A focused Grade 7 learning session for Circumference of a Circle using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving circumference of a circle.
Circumference of a Circle is part of Grade 7 Measurement Geometry. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of circumference of a circle 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 Circumference of a Circle, 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 circumference of a circle.
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.
A circle has a radius of \(5\) meters. Approximately, what is its circumference? Use \(\pi\approx3.14\).
Answer C: \(31.4\) m
Circumference \(=2\pi r\approx2\times3.14\times5=31.4\) m.
A circle has a diameter of \(12\) cm. What is the circumference? Use \(\pi\approx\frac{22}{7}\).
Answer A: \(\frac{264}{7}\) cm
\(C=\pi d=\frac{22}{7}\times12=\frac{264}{7}\approx37.7\) cm.
If a circle's radius is \(7\) inches, which expression gives its circumference?
Answer B: \(14\pi\)
\(C=2\pi r=2\pi(7)=14\pi\) in.
A circle has diameter \(20\) ft. What is its circumference to the nearest tenth? Use \(\pi\approx3.14\).
Answer B: \(62.8\) ft
\(C=\pi d=3.14\times20=62.8\) ft.
A wheel has radius \(0.5\) m. If it rotates exactly once, how far does it travel? Use \(\pi\approx3.14\).
Answer C: \(3.14\) m
Distance = circumference = \(2\pi r=2\times3.14\times0.5=3.14\) m.
A circular pond has circumference \(44\) meters. Using \(\pi\approx\frac{22}{7}\), what is its diameter?
Answer B: \(14\) m
\(C=\pi d \Rightarrow 44=\frac{22}{7}d \Rightarrow d=44\div\frac{22}{7}=44\times\frac{7}{22}=14\) m.
Which circle below has a circumference of approximately \(37.7\) cm? Use \(\pi\approx3.14\).
Answer A: Radius \(6\) cm
\(C=2\pi r=2\times3.14\times6=37.68\approx37.7\) cm (A); B: \(C=\pi d=3.14\times6=18.84\) cm (wrong); C: confuses formula; D: \(C=\pi d=3.14\times12=37.68\) cm (close, but uses diameter not radius).
A circular track has radius \(50\) meters. A runner completes \(3\) laps. Approximately how far does the runner travel? Use \(\pi\approx3.14\).
Answer D: \(942\) m
One lap = \(C=2\pi r=2\times3.14\times50=314\) m. Three laps = \(3\times314=942\) m.
If a circle has circumference \(100\) cm, what is its radius? (Use \(\pi\approx3.14\), round to nearest whole.)
Answer A: About \(16\) cm
\(C=2\pi r \Rightarrow 100=2\times3.14\times r \Rightarrow r=100\div6.28\approx16\) cm.
A plate has diameter \(10\) inches. Using \(\pi\approx\frac{22}{7}\), approximately what is its circumference?
Answer A: \(\frac{220}{7}\) in
\(C=\pi d=\frac{22}{7}\times10=\frac{220}{7}\) in \(\approx31.4\) in.
Based on the diagram, what is the circumference of the circle? Use \(\pi\approx3.14\).
Answer B: \(18.84\) cm
\(C=2\pi r=2\times3.14\times3=18.84\) cm.
