Sampling and making inferences – Grade 11 math lesson

Lesson 23 of 23 in the Grade 11 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 11 (ages 16–17) 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 11 (ages 16–17)
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

45 minutes in 5 parts
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

All Grade 11 math lessons and tests · Math Department

Curriculum

Common Core State Standards HSS.IC.B.3: “Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.”

Common Core State Standards HSS.IC.B.4: “Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.”

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