Myths about teaching can hold you back
- Year 9
Exploring the shapes of graphs using technology
I can appreciate that different types of equations give rise to different graph shapes, identifying quadratics in particular.
- Year 9
Exploring the shapes of graphs using technology
I can appreciate that different types of equations give rise to different graph shapes, identifying quadratics in particular.
Lesson details
Key learning points
- There are many different types of equations.
- You can plot the graph of an equation if you have two variables (one for each axis).
- Certain types of equation give rise to certain graph shapes.
- Linear equations produce a straight line.
- Quadratic equations produce a parabola.
Keywords
Quadratic - A quadratic is an equation whereby the highest exponent of the variable is 2; the graph of which forms a parabola.
Parabola - A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus) and a fixed straight line (a directrix).
Common misconception
After plotting the integer coordinate pairs of a quadratic, they should be joined with a straight line.
Use graphing technology to plot coordinate pairs that use smaller and smaller non-integer steps between $$x$$-coordinates. This will reveal the true, curved nature of the line.
To help you plan your year 9 maths lesson on: Exploring the shapes of graphs using technology, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: Exploring the shapes of graphs using technology, 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 Graphical representations unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.The linear equation $$y=3x-7$$ will form a __________ graph.
Q2.Which of these coordinates will be on the linear graph $$y=3x-7$$?
Q3.How many points can be plotted on the graph of the linear equation $$y=3x-7$$?
Q4.If you were populating this table of values for the linear equation $$y=8-5x$$, what is highest value of $$y$$ you will get?

Q5.If you were populating this table of values for the linear equation $$y=8-5x$$, what is lowest value of $$y$$ you will get?

Q6.Which of these equation will produce a non-linear graph?
Assessment exit quiz
6 Questions
Q1.A __________ equation is an equation where the highest exponent of the variable is 2.
Q2.Select all the quadratic equations.
Q3.__________ is a special symmetrical curve which can be bowl-shaped or archlike.
Q4.Which of the below equations will form a parabola when plotted?
Q5.Match each equation to the description of its shape when graphed.
$$2x+3y=12$$ -
Straight graph.
$$y=x^2+3x$$ -
Parabola.
$$y=x^3+2x$$ -
Cubic curve.