New
New
Year 9

Problem solving with graphical representations

I can use my knowledge of graphical representations to solve problems.

New
New
Year 9

Problem solving with graphical representations

I can use my knowledge of graphical representations to solve problems.

Lesson details

Key learning points

  1. When presented with a real-life problem, it can help to sketch what is happening.
  2. A sketch can provide a visual aid for understanding.
  3. In there is a context to the problem then the solution should be given in context.

Common misconception

A distance time graph will always be constructed with straight lines.

A straight line represents a consistent rate of a change, a consistent speed. In reality we need to model acceleration and deceleration which will involve curved lines.

Keywords

  • Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

  • Gradient - The gradient is a measure of how steep a line is.

  • Intercept - An intercept is the coordinate where a line or curve meets a given axis.

  • 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 (the directrix).

In each case, encourage pupils to verbalise what it is that the sketch shows them.
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).

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6 Questions

Q1.
The diagram shows the lines $$y=2x-1$$ and $$y=5-x$$. The point A will help you find the solution to the __________ equations $$y=2x-1$$ and $$y=5-x$$.
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intersecting
non-linear
quadratic
Correct answer: simultanous
Q2.
Sam plots the graphs of $$y=3x+1$$ and $$y=3x-4$$ on the same coordinate grid. How many points will lie on both lines?
Correct Answer: 0, zero, none
Q3.
The linear equations $$y = 2x -9$$ and $$y = 3 − x$$ intersect at the point with coordinates (4, -1). What is the solution to the equation $$2x-9=3-x$$?
$$x=-1$$
$$x=4$$
$$y=-1$$
$$y=4$$
Q4.
Use the graph to solve the simultaneous equations $$y=2x-1$$ and $$y=5-x$$.
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$$x=3$$, $$y=2$$
$$x=7$$, $$y=-2$$
$$x=1$$, $$y=1$$
$$x=-2$$, $$y=7$$
Correct answer: $$x=2$$, $$y=3$$
Q5.
The diagram shows 6 points and the the lines $$y=2x-1$$ and $$y=5-x$$. Which points satisfy the inequality $$y<5-x$$ ?
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Correct answer: A
C
D
Correct answer: F
B and E
Q6.
The diagram shows 6 points and the the lines $$y=2x-1$$ and $$y=5-x$$. The point that is the region $$y>5-x$$ and $$y>2x-1$$ is .
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Correct Answer: C, c

6 Questions

Q1.
The y- is the point where a line or curve meets the $$y$$-axis.
Correct Answer: intercept
Q2.
Four pupils are solving a pair of simultaneous equations. The diagram shows the graphs of the equations they are solving. Which pupils are definitely incorrect?
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Correct answer: Alex says $$x=2$$, $$y=3$$
Correct answer: Izzy says $$x=-2$$, $$y=-3$$
Jun says $$x=2$$, $$y=-3$$
Correct answer: Laura says $$x=-2$$, $$y=3$$
Q3.
The graph models the time taken for three people to run 100 metres. Which line represents the fastest runner?
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Correct answer: Line a
Line b
Line c
Q4.
The parabola is used to model the throw of a tennis ball. The ball reaches a height of 10 metres times.
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Correct Answer: 2, twice
Q5.
The graphs models Laura running a 100 metre race. The graph covers a distance of 110 metres. Match each section of the graph to the correct statement.
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Correct Answer:A,Laura is accelerating

Laura is accelerating

Correct Answer:B,Laura is running fast

Laura is running fast

Correct Answer:C,Laura is slowing down

Laura is slowing down

Correct Answer:D,Laura has nearly stopped

Laura has nearly stopped

Q6.
A container is filled with water at a constant rate. The graph shows the depth of water in a container as it is filled. Which of these could be a cross section of the container?
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An image in a quiz
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Correct Answer: An image in a quiz
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