Fractions

Students learn to add, subtract, multiply, and divide fractions and apply the order of operations to solve more complex problems.
By Anonymous
Part of Introduction to Math (SAMPLE)
Public

Lesson Steps

Overview
1
Introduction to Fractions
10 minutes
2
Adding and Subtracting Fractions
15 minutes
3
Multiplying Fractions
15 minutes
4
Dividing Fractions
15 minutes
5
Order of Operations with Fractions
20 minutes
6
Practice and Application
15 minutes
Show All Steps

Lesson Overview

Fractions

This lesson introduces students to the essential idea of fractions and how they are used to represent parts of a whole. Through guided practice and problem-solving, students build confidence in identifying, comparing, and working with fractions in meaningful ways.

The lesson also supports students in developing a strong foundation for more advanced mathematical thinking by exploring the four operations with fractions and applying the order of operations to solve multi-step problems. By the end of the lesson, students are beginning to connect fraction skills to a wider range of mathematical situations and use them with greater accuracy and understanding.

Key Objectives

Key Objectives
  • Students develop a secure understanding of fractions and the meaning of numerator and denominator, and they build confidence in identifying, comparing, and representing fractions accurately. They practise adding, subtracting, multiplying, and dividing fractions, applying appropriate methods with increasing accuracy, and they use the order of operations to solve more complex fraction problems. Students also use clear mathematical reasoning, show their working neatly, and check answers for reasonableness. Throughout the lesson, they follow classroom expectations, handle resources carefully, and work safely and responsibly during individual and collaborative tasks.
Equipment required
  • Whiteboard
  • Whiteboard markers
  • Fraction strips or fraction circles
  • Printed fraction worksheets or task cards
  • Pencils
  • Erasers
  • Rulers
  • Exercise books or maths books
  • Calculator, if required for checking answers
  • Projector or interactive display, if used for modelling examples
Get Started
Step 1 of 6

Introduction to Fractions

10 minutes

Students explore fractions as equal parts of a whole and use pictures and objects to identify numerator and denominator.

🌟 Learning goal

  • I can explain a fraction as equal parts of one whole.
  • I can name the top number and bottom number in a fraction.
  • I can match a fraction to a picture, shape, or set.

🔎 Key words

fraction whole equal parts numerator denominator

These words stay visible during the lesson so students can connect language to meaning.

🧠 Teacher move: build meaning with real objects

Use a paper strip, an apple picture, a pizza shape, or a set of counters. Show one whole item first, then divide it into equal parts.

  • Point to the whole object.
  • Split it into equal sections.
  • Shade or mark one part.
  • Say the fraction aloud: 1/2, 1/3, 3/4.

🧩 Quick visual model

1 out of 4 equal parts is shaded
1/4 means 1 shaded part out of 4 equal parts.

📘 Fraction parts at a glance

Part What it means Example
Numerator The top number shows how many parts are being used or shown. 3 in 3/5
Denominator The bottom number shows how many equal parts make the whole. 5 in 3/5
Whole The complete shape, set, or amount before it is split. One pizza, one strip, one group

💬 Guided talk prompts

  • What is the whole in this picture?
  • How many equal parts do you see?
  • How many parts are shaded or shown?
  • Which number tells the parts counted? Which number tells the total equal parts?

✅ Simple practice examples

Situation Fraction Student response
A circle is split into 2 equal parts and 1 part is shaded. 1/2 “One out of two equal parts is shaded.”
A bar is split into 3 equal parts and 2 parts are shaded. 2/3 “Two parts are shaded out of three equal parts.”
A set of 4 apples has 1 red apple. 1/4 “One apple in the set is red.”

🚀 Exit check

Students point to a model and say: “This fraction shows equal parts. The numerator tells how many. The denominator tells how many altogether.”

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Step 2 of 6

Adding and Subtracting Fractions

15 minutes

Students use visual models, number sentences, and simple explanation prompts to add and subtract fractions with the same denominator, then extend to fractions with common denominators.

1) Warm-up: Fraction parts in a bar model

Model A
Model B

Students notice that the denominator stays the same because the parts are the same size.

