Rates and unit rates – Grade 6 math lesson
Lesson 7 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: “Why does a car travelling at 60 km/h go 1 km every minute?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using 30 minutes as 0.3 hours. 30 minutes is half an hour: 0.5.
- Multiplying when you should divide. Check the units: km/h means km ÷ h.
Tip for home: Work out average speed on a journey from the distance and time.
What your child will learn
Learning goal: use compound measures such as speed, density and pressure.
Success looks like
- I can use the speed formula.
- I can use density and pressure.
- I can convert units in compound measures.
Key words
- speed
- distance covered in a unit of time
- density
- mass of one unit of volume
- pressure
- force on one unit of area
- rate
- how much of one quantity per unit of another
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Time how long it takes to walk 100 m and work out your speed in meters per second.
The big ideas (for the adult)
A compound measure combines two measures: speed = distance ÷ time, density = mass ÷ volume, pressure = force ÷ area.
Rearrange the formula to find another part: distance = speed × time.
Check the units match: a speed in km/h needs time in hours, so 30 minutes is 0.5 hours.
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
- 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.3.b: “Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?”
Common Core State Standards HSN.Q.A.1: “Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.