Find Pairs of Values

Overview

• Unit: Algebra Adventures Unlocked
• Lesson: 9 of 10
• Duration: 45 minutes
• Class Size: 30 students
• Year Group: 6
• Curriculum Reference: Mathematics Program of Study – Key Stage 2, Years 5 & 6
• Focus: Algebra – understanding and solving simple equations

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National Curriculum Links

Mathematics: Key Stage 2 – Years 5 & 6

• Number – Algebra:
  • Use simple formulae [National Curriculum Ref: Y6-NS3]
  • Generate and describe linear number sequences [NC Ref: Y6-NS4]
  • Express missing number problems algebraically [NC Ref: Y6-NS5]
  • Enumerate possibilities of combinations of two variables [NC Ref: Y6-NS6]

Assessment Focus:

• Solve problems by finding pairs of values that satisfy an equation.
• Understand and represent ordered pairs in an algebraic context.

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Learning Objectives

By the end of this lesson, students will:

1. Understand the concept of ordered pairs (x, y) as solutions to equations.
2. Find pairs of values that satisfy simple algebraic equations (e.g., y = 2x + 1).
3. Develop strategies to systematically identify pairs of values within given constraints.
4. Begin to appreciate the connection between algebraic notation and numerical solutions.

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Resources Needed

• Whiteboard and markers
• A4 graph paper (one per student)
• Worksheets with equations for practice (e.g., y = 3x, y = x + 5)
• Pre-prepared sets of number cards (0–10) for group activities
• Mini whiteboards and pens for all students
• Projector or visualiser (to model examples and show students' work)

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Lesson Structure

1. Starter Activity (5 minutes)

Objective: Activate prior knowledge about coordinates and simple equations.

• Begin with a quick recall: What is an ordered pair?
• Use the whiteboard to plot a few points (e.g., (1, 2), (2, 5)) and ask students to identify them.
• Ask: "If y = 2x, what would be the y-values for x = 1, 2, 3?"
• Students answer chorally and individually on mini whiteboards.

Curriculum link: Reinforces understanding of coordinates following Y5-NS7 (read and plot points in four quadrants).

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2. Direct Teaching & Modelling (10 minutes)

Objective: Introduce finding pairs that satisfy an equation algebraically and visually.

• Present a simple linear equation on the board: e.g., y = 2x + 1
• Explain what it means for a pair (x, y) to satisfy this equation.
• Model step-by-step how to find pairs of values: substitute values for x, calculate y, and write down the ordered pairs.
• Use a table format on board for x values 0–5:

x	y = 2x + 1	(x, y)
0	1	(0, 1)
1	3	(1, 3)
2	5	(2, 5)
…	…	…

• Show how this can also be represented graphically on graph paper.

Curriculum link: Supports Y6-NS3 (Use simple formulae) and Y6-NS6 (Enumerate possibilities for combinations of two variables).

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3. Guided Practice (15 minutes)

Objective: Apply understanding by completing tables and finding pairs in groups.

• Hand out worksheets with 3 different linear equations (e.g., y = x + 4, y = 3x, y = 5 - x).

• Students work in pairs to fill in tables of x and y values (0–5) and write down pairs.

• Circulate to assist and challenge with "What if x is negative?" or "Can you find pairs for x = 6?"

• Use mini whiteboards to share examples; invite pairs to write good examples on the board.

• Extension challenge:
  Given a pair (x, y), check if it satisfies the equation. For example, does (3, 10) satisfy y = 3x + 1?

Curriculum link: Algebraic problem solving and substitution as per NC Year 6 requirements.

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4. Activity: Pair Matching Game (10 minutes)

Objective: Deepen understanding through a kinaesthetic learning approach.

• In groups of 5, use number cards labelled 0–10 for x and y values.
• Teacher reads out an equation, for example, y = 2x - 1.
• Groups must find all card pairings (x, y) that satisfy it, physically pairing cards and arranging them in order on the desk.
• First group to correctly find all 6 pairs for x values 0 to 5 wins a small reward.
• Recap with the whole class by asking groups to share their pairs and reasoning.

Curriculum connection: Consolidates enumeration of possibilities and visualisation of solutions (Y6-NS6).

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5. Plenary & Assessment (5 minutes)

Objective: Evaluate understanding and consolidate learning through questioning and reflection.

• Quick exit quiz on mini whiteboards: Given y = x + 2, write down three pairs of values.
• Ask students to explain why these pairs work and what an ordered pair means.
• Use thumbs up/down to gauge confidence on today’s learning objectives.
• Collect worksheets to assess individual progress.

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Differentiation

• Support: Provide ready-made tables with partially filled values, visual aids for pairing, and sentence starters for explaining answers.
• Challenge: Encourage finding pairs with negative x-values and real-life context problems (e.g., number of wheels on bikes vs number of bikes).
• EAL/SEN: Pre-teach key vocabulary (ordered pair, satisfy, variable, equation), use visual representations constantly.

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Assessment for Learning

• Monitor paired work and discussions for misconceptions (e.g., confusing x and y or incorrect substitution).
• Evaluate partnership worksheets for accuracy in pairs found.
• Use exit quiz and plenary responses to evaluate individual confidence and conceptual understanding.

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Homework Suggestion

• Choose an equation (provided or student-created) and find 5 pairs of values. Draw these on graph paper, label the pairs, and write a sentence explaining how you know they satisfy the equation.

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Reflection Notes for Teacher

• Students tend to confuse the components of pairs; extra emphasis on (x, y) order is critical.
• Use of games and kinaesthetic activity elevated engagement noticeably.
• Consider digital tools (like simple graphing calculators or apps) for next lesson to extend learning further.

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This lesson plan carefully aligns with the England National Curriculum for Mathematics at Year 6 and incorporates varied teaching methods to ensure deep conceptual understanding and engagement.