Fractions, decimals and percentages – Grade 6 math lesson

Lesson 2 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: “Which is greater: 3/5, 0.58 or 61%? How did you decide?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Writing 0.5 as 5%. Multiply by 100: 0.5 × 100 = 50, so 50%.
Thinking 1/4 is 0.4. A fraction is a division: 1 ÷ 4 = 0.25.

Tip for home: Look for "50% off" or "1/3 extra free" on packets and say what they mean.

What your child will learn

Learning goal: change between fractions, decimals and percentages.

Success looks like

I know common equivalents such as 1/4 = 0.25 = 25%.
I can convert between the three forms.
I can compare amounts written in different forms.

Key words

percent: out of 100 (%)
equivalent: worth the same
denominator: the bottom number of a fraction
decimal: a number with a decimal point

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Shade a 100 square to show one amount, then write it as a fraction, a decimal and a percentage. No squared paper? Draw a 10 by 10 grid.

The big ideas (for the adult)

Fractions, decimals and percentages are three ways of writing the same amount: 1/2 = 0.5 = 50%.

Per cent means out of 100. To change a fraction to a percentage, make it out of 100: 3/20 = 15/100 = 15%.

To change a decimal to a percentage, multiply by 100: 0.35 = 35%. Divide by 100 to go back.

The lesson, step by step

45 minutes in 5 parts
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

Grade 6 Math: Ratios and Rates Practice TestGraded instantly

All Grade 6 math lessons and tests · Math Department

Curriculum

Common Core State Standards 6.RP.A.3.c: “Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.