✨ same-size parts 🧠 numerator changes 📏 denominator stays fixed

Learning focus

  • Students add fractions with the same denominator by combining the numerators.
  • Students subtract fractions with the same denominator by taking away numerators.
  • Students use common denominators when the parts are not already the same size.
  • Students explain each step using clear fraction language.

Step-by-step fraction thinking

1️⃣ Look at the denominator
Students check whether the parts are already equal in size.
2️⃣ Work with the numerators
Students add or subtract the top numbers while keeping the denominator the same.
3️⃣ Say the answer clearly
Students read the result and explain what the fraction means in the model.

Guided examples

Problem Thinking Answer
1/5 + 2/5 Combine 1 part and 2 parts of the same fifths. 3/5
4/6 - 1/6 Take 1 sixth away from 4 sixths. 3/6
1/3 + 1/6 Change to a common denominator: 2/6 + 1/6. 3/6

Quick visual rule

When the denominator matches, students add or subtract only the numerator.

Talk it out

  • “I notice the denominator is the same.”
  • “I add the numerators because the parts match.”
  • “I keep the denominator because the whole is split the same way.”
  • “I check my answer with the bar model.”

Mini challenge

Students solve each expression and then name the strategy used.

Expression Strategy Result
3/8 + 2/8 Add numerators 5/8
7/10 - 3/10 Subtract numerators 4/10
1/2 + 1/4 Use common denominators 2/4 + 1/4 = 3/4
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Step 3 of 6

Multiplying Fractions

15 minutes

Part 3 • Multiplying Fractions

Students see fraction multiplication as “a fraction of a fraction” and connect the rule to visual models.

➗ Part of a part ▭ Area model 📏 Number line 🧠 Explain the pattern

Core idea

When students multiply fractions, they are finding a fraction of another fraction. For example, 1/2 of 3/4 means taking half of three quarters.

1. Shade the whole shape Show one fraction across and one fraction down.
2. Find the overlap The overlapping region shows the product.
3. Write the product Multiply numerators and denominators.
Area model for 1/2 × 3/4 A rectangle split into 4 columns and 2 rows. Three of four columns are shaded one way, one of two rows is shaded another way, and the overlap is highlighted as three eighths. 3/4 1/2 Overlapping part = 3/8 Multiply: 1/2 × 3/4 = 3/8 numerator × numerator denominator × denominator

Quick teaching language

  • “Of” means multiply. Students link words to the operation.
  • Shading shows the answer. The overlap is the product.
  • Count the pieces. The model and the equation match.
Expression Product Meaning
1/2 × 1/3 1/6 Half of one third.
2/3 × 3/5 2/5 Two thirds of three fifths.
1/4 × 2/3 1/6 One quarter of two thirds.

Practice and connect

Problem Think about Answer space
1/2 × 2/5 Take half of two fifths. ____ / ____
3/4 × 2/3 Find the overlap in an area model. ____ / ____
1/3 × 3/8 Multiply the fractions and simplify if needed. ____ / ____

Teacher prompt: “Show me how the shaded part changes when I take a fraction of a fraction.” Invite students to point to the model, say the equation, and name the product in full sentences.

Worksheet
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Step 4 of 6

Dividing Fractions

15 minutes
Fractions • Operation focus Visual reasoning + equation steps

Learning focus

Students explore division with fractions using sharing, grouping, and the idea of multiplying by the reciprocal. They connect each example to a model and explain the calculation in clear mathematical language.

Guided idea

1
Keep
the first fraction
2
Change
division to multiplication
3
Flip
the second fraction

Think: “How many groups?” and “How much is in each group?”

Worked example with clear steps

🧠 Example: 2 ÷ 1/3

  • 2 means 2 wholes.
  • 1/3 means one third in each group.
  • There are 3 thirds in 1 whole, so there are 6 thirds in 2 wholes.

Equation:

2 ÷ 1/3 = 2 × 3/1 = 6

The reciprocal of 1/3 is 3/1, so the operation becomes multiplication.

