Finding a Third

Overview

Duration: 60 minutes
Class Size: 28 pupils (Year 2)
Curriculum Area: Mathematics
Key Stage: KS1
National Curriculum Objective (England, 2014):

Pupils should be taught to: recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity.

Focus of Lesson: Recognising and finding one third (1/3)
Differentiation Focus: Middle ability group
School Ethos: No-worksheet setting – all outcomes to be recorded in books through active, engaging, and practical experiences

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Intended Learning Objectives

By the end of this session, most pupils will be able to:

• Recognise when a shape, quantity or group has been split into thirds
• Find one third of a shape or quantity using practical, visual methods
• Record learning clearly in books through drawings, mathematical language, and explanations

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Vocabulary

• Fraction
• Third (1/3)
• Whole
• Equal
• Divide
• Share

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Resources

• Coloured paper strips (cut into 'whole-bars' for group work)
• Large whiteboard or floor grid for whole-class anchor modelling
• Mini-whiteboards and pens for active engagement
• Plastic fruit or fake food items (play food ideal)
• String, chalks, Unifix cubes
• Fraction circle cards (non-worksheet, manipulative style)
• Maths books, pencils, crayons
• Digital timer or sand timer
• Camera/iPad for evidence capture if allowed by school policy

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Lesson Breakdown

🔵 Starter (10 minutes) – ‘What’s the Whole?’

Objective: Warm-up to review understanding of ‘whole’ and introduce fractions as parts

• Use a large coloured circle or rectangle. Cut it into 2, then 3 then 4 parts with scissors in front of class.
• Ask: “What do you notice about these parts?” “Are they the same size?”
• Discuss importance of equal parts when dividing into thirds.
• Emphasise: “Third means three equal parts.”

Active Engagement:
Pupils use mini whiteboards to draw a rectangle and divide it into 3 equal and 3 unequal parts. Discuss which show “one third” correctly.

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🔵 Main Input (15 minutes) – Fraction Detectives

Objective: Explicit teaching of how to find one third in different contexts (shapes, sets, and amounts)

1. Use magnetic visuals or a smartboard shape – e.g. a pizza. Divide it into 3 to model one third.
2. Next, model sharing 12 cubes into 3 equal groups to find 1/3 of 12.
3. Whole class chants to reinforce:
   “To find one third, we must share,
   Split into three – be fair!”

Quick-fire practise:
“What is one third of 9?”
Use Unifix to show and count.

Check for Understanding:
Ask different pupils how they knew it was one third. Use stems:

• “I know it is one third because...”

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🔵 Main Activity (25 minutes) – Pudding Platers 🍮 (Middle Ability Focus)

Objective: Practise finding 1/3 of quantities in engaging, practical context

Pupils work in groups of 4 (ability grouped).

Scenario:
The school has 12 puddings to share between 3 tables. Can you help each table get exactly one third?

Each group is given:

• A pretend tray with 12 ‘puddings’ (plastic counters or paper circles)
• Labels with 'Table A', 'Table B', 'Table C'

Instructions:

1. Pupils physically share the ‘puddings’ into 3 fair piles.
2. Once shared, they choose any pile and draw it in their books.
3. Above drawing, pupils write:
   “One third of 12 is 4.”
4. Extension: Pupils must explain with sentences:
   “We had 12 puddings. We shared them into 3 equal groups. Each group got 4. So one third is 4.”

Scaffolding Available for Middle Group:

• Use of sharing dishes or plates to help categorise
• Adult or TA supports with language and checking equal shares
• Digit cards available to self-check their ‘third’ answer.

Adaptation Ideas:

• Add challenge: “What would one third of 15 puddings look like?”

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🔵 Plenary (10 minutes) – Human Fractions

Objective: Conclude and reinforce understanding through physical movement and peer-led reflections

1. Ask 9 pupils to line up.
2. Ask rest of class: “If we have 9 pupils, what is one third?”
3. Direct children to physically move themselves into 3 equal groups.
4. Use rest of class to predict, check, and reflect.

Verbal Prompt:
“Because 9 is split into how many groups...? How many in each?”

Peer Teach:

• Choose 2 pupils to explain to the class:
  “We made 3 equal lines. Each had 3 people. That shows one third of 9 is 3.”

Recording Task (5 minutes):
Back in seats, pupils draw 3 stick groups for 9 and shade one group. Label:
“One third of 9 is 3.”

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Assessment for Learning

• Use of questioning during mini-whiteboard activities and group tasks
• Review books for accuracy in pictorial representations and written language
• Class discussion and peer explanation during plenary
• Observations during “Pudding Platers” of ability to divide and verbalise reasoning

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Opportunities for Challenge

• “Can you find one third of 18? What if there were 21 puddings?”
• Reasoning prompts:
  • “Is it always possible to divide into thirds?”
  • “If we can’t share fairly, is it still a third?”

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Cross-Curricular Links

• PSHE: Turn-taking, group discussion, fairness
• Language: Sentence structure, using stem language to explain reasoning
• Physical Development: Movement in plenary, handling manipulatives

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Wow Factor / Outside-the-Box Element

“Pudding Platers” scenario brings real context from the dining hall – practical, visual and food-themed activity ensures high engagement without reliance on worksheets. Recording in books is fully embedded through drawing, reasoning, and sentence work, meeting the school’s ethos while remaining mathematically robust.

Use of role-play, chanting, and physical movement (Human Fractions) reinforces core concepts in memorable ways.

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Teacher Reflection Prompts (Post-Lesson)

• Did pupils use correct vocabulary consistently?
• Were pupils able to explain why something was (or wasn’t) one third?
• Which children showed strong visualisation skills?
• Did middle group show more confidence when 1/3 involved objects instead of numbers?

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Great teaching doesn’t need worksheets – just imagination, movement and meaningful maths!