Solving equations – Grade 8 math lesson
Lesson 6 of 16 in the Grade 8 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 8 (ages 13–14) 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 8 (ages 13–14)
- 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 can you check your solution is right?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Doing an operation to one side only. Write the operation on both sides each time.
- Subtracting when the term is negative (−2x = 8 gives x = 10). Divide both sides by −2: x = −4.
Tip for home: Make up "think of a number" puzzles and solve them with equations.
What your child will learn
Learning goal: solve linear equations, including with parentheses and unknowns on both sides.
Success looks like
- I can solve one-step and two-step equations.
- I can solve equations with parentheses.
- I can solve equations with unknowns on both sides.
Key words
- equation
- two expressions that are equal
- solve
- find the value that makes it true
- inverse operation
- the operation that undoes another
- solution
- the value of the unknown
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Model equations with a balance: cups with hidden counters and loose counters.
The big ideas (for the adult)
An equation is like a balance: whatever you do to one side, do to the other.
Undo operations in reverse order: for 3x + 5 = 20, subtract 5, then divide by 3, so x = 5.
With unknowns on both sides, first collect the x terms on one side. Expand any parentheses first. Check by substituting.
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 8 math lessons
- Repeating decimals
- Scientific notation
- Laws of exponents
- Square roots and cube roots
- Simplifying expressions
- Systems of equations
- Arithmetic and geometric sequences
- Linear functions and slope
- Functions
- Graphing functions
- Angle relationships
- Volume and surface area
- The Pythagorean theorem
- Transformations
- Scatter plots and lines of fit
Curriculum
Common Core State Standards 8.EE.C.7.b: “Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.”
Common Core State Standards 8.EE.C.7.a: “Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.