Myths about teaching can hold you back
- Year 8
Solution to an equation
I can appreciate that a solution is a value that makes the two sides of an equation balance.
- Year 8
Solution to an equation
I can appreciate that a solution is a value that makes the two sides of an equation balance.
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Lesson details
Key learning points
- In an expression the variable can take any value.
- In a linear equation there is a particular value that makes the equation balance.
- The value is the solution to the linear equation.
- When graphing a linear expression this value represents a single point.
Keywords
Solution - A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
Common misconception
When reading solutions from a graph pupils may read the solution as the y-coordinate.
The solution to the equation is the value of the variable that makes both sides balance.
To help you plan your year 8 maths lesson on: Solution to an equation, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 8 maths lesson on: Solution to an equation, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Solving linear equations unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.What is the value of the expression $$5x − 4$$ when $$x = 3$$?
Q2.What is the value of the expression $$5x − 4$$ when $$x = −1$$?
Q3.The table of values for the equation $$y = 7 − 2x$$ is shown. The missing number is .
Q4.To find the value of the expression $$21 − 1.5a$$ when $$a = 5$$, you should the variable $$a$$ for the number 5.
Q5.The graph shows 5 lines labelled A, B, C, D and E. Match each line to the equation for that line.
A (blue) -
$$x = −1$$
B (pink) -
$$y = x$$
C (purple) -
$$y = −1$$
D (green) -
$$y = 1$$
E (black) -
$$y = −x$$
Q6.Match each fraction calculation to its answer.
$$4\times {1\over 2}$$ -
2
$$4\times {3\over 2}$$ -
6
$$4\times {5\over 2}$$ -
10
$$4\times {1\over 4}$$ -
1
$$4\times {3\over 4}$$ -
3
$$4\times {5\over4}$$ -
5
Assessment exit quiz
6 Questions
Q1.Which of these best describes what a solution is?
Q2.Which of these equations have a solution when $$x = 4$$?
Q3.Which of these is a solution to the equation $$3a + 5 = 2a + 2$$?
Q4.Which of these equations have no solution?
Q5.The graph shows the lines with equations $$y = 2 − 2x$$ and $$y = 2x - 2$$. What is the solution to the equation $$2x − 2 = 2 − 2x$$?
Q6.Use the graph to match each equation to its solution.
$$1 − x = 2$$ -
solution when $$x = −1$$
$$1 − x = −4$$ -
solution when $$x = 5$$
$$2x = 2$$ -
solution when $$x = 1$$
$$2x = −4$$ -
solution when $$x = −2$$