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Year 5 Mathematics • AC9M5N04

Improper Fractions & Mixed Numbers

Exploring, visualising, and converting fractions greater than 1

🎯 WALT (We Are Learning To)

Understand, visualise, and convert between mixed numbers and improper fractions using concrete representations and numerical steps.

⭐ WILF (What I'm Looking For)

  • Identify mixed numbers vs improper fractions.
  • Convert mixed numbers → improper ("Multiply then add").
  • Convert improper fractions → mixed ("Divide bottom into top").

Concept Discovery: Pizza Fraction Visualiser

Imagine ordering pizzas cut into equal slices. When we have more slices than one whole pizza, we can name the amount in two different ways!

Number of Slices: 5
As an Improper Fraction:
54
(Total Slices over Denominator)
As a Mixed Number:
114
(Whole Pizzas + Remaining Slices)

Key Definitions & Number Line Model

Mixed Number

Has a whole number part AND a fraction part.

312   (3 wholes and 1 half)

Improper Fraction

The numerator (top) is larger than or equal to the denominator (bottom).

72   (7 halves)

Interactive Fraction Number Line ($0$ to $2$)

Click any fraction position below:
Click a tick mark on the number line above to compare its Mixed Number and Improper Fraction form!

Method 1: Mixed Number → Improper Fraction

The Golden Rule:
"Multiply the whole number by the denominator, then add the numerator!"
Multiply then Add ✖️ ➕
Worked Formula Model:
314 = (3 × 4) + 14 = 134
3 wholes of 4 quarters = 12 quarters + 1 extra quarter = 13 quarters!
1
Multiply the whole number by the bottom number (denominator).
2
Add the top number (numerator) to your result.
3
Write the total over the same denominator!

Method 2: Improper Fraction → Mixed Number

The Division Rule:
"Divide the top by the bottom. The answer is the whole, remainder is the fraction!"
Divide Bottom into Top ➗
Worked Division Model:
114 = 11 ÷ 4 = 2 rem 3
= 234
4 goes into 11 two whole times (8), leaving 3 quarters remaining!
1
Divide the numerator (top) by the denominator (bottom).
2
The whole number answer becomes your whole number.
3
The remainder becomes the new top fraction number!

Class Practice: Check Your Understanding

Work out these 4 conversions on your mini-whiteboard or exercise book. Click each card to check your steps!

Q1. Mixed → Improper Tap to Reveal
234 = ?
Q2. Improper → Mixed Tap to Reveal
143 = ?
Q3. Mixed → Improper Tap to Reveal
415 = ?
Q4. Improper → Mixed Tap to Reveal
3110 = ?

Three-Tiered Differentiated Task Stations

Select your entry tier or work through in order with your partner!

🟢 Tier 1: Support

Visuals & Halves/Thirds

A. Convert to Improper:

  1. 113
  2. 212
  3. 134

B. Convert to Mixed:

  1. 53
  2. 72

🔵 Tier 2: Core

Standard Conversions

A. Convert to Improper:

  1. 235
  2. 314
  3. 1910

B. Convert to Mixed:

  1. 134
  2. 175
  3. 2710

🟣 Tier 3: Extension

Reasoning & Context

1. Compare: Which is larger: 325 or 165? Show why!

2. Pizza Context: Sam ordered 5 pizzas cut into 6 slices each. Friends ate 22 slices. Express the eaten pizza as a mixed number and improper fraction.

3. Convert: 578 to improper fraction.

Ready for Independent Practice!

You are now ready to complete Page 1:11 (Improper fractions, mixed numbers) in your workbook!

Task 1: Mixed → Improper

Multiply whole number by denominator, add numerator!
(Questions 1a to 1l)

Task 2: Improper → Mixed

Divide bottom into top! Remainder is new numerator.
(Questions 2a to 2l)

🖐️ Self-Assessment Check (Fist to Five)

How confident do you feel starting Page 1:11? Show your teacher 1 to 5 fingers before picking up your workbook!

Teacher Notes

Select a slide to see accompanying pedagogical notes and teaching tips.

Interactive Virtual Whiteboard