Expected value – Grade 11 math lesson

Lesson 20 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: “Would you play a game that costs 2 to enter if the expected prize is 1.50? Why?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Averaging the values without the probabilities. Weight each value by its probability.
Expecting the expected value to happen in one go. It is an average over many trials.

Tip for home: Talk about why games of chance are designed so the house wins on average.

What your child will learn

Learning goal: find expected values and use probability distributions to make decisions.

Success looks like

I can make a probability distribution.
I can calculate an expected value.
I can use expected values to decide.

Key words

random variable: a quantity whose value depends on chance
probability distribution: all values with their probabilities
expected value: the long-run average value
fair game: expected gain of zero

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Design a simple dice game with prizes and work out whether it is fair.

The big ideas (for the adult)

A probability distribution lists each value and its probability; the probabilities add up to 1.

The expected value is the long-run average: multiply each value by its probability and add.

Use expected values to compare choices, such as two games or two insurance plans.

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.MD.A.1: “(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.”

Common Core State Standards HSS.MD.A.2: “(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.”

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