Operations with fractions – Grade 6 math lesson
Lesson 13 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 can dividing by a fraction give a bigger answer?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Adding denominators (1/2 + 1/3 = 2/5). Find a common denominator: 3/6 + 2/6 = 5/6.
- Flipping the first fraction when dividing. Keep the first, change ÷ to ×, flip the second.
Tip for home: Halve or double a recipe that uses fractions of cups or teaspoons.
What your child will learn
Learning goal: add, subtract, multiply and divide fractions and mixed numbers.
Success looks like
- I can add and subtract fractions.
- I can multiply fractions.
- I can divide by a fraction.
Key words
- reciprocal
- a fraction turned upside down
- mixed number
- a whole number and a fraction
- improper fraction
- numerator bigger than denominator
- common denominator
- a shared bottom number
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use fraction bars to show 3 ÷ 1/4: how many quarters fit into 3?
The big ideas (for the adult)
To add or subtract fractions, write them with a common denominator first.
To multiply, multiply the numerators and multiply the denominators, then simplify.
To divide by a fraction, multiply by its reciprocal: 2/3 ÷ 4/5 = 2/3 × 5/4. Change mixed numbers to improper fractions 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
- Proportional relationships
- Rates and unit rates
- Unit prices and best buys
- Converting units
- Negative numbers and temperature
- Integers and absolute value
- Operations with multi-digit decimals
- 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.NS.A.1: “Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.