3x=9\). Divide by \(-3\): \(x=-3\).
Solve for \(x\): \(5(x-4)=45\)
Answer C: \(x=13\)
Distribute: \(5x-20=45\). Add \(20\): \(5x=65\). Divide by \(5\): \(x=13\).
Which equation is equivalent to \(3(x-5)=24\)?
Answer A: \(3x-15=24\)
The distributive property gives \(3 \cdot x - 3 \cdot 5 = 24\), so \(3x-15=24\).
