A focused Grade 7 learning session for Writing Two-Step Equations from Word Problems using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving writing two-step equations from word problems.
Writing Two-Step Equations from Word Problems 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 writing two-step equations from word 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 Writing Two-Step Equations from Word 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 writing two-step equations from word 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.
Naomi buys \(3\) books at \($8\) each and a \($5\) bookmark. Let \(t\) be her total cost. Which equation models this situation?
Answer C: \(t=3(8)+5\)
The books cost \(3\times8=$24\) and the bookmark adds \($5\), so \(t=3(8)+5=29\).
A car rental company charges a base fee of \($45\) and then \($0.25\) per mile. Which equation represents the total cost \(C\) for \(m\) miles?
Answer B: \(C=0.25m+45\)
The per-mile cost \(0.25m\) is added to the fixed base fee \($45\).
A phone company charges \($20\) per month plus \($0.15\) for each text message over the limit. If Marcus pays \($35.60\) in a month, which equation could be used to find \(n\), the number of text messages over the limit?
Answer A: \(0.15n+20=35.60\)
Base charge is \($20\); each extra text adds \($0.15\). So \(0.15n+20=35.60\).
A delivery service charges an initial fee of \($8\) plus \($3\) per package. If the total charge is \($26\), which equation represents this, where \(p\) is the number of packages?
Answer B: \(3p+8=26\)
Initial fee is \($8\); each package adds \($3\). Equation: \(3p+8=26\).
Jenna joins a gym with a membership fee of \($50\) and monthly charges of \($25\). Let \(m\) represent the number of months. Which equation shows the total cost \(T\) including the membership fee?
Answer C: \(T=50+25m\)
The one-time membership is \($50\) plus \($25\) each month, so \(T=50+25m\).
A plumber charges \($65\) for a service call and \($40\) per hour of work. The total bill was \($185\). Which equation helps find \(h\), the number of hours worked?
Answer B: \(65+40h=185\)
Service call is \($65\) plus \($40\) per hour. So \(65+40h=185\).
A baker buys flour in \(5\)-pound bags at \($3\) per bag. She also buys yeast for \($2\). If she spends \($17\) total, which equation represents the number of bags \(b\) she bought?
Answer C: \(3b+2=17\)
Each bag costs \($3\) and yeast is \($2\). Equation: \(3b+2=17\).
A streaming service costs \($12.99\) per month plus a one-time setup fee of \($19.99\). Which expression shows the total cost \(C\) for \(n\) months?
Answer A: \(C=19.99+12.99n\)
Setup fee is \($19.99\) plus \($12.99\) per month, so \(C=19.99+12.99n\).
A skateboard costs \($85\), and safety gear costs \($12\) per item. Marcus buys a skateboard and \(4\) safety items. Which equation represents his total cost \(C\)?
Answer C: \(C=85+4(12)\)
Skateboard is \($85\) and safety gear is \(4 \times $12=$48\). Total equation: \(C=85+4(12)=$85+$48=$133\).
A tutoring center charges an enrollment fee of \($30\) and \($45\) per session. Write an equation that models the total cost \(T\) for \(s\) sessions.
Answer C: \(T=30+45s\)
Enrollment fee (constant \($30\)) plus per-session charge (\($45s\)). Equivalent forms: \(T=30+45s\) or \(T=45s+30\) (commutativity).
Which situation matches the equation \(2x+7=21\)?
Answer D: A number is doubled, then \(7\) is added, resulting in \(21\).
Option D matches \(2x+7=21\): multiply \(x\) by \(2\), add \(7\). Others do not use the form correctly.
