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Year 10
Foundation

Checking and securing understanding of forming linear equations

I can use a letter to represent a generalised number and form a linear equation from a context.

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Year 10
Foundation

Checking and securing understanding of forming linear equations

I can use a letter to represent a generalised number and form a linear equation from a context.

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Lesson details

Key learning points

  1. Quantities that change can be assigned a variable.
  2. If there is a relationship between these quantities, we can write this algebraically.
  3. With two quantities, the algebraic statement can form an equation.

Keywords

  • Equation - An equation is used to show 2 expressions that are equal to each other.

  • Interior angle - An interior angle is an angle formed inside a polygon by two of its edges.

  • Vertically opposite angles - Vertically opposite angles are pairs of opposite angles formed when two lines intersect at a point. They are equal.

Common misconception

When forming expressions brackets can be missed out or incorrectly used.

Review priority of operations. Testing algebraic manipulations with numerical values can be useful when pupils are unsure if things are equivalent. E.g. the difference between 2(x + 4) and 2x + 4 can be shown with 2(5 + 4) and 2(5) + 4


To help you plan your year 10 maths lesson on: Checking and securing understanding of forming linear equations, download all teaching resources for free and adapt to suit your pupils' needs...

This is a good chance to revise geometry topics such as angle facts, as forming equations will be used to solve problems in all topic areas.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Expand and simplify $$5(x - 2) - 2(3x + 4)$$
$$3x - 18$$
Correct answer: $$-x - 18$$
$$x - 14$$
Q2.
Simplify the expression $$\frac{x^2 - 9}{x - 3}$$
Correct answer: $$x + 3$$
$$x - 3$$
$$x^2 + 3x$$
Q3.
Fully factorise the expression $$5x + 20$$
$$x + 25$$
$$5(x - 4)$$
Correct answer: $$5(x + 4)$$
Q4.
Fully factorise the expression $$3x^2 - 12$$
$$x^2 - 4$$
Correct answer: $$3(x + 2)(x - 2)$$
$$3(x^2 - 4)$$
Q5.
Fully factorise the expression $$x^2 - 9$$
$$x(x-3)$$
$$(x + 3)(x + 3)$$
Correct answer: $$(x + 3)(x - 3)$$
Q6.
Fully factorise the expression $$2x^2 + 8x$$
Correct answer: $$2x(x + 4)$$
$$2(x + 4)^2$$
$$x(2x + 8)$$

Exit quiz

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6 Questions

Q1.
A rectangle has side lengths of $$3x + 5$$ and $$2x - 3$$. Write an expression for the perimeter of the shape.
Correct Answer: 10x + 4, 2(5x+2)
Q2.
A triangle has side lengths of $$x + 2$$, $$2x + 3$$, and $$3x + 4$$. Write an expression for the perimeter of the shape.
Correct Answer: 6x + 9, 3(2x + 3)
Q3.
A regular quadrilateral (square) has side length $$4y - 5$$. Write an expression for the perimeter of the shape.
Correct Answer: 16y-20, 4(4y-5)
Q4.
A rectangle has side lengths of $$5a - 6$$ and $$3a + 2$$. Write an expression for the perimeter of the shape.
Correct answer: $$16a - 8$$
$$16a + 8$$
$$8a - 4$$
$$8a + 4$$
Q5.
A regular pentagon has side length $$2z + 1$$. Write an expression for the perimeter of the shape.
Correct Answer: 10z + 5, 5(2z + 1)
Q6.
A regular hexagon has side length $$3n - 4$$. Write an expression for the perimeter of the shape.
Correct Answer: 18n - 24, 6(3n-4)