Proportional relationships – Grade 6 math lesson
Lesson 6 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: “If 4 people take 6 hours to paint a fence, how long do 3 people take? Why not 4.5 hours?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using direct proportion when it is inverse (more painters take longer). Ask: if one doubles, does the other double or halve?
- Adding instead of multiplying to scale. Proportion is about multiplying, not adding.
Tip for home: Compare prices per item for different pack sizes.
What your child will learn
Learning goal: recognize and use direct and inverse proportion.
Success looks like
- I can spot direct and inverse proportion.
- I can find the constant of proportionality.
- I can solve proportion problems.
Key words
- direct proportion
- both increase at the same rate
- inverse proportion
- one increases as the other decreases
- constant of proportionality
- the number k that links them
- unitary method
- find one first, then scale
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use a recipe (direct) and sharing a job between friends (inverse) to compare the two kinds.
The big ideas (for the adult)
Two quantities are in direct proportion when one is always the same multiple of the other: double one and the other doubles. y = kx.
In inverse proportion, when one doubles the other halves: more workers, less time. y = k/x.
Find the constant k from one pair of values, then use it for the rest. The unitary method finds the value of one first.
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
- 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
- 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.RP.A.2: “Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."”
Common Core State Standards 6.RP.A.3.a: “Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.