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YEAR 9: AUTUMN TERM
Teaching objectives for the oral and mental activities
a) Order, add, subtract, multiply and divide integers.
b) Multiply and divide decimals by 10, 100, 1000, 0.1 and
0.01.
c) Count on and back in steps of 0.4, 0.75, 3/4…
d) Round numbers, including to one or two decimal places.
e) Know and use squares, cubes, roots and index notation.
f) Know or derive quickly prime numbers less than 30 and
factor pairs for a given number.
g) Convert between fractions, decimals and percentages.
Know that 0.005 is half of one per cent.
h) Find fractions and percentages of quantities.
i) Know or derive complements of 0.1, 1, 10, 50, 100, 1000.
j) Add and subtract several small numbers or several
multiples of 10, e.g. 250 + 120 – 190.
k) Use jottings to support addition and subtraction of whole
numbers and decimals.
l) Use knowledge of place value to multiply and divide, e.g.
432  0.01, 37  0.01, 0.04  8,
0.03  5, 13  1.4.
m) Recall multiplication and division facts to 10  10. Derive
products and quotients of multiples of 10, 100, 1000.
n) Use factors to multiply and divide mentally, e.g. 22  0.02,
420  15.
o) Multiply and divide a two-digit number by a one-digit
number.
p) Use approximations to estimate the answers to
calculations, e.g. 39  2.8.
q) Solve equations, e.g. n(n – 1) = 56,  +  = –46.
r) Visualise, describe and sketch 2-D shapes.
s) Recall and use formulae for the perimeter of a rectangle,
and areas of rectangles and triangles.
t) Calculate volumes of cuboids.
u) Estimate and order acute, obtuse and reflex angles.
v) Use metric units (length, mass, capacity) and units of time
for calculations.
w) Use metric units for estimation (length, mass, capacity).
x) Convert between metric units, including area, volume and
capacity measures.
y) Discuss and interpret graphs.
z) Calculate a mean using an assumed mean.
aa) Apply mental skills to solve simple problems.
YEAR 9: AUTUMN TERM
Algebra 1 & 2 (6 hours)
Sequences, functions and graphs (148–163, 172–177)
Solving problems(26–27)
Teaching objectives for the main activities
CORE
From the Y9 teaching programme
A. Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper
and using ICT.
B. Generate sequences from practical contexts and write an expression to describe the nth term of an arithmetic
sequence.
C. Find the inverse of a linear function.
D. Construct functions arising from real-life problems and plot their corresponding graphs.
E. Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form to
another to gain a different perspective on the problem.
Unit:
Algebra 1 & 2
Year Group:
Y9
Number of 1 Hour Lessons:
6
Class/Set:
Core
Oral and Mental
Objective b & c and A
Counting on and back activities in
steps of 0.4, 0.25, ¼, ¾ etc.
Main Teaching
Lesson 1 – (Could be 2 lessons)
Objective A and B
Revisit or introduce ‘T’ notation for
sequences.
Choose different starting numbers.
T(1) = first term T(2) = 2nd term etc.
Establish these are sequences and
Model T(n) = nth term = 2n
remind about need for a starting value Model other functions.
and a rule.
(See page 149 of framework)
Extend to multiplying by 10, 100,
1000 etc.,
By 0.1, 0.2, by 0.01 etc.
Set question like if T(n) = 2n – 7 what is
T(6)?
Establish than adding on and taking
off is an arithmetic sequence.
Revisit finding rules from input and output
tables. Establish difference between term to
term and nth term rules.
(See www.eril.net following links to
learning worlds – maths – interactive
whiteboard – sequences and rules)
Distinguish between these and
geometric sequences.
Notes
Key Vocabulary
Sequence
Arithmetic
Linear
Term to term
nth term
Difference
Plenary
 Give me an example of an arithmetic
sequence
 Give me a non-arithmetic sequence
 What is a term to term rule – give an
example.
 How else can we describe a sequence?
 What does T(n) = 2n – 6 mean?
 6, 10, 14, 18….. T(n) = ?
How do we find the rule?
 Extension – what about this sequence
1, 4, 9, 16?
How do we describe it?
Oral and Mental
Objective B
(Writing expressions)
My starting number is always n.
Give me an expression for:
Twice n
n multiplied by itself
Half n
The reciprocal of n
25% of n
8 more than n
n doubled and six added
Six added to n and then doubled
Etc.
(Pupils respond with white boards
etc.)
Pupils sketch graphs of functions
y = x,
y = 2x,
y = 2x + 1 etc. in pairs on
whiteboards.
Main Teaching (2 lessons)
Objective D and E
Revisit/model function like y = 2x,
y = 2x + 2 etc relate x and y values to
n 2n, n  2n + 2 etc. show links.
Revisit sequence 1, 4, 9, 16, model graph –
establish why it is non-linear.
Model everyday life situation.
e.g. a cement mixer cost £20 to hire plus £5
for each day.
Produce Table of Values for up to one
week.
Day
Cost
1
25
2
30
3
35
4
40
Model term to term rules
Model nth term rule.
Plot graph, make links.
Questions needed on practical situations
using real life problems.
Pupils undertake surround activity
(worksheet Surround 9Alg 1&2a )
Notes
Plenary
 Revisit cement mixer activity


Compare
Table
Graph
Algebraic rule
(T(n) = 5n + 20) and worded rule “£20 +
£5 per day”
How does each present the situation?
Model other questions.
Oral and Mental
Objective y
What type of rules might give these
graphs:
f(n)
n
f(n)
n
f(n)
n
Main Teaching 2 lessons
Objective C
Pupils list sequence generated by
T(n) = 10 – n
e.g. 9, 8, 7, 6 …
If I know the number in a sequence, how
can I tell which term it is?
Establish 10 – sequence number = term
number.
What about T(n) = 15 – n T(n) = 13 – n
What do you notice?
Note that ‘undoing’ the sequence we use the
same function.
Introduce the idea of ‘inverse’ of a function.
Model in words a function and then the
inverse.
Relate to number machines and mappings.
e.g. ‘I take a number, double it and then add
one’. Inverse is ‘ I take one and halve’.
Model the algebra.
n
2n + 1
confusion may occur
n
n - 1
using the n notation
2
f(n)
To simplify this you could use y = 2x + 1
with and inverse
x=y - 1
2
n
Graded questions needed – some students
may remain at the function/number machine
stage.
f(n)
n
Pupils discuss each on in pairs.
Teacher collects responses – class
discuss.
Notes
Key Vocabulary
Inverse
Self inverse
Plenary
 Model graphs of:
T(n) = 10 – n
i.e. y = 10 – x


T(n) = 13 – n
y = 13 – x etc.
What do you notice?
Talk about self inverses.
Plot y = x …… is this a self inverse?
What do you notice:
OR


Carefully remodel functions and
inverses.
How do inverse functions help?
Oral and Mental
Objective C
‘I think of a number’
e.g.
I think of a number double it and add
6. The answer is 10. What was the
number?
What was the function?
What was the inverse function?
Grade questions carefully and
support/model responses.
Main Teaching
Objective A, B, C, D, E (Model the
following with help from students)
A taxi driver charges £2 as soon as you sit
in his cab and the £1 per mile.
Write out a table of values for each
increasing mile.
What is the term to term rule?
What is the nth term rule?
Write this as a function. Plot the graph.
Use all the above to answer the following:
How much to travel 12 miles?
If I was charged £28, how many miles
did I travel?
Further questions of this type for pupils to
solve.
Notes
A function’s graph
line reflected in the
line y = x will give
the inverse function.
Plenary
 Discuss solutions
 Compare graphs of function and inverse
 Function example with graph line y = x
 Conjecture?
 Is this always true?
 Check with further functions.