Mathematics · Year 5 · Fractions, Decimals, and Percentages · Spring Term

Improper Fractions and Mixed Numbers

Students will convert between improper fractions and mixed numbers.

• National Curriculum Attainment Targets
• KS2: Mathematics - Fractions

About This Topic

The concept of percent introduces students to a specific type of fraction where the denominator is always 100. In Year 5, the goal is to understand 'percent' as 'parts per hundred' and to establish the fundamental links between percentages, decimals, and fractions. This is one of the most applicable areas of mathematics, appearing in everything from shop sales to battery life.

Students learn to find percentages of amounts by relating them to known fractions (e.g., 50% is half, 25% is a quarter). They use visual aids like 100-squares to represent these values. Students grasp this concept faster through structured discussion and peer explanation, where they can apply their knowledge to real world scenarios like calculating discounts or interpreting data from a survey.

Key Questions

1. Explain the difference between an improper fraction and a mixed number.
2. Construct a mixed number from an improper fraction like 7/3.
3. Justify why converting to an improper fraction can simplify addition of mixed numbers.

Learning Objectives

• Convert improper fractions to mixed numbers with 90% accuracy.
• Convert mixed numbers to improper fractions with 90% accuracy.
• Compare and order improper fractions and mixed numbers.
• Explain the relationship between improper fractions and mixed numbers using visual representations.

Before You Start

Understanding Fractions

Why: Students need a solid grasp of what fractions represent (parts of a whole) and the roles of the numerator and denominator.

Division as Sharing

Why: Converting between improper fractions and mixed numbers relies on understanding division with remainders, which is foundational to this topic.

Key Vocabulary

Improper Fraction	A fraction where the numerator is greater than or equal to the denominator, indicating a value of one or more.
Mixed Number	A number consisting of a whole number and a proper fraction, representing a value greater than one.
Numerator	The top number in a fraction, representing the number of parts being considered.
Denominator	The bottom number in a fraction, representing the total number of equal parts in a whole.
Whole Number	A non-negative integer (0, 1, 2, 3, ...) that does not have a fractional or decimal part.

Watch Out for These Misconceptions

Common Misconception

Students may think that 100% is the maximum possible value for any percentage.

What to Teach Instead

While 100% is 'the whole' in most Year 5 contexts, use examples like '200% growth' in a plant's height to show that percentages can exceed 100. This is best explored through visual bar models.

Common Misconception

Pupils often struggle to find 10% of a number, trying to divide by 100 instead of 10.

What to Teach Instead

Relate 10% back to the fraction 10/100, which simplifies to 1/10. Using place value grids to show that finding 10% is the same as dividing by 10 helps clarify the process.

Active Learning Ideas

Simulation Game: The High Street Sale

The classroom becomes a shop where items have price tags and 'discount' signs (10%, 25%, 50%). Students work in pairs to calculate the new prices and the total savings, using their knowledge of equivalent fractions.

45 min·Pairs

Inquiry Circle: The 100-Square Mosaic

Students create a mosaic design on a 10-by-10 grid using different colours. They must then calculate the percentage, decimal, and fraction representation for each colour used in their design.

40 min·Individual

Gallery Walk: Data Detectives

Display various 'stats' from newspapers or cereal boxes (e.g., '30% less sugar'). Students rotate to explain what that percentage means in terms of 'parts per hundred' and what the equivalent fraction would be.

30 min·Small Groups

Real-World Connections

• Bakers use mixed numbers when measuring ingredients for recipes, such as 2 1/2 cups of flour. Converting this to an improper fraction, 5/2, can simplify calculations when scaling a recipe up or down.
• Construction workers might measure materials using fractions. For example, a length of wood might be 7/4 feet long, which is equivalent to the mixed number 1 3/4 feet. Understanding both forms helps in precise measurement and cutting.

Assessment Ideas

Exit Ticket

Provide students with three cards. Card 1 has an improper fraction (e.g., 11/4). Card 2 has a mixed number (e.g., 2 3/5). Card 3 has a blank space. Ask students to convert the improper fraction to a mixed number and write it on Card 3. Then, ask them to convert the mixed number to an improper fraction and write it on Card 3 below their first answer.

Quick Check

Display a set of fractions and mixed numbers on the board (e.g., 5/3, 1 1/2, 7/2, 2 1/4). Ask students to write each one in its alternative form on a mini-whiteboard. Observe student responses and address common misconceptions immediately.

Discussion Prompt

Pose the question: 'Imagine you have 9/4 pizzas. How many whole pizzas and extra slices do you have? Explain your thinking using drawings or words.' Facilitate a class discussion where students share their methods for converting the improper fraction to a mixed number.

Frequently Asked Questions

What are the best hands-on strategies for teaching percentages?

Using 100-squares is the gold standard for Year 5. It allows students to physically colour in 'parts per hundred' and see the relationship between the percentage and the whole. Linking percentages to money in a 'shop simulation' is also highly effective, as it provides a concrete context for why we need to calculate parts of an amount.

How do you find 25% of a number easily?

The easiest way for Year 5 is to recognise that 25% is equivalent to one quarter. Therefore, they can just divide the amount by 4, or halve it and halve it again.

Why do we use percentages instead of just fractions?

Percentages provide a standardised way to compare different amounts. It is much easier to compare 30% and 40% than it is to compare 3/10 and 2/5 at a glance.

What is the meaning of the word 'percent'?

It comes from the Latin 'per centum', meaning 'by the hundred'. Teaching this etymology helps students remember that every percentage is just a fraction with 100 as the denominator.