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Year 8

Problem solving with linear equations

I can use my knowledge of solving linear equations to solve problems.

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New
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Year 8

Problem solving with linear equations

I can use my knowledge of solving linear equations to solve problems.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Problems in context can be expressed algebraically as equations.
  2. These equations can be solved.
  3. The solution can be interpreted in context.
  4. Real life problems can be solved using linear equations.

Keywords

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

  • Solution - The solution to an equality is the value which, when substituted, maintains the equality between the expressions.

Common misconception

That algebra, in particular solving equations, is abstract and not related to the world around us.

Ask pupils to solve $$4(x+3)=20$$. Then show a square with length $$x+3$$, tell them the perimeter is $$20$$ and ask them to find $$x$$.

Give pupils some equations as a starter. For example, $$2m+5=17$$. Then later give them the matching contextual example; "A taxi firm charge a $$£5$$ flat rate plus $$£2$$ per mile. How many miles is a ride costing $$£17$$?".
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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.
$$4(7x-13)$$ is an for the perimeter of this square.
An image in a quiz
Correct Answer: expression, Expression
Q2.
Evaluate $$2(3x-4)+2(5x+9)$$ when $$x=6$$. The value of the expression is .
Correct Answer: 106, one hundred and six
Q3.
Expand and simplify $$2(6x-4)+2(x-7)$$.
$$8x-8+2x-14=10x-22$$
$$12x-8+2x-14=14x+22$$
Correct answer: $$12x-8+2x-14=14x-22$$
$$12x-4+2x-7=14x-11$$
Q4.
The solution to the equation $$4(7x-3)=128$$ is $$x=$$ .
Correct Answer: 5, five, x=5, x = 5
Q5.
Solve $$4x+7=8x-9$$.
$$x=-4$$
$$x=-0.5$$
$$x=0.5$$
Correct answer: $$x=4$$
Q6.
Laura thinks of a number. She multiplies it by 8 and subtracts 12. Her answer is 60. Laura's number is .
Correct Answer: 9, nine

Exit quiz

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6 Questions

Q1.
The perimeter of this square is $$80$$ units. You can find the value of $$x$$ using the $$4(7x-8)=80$$.
An image in a quiz
Correct Answer: equation, Equation
Q2.
The perimeter of this square is $$80$$ units. What is the value of $$x$$? $$x=$$ .
An image in a quiz
Correct Answer: 4, four
Q3.
Find the perimeter of this square. $$P=$$ .
An image in a quiz
Correct Answer: 40, 40 units, forty
Q4.
An electrician has a call-out fee of £120 and then charges an hourly rate for their work. For a six hour job they charge £480. Calculate their hourly rate.
£100
£80
Correct answer: £60
£20
Q5.
Sofia thinks of a number. She multiplies it by 6 and then subtracts 24. Sofia multiplies her original number by 4 and adds 6. She gets the same answer both times. Sofia's number is .
Correct Answer: 15, fifteen
Q6.
Three children share 65 sweets. Lucas takes 5 more sweets than Jacob does. Izzy takes four times as many sweets as Jacob does. Jacob takes sweets.
Correct Answer: 10, ten