Comparing and simplifying fractions – Grade 3 math lesson
Lesson 10 of 15 in the Grade 3 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 3 (ages 8–9) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 15 min homework
- Grade
- Grade 3 (ages 8–9)
- 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: “How can you tell 3/7 is less than a half without drawing it?”
- Later that day or the next day: the homework (15 minutes), then a practice test.
Watch out for
- Thinking 1/8 is bigger than 1/4 because 8 is bigger. Draw both: more parts means smaller parts.
- Simplifying by dividing only the top or only the bottom. Whatever you do to the top, do to the bottom.
Tip for home: Share a pizza or cake and compare who has the bigger fraction.
What your child will learn
Learning goal: compare, order and simplify fractions.
Success looks like
- I can compare fractions with the same denominator or numerator.
- I can compare by finding a common denominator.
- I can simplify fractions.
Key words
- numerator
- the top number
- denominator
- the bottom number
- common denominator
- a denominator both fractions can share
- simplest form
- the numbers cannot be divided by the same number any more
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use fraction strips or a fraction wall to compare fractions side by side. No fraction strips? Draw equal-length bars and split them into parts.
The big ideas (for the adult)
Fractions with the same denominator: the bigger numerator is the bigger fraction. Same numerator: the smaller denominator is bigger.
To compare other fractions, make the denominators the same using equivalent fractions.
To simplify, divide the numerator and denominator by the same number until no number above 1 divides both.
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
15 minutes: 8 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 3 math lessons
- Multiplication facts
- Multiplication and division
- Solving word problems
- Rounding to the nearest 10, 100 or 1,000
- Adding with the standard algorithm
- Subtracting with the standard algorithm
- Number lines
- Equivalent fractions
- Recognizing fractions
- Area of rectangles
- Perimeter
- Line plots
- Bar graphs, picture graphs and tables
- Elapsed time and schedules
Curriculum
Common Core State Standards 3.NF.A.3.d: “Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.