Ratios – Grade 7 math lesson
Lesson 1 of 21 in the Grade 7 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 7 (ages 12–13) 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 7 (ages 12–13)
- 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 is 2 : 3 not the same as 3 : 2?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Dividing the amount by one part instead of the total of the parts. Draw a bar split into all the parts first.
- Swapping the order of the ratio. Write the labels above the numbers.
Tip for home: Look for ratios in recipes and on drink bottles ("1 part squash to 4 parts water").
What your child will learn
Learning goal: write and simplify ratios, share in a ratio and solve ratio problems.
Success looks like
- I can simplify a ratio.
- I can share an amount in a ratio.
- I can solve ratio problems.
Key words
- ratio
- a comparison of the sizes of parts
- simplest form
- no whole number above 1 divides every part
- share
- split an amount into parts
- unit ratio
- a ratio written as 1 : n
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Mix a drink or paint in a ratio such as 1 : 4, then make twice as much.
The big ideas (for the adult)
A ratio compares the sizes of parts: 2 : 3 means 2 parts to every 3 parts.
Simplify by dividing every part by the same number. Make sure both parts are in the same units first.
To share an amount in a ratio, add the parts, find the value of one part, then multiply.
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 7 math lessons
- Percent
- Proportional relationships
- Operations with integers
- Repeating decimals
- Evaluating expressions
- Simplifying expressions
- Expanding expressions
- Solving equations
- Inequalities
- Scale drawings and maps
- Angle relationships
- Area of triangles, parallelograms and trapezoids
- Circles: circumference and area
- Volume and surface area
- Cross sections of 3-D figures
- Probability
- Experimental probability
- Compound events
- Box plots and interquartile range
- Sampling and making inferences
Curriculum
Common Core State Standards 7.RP.A.2.c: “Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.”
Common Core State Standards 6.RP.A.1: “Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.