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Oak National Academy
Oak National Academy
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New
New
Year 10
Higher

Equations from complex shapes

I can form and solve equations with more complex shapes.

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Share activities with pupils
New
New
Year 10
Higher

Equations from complex shapes

I can form and solve equations with more complex shapes.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Sometimes you are given a problem with insufficient information to reach a numerical value.
  2. Depending on the problem, it may be possible to write more than one equation.
  3. It is possible these equations can be combined to write a new, more succinct, equation.

Common misconception

Some pupils may have an equivalent algebraic expressions without noticing.

Tell pupils to always check if their expressions can be simplified or factorised before deeming themselves incorrect.

Keywords

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

  • Perimeter - The perimeter is the distance around a 2D shape.

  • Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

Provide pupils with a shape, such as a kite, with algebraic expressions for each edge and ask them to come up with as many equations as they can from the given information.
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).

Video

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Starter quiz

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6 Questions

Q1.
$$3n+5=2+n$$ is an example of an .
Correct Answer: equation
Q2.
The solution to $$6(2m-7)=42$$ is $$m=$$ .
Correct Answer: 7, seven
Q3.
The solution to $$6y-5=2y+25$$ is $$y=$$ .
Correct Answer: 7.5, 15/2
Q4.
The solution to $$8x+9=28-2x$$ is $$x=$$ .
Correct Answer: 1.9, 19/10
Q5.
The solution to $$\frac{5t+12}{3}=9$$ is $$t=$$ .
Correct Answer: 3
Q6.
The solution to $$6(5d+2)=3(9d-1)$$ is $$d=$$ .
Correct Answer: -5, - 5, minus 5, negative 5

Exit quiz

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6 Questions

Q1.
Given that the perimeter of this rectangle is 76 cm, then $$x=$$ .
An image in a quiz
Correct Answer: 5, five, 5 cm, 5cm
Q2.
Which of these equations are true for this square?
An image in a quiz
$$2(x+1)+2(3x-7)+(18-2x)=7x-18$$
Correct answer: $$7x-18=18-2x$$
Correct answer: $$2(3x-7)=18-2x$$
$$2(3x-7)-(7x-18)=2(x+1)$$
Correct answer: $$(18-2x)^2=(7x-18)(2(3x-7))$$
Q3.
The perimeter of this isosceles triangle is 53 cm. The length of the unmarked edge is cm.
An image in a quiz
Correct Answer: 7, seven
Q4.
Given that this is a parallelogram, complete the equation: $$5x-9=$$___________.
An image in a quiz
$$11y+3$$
Correct answer: $$6y$$
$$7(x-1)$$
Q5.
Given that these two shapes have equal areas, then $$x=$$ .
An image in a quiz
Correct Answer: 3, three, 3 cm, 3cm
Q6.
The area of this rectangle is 48 square centimetres. The perimeter is cm.
An image in a quiz
Correct Answer: 28, twenty eight, 28 cm, 28cm