Myths about teaching can hold you back
- Year 10•
- Higher
Advanced problem solving with linear graphs
I can use my knowledge of linear graphs to solve problems.
- Year 10•
- Higher
Advanced problem solving with linear graphs
I can use my knowledge of linear graphs to solve problems.
Lesson details
Key learning points
- Knowledge of the geometric properties of shapes can be used here.
- Knowledge of ratio can be used here.
Keywords
Tangent (of a circle) - The tangent (of a circle) is a line that intersects the circle exactly once.
Common misconception
P is a point such that AP : PB is in the ratio of 1 : 3 means that point P is a third of the distance of AB from A.
There are 4 equal parts in total, meaning that point P is a quarter of the distance of AB from A.
To help you plan your year 10 maths lesson on: Advanced problem solving with linear graphs, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Advanced problem solving with linear 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 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.Two lines are perpendicular if their gradients are the negative __________ of one another.
Q2.Match each line with a line that is perpendicular to it.
$$y=3x-8$$ -Â
$$y=-{1\over3}x-11$$
$$y={1\over2}x+8$$ -Â
$$y=10-2x$$
$$y=7-{2\over3}x$$ -Â
$$y={3\over2}x-3$$
$$y={3\over2}x-10$$ -Â
$$y=-{2\over3}x+8$$
Q3.What is the equation of this line?

Q4.What is the equation of the straight line that goes through the coordinates (-5, -23) and (3, 17)?
Q5.Find the coordinates of the point P when AP : PB is in the ratio 1 : 5.

Q6.What is the coordinate of C when AB : BC is in the ratio 1 : 2?

Assessment exit quiz
6 Questions
Q1.In a circle, a tangent and a __________ meet at a right angle.
Q2.The grid shows a circle, its radius and a tangent which touches the circumference at (3, -4). What is the equation of the tangent line?

Q3.The grid shows a circle, its radius and a tangent which touches the circumference at (3,-4). The radius is a line segment of the line ...

Q4.In this graph the radius is a line segment of the line $$y=-{1\over2}x-{5\over2}$$ and the tangent is line $$y=2x-10$$. How can you tell they meet at a right angle?

Q5.Point P is such that AP : PB is in the ratio 1 : 2. Find the area of triangle OPB.

Q6.Point P is such that AP : PB is in the ratio 5 : 1. The area of triangle OAP is square units.
