Expanding expressions – Grade 12 math lesson
Lesson 2 of 5 in the Grade 12 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 12 (ages 17–18) 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 12 (ages 17–18)
- 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
| 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 12 math lessons
Curriculum
Common Core State Standards HSA.APR.C.5: “(+) Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.