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One quantity as a fraction or percentage of another – Grade 6 math lesson

Lesson 4 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.

  1. Read what your child will learn and the big ideas together.
  2. Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
  3. 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.
  4. Finish with the exit ticket and the talk question: “Which is the better test score: 17 out of 20 or 40 out of 50?”
  5. Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

  • Mixing units (30 minutes as a fraction of 2 hours as 30/2). Change both to minutes first.
  • Putting the whole on top. Part on top, whole on the bottom.

Tip for home: Work out what percentage of a packet is sugar or fat from the label.

What your child will learn

Learning goal: write one quantity as a fraction or percentage of another.

Success looks like

  • I can write one amount as a fraction of another.
  • I can write it as a percentage.
  • I can compare using fractions or percentages.

Key words

fraction
part over whole
percentage
out of 100
units
what each amount is measured in
simplify
divide top and bottom by the same number

What to have ready

  • Paper and a pencil
  • This page on a computer, tablet or phone
  • For the hands-on part: Find what fraction and percentage of a day you spend asleep, at school and eating.

The big ideas (for the adult)

To write a as a fraction of b, write a/b and simplify. Make sure both are in the same units.

To write it as a percentage, change the fraction to hundredths, or divide and multiply by 100.

30 minutes as a fraction of 2 hours is 30/120 = 1/4 = 25%.

The lesson, step by step

45 minutes in 5 parts
PartTimeHow it is checked
Starter: quick recall5 minGraded by Classfern
Teaching input10 minNot assessed, self-checked
Worked examples and guided practice9 minNot assessed, graded by Classfern
Independent practice15 minGraded by Classfern
Closure and exit ticket6 minGraded 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

All Grade 6 math lessons and tests · Math Department

More Grade 6 math lessons

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.