Algebraic Expressions and Fractions

Worksheets that build algebra from meaning to rules. Students start with growing patterns and letters as numbers, and check that expressions are equivalent by substituting. Multiplying, squaring a binomial and squaring a trinomial are shown with the area model and algebra tiles, and the cube of a binomial and the sum and difference of cubes with a cube that comes apart. Then come factorising and algebraic fractions, always linked to number fractions. The last sheet is a group game with a check.

Expressions and Patterns

PDFPatterns and Generalisingstick and tile patterns, an expression in n, equivalent expressions · 2 pagesPRI
PDFThe Value of an Expressionsubstituting, negative numbers in brackets, words into expressions · 2 pagesPRI
PDFEquivalent Expressionslike terms, checking by substituting, matching expressions · 2 pagesPRI
PDFThe Distributive Lawthe area model, multiplying out a bracket, signs · 2 pagesPRI

Factoring Out and Special Products

PDFFactoring Out a Common Factorthe greatest common factor, checking by multiplying · 2 pagesPRISEC
PDFMultiplying Binomialsalgebra tiles, the area model, checking with numbers · 2 pagesPRISEC
PDFSquaring a Binomialthe formula as a picture of a square, mental maths · 2 pagesPRISEC
PDFThe Difference of Squarescutting and rearranging, factorising, mental maths · 2 pagesPRISEC
PDFSquaring a Trinomiala 3 × 3 grid, signs, the number 111² · 2 pagesSEC
PDFThe Cube of a Sum and of a Differencea cube of 8 pieces, Pascal's triangle · 2 pagesSEC
PDFThe Sum and Difference of Cubesa cube with a cube taken out, the sign rule · 2 pagesSEC

Factorising

PDFFactorising Trinomialsx² + bx + c, sum and product, algebra tiles · 2 pagesSEC
PDFGrouping and Choosing a Methodgrouping, a flow chart, factorising completely · 2 pagesSEC

Algebraic Fractions

PDFAlgebraic Fractions: Simplifyingcancelling factors, conditions, common mistakes · 2 pagesSEC
PDFMultiplying and Dividing Algebraic Fractionsfactorise, cancel, multiply; the reciprocal · 2 pagesSEC
PDFAdding Algebraic Fractions: Simple Denominatorsthe same and simple denominators, a common mistake, working together · 2 pagesSEC
PDFAdding Algebraic Fractions: Factorising Denominatorsfactorising denominators, the lowest common denominator, compound fractions · 2 pagesSEC

Review

PDFAlgebraic Expressions: Practice and CheckFind the pair group game, a check, self-assessment · 2 pagesPRISEC

Students can also use the free Parabola app (tables and differences, three forms, sign and inequalities) and Algebra Tiles (completing the square) in the browser.