Writing equations for situations – Grade 6 math lesson
Lesson 21 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 tell from a table that the rule is "multiply by 4"?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Swapping the two variables. Ask: which one depends on the other?
- Adding when the rule multiplies. Check the rule with every row of the table.
Tip for home: Write equations for everyday rates: pay per hour, cost per item.
What your child will learn
Learning goal: write equations to show how two quantities are related.
Success looks like
- I can identify the dependent and independent variables.
- I can write an equation from a table.
- I can use the equation to solve problems.
Key words
- independent variable
- the input you choose
- dependent variable
- the output that depends on it
- rate
- how much one changes for each unit of the other
- equation
- a statement that two expressions are equal
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Record the cost of 1, 2, 3 and 4 items at a shop and write an equation for the cost.
The big ideas (for the adult)
When one quantity depends on another, an equation shows the rule: if each ticket costs 8, the cost c for t tickets is c = 8t.
A table of values helps you see the rule: look at how the output changes as the input goes up by 1.
The variable that depends on the other is the dependent variable; the one you choose is the independent variable.
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
- Solving equations
- Inequalities
- 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.C.9: “Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.