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      Checking and securing understanding of plotting coordinates generated from a rule

      Lesson details

      Learning outcome

      I can represent, algebraically and graphically, a set of coordinates constructed according to a mathematical rule.

      Key learning points

      1. An arithmetic sequence can be generated using an n^th term rule..
      2. The term numbers and terms of a sequence can be converted onto coordinates.
      3. These coordinates will lie on a straight line when plotted.
      4. Often the rule will be written using a pair of variables.
      5. The points can be generated and plotted in the same way as with a sequence.

      Keywords

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

      Common misconception

      The plotted points of an arithmetic sequence form a line so we draw a line connecting them.

      Sequences are an ordered list and do not always need to follow a rule, so we often only find and use the positive integer term numbers.

      Teacher tip

      Get pupils to notice features of the points they plot and how they relate to the n^th term or the algebraic rule. Ask things like, "what do increasing sequences look like?", "what is the same/different about plotting sequences and algebraic rules?"

      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 words describes the sequence $$11,15,19,23, ...$$?

      Correct answer: linear
      quadratic
      Correct answer: arithmetic
      geometric
      counting

      Q2.
      What are the first three terms of the arithmetic sequence $$10n−2$$?

      $$8,6,4$$
      $$10,8,6$$
      Correct answer: $$8,18,28$$
      $$12,22,32$$
      $$−2,8,18$$

      Q3.
      Match the verbal description to the $$n^{\text{th}}$$ term expression.

      Correct Answer:$$3n$$,Multiply $$n$$ by $$3$$

      Multiply $$n$$ by $$3$$

      Correct Answer:$$3n+5$$,Multiply $$n$$ by $$3$$ and add $$5$$

      Multiply $$n$$ by $$3$$ and add $$5$$

      Correct Answer:$$5n+3$$,Multiply $$n$$ by $$5$$ and add $$3$$

      Multiply $$n$$ by $$5$$ and add $$3$$

      Correct Answer:$$5(n+3)$$,Add $$3$$ to $$n$$ and then multiply $$5$$.

      Add $$3$$ to $$n$$ and then multiply $$5$$.

      Correct Answer:$$n+3$$,Add $$3$$ to $$n$$

      Add $$3$$ to $$n$$

      Q4.
      Match the point to its coordinate pair.

      An image in a quiz
      Correct Answer:A,$$(2, 4)$$

      $$(2, 4)$$

      Correct Answer:B,$$(3, 3)$$

      $$(3, 3)$$

      Correct Answer:C,$$(4, 2)$$

      $$(4, 2)$$

      Correct Answer:D,$$(5, 1)$$

      $$(5, 1)$$

      Q5.
      Which of these coordinates fits the rule $$y=7−2x$$?

      Correct answer: $$(0, 7)$$
      $$(7, 2)$$
      $$(7, 0)$$
      Correct answer: $$(1, 5)$$
      $$(2, 7)$$

      Q6.
      Which rule links $$n$$ to $$T$$ in this arithmetic sequence?

      An image in a quiz
      $$4n$$
      $$n+4$$
      $$1+4n$$
      Correct answer: $$4n−3$$
      $$n\times4 + 1$$

      6 Questions

      Q1.
      This table of values tells us the to plot the relationship $$y=3x+4$$.

      An image in a quiz
      Correct Answer: coordinates, Coordinates, cartesian coordinates, Cartesian coordinates

      Q2.
      What is wrong with this plotting of the arithmetic sequence $$2n−1$$?

      An image in a quiz
      The coordinates are wrong.
      The line should extend to the edges of the grid.
      Correct answer: There shouldn't be a line through the points.
      The points should not line up.
      You need more than $$5$$ term numbers.

      Q3.
      Which of these arithmetic sequences could this graph represent?

      An image in a quiz
      Correct answer: $$17−5n$$
      $$5n−17$$
      $$n−17$$
      $$5−n$$
      $$5−17n$$

      Q4.
      What are the two missing $$y$$ coordinate values for this linear rule?

      An image in a quiz
      Correct answer: $$−1$$
      $$−4$$
      $$−5$$
      Correct answer: $$−6$$
      $$−9$$

      Q5.
      This is a table of values for a linear rule but there is an error. Which value is the error?

      An image in a quiz
      $$y=26$$
      $$y=19$$
      $$y=5$$
      Correct answer: $$y=−3$$
      $$y=−16$$

      Q6.
      For the linear rule $$y=13−2x$$ what is the $$y$$ coordinate when $$x=−5$$?

      Correct answer: $$23$$
      $$18$$
      $$11$$
      $$8$$
      $$3$$

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