Fractions of Quantities

I want the plan to focus on develop further understanding on how to calculate fractions of a quantity

Create a success criteria for this lesson

Create a high engaging introduction and a range of questioning for this maths lesson Identify common misconceptions and areas of difficulty for develop further understanding on how to calculate fractions of a quantity

Create use of targeted whole class questions- Questions shouldn't just ask for the correct answer they should require pupils to explain their thinking justifying their reasoning. (Use Bloom's taxonomy to help create questions beyond basic thinking and encourage deeper thinking)

Create an example for children to copy into books and use to support work

Include AfL points throughout teaching and modelling stage ( tell me What AfL to use, where to use it?) Modelling

Plan a task that gradually increases in complexity, e.g. by adding more elements pupils need to think about or having them apply what they have been taught to different situations.

plenary

Align with White Rose Maths Scheme

National Curriculum Links

Year 4 Maths - Number - Fractions

Solve problems involving increasingly harder fractions to calculate quantities (including non-unit fractions)
Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
Understand how to find fractions of a quantity

Learning Objectives

By the end of this lesson, pupils will:

Be able to calculate unit and non-unit fractions of a given quantity confidently
Understand and apply strategies to solve problems involving fractions of quantities
Justify their reasoning when calculating fractions of quantities

Success Criteria

I can identify the fraction part to find (unit or non-unit)
I can divide the quantity correctly before multiplying by the numerator
I can explain my method clearly and justify why it works
I can solve increasingly complex fraction of quantity problems involving different contexts

Lesson Overview (45 minutes)

Time	Activity	Details
0-7m	Engaging Introduction	Real-life scenario introduction with interactive questioning to link fractions to everyday quantities
7-15m	Modelling & Whole-Class Teaching	Step-by-step example with detailed explanation, including AFL checks and questioning based on Bloom’s Taxonomy
15-30m	Guided Practice Task	Task with gradual increase in difficulty, differentiated questioning and peer discussion
30-40m	Independent Work	Pupils solve related problems with AFL mini-plenaries to assess understanding in real time
40-45m	Plenary and Reflection	Share solutions, misconceptions addressed, reflective questioning and success criteria review

Detailed Plan

1. Introduction (0-7 minutes)

Hook: Show a large jar containing 60 sweets. Ask:

If I want to give 1/4 of sweets to my friend, how many sweets should I give?
But what if I want to find 3/4? How can I work this out?

Class discussion questions:

Why do we divide the number of sweets by 4 here?
What does the numerator (top number) tell us in the fraction 3/4?
How is finding 3/4 different from finding 1/4?

Higher-order questions to spark thinking:

Can you think of other examples where we might use fractions of quantities in daily life? (Apply)
How can knowing the denominator and numerator help you find the fraction quickly? (Analyse)

2. Modelling & Whole-Class Teaching (7-15 minutes)

Step-by-step example to copy into books:

Find 3/5 of 40

Understand the denominator - 5 means we split the total into 5 equal parts.
Divide 40 ÷ 5 = 8 (find the value of 1/5)
Multiply 8 × 3 = 24 (then find 3 parts)

Worked example written neatly:
3/5 of 40 = (40 ÷ 5) × 3 = 8 × 3 = 24

AfL points during modelling:

After dividing, ask: Is everyone confident that 8 is 1/5 of 40? How do you know? (Show thumbs up/down)
After multiplying, prompt: How do we know multiplying by 3 gives us 3/5? (Hands-down, give reasoning)
Use mini-whiteboards for children to show the division step before the multiplication

3. Questioning Throughout Teaching (Bloom’s Taxonomy)

Cognitive Level	Question example	Purpose
Remembering	What is the denominator in the fraction?	Recall fraction parts
Understanding	Why do we divide first when finding fractions of quantities?	Understand procedure
Applying	How would you find 2/7 of 49?	Apply steps to new problem
Analysing	Why is it important to divide before multiplying?	Analyse the process
Evaluating	Is there more than one way to solve 4/6 of 36? Explain.	Evaluate different strategies
Creating	Create a word problem involving finding a fraction of a quantity and solve it.	Encourage creation and application

4. Guided Practice Tasks (15-30 minutes)

Task 1 (Simple): Find 2/4 of 20
Task 2 (Moderate): Find 5/8 of 64
Task 3 (Challenging): A farmer has 72 eggs. He sells 3/6 of them and uses 1/4 of the remaining eggs. How many eggs does he use?

Differentiation:

Support: Use counters or visual fraction bars to represent quantities
Extension: Find the fraction of quantities involving mixed numbers

Peer discussion: After each task, pupils explain their reasoning in pairs or groups using sentence starters, e.g. “I divided by... because...” or “Multiplying by... gave me...”

5. Independent Work with AFL Checks (30-40 minutes)

Pupils attempt problems independently in books:

Find 3/7 of 56
Find 4/9 of 81
If 3/5 of a number is 36, what is the whole number?

AfL:

Use thumbs up/down after the first two problems to see who needs further support
Pause after the last question to discuss reverse operations and reasoning—get pupils to explain their strategies aloud

6. Plenary (40-45 minutes)

Invite pupils to share answers and explanations to discuss different problem-solving approaches
Clarify common misconceptions such as:
- Mistaking multiplying before dividing
- Dividing by numerator instead of denominator
- Confusing fraction of a quantity with division by the fraction
Recap success criteria, asking pupils to self-assess: “Which parts of the success criteria did I meet confidently?”
Reflective question for deeper learning—“How would your method change if the problem involved parts of money or measurements rather than whole numbers?”

Common Misconceptions & Difficulties

Dividing by numerator instead of denominator (e.g., doing 40 ÷ 3 instead of 40 ÷ 5 for 3/5)
Confusing ‘of’ with ‘multiply’ – trying to multiply numerator and denominator by the quantity
Not understanding why to divide first before multiplying
Difficulty applying knowledge to word problems or missing the context
Forgetting to simplify answers or leaving answers as just multiplication results

Alignment With White Rose Maths Scheme

This lesson supports small steps in "Year 4 - Fractions: Calculate fractions of a quantity"
Builds on prior understanding of unit fractions and links calculation strategies
Encourages reasoning and problem solving consistent with White Rose expectations

WOW factor idea: Use real physical objects or animations (e.g., outdoor counting with fraction cards on sets of leaves/fruits) for conceptual clarity. Encourage pupils to create their own fraction of quantity problems based on their interests and share using mini whiteboards — fostering ownership and creativity in maths.

Teacher’s Notes:

Use mini whiteboards regularly for AFL to quickly gauge understanding
Emphasise mathematical vocabulary (‘numerator’, ‘denominator’, ‘quantity’) and ensure children articulate process clearly
Scaffold rigor gradually so no pupil is left behind while extending able pupils with richer problems and reasoning discussions

End of Plan.

Teaching Instructions