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Plotting coordinates generated from a rule using technology

I can use technology to quickly represent a set of coordinates graphically.

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Lesson 5 of 7

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Year 7

Plotting coordinates generated from a rule using technology

I can use technology to quickly represent a set of coordinates graphically.

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Lesson slides

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Lesson details

Key learning points

Coordinates can be entered onto Desmos and they will be plotted.
A rule can be entered in Desmos to generate coordinates.
It is possible to spot coordinates that are not following the rule easily using Desmos.
Desmos can be used to create mathematical shapes and pictures using coordinates.

Keywords

Origin - The origin is where the $$x$$-axis and $$y$$-axis cross. It has the coordinate pair (0,0).

Common misconception

Pupils may think that coordinates that make a square/ rectangle follow a linear pattern.

In order for coordinates to follow a rule written as an equation, there needs to be a relationship between the values within a coordinate.

Plan ahead so pupils can have access to technology for this lesson. Allow time to explore Desmos freely so pupils are confident using it for future graph work.

Teacher tip

Licence

This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
What coordinate has been plotted on this set of axes?

Correct Answer: (-3,4)

Q2.
What coordinate has been plotted on this set of axes?

Correct Answer: (2.5,-1.5)

Q3.
Which of these statements about the scale on a set of axes are true?

The $$x$$ axis and the $$y$$ axis have to have the same scale as each other.

Correct answer: The scale has to be the same in the positive and negative $$x$$ direction.

The $$y$$ axis has to have a step of 1.

Correct answer: The $$x$$ axis can have a step of 5.

The $$x$$ axis can increase in 1s until the number 10 then increase in 10s.

Q4.
What word can we use to refer to the point where the $$x$$ axis and $$y$$ axis cross?

Correct Answer: origin, the origin

Q5.
What rule links the coordinates plotted on the graph shown?

$$y=4$$

$$x=4$$

$$x=-4$$

Correct answer: $$y=-4$$

$$y=-x$$

Q6.
These three coordinates are plotted: $$(-3,-10)\;(4.5,8)\;(-3, 8)$$. What fourth coordinate would you need to plot to form a rectangle?

Correct Answer: (4.5,-10)

Assessment exit quiz

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6 Questions

Q1.
What is the coordinate of the origin?

Correct Answer: (0,0)

Q2.
Plot these 4 coordinates on Desmos. What shape do they form? $$(2.5,-4)\;(7,-2.2)\;(10.6,-11.2)\;(6.1,-13)$$

square

Correct answer: rectangle

rhombus

kite

Q3.
Write down the coordinate which does not follow the same rule as the others on this graph. The coordinate pairs are: $$(-2,-11)\;(0,-5)\;(1,5)\;(4,7)\;(6.1,13.3)\;(8.5,20.5)$$

Correct Answer: (1,5)

Q4.
Aisha has plotted these 4 coordinates. Why do they not lie on a straight line? $$(1,3)\;(7,5)\;(-6,-4)\;(-2,0)$$

Correct answer: They do not follow the same rule.

They do not have the same $$x$$ coordinate.

She has plotted them wrong.

They do not have the same $$y$$ coordinate.

The $$y$$ axis has been stretched .

Q5.
What is the rule which links the coordinates: $$(6,14)\;(-2,-18)\;(-5,-30)\;(-11,-54)$$? Plot the coordinates and the lines in Desmos to help you.

$$y=3x-4$$

$$y=-2x+8$$

Correct answer: $$y=4x-10$$

$$y=5x+1$$

Q6.
These three coordinates are plotted: $$(3,5)\;(5,9)\;(9,7)$$. What are the coordinates of the 4th point needed to form a square? Plot them on Desmos to help you.

Correct Answer: (7,3)

Lesson appears in

UnitMaths / Plotting coordinates

Maths

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Plotting coordinates generated from a rule using technology

Plotting coordinates generated from a rule using technology

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.What coordinate has been plotted on this set of axes?

Q2.What coordinate has been plotted on this set of axes?

Q3.Which of these statements about the scale on a set of axes are true?

Q4.What word can we use to refer to the point where the $$x$$ axis and $$y$$ axis cross?

Q5.What rule links the coordinates plotted on the graph shown?

Q6.These three coordinates are plotted: $$(-3,-10)\;(4.5,8)\;(-3, 8)$$. What fourth coordinate would you need to plot to form a rectangle?

Assessment exit quiz

6 Questions

Q1.What is the coordinate of the origin?

Q2.Plot these 4 coordinates on Desmos. What shape do they form? $$(2.5,-4)\;(7,-2.2)\;(10.6,-11.2)\;(6.1,-13)$$

Q3.Write down the coordinate which does not follow the same rule as the others on this graph. The coordinate pairs are: $$(-2,-11)\;(0,-5)\;(1,5)\;(4,7)\;(6.1,13.3)\;(8.5,20.5)$$

Q4.Aisha has plotted these 4 coordinates. Why do they not lie on a straight line? $$(1,3)\;(7,5)\;(-6,-4)\;(-2,0)$$

Q5.What is the rule which links the coordinates: $$(6,14)\;(-2,-18)\;(-5,-30)\;(-11,-54)$$? Plot the coordinates and the lines in Desmos to help you.

Q6.These three coordinates are plotted: $$(3,5)\;(5,9)\;(9,7)$$. What are the coordinates of the 4th point needed to form a square? Plot them on Desmos to help you.

Lesson appears in

UnitMaths / Plotting coordinates

Maths

Q1.
What coordinate has been plotted on this set of axes?

Q2.
What coordinate has been plotted on this set of axes?

Q3.
Which of these statements about the scale on a set of axes are true?

Q4.
What word can we use to refer to the point where the $$x$$ axis and $$y$$ axis cross?

Q5.
What rule links the coordinates plotted on the graph shown?

Q6.
These three coordinates are plotted: $$(-3,-10)\;(4.5,8)\;(-3, 8)$$. What fourth coordinate would you need to plot to form a rectangle?

Q1.
What is the coordinate of the origin?

Q2.
Plot these 4 coordinates on Desmos. What shape do they form? $$(2.5,-4)\;(7,-2.2)\;(10.6,-11.2)\;(6.1,-13)$$

Q3.
Write down the coordinate which does not follow the same rule as the others on this graph. The coordinate pairs are: $$(-2,-11)\;(0,-5)\;(1,5)\;(4,7)\;(6.1,13.3)\;(8.5,20.5)$$

Q4.
Aisha has plotted these 4 coordinates. Why do they not lie on a straight line? $$(1,3)\;(7,5)\;(-6,-4)\;(-2,0)$$

Q5.
What is the rule which links the coordinates: $$(6,14)\;(-2,-18)\;(-5,-30)\;(-11,-54)$$? Plot the coordinates and the lines in Desmos to help you.

Q6.
These three coordinates are plotted: $$(3,5)\;(5,9)\;(9,7)$$. What are the coordinates of the 4th point needed to form a square? Plot them on Desmos to help you.