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Year 8

Checking and securing understanding of plotting coordinates generated from a rule

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

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New
New
Year 8

Checking and securing understanding of plotting coordinates generated from a rule

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

Download all resources
Share activities with pupils

Lesson details

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.

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.

Keywords

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

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?"
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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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: $$4n−3$$
$$n\times4 + 1$$

Exit quiz

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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: $$23$$
$$18$$
$$11$$
$$8$$
$$3$$