Simplifying expressions – Grade 9 math lesson
Lesson 4 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 can 3x + 2x be simplified but 3x + 2y cannot?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Combining unlike terms (3x + 2y = 5xy). Only like terms can be added: apples and bananas stay separate.
- Losing the minus sign of a term. Circle each term with the sign in front of it.
Tip for home: Make up expressions for shopping: 3 apples + 2 bananas + 1 apple.
What your child will learn
Learning goal: simplify expressions by collecting like terms and using index laws.
Success looks like
- I can spot like terms.
- I can collect like terms.
- I can multiply and divide terms.
Key words
- like terms
- terms with the same letters and powers
- coefficient
- the number in front of a letter
- simplify
- write in the shortest form
- exponent
- a power
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Sort algebra cards into groups of like terms, then simplify each group.
The big ideas (for the adult)
Like terms have exactly the same letters and powers: 3x and 5x are like terms; 3x and 3x² are not.
Collect like terms by adding or subtracting their coefficients: 3x + 5y − x + 2y = 2x + 7y. The sign belongs to the term after it.
When multiplying terms, multiply the numbers and add the powers of the same letter: 2a³ × 4a² = 8a⁵.
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 9 math lessons
- Rates and unit rates
- Converting units
- Upper and lower bounds
- Expanding expressions
- Factoring
- Solving equations
- Inequalities
- Rearranging formulas
- Systems of equations
- Quadratic equations
- Identities and proof
- Arithmetic and geometric sequences
- Linear functions and slope
- Functions
- Graphing functions
- Exponential functions
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.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.