Solving equations – Grade 6 math lesson
Lesson 19 of 26 in the Grade 6 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 6 (ages 11–12) 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 6 (ages 11–12)
- 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 6 math lessons
- Solving word problems
- Fractions, decimals and percentages
- Ratios
- One quantity as a fraction or percentage of another
- Percent
- Proportional relationships
- Rates and unit rates
- Unit prices and best buys
- Converting units
- Negative numbers and temperature
- Integers and absolute value
- Operations with multi-digit decimals
- Operations with fractions
- Greatest common factor and least common multiple
- Square and cube numbers
- Writing expressions
- Evaluating expressions
- Simplifying expressions
- Inequalities
- Writing equations for situations
- 3-D shapes and nets
- Coordinates
- Volume and surface area
- Mean, median and mode
- Box plots and interquartile range
Curriculum
Common Core State Standards 6.EE.B.5: “Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.”
Common Core State Standards 6.EE.B.7: “Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.