Talk and explain

  • Students say what the dividend and divisor mean in the context of the problem.
  • Students describe why changing to multiplication gives the same result.
  • Students check answers using a quick model, number line, or repeated groups.

Quick practice

Problem Hint Answer
1 ÷ 1/2 How many halves make 1? 2
3 ÷ 1/4 How many quarter groups fit into 3? 12
2 ÷ 2/3 Change division to multiplication by the reciprocal. 3
4 / 6
Step 5 of 6

Order of Operations with Fractions

20 minutes

Students solve mixed fraction expressions by following the order of operations step by step: brackets first, then multiplication and division, then addition and subtraction.

What students do

  • They look for grouping symbols such as brackets or parentheses.
  • They decide which operation comes first in each expression.
  • They solve one part at a time and keep the fraction work neat.
  • They explain why they choose each step using mathematical language.
1️⃣ Grouping
( ) or [ ]
→
2️⃣ × and ÷
left to right
→
3️⃣ + and −
left to right

Worked example

1/2 + (3/4 × 2/3)

Step 1: Solve inside the brackets: 3/4 × 2/3 = 1/2

Step 2: Add the results: 1/2 + 1/2 = 1

⭐ The bracket helps students see that multiplication happens before addition in this expression.

Key reminder

Brackets first Multiply and divide next Add and subtract last
Expression First step Reason
(1/3 + 1/6) × 2 Add inside the brackets Grouping symbols come first
3/5 ÷ 1/10 + 1/2 Divide first Division happens before addition
2/3 - (1/6 × 3) Multiply inside the brackets Work inside the grouping symbol first

Try it together

2/5 + 1/2 × 4/5

  • Students identify the multiplication first.
  • They solve 1/2 × 4/5 = 2/5.
  • They add 2/5 + 2/5 = 4/5.

Guided practice prompts

  • Which operation comes first in this expression?
  • What do you solve before you add or subtract?
  • How do you know the answer is reasonable?

Mixed practice expressions

Students solve each expression and name the first operation they use.

  • (3/8 + 1/8) ÷ 1/2
  • 5/6 - 1/3 × 3/4
  • 1/4 + (2/3 ÷ 2)
  • (1/2 × 3/5) + 1/10
5 / 6
Step 6 of 6

Practice and Application

15 minutes

🧠 Practice & Application: Fraction Skills in Action

Students use what they know about fractions to solve mixed problems, explain their thinking, and choose the correct operation in each situation.

🎯 Learning focus

  • Add and subtract fractions with confidence.
  • Multiply fractions to find part of a part.
  • Divide fractions using sharing, grouping, or the reciprocal.
  • Apply the order of operations in expressions with fractions.
  • Give a short explanation that matches the solution.
➕ Add ➖ Subtract ✖ Multiply ➗ Divide 📏 Order of operations

🔎 Quick reminder

1) Same denominator? Add or subtract the numerators. 2) Multiply straight across. 3) Flip and multiply for division. 4) Brackets first. 5) Multiply and divide next. 6) Add and subtract last. Example path: (1/2 + 1/4) × 2 ↓ 3/4 × 2 ↓ 3/2

Students check each step and state why the chosen operation works.

✍️ Independent practice set

Problem What students do Expected thinking
1/3 + 1/3 Solve and say the answer in a sentence. Same denominator, so add the numerators.
5/6 - 1/6 Find the difference. Subtract the numerators and keep the denominator.
2/5 × 3/4 Multiply the fractions. Multiply numerator by numerator and denominator by denominator.
3/4 ÷ 1/2 Divide using a strategy that makes sense. Multiply by the reciprocal or think about how many halves fit in three quarters.
(1/2 + 1/4) × 2 Use the order of operations. Solve inside the brackets first, then multiply.
2/3 + 1/6 Use a common denominator. Rename the fractions, then add.

🗣️ Short explanation frames

  • I choose this operation because ________.
  • I solve the bracket first because ________.
  • I know my answer is reasonable because ________.

✅ Success look-for

  • Students select the correct operation for each problem.
  • Students show steps clearly and keep fractions in simplest form when possible.
  • Students explain the solution using mathematical words such as numerator, denominator, reciprocal, and order.
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