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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to scale a sample proportion to an estimated count.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Proportions, fractions, and multiplication.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
In a random sample of 80 students from a school of 600, 28 report walking to school. Estimate how many students in the school walk.
Why this math matters
A sample proportion can support a population estimate while leaving sampling uncertainty. Label an extrapolated count as an estimate and describe how its sample was chosen.
Set up the model
A useful answer starts with clear assumptions:
- The sample was randomly drawn from the full school roster.
- Reported walking status is accurate and refers to the same time period.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Scale a sample proportion to an estimated count
PausedQuestion: Start with the question. Paused.
Question
Start with the question
In a random sample of 80 students from a school of 600, 28 report walking to school. Estimate how many students in the school walk.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
sample proportion = 28/80 = 0.35
Estimate the population's walking proportion using the observed sample fraction.
Apply the relationship
estimated count = 0.35 × 600
Apply the estimated proportion to the population size.
Check and interpret
estimated count = 210 students
This is an estimate, not a census count; a different random sample can produce a different result.
The result
estimated count = 210 students
This is an estimate, not a census count; a different random sample can produce a different result.
Common mistakes to catch
- The estimated population count is not the number actually observed.
- Multiplying a biased sample proportion by the population size preserves the bias.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A random sample has 18 bus riders among 50 students. Estimate bus riders in a population of 400.
Show a hint
Multiply 18/50 by 400.
Reveal answer and explanation
144 students
0.36 × 400 = 144.
Practice 2
Two random samples give 34% and 38%. Must one have been collected dishonestly?
Show a hint
Consider ordinary sample-to-sample variation.
Reveal answer and explanation
No
Different random samples can yield different proportions even when both are collected correctly.
Take the idea with you
Label an extrapolated count as an estimate and describe how its sample was chosen.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
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