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Foundation - Algebraic Manipulation

infoWhy this? We are teaching this unit so that pupils can confidently manipulate algebraic expressions, including expanding, factorising and substituting, and use algebra to represent situations and construct clear mathematical arguments.

scheduleWhy now? We are teaching it now in Year 10 so that pupils develop a strong algebraic foundation before moving on to more complex GCSE topics such as equations, graphs and functions later in the course

neurologyYou need to know

  • List all square, cube, and prime numbers up to a given value.
  • List all factors and multiples of a given number.
  • Identify the LCM and HCF of any two or more numbers, including using prime factorisation.
  • Round numbers to the nearest integer, 10, 100, 1000, decimal place, or significant figure as specified.
  • Estimate answers to calculations by rounding each number to one significant figure and performing the calculation.
  • Truncate numbers to a specified number of decimal places or significant figures.
  • Express any number as a product of its prime factors, using index notation where appropriate.
  • Use prime decomposition to find the LCM and HCF of two or more numbers.
  • Solve worded problems involving LCM and HCF in real-life contexts (e.g., finding when events coincide, grouping items).
  • Find upper and lower bounds for a value given a degree of accuracy (e.g., rounding or measurement).
  • Write error intervals for numbers rounded to a given degree of accuracy, using correct mathematical notation.

rocket_launchYou must be able to

  • Simplify algebraic expressions by collecting like terms.
  • Multiply and divide algebraic terms, using the laws of indices.
  • Expand single brackets and simplify the resulting expressions.
  • Expand and simplify expressions involving multiple single brackets.
  • Substitute positive and negative values into basic linear expressions.
  • Form algebraic expressions from worded problems or statements.
  • Use algebraic expressions to form and construct simple mathematical arguments or proofs.
  • Factorise basic linear expressions by taking out a common factor
  • Expand and simplify double brackets (e.g., (x + 2)(x + 3)).
  • Substitute values into non-linear expressions (e.g., quadratic or cubic expressions).
  • Factorise quadratic expressions into single brackets (when possible, e.g., x² + 2x = x(x + 2)).
  • Factorise quadratic expressions with a unitary coefficient of x² into double brackets (e.g., x² + 5x + 6 = (x + 2)(x + 3)), including the difference of two squares (e.g., x² - 9 = (x + 3)(x - 3)).


Revision Quiz

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