Sampling and making inferences – Grade 7 math lesson
Lesson 21 of 21 in the Grade 7 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 7 (ages 12–13) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 7 (ages 12–13)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why might asking people at a gym about exercise give a biased result?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using a sample of only friends or one class. Ask: does every member have an equal chance of being picked?
- Thinking a sample result is exactly right for the population. It is an estimate; bigger samples are usually better.
Tip for home: Talk about polls in the news: who was asked, and how many?
What your child will learn
Learning goal: choose fair samples and use them to estimate facts about a population.
Success looks like
- I can explain population and sample.
- I can spot a biased sample.
- I can make an estimate from a sample.
Key words
- population
- the whole group being studied
- sample
- part of the population
- random
- every member has an equal chance
- bias
- a sample that is not fair
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Pick a random sample of words from a book page and estimate the average word length.
The big ideas (for the adult)
A population is everyone or everything you want to know about; a sample is a smaller group you actually ask or measure.
A random sample gives everyone the same chance of being chosen, which helps avoid bias.
Use a sample to estimate: if 12 out of 40 in the sample like a song, about 30% of the population might.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 7 math lessons
- Ratios
- Percent
- Proportional relationships
- Operations with integers
- Repeating decimals
- Evaluating expressions
- Simplifying expressions
- Expanding expressions
- Solving equations
- Inequalities
- Scale drawings and maps
- Angle relationships
- Area of triangles, parallelograms and trapezoids
- Circles: circumference and area
- Volume and surface area
- Cross sections of 3-D figures
- Probability
- Experimental probability
- Compound events
- Box plots and interquartile range
Curriculum
Common Core State Standards 7.SP.A.1: “Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.”
Common Core State Standards 7.SP.A.2: “Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.