|
|
|
|
|
| - express simple
functions in word, then using symbols; represent
in mappings |
|
Previous
list plus:
input
output
function
function machine
mapping
and Ma 1 words: any of -
answer
evidence
explain
explore
investigate
method
problem
reason
results
solution, solve
true, false |
|
Sparks 8: Sequences
1
OR
Sparks 9: Sequences 2
Represent with mapping, function machine.
Mappings from other sequences:
Given inputs & outputs, what is the rule?
Inverse: Given output & rule, input?
What is a mapping? |
|
1) Sequences requiring
pupils to produce mapping / inputs / outputs.
2) Link to nth term, eg: nth
term is 3n +1
3) Link to Equations (A2), eg: y
= 3n + 1
OR
Review sequence patterns and general rules, using:
Revising
Patterns and Rules |
|
Use mappings produced
to introduce term function
& notice some properties of expressions:
Can write in > 1 way,
eg: (c-1)x2 or c x 2 - 2
Can say more simply, eg;
d+1 +2 or d+3
Can invert it, eg:
X + 4 = Y or X = Y - 4 |
|
|
|
Use counting
stick to generate sequences from a rule:
Eg: start with 3. Keep doubling and adding 1; finishing
number (end of stick)?
(Review / extend sequences used in A1). |
|
- generate terms
of a simple sequence, given a rule:
- term-to-term &
- position-to-term)
- solve word problems & investigate in range
of number & algebra contexts
- identify information necessary to solve a problem
and
- represent problems mathematically: symbols / diagrams
/ tables / graphs |
|
Q: 'What
is 4 x 8? How did you work it out if you didn't
know it by heart?'
Compare term-to-term approach - (Start
No is 8, keep adding 8: 8, 16, 24, 32)
with position-to-term approach - (1st.
term is 1 x 8, 2nd is 2x 8, 3rd is 3 x 8, 4th is
4 x 8)
Highlight difference, which is easier for early
terms, late terms...?
Link to mappings |
|
Activities
that require
- term-to-term approach,
eg:
1st term is 100, each term is 10 times the one before;
1st 5 terms? describe sequence in words
- position-to-term approach,
eg:
nth term of a sequence
is 2n - 1, 1st 5 terms? Describe sequence (eg: odd
nos)
OR
Graphical Calculator Investigation: p 148
OR
(Spreadsheets to explore both approaches, see page
148)
Extend to word problems, eg:
Crossing
the River from BGfL |
|
Harry & Rajid
start with £1 pocket money in week 1 of the
new year. Which pocket money rule is better? - Why?
-
Harry: 2 x week no. + 1
Rajid: 2 x (week no. + 1)
What do they each get in Week 100? (position- term). |
|
pp 148 - 153
Counting sticks
Graphical calculators |
|
|
Review plotting
& reading coordinates in 1st quadrant (>
4th quadrant).
Eg:
OHS
A4/2: Car Hire |
|
- generate co-ordinate
pairs that satisfy a simple linear rule; plot
graphs of simple linear functions, (in form
y = ..x...) using paper & ICT and
- recognise straight-line graphs parallel to x-axis
or y-axis |
|
co-ordinates
co-ordinate pair/point
x-coordinate
y-coordinate
grid, origin
axis, axes
graph variable
straight-line graph
equation (of a graph) |
|
Introduce co-ordinate
pairs, eg:
"Give rule such as
C = 3D+ 4, tell me a pair of co-ordinates that C
and D could be".
Plot on a coordinate grid.
OHS
A3/2: Co-ordinate Grid
Link with secure learning of previous A3 lessons,
eg; sequences, mappings, nth term & formulae
|
|
Activities
to include:
1) generating co-ordinate pairs from equation
2) generating table of x, y values from equation
3) plotting points, drawing
a line through points & extending line
4) read off intermediate points; check they fit
rule
5) extend this to fractions & negative nos
6) begin to notice key graph features (of form y
= mx)
OR plot given shapes, using:
Coordinate
Shapes from BGfL
OR
The
Coordinate Game from BGfL |
|
OHS
A3/2: Co-ordinate Grid
Oral work with whole class: generate family of graphs
for y=x, y=2x, y=3x, y=4x
Use to recap correct methods for plotting and line
drawing.Use to highlight that;
all go through origin
all are straight lines
vary in steepness |
|
|
