Algebra Revision Boost

Overview

Duration: 30 minutes
Class size: 6 students
Age group: Year 7 (11-12 years)
Curriculum Alignment: National Curriculum for England (Mathematics)
Curriculum Ref:

• Number: b) Use and understand negative numbers in context (Y7)
• Algebra: a) Use symbols, letters and words to describe aspects of mathematics; c) Simplify and manipulate algebraic expressions; d) Expand and factorise single brackets (Years 6-7)

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Learning Objectives

By the end of this lesson, students will:

• Understand and confidently operate with negative numbers.
• Simplify algebraic expressions by combining like terms.
• Expand single brackets accurately.
• Factorise expressions involving single brackets.

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Lesson Structure & Activities

1. Introduction to Negative Numbers (5 minutes)

Objective: Recall and revise adding, subtracting, multiplying, and dividing negative numbers.
Curriculum Link: Number - use negative numbers in context
Slide:

• Brief explanation of negative numbers on a number line.
• Rules for addition, subtraction, multiplication, and division with negatives.

Teacher Model Example:
Calculate: (-3 + 5 = ?) and (-4 \times (-2) = ?)

Follow Up Questions:

1. What is (-7 + 4)?
2. Calculate (-6 - (-3)).
3. Work out (-5 \times 3).
4. Find the result of (-8 \div (-2)).
5. Simplify (-2 + (-9)).

2. Simplifying Algebraic Expressions (7 minutes)

Objective: Combine like terms using correct algebraic notation.
Curriculum Link: Algebra - simplify and manipulate algebraic expressions

Slide:

• Explanation of like terms (same variable and power) e.g., (3x) and (-5x).
• How to combine like terms: Add or subtract coefficients.

Teacher Model Example:
Simplify: (4x + 3 - 2x + 7)

Follow Up Questions:

1. Simplify (5a - 3a + 6).
2. Simplify (2y + 7 - y + 4).
3. Simplify (9b - 4b - 2b + 1).
4. Simplify (3m + 2n - m + 5) (note: only combine like terms).
5. Simplify (-2x + 8 - x - 3).

3. Expanding Single Brackets (8 minutes)

Objective: Apply distributive law to expand expressions.
Curriculum Link: Algebra - expand brackets

Slide:

• Explanation: Multiply each term inside the bracket by the outside term.
• Example of the distributive property: (a(b + c) = ab + ac).

Teacher Model Example:
Expand: (3(x + 4))

Follow Up Questions:

1. Expand (2(y + 5)).
2. Expand (-4(x - 3)).
3. Expand (5(a + 2b)).
4. Expand (-3(2x + 1)).
5. Expand (6(m - 4)).

4. Factoring Single Brackets (8 minutes)

Objective: Factor expressions by taking out common factors.
Curriculum Link: Algebra - factorise expressions involving single brackets

Slide:

• Explanation of common factor extraction.
• Factor out the highest common factor (HCF) from terms.

Teacher Model Example:
Factorise: (6x + 9)

Follow Up Questions:

1. Factorise (4y + 12).
2. Factorise (10a - 15).
3. Factorise (9m + 3n) (factor out integer only).
4. Factorise (-8x - 20).
5. Factorise (14p + 7).

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Assessment & Differentiation

• Formative Assessment: Monitor students' answers to follow-up questions live using mini whiteboards or verbally.
• Extended Challenge: For faster students, ask them to simplify or factorise expressions with three terms or introduce negative coefficients.
• Support: One-to-one explanation during activities for any student struggling with foundational concepts like negative numbers.

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Resources Needed

• Interactive slides with clear step-by-step animations for each topic.
• Mini whiteboards and pens per student or paper for working out problems.
• Visual aids for number line showing negative values.

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Reflection for Next Steps

• Check understanding of negative number operations through verbal questioning.
• Identify common errors in simplifying and factoring for follow-up mini-lessons or homework exercises.
• Encourage students to verbalise reasoning to consolidate conceptual knowledge.

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Teacher Tip: Use real-life contexts (e.g., temperature below zero for negatives) during introduction to engage curiosity. Also, encourage students to explain their working aloud to build confidence with algebraic manipulation language.

End of Plan