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Maths

Writing and Simplifying Algebraic Expressions

Overview

Students take their first steps into formal algebra by translating English into algebraic notation and simplifying expressions by grouping like terms.

Learning Objective
Students write simple algebraic expressions from word descriptions, understand the difference between terms and expressions, and simplify by collecting like terms.

Resources needed

  • Mini whiteboards

Lesson stages

0 / 7 done
  1. 1 'I think of a number and add 5.' Call the unknown n. Expression: n + 5. 'I think of a number, multiply by 3, and subtract 2.' Expression: 3n − 2. 'Why use n instead of a number?' (It works for any number.)
  2. 2 3 × n = 3n (write coefficient before letter, drop × sign). n × n = n² (indices). 1n = n (drop the 1). n ÷ 3 = n/3. Students rewrite six expressions using correct notation.
  3. 3 'The total cost of n books at £4 each' = 4n. 'The number of days in w weeks' = 7w. 'Three more than a number p' = p+3. 'Half of q' = q/2. Students write 8 expressions from similar descriptions.
  4. 4 Display: 3x, 5x, 4y, 2x². 'Which can be combined?' Like terms have the same letter AND power. 3x and 5x are like (both x). 3x and 4y are unlike. 3x and 2x² are unlike (different powers). Students sort a set of terms.
  5. 5 Simplify 3x + 5y + 2x − y. Group: (3x+2x) + (5y−y) = 5x + 4y. Key: do NOT try to combine unlike terms. Simplify 4a + 3b − 2a + 5b + 1. Students show each step.
  6. 6 A rectangle has length (2x+3) and width x. Write the perimeter as an expression. 2(2x+3) + 2x = 4x+6+2x = 6x+6. 'This expression works for ANY value of x.' Students find perimeter expressions for two more shapes.
  7. 7 Show: 3x + 2y = 5xy (wrong — unlike terms). 4a + 4a = 8a² (wrong — correct is 8a). 5p − 5p = 1 (wrong — correct is 0). Students identify and correct each error.

Tap a step to mark it as done.

Variations

  • Extend to substituting values into expressions
  • Include expressions with brackets (expand single brackets)
  • Link to formulae in science or geography
More information

Display: term, expression, coefficient, variable, like terms. Use: 'A term is a number, letter, or product. An expression is a collection of terms.'

Use concrete examples (bags of apples: each bag has x apples, 3 bags = 3x apples). Restrict to one variable before introducing two. Provide a sorting card set for like terms.

Do students use correct notation (3n not 3×n)? Do they collect only like terms? Are their perimeter expressions correct?

All on mini whiteboards. No printed resources needed.

Students may add unlike terms (3x+4y=7xy). Reinforce: 'you can only add the same fruits — 3 apples and 4 oranges are still 3 apples and 4 oranges, not 7 appleoranges.'

Activity details
Primary Medium 35 minutes No prep Solo, Pairs Indoor
Topics
Algebra Expressions Simplifying Collecting Like Terms