A focused Grade 7 learning session for Solving Multi-Step Problems with Rational Numbers using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving solving multi-step problems with rational numbers.
Solving Multi-Step Problems with Rational Numbers 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 multi-step problems with rational numbers 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 Multi-Step Problems with Rational Numbers, 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 multi-step problems with rational numbers.
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: \(\frac{1}{2}x-3=5\) and check that your answer is reasonable.
Answer C: \(x=16\)
Add \(3\) to both sides: \(\frac{1}{2}x=8\). Multiply by \(2\): \(x=16\). Check: \(\frac{1}{2}(16)-3 = 8-3 = 5\) ✓. Reasonableness: Half of 16 is 8; minus 3 gives 5. ✓
Solve \(3x+7=22\) and explain why your answer is reasonable.
Answer A: \(x=5\)
Subtract \(7\): \(3x=15\). Divide by \(3\): \(x=5\). Check: \(3(5)+7 = 15+7 = 22\) ✓. Reasonable: three times 5 is 15; add 7 gives 22.
Solve for \(y\): \(2y-8=-14\) and check your answer makes sense.
Answer A: \(y=-3\)
Add \(8\): \(2y=-6\). Divide by \(2\): \(y=-3\). Check: \(2(-3)-8 = -6-8 = -14\) ✓. Reasonable: negative answer expected (result is negative).
Which value of \(x\) satisfies \(\frac{x}{4}+2=5\)? Use mental math to verify.
Answer B: \(x=12\)
Subtract \(2\): \(\frac{x}{4}=3\). Multiply by \(4\): \(x=12\). Mental math check: \(\frac{12}{4}+2 = 3+2 = 5\) ✓. Reasonable: one-quarter of 12 is 3; add 2 gives 5.
Solve: \(5(x-2)=30\) and verify using inverse operations.
Answer B: \(x=8\)
Divide by \(5\): \(x-2=6\). Add \(2\): \(x=8\). Check: \(5(8-2) = 5(6) = 30\) ✓. Reasonable: five groups of 6 equals 30.
A savings account has a balance of \(-$15\) (overdraft). After depositing $50, what is the new balance? Write and solve an equation.
Answer B: \($35\)
Equation: \(-15 + d = b\) where \(d = 50\) (deposit). Or: \(-15 + 50 = 35\). Check: Starting with \(-$15\) debt, adding \($50\) leaves \($35\) surplus. Reasonable.
Marcus earns $12 per hour. After working 8 hours, he spent $15 on lunch. How much money does he have left?
Answer A: \($81\)
Earnings: \(12 \times 8 = 96\). After spending: \(96 - 15 = 81\).
Solve: \(-2x+6=18\) and check that a negative answer is reasonable.
Answer A: \(x=-6\)
Subtract \(6\): \(-2x=12\). Divide by \(-2\): \(x=-6\). Check: \(-2(-6)+6 = 12+6 = 18\) ✓. Reasonable: negative coefficient times negative answer yields positive; add 6 gives 18.
What is the solution to \(\frac{3}{4}x=12\)? Use a reciprocal to solve and verify.
Answer C: \(x=16\)
Multiply both sides by \(\frac{4}{3}\) (reciprocal): \(x = 12 \times \frac{4}{3} = 16\). Check: \(\frac{3}{4}(16) = \frac{3 \times 16}{4} = \frac{48}{4} = 12\) ✓. Reasonable: three-quarters of 16 is 12.
Solve: \(2x-5=7\)
Answer B: \(x=6\)
Add \(5\): \(2x=12\). Divide by \(2\): \(x=6\).
A taxi charges $3 per mile plus a $2 fee. If a trip costs $17, how many miles was the trip? Check your answer is reasonable.
Answer B: \(5\) miles
Set up: \(3m + 2 = 17\). Subtract \(2\): \(3m = 15\). Divide by \(3\): \(m = 5\) miles. Check: \(3(5) + 2 = 15 + 2 = 17\) ✓. Reasonable: ~5 miles at $3/mile plus $2 fee totals $17.
