YEAR 9: SPRING TERM
Number 2
(8-10 hours)
Place value (36–47)
Fractions, decimals, percentages, ratio and proportion (60–81)
Calculations (82–107, 110–111)
Calculator methods (108–109)
Solving problems (28–29)
Teaching objectives for the main activities
CORE
From the Y9 teaching programme
A. Understand the order of precedence and effect of powers.
B. Use known facts to derive unknown facts; extend mental methods of calculation, working with
decimals, fractions, percentages, factors, powers and roots; solve word problems mentally.
C. Make and justify estimates and approximations of calculations.
D. Use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a
multiplicative inverse; cancel common factors before multiplying or dividing.
E. Check results using appropriate methods
F. Extend knowledge of integer powers of 10; multiply and divide by any integer power of 10.
G. Use rounding to make estimates; round numbers to the nearest whole number or to one or two decimal
places.
H. Know that a recurring decimal is an exact fraction.
I. Use standard column procedures to add and subtract integers and decimals of any size, including a
mixture of large and small numbers with differing numbers of decimal places; multiply and divide by
decimals, dividing by transforming to division by an integer.
J. Check results using appropriate methods.
K. Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size,
knowing not to round during intermediate steps of a calculation; use the constant,  and sign change
keys, function keys for powers, roots and fractions, brackets and the memory.
L. Enter numbers into a calculator and interpret the display in context (negative numbers, fractions,
decimals, percentages, money, metric measures, time). (reduce since added into Number 1)
M. Solve substantial problems by breaking them into simpler tasks, using a range of efficient
techniques, methods and resources, including ICT; use trial and improvement where a more
efficient method is not obvious.
Unit:
Number 2
Year Group:
Y9
Number of 1 Hour Lessons:
8 to 10
Class/Set:
Core
Oral and mental
Objectives j, h, k, i.
Complements of decimals
to 1, 10, 20 etc. Explore
methods extend as
appropriate.
How would you calculate
36 x 25?
So what is 36 x 26?
So what is 36 x 24?
Main Teaching
(2 to 3 ) lessons
Objective I (+ and -)
Consolidate column addition and subtraction of
decimals as needed. (Discuss jottings and number
lines - objective i)
Use in context of money and measurement of length
etc.
Objective F, I ( x)
Consolidate understanding of decimals and their
multiplication by 10, 100, 1000 etc.
Extend to multiplication by 101, 102, 103 etc.
making explicit the clues given by the powers.
Move to division and set scenarios as below.
Notes
Key Vocab.
Product.
Powers
Plenary
What are the main mistakes people
make when adding and subtracting
decimals?
Why is 0.3 x 0.2 = 0.06?
How many ways can you express
nine hundredths?
Give me an informal jotting method
of using 16 x 25 to get 1.6 x 24.
Focus on solutions to some of the
solutions to key problems set in the
lesson.
Note and reinforce techniques
developed.
0.4 = 4 ÷ 10 = 4/10
0.07 =
Model practical application from
the lesson.
0.005 =
Extend to 3.6 x 25 then
3.6 x 2.5 to assess
knowledge and
understanding. Try
estimates to check
answers and or
calculators.
If possible model 3.6 x 2.5 =
36 25 900
x

9
10 10 100
Linking the two skills. Use these techniques to solve
problems including written questions on area and
percentages which lead to the product of decimals.
(Integrate or teach specifically, rounding answers objective G).
Oral and mental
Objectives g and f.
Simplifying fractions by
cancelling.
Find equivalent fractions
with larger numerators
and denominators.
How does this relate to
36 36  10

 3.6 ?
10 10  10
What happens to a
fraction if we increase the
denominator?
What happens to a
fraction if we increase the
numerator?
Main Teaching
(1 – 2 lessons)
Revisit skills from previous lessons.
Objective I (division)
Explore the meaning of division.
Model and develop understanding that
1
 3  10  30 (obj. D interpret
10
division is a multiplicative inverse).
Develop into practical situation. E.g. how many
10cm strips could I cut from a 3metre wooden
board?
If possible extend to negative index notation for
powers of 10.
3
3  10
30


 30
Model 3  0.1 
0.1 0.1  10
1
Develop this technique to support division by
decimals e.g. making the denominator or divisor a
whole number whilst keeping the same ratio.
3 ÷ 0.1 = 3 
Notes
Key Vocab.
Multiplicative inverse
Generalise
Divisor
Plenary
If I say 23 ÷ 0.1 = 2.3 how do you
know this is wrong?
If I say 23 ÷ 0.1 = 230 how does
1
this help me tackle 23  ?
10
How can I extend this to help me
with other questions?
What generalisations can we make?
How do powers of 10 help us with
multiplication and division?
Highlight what has to be
remembered.
Oral and mental
Obj l, m, n,
Revisit mult. and division
by powers of 10
 Match answers to
questions and
solutions.
 Use a target board
 Use a mixture of
numbers and signs
on the board
pointing to two
numbers and a
sign and asking
for a solution.




Matching
equivalent
fractions
Converting mixed
numbers to
improper fractions
etc.
Mental addition of
fractions.
Counting up in
eighths on a
number line with
cancelling etc
Main Teaching
Objectives D, B, C and E
(2 - 3 lesson).
Revisit understanding of fractions cancelling and
equivalent fractions – make links to percentages
and decimals.
Revisit or teach addition and subtraction of fractions
– extend to mixed number techniques. (Objective L
Model with calculator).
Notes
Key Vocab.
Cancel
Simplest
Lowest terms
Mixed number
Improper fraction.
Proportional
Common factor
Plenary
Generalise on findings.
Model cancelling with pictures or
ask students to give a pictorial
explanation of cancelling.
Ask students to invent some
common mistakes in adding or
subtracting fractions. Share the
inventions and ask other students to
say what is wrong.
Model some addition of fractions
and equivalent additions using
decimals.
Model multiplication of fractions e.g.
3 2 3 2
  of
4 3 4 3
2
Draw a 4 by 3 table and shade in
.Then shade in
3
2
6
3
of the . Show the result is
of the original
3
12
4
table and develop a system for efficiently
multiplying fractions. Look at short cuts in
cancelling. Extend to mixed numbers. (Partitioning
perhaps and using the grid multiplication method).
Model division with concrete examples with
3 3
diagrams e.g how many in ? Develop a system
8 4
using multiplicative inverse idea.
(Objective L Model with calculator)
Revisit generalisation
Ask students to model a solution
pictorially.
Relate to percentages.
Model common mistakes.
Model some questions that can be
1 2
1 1
done mentally. E.g  , 1 
2 3
2 2
Why is multiplying by one tenth the
same as dividing by 10 etc.?
Relate to percentages.
Oral and mental
Objective g
Increase $1.20 by 25%.
Ask groups of students or
all the students to do it.
 Mentally
 Using
multiplication of
decimals.
 Using
multiplication by
a¼
 Using
multiplication by
a mixed number
(1 ¼).
 By ratio
Main Teaching
Objectives K, L, M and E. (2 