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      Plotting non-integer coordinates

      Lesson details

      Learning outcome

      I can describe and plot coordinates, including non-integer values, in all four quadrants.

      Key learning points

      1. Coordinates with any values can be plotted.
      2. Coordinates can be described in all four quadrants.
      3. Shapes can be described using coordinates.

      Keywords

      • Integer - An integer is any positive or negative whole number or zero.

      Common misconception

      That coordinates only exist, and can only be plotted, on the lines of graph paper.

      Between any two vertices there are infinitely more points. Ask pupils to consider what numbers are between 1 and 2.

      Teacher tip

      Some verbal play can warm your class up for this topic. "Give me a number between 0 and 5". 1, 2, 3 and 4 will quickly be exhausted. Keep asking. 0.5, 1.5, 1.6 etc. may emerge. The game can go on infinitely.

      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.
      $$2, 27, 327, -7, -107$$ and $$0$$ are all examples of __________.

      whole numbers
      natural numbers
      Correct answer: integers
      non-integers

      Q2.
      Match the equivalent fractions and decimals.

      Correct Answer:$$0.25$$,$${1 \over 4}$$

      $${1 \over 4}$$

      Correct Answer:$$0.2$$,$${1 \over 5}$$

      $${1 \over 5}$$

      Correct Answer:$$0.5$$,$${1 \over 2}$$

      $${1 \over 2}$$

      Correct Answer:$$0.75$$,$${3 \over 4}$$

      $${3 \over 4}$$

      Correct Answer:$$0.6$$,$${3 \over 5}$$

      $${3 \over 5}$$

      Q3.
      Find the midpoint for each pair of numbers.

      Correct Answer:1 and 9,5

      5

      Correct Answer:1 and 7,4

      4

      Correct Answer:1 and 8,4.5

      4.5

      Correct Answer:1 and 10,5.5

      5.5

      Correct Answer:2 and 10,6

      6

      Correct Answer:2 and 11,6.5

      6.5

      Q4.
      What is this coordinate?

      An image in a quiz
      $$(2,-5)$$
      $$(-2,-5)$$
      $$(5,-2)$$
      Correct answer: $$(-2,5)$$

      Q5.
      What's wrong with the labelling of this coordinate?

      An image in a quiz
      Correct answer: The signs are the wrong way round on both coordinates. It should read $$(3,-4)$$
      It's below the $$x$$-axis so both need to be negative. $$(-3,-4)$$
      Nothing. That is the coordinate $$(-3,4)$$

      Q6.
      The sides of this rectangle are parallel to the $$x$$ and $$y$$ axes. What is the missing fourth coordinate?

      An image in a quiz
      $$(-11,-12)$$
      $$(-12,-10)$$
      $$(-12,-11)$$
      Correct answer: $$(-12,-9)$$
      $$(-9,-12)$$

      6 Questions

      Q1.
      Coordinates can take integer values such as $$(2,5)$$ and $$(13,-27)$$ and also __________ values such as $$({1 \over 2},{1 \over 5})$$ and $$(1.3,-2.7)$$

      smaller
      whole number
      Correct answer: non-integer
      decimal

      Q2.
      What is this coordinate?

      An image in a quiz
      $$(5,3)$$
      $$(3,5)$$
      Correct answer: $$(1.5,2.5)$$
      $$(2.5,1.5)$$
      $$(1.5,5)$$

      Q3.
      What is this coordinate?

      An image in a quiz
      Correct answer: $$(0.2,0.6)$$
      $$(0.1,0.3)$$
      Correct answer: $$ ({1 \over 5},{3 \over 5})$$
      $$ (1,{3 \over 5})$$
      $$(1,3)$$

      Q4.
      What is this coordinate?

      An image in a quiz
      Correct answer: $$(-1.25, {3 \over 4})$$
      $$(-1.25, -{3 \over 4})$$
      Correct answer: $$(-{5 \over 4}, {3 \over 4})$$
      $$(-0.75, 1.25)$$
      Correct answer: $$(-1.25, 0.75)$$

      Q5.
      What could this coordinate be?

      An image in a quiz
      $$(2.1,-2)$$
      Correct answer: $$(2,-1.9)$$
      $$(2,-2.1)$$
      $$(2.1,-1.9)$$
      $$(1.9,-1.9)$$

      Q6.
      This rectangle is parallel to the $$x$$ and $$y$$ axes. What is the missing fourth coordinate?

      An image in a quiz
      Correct answer: $$(4.3,-3.5)$$
      $$(4.3,-2.8)$$
      $$(-2.9,2.8)$$
      $$(-2.9,3.5)$$

      To help you plan your 7 maths lesson on: Plotting non-integer coordinates, download all teaching resources for free and adapt to suit your pupils' needs...