Expanding expressions – Grade 9 math lesson

Lesson 5 of 17 in the Grade 9 math course

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

A complete 45-minute lesson for grade 9 (ages 14–15) 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 9 (ages 14–15)
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 is (x + 3)² not equal to x² + 9? Use a diagram.”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Only multiplying the first term (3(x + 4) = 3x + 4). Draw arrows from the outside to every term inside.
Getting (x + 3)² = x² + 9. Write it as (x + 3)(x + 3) and use a grid: x² + 6x + 9.

Tip for home: Use the area of a garden split into parts to show expanding parentheses.

What your child will learn

Learning goal: use the distributive property to multiply out parentheses, including two binomials.

Success looks like

I can expand a single parenthesis.
I can expand double parentheses.
I can expand and simplify.

Key words

expand: multiply out
parentheses: group terms together
binomial: an expression with two terms
like terms: terms that can be collected

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Draw a rectangle split into parts to show 3(x + 4) as an area.

The big ideas (for the adult)

To expand, multiply every term inside the parentheses by the term outside: 3(x + 4) = 3x + 12.

For two binomials, multiply each term in the first by each term in the second, then collect like terms. An area model helps.

Watch the signs: −2(x − 5) = −2x + 10.

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

Algebra 1: Polynomials Practice TestGraded instantly

All Grade 9 math lessons and tests · Math Department

More Grade 9 math lessons

Curriculum

Common Core State Standards HSA.APR.A.1: “Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.”

Common Core State Standards HSA.SSE.A.2: “Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ - y⁴ as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).”

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