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      Checking and securing understanding of plotting coordinates with technology

      Lesson details

      Learning outcome

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

      Key learning points

      1. A table can be used to plot coordinates on Desmos.
      2. It is easy to see if any of the points do not fit the pattern.
      3. It is possible to draw a line through the points using Desmos.
      4. Using the line you can determine if points do or do not fit the rule.

      Keywords

      • Arithmetic (linear) sequence - A sequence where the difference between successive terms is a constant.

      Common misconception

      When plotting the sequence $$3n-1$$ using technology you need to type each coordinate individually.

      "We use technology to make things easier. There must be a quicker way!" Look for the 'table' function.

      Teacher tip

      Get pupils to plot the first ten terms of $$3n-1$$ then say, "Do it for 100 terms". Allow a minute before interrupting with, "There is a quicker way! A table function which plots multiple points in seconds. Can you find it?". Allow pupils to explore.

      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.
      The vertical and horizontal lines that divide our coordinate grid into the four quadrants are called ...

      Correct answer: axes
      grid lines
      parallel lines

      Q2.
      Which of these is a correctly formatted coordinate?

      $$2,7$$
      $$(2/7)$$
      $$2:7$$
      $$(2$$ $$7)$$
      Correct answer: $$(2, 7)$$

      Q3.
      Which of these coordinates fits the rule "The $$y$$ coordinate is five times the $$x$$ coordinate minus $$1$$?

      $$(0, 1)$$
      Correct answer: $$(0, −1)$$
      $$(5, 4)$$
      Correct answer: $$(5, 24)$$
      $$(5, −1)$$

      Q4.
      Which arithmetic sequence is represented by this table of values?

      An image in a quiz
      $$n+7$$
      $$7n+7$$
      $$7(n+7)$$
      Correct answer: $$7n$$

      Q5.
      Arithmetic sequences have which features?

      Correct answer: A constant difference between terms.
      Correct answer: They form a straight line when plotted.
      They form a curve when plotted.
      Increasing values.

      Q6.
      Which relationship is represented by this table of values?

      An image in a quiz
      Correct answer: $$y=6−2x$$
      $$y=x−2$$
      $$y=2x−6$$
      $$y=8−2x$$

      6 Questions

      Q1.
      Which words describe this plotted sequence?

      An image in a quiz
      Correct answer: linear
      Correct answer: arithmetic
      increasing
      Correct answer: decreasing
      quadratic

      Q2.
      Why did the software not plot the coordinate $$(3, 5)$$ in this image?

      An image in a quiz
      Because $$3$$ and $$5$$ aren't labelled on the $$x$$ and $$y$$ axes.
      The scale on the axes is wrong.
      We are zoomed in on the wrong region of the graph to see it.
      Correct answer: You have to write the coordinate pair in brackets.

      Q3.
      Which arithmetic sequence is represented here?

      An image in a quiz
      $$n$$
      $$−2n$$
      $$5−2n$$
      Correct answer: $$7−2n$$

      Q4.
      How do we know that $$(2,−3)$$ does not follow the same linear rule as the other coordinates?

      An image in a quiz
      It's in the wrong quadrant.
      It's plotted wrong.
      Correct answer: It doesn't align with the other coordinates.
      Because the $$y$$ coordinate is less than the $$x$$ coordinate.

      Q5.
      Which term is incorrect in this arithmetic sequence?

      An image in a quiz
      The $$1^{\text{st}}$$ one
      The $$3^{\text{rd}}$$ one
      Correct answer: The $$5^{\text{th}}$$ one
      The $$7^{\text{th}}$$ one

      Q6.
      Which coordinate fits both of the rules $$y=8−x$$ and $$y=3x−4$$?

      An image in a quiz
      $$(0, 8)$$
      $$(8, 0)$$
      Correct answer: $$(3, 5)$$
      $$(5, 3)$$
      No coordinate fits both rules.

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