Counting outcomes – Grade 11 math lesson

Lesson 16 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: “How many 3-digit codes can be made from the digits 1 to 5 with no repeats? How do you know?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Listing in a random order and missing some. Fix one choice at a time and list all the others.
Adding the choices instead of multiplying. Draw a tree: each starter branches into every main.

Tip for home: Count the possible combinations of outfits or meals at home.

What your child will learn

Learning goal: list outcomes systematically and use the product rule for counting.

Success looks like

I can list outcomes systematically.
I can use the product rule.
I can count arrangements without repeats.

Key words

outcome: one possible result
systematic: in a careful order
product rule: multiply the number of choices at each step
arrangement: an order of items

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: List all the outfits you can make from 3 tops and 2 pairs of trousers.

The big ideas (for the adult)

Listing systematically means working in an order so nothing is missed or repeated: fix the first choice, list all the second choices, then move on.

The product rule: if there are 3 starters and 4 mains, there are 3 × 4 = 12 different meals.

If items cannot be repeated, the number of choices goes down at each step: 5 × 4 × 3 ways to fill three places from five people.

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.CP.B.9: “(+) Use permutations and combinations to compute probabilities of compound events and solve problems.”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.