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      Problem solving with plotting coordinates

      Lesson details

      Learning outcome

      I can use my knowledge of plotting coordinates to solve problems.

      Key learning points

      1. You can describe the relationship between coordinate pairs in words.
      2. It is possible to identify points which do or do not follow a rule.
      3. A line represents an infinity of points that follow a rule.
      4. You can describe the relationship between coordinate pairs using algebra.

      Keywords

      • Plot - Drawing on a graph or map is known as plotting.

      Common misconception

      Adding the length of the side onto the wrong value within a coordinate.

      Use sketches/ erasable axis/ Desmos to plot points and see if they are reasonable. Encourage writing/drawing on diagrams as working out.

      Teacher tip

      You may wish to allow some students use of graphing software such as Desmos to help. Other students may benefit from checking their answers using Desmos.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Which of these are properties of a square

      Correct answer: It has 4 right angles
      Correct answer: All sides are the same length
      It has angles of 60 degrees
      Two sides are the same length but the other two are different.
      It has 5 sides

      Q2.
      Jun marks the coordinate (3,4) on a set of axes with a cross. What word best describes what he has done?

      Correct answer: plotted
      drawn
      estimated
      generalised
      multiplied

      Q3.
      Lucas has put -3 and 4 on a number line. What calculation will give him the distance between these numbers on his number line?

      $$-3+4$$
      $$-3\div 4$$
      Correct answer: $$4-(-3)$$
      $$4-3$$
      $$-4+3$$

      Q4.
      Calculate $$(-8)-(-10)$$

      Correct Answer: 2, two

      Q5.
      Match the coordinate with the equation for the line it will lie on

      Correct Answer:(2,3),$$y=3$$

      $$y=3$$

      Correct Answer:(3,6),$$x=3$$

      $$x=3$$

      Correct Answer:(-3,-3),$$y=x$$

      $$y=x$$

      Correct Answer:(5,-5),$$y=-x$$

      $$y=-x$$

      Correct Answer:(-2,-3),$$y=2x+1$$

      $$y=2x+1$$

      Correct Answer:(-3,4),$$y=-3x-5$$

      $$y=-3x-5$$

      Q6.
      These three coordinates are plotted on an axis. (-10,3) (-8,3) (-10,1). What coordinate needs to be plotted to form a square?

      Correct Answer: (-8,1)

      6 Questions

      Q1.
      Which of the rules below does the coordinate (2,-12) follow?

      Correct answer: $$x=2$$
      $$x=y$$
      $$y=x+10$$
      $$y=12$$
      Correct answer: $$y=-12$$

      Q2.
      What is the length of one side of this square

      An image in a quiz
      Correct Answer: 11, eleven, 11 squares, eleven squares

      Q3.
      Work out the coordinate of the top right corner of this square

      An image in a quiz
      Correct Answer: (9,-6)

      Q4.
      Match the coordinate with the two rules it follows

      Correct Answer:(5,5),$$x=5$$ and $$y=x$$

      $$x=5$$ and $$y=x$$

      Correct Answer:(5,15),$$y=3x$$ and $$y=x+10$$

      $$y=3x$$ and $$y=x+10$$

      Correct Answer:(5,-5),$$y=x-10$$ and $$y=-x$$

      $$y=x-10$$ and $$y=-x$$

      Correct Answer:(-5,5),$$y=x+10$$ and $$y=-x$$

      $$y=x+10$$ and $$y=-x$$

      Correct Answer:(5,-15),$$y=-3x$$ $$y=-15$$

      $$y=-3x$$ $$y=-15$$

      Q5.
      Which statements concerning intersection points are true?

      Any two lines will intersect
      The lines $$x=4$$ and $$y=3$$ intersect at (3,4)
      Correct answer: The lines $$y=x+15$$ and $$y=2x$$ intersect at (15,30)
      Correct answer: The lines $$y=x$$, $$x=4$$ and $$y=4$$ as intersect at (4,4)
      Two straight lines can intersect at 2 different coordinates

      Q6.
      At which coordinate do the lines $$y=4x$$ and $$y=x-9$$ intersect?

      Correct Answer: (-3,-12)

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