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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

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

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Lesson details

Key learning points

An arithmetic sequence can be generated using an n^th term rule..
The term numbers and terms of a sequence can be converted onto coordinates.
These coordinates will lie on a straight line when plotted.
Often the rule will be written using a pair of variables.
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.

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).

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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.

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?

$$4n$$

$$n+4$$

$$1+4n$$

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 $$y=3x+4$$.

Correct Answer: coordinates, Coordinates, cartesian coordinates, Cartesian coordinates

Q2.

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

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?

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?

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?

$$y=26$$

$$y=19$$

$$y=5$$

Correct answer: $$y=−3$$

$$y=−16$$

Q6.

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

Correct answer: $$23$$

$$18$$

$$11$$

$$8$$

$$3$$