Teach all of the algebra content for Key Stage 3 with these problem-solving numeracy investigations. They will give students a numerical grounding for understanding KS3 algebra while helping them develop numeracy confidence and meta skills. Students will also learn resilience and tactics for approaching mathematical problem solving.

Each unit consist of three lessons. The first lesson provides teaching, activities, practice and homework materials to teach a piece of algebra. The second lesson provides a problem-solving, investigative activity involving an aspect of number work. This is designed to stimulate students’ logical reasoning skills. The third lesson draws on the algebra taught in lesson 1 to generalise the solution to the investigation.

There could not nee a better context in which to teach all the algebra for KS3!

Unit 1 Four of the Best (free)

Objectives

KS3 Programme of Study Statements
-- Simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms.

-- Substitute numerical values into expressions.

-- Use the four operations applied to decimals.

-- Solve problems.

-- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

Teaching and Activities

Algebra
Write and simplify algebraic expressions; substitute into algebraic expressions.

Numeracy and problem solving
Investigation: Four of the Best (involving revision of adding decimals)

Algebra and problem solving
Continuation of investigation: Four of the Best (including generalisation, using algebra learnt in A1)

Unit 2 Stars and Crosses

Objectives

KS3 Programme of Study Statements
-- Model situations by translating them into algebraic expressions.

-- Use and interpret algebraic notation.

-- Simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms.

-- Use the 4 operations, including formal written methods, applied to integers.

-- Solve problems.

-- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

Teaching and Activities

Algebra
Model situations using algebraic expressions; Simplify algebraic expressions involving adding negative integers

Numeracy and problem solving
Investigation: Stars and Crosses (involving revision of adding five or more two-digit numbers; developing fluency)

Algebra and problem solving
Continuation of investigation: Stars and Crosses (including generalisation, using algebra learnt in B1)

Unit 3 Four in a Row

Objectives

KS3 Programme of Study Statements
-- Solve problems.

-- Use the 4 operations applied to integers.

-- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

-- Use and interpret algebraic notation.

-- Make connections between number relationships, and their algebraic representations.

-- Simplify algebraic expression.

Teaching and Activities

Numeracy and problem solving
Introduce/consolidate mathematical language: ‘consecutive’ and ‘integer’. Practice ‘looking for patterns’ and become familiar with the problem solving skill of ‘simplifying a problem’. Practice a range of numeracy skills.

Algebra
Recognise expressions that represent even numbers.

Algebra and problem solving
Investigation: Four in a Row (including generalisation, applying the algebraic concepts learnt in C2)

Unit 4 On Cloud Nine

Objectives

KS3 Programme of Study Statements
-- Model situations by translating them into algebraic expressions.

-- Use and interpret algebraic notation.

-- Substitute numerical values into expressions.

-- Simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms. Use the concept and vocabulary of multiples.

-- Use the 4 operations, including formal written methods, applied to integers.

-- Use the concept and vocabulary of multiples.

-- Solve problems.

-- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

Teaching and Activities

Numeracy and Algebra
Write in expanded form (using digits or algebra); substitute into expressions; look for patterns; collect like terms and simplify; recognise multiples.

Numeracy and problem solving
Investigation: On Cloud 9 (involving revision of subtracting two-digit numbers; recognising multiples; developing fluency.)

Algebra and problem solving
Continuation of investigation: On Cloud Nine (including generalisation, using algebra learnt in 1.)

Unit 5 Riveting Reversals

Objectives

KS3 Programme of Study Statements
-- Use and interpret algebraic notation.

-- Model situations or procedures by translating them into algebraic expressions.

-- Simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms.

-- Substitute numerical values into expressions.

-- Solve problems.

-- Use the four operations, including formal written methods.

-- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

Teaching and Activities

Algebra
Write consecutive numbers, expressed algebraically; simplify algebraic expressions involving adding and subtracting positive and negative integers; substitute into algebraic expressions.

Numeracy and problem solving
Investigation: Riveting reversals (involving revision of long multiplication of 3-digit and 4-digit numbers by 2-digit numbers; and finding the difference between 4-, 5- and 6-digit numbers.)

Algebra and problem solving
Continuation of investigation: Riveting reversals (including generalisation, using algebra learnt in Unit 4 and Lesson 1)

Unit 6 Queued Cubes

Objectives

KS3 Programme of Study Statements
-- Use integer powers (square and cube).

-- Use and interpret algebraic notation.

-- Make and test conjectures about patterns and relationships.

-- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

-- Model situations or procedures by translating them into algebraic formulae.

-- Substitute numerical values into formulae.

-- Solve problems.

-- Derive and apply formulae to calculate and solve problems involving volume of cuboids (including cubes)

Teaching and Activities

Algebra
Use algebra to generalise the structure of arithmetic, including to devise formulae; use algebraic notation; substitute numerical values into formulae.

Numeracy and problem solving
Investigation: Queued Cubes (involving revision of surface areas and volumes of cubes, and division)

Algebra, Geometry and Measures and problem solving
Continuation of investigation: Queued Cubes (including devising formulae, using algebra learnt in Lesson 1)

Unit 7 Incredible Coordinates

Objectives

KS3 Programme of Study Statements
-- Work with coordinates in all four quadrants.

-- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships

-- Make and test conjectures about patterns and relationships

-- Use the 4 operations, including formal written methods, applied to integers.

-- Calculate and solve problems involving perimeters of 2-D shapes

-- Solve problems.

-- Interpret mathematical relationships both algebraically and geometrically

Teaching and Activities

Algebra
Plot coordinates in all four quadrants; recognise and interpret patterns in x- and y-coordinates; write coordinates in general form (a , b)

Numeracy and problem solving
Investigation: Incredible coordinates (involving revision of number bonds, mental addition – including negative numbers –, multiplication and perimeters)

Algebra and problem solving
Continuation of investigation: Incredible coordinates (including generalisation, using algebra learnt in Lesson 1)