Myths about teaching can hold you back
- Year 10•
- Foundation
Drawing cubic graphs
I can generate coordinate pairs for a cubic graph from its equation and then draw the graph.
- Year 10•
- Foundation
Drawing cubic graphs
I can generate coordinate pairs for a cubic graph from its equation and then draw the graph.
Lesson details
Key learning points
- A table of values can be useful to identify coordinate pairs which satisfy the equation.
- By substituting the values for x, you can calculate corresponding values for y.
- If used correctly, your calculator can be a powerful tool to speed up calculations.
Keywords
Cubic - A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3
Common misconception
To draw a graph, points should always be joined with line segments.
For the graph of $$y=x^3$$ show the line joining $$(0,0)$$ and $$(1,1)$$ and ask pupils to test some coordinate pairs from that line in the original equation. For example, $$(1/2,1/2)$$ does not satisfy the equation.
To help you plan your year 10 maths lesson on: Drawing cubic graphs, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Drawing cubic graphs, 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 4 maths lessons from the Non-linear graphs 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.In the equation $$y=5x^3-7$$, the $$3$$ is the __________ of $$x$$.
Q2.What is the value of $$x^3$$ when $$x=4$$?
Q3.What is the value of $$x^3$$ when $$x=-2$$?
Q4.Match each $$x$$ value to its corresponding $$y$$ value for the equation $$y=x^3-2$$.
$$x=-2$$ -
$$y=-10$$
$$x=-1$$ -
$$y=-3$$
$$x=0$$ -
$$y=-2$$
$$x=1$$ -
$$y=-1$$
$$x=2$$ -
$$y=6$$
$$x=3$$ -
$$y=25$$
Q5.Where is the $$y$$-intercept of the equation $$y=x^2-7x+8$$?
Q6. Use a calculator to find the $$y$$ value when $$x=4$$ in the equation $$y=x^{3}-3x^{2}+2x$$.
Assessment exit quiz
6 Questions
Q1.$$y=x^3-7$$ is a __________ equation.
Q2.Which $$y$$ value is incorrect in this table of values for the equation $$y=x^3-9$$? Use a calculator.
Q3.What is the $$y$$ value when $$x=-3$$ for the equation $$y=12-x^3$$? Do not use a calculator for this question.
Q4.What is the general form for a cubic?
Q5.The diagram shows the graph of a cubic of the form $$y=ax^3+d$$. Which of these statements are correct?
Q6.Which of these will be $$y$$ values in this table for the equation $$x^{3}-5x^{2}+3x-4$$? Use a calculator.
