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Whole class chanting
for 6 times tables.
Record on board as
1 2 3 4 …
6 12 18 24 …
Term-to-term
rule? (+ 5)
Position-to-term
rule? (x 5)
Agree that nth term is 5n.
What
is the sequence for:
6n + 1? 6n +3? 6n – 6?
What do they all have in common?
(Position-to-term rule has a x 6 and term-to-term
rule is +6).
What is
the difference between them? |
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- Generate coordinate
pairs that satisfy a simple linear rule with 2 or
more steps
- Plot the graphs of simple
linear functions, where y is given in terms
of x, on paper and using ICT |
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sequence
term
nth term
consecutive
predict
rule
generate
continue
symbol
expression
equation
formula
linear
parallel
axis
axes
coordinate
squadrant
slope
intercept |
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1. Use starter to highlight the fact
that a constant difference of + 4 means that x 4
is part of position-to-term rule.
2. Demonstrate how to apply the same process as
above to linear functions with more than one step:
sequence
term-to-term rule
position-to-term rule
formula
mapping
function machine
coordinate pairs
graph |
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Eg: Shape
pattern sequence based on multiplication tables:
Pupils to:
1. - derive sequence
term-to-term rule
position-to-term rule
formula
mapping
function machine
coordinate pairs
graph
2. - explain the (number)
link to times tables.
Eg: the sequence is 1 more
than the 5 times tables
v = 5n + 1
3. - begin to identify
the (graphical) link to times tables.
Eg: Graphs of: v = 5n &
v = 5n + 1 they have the same slope, but different
intercept.
Predict other graph shapes. |
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What is the nth term foe these
sequences?
5, 8, 11, 14, 17, …Ans: 3n + 2
6, 13, 20, 27, 34, …Ans: 7n – 1
8, 6, 4, 2, 0, …10 – 2n
8, 10, 12, 14, 16, …Ans: 2(n +3) or 2n + 6 |
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OHS
A5b/1: Shopping
1
jar of coffee costs £2. What would 2 jars
cost? 3 jars? 4 jars? … 10 jars?
As pupils give an answer plot on coordinate grid,
labelled:
Total cost v Quantity.
What
pattern does the graph make? (straight line) Why?
(number proportional to cost)
Can I join up the points?
Why not? (discrete – 1 ½ cans
cannot exist)
1
kg of grapes costs £2. Cost of 2kg? 3kg? 4kg?
… 10kg?
Repeat graph and questions. Why
can the points be joined up now? (continuous) |
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- Begin to plot and interpret the
graphs of simple linear functions arising from real-life
situations.
- Suggest extensions: asking ‘What if…?’;
begin to generalise |
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Present two or three
real-life graphs, and ask pupils to make statements
about them.
Eg:
- simple travel graphs
- conversion graphs
- rental graphs
- total cost v number of items bought
Agree on how to interpret:
- differences on gradient
- intercept
- horizontal graphs
- linear and non-linear graphs |
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- extend to graphs
of simple linear functions in real-life situations,
asking 'What if
…?' type questions.
Eg: Sketch a line graph
for these containers:
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£1 is approximately
70 euros according to today's exchange rate.
Sketch / draw conversion graph to include up to
£100.
Can you join up the points?
Why?
Read off some interpolated points. |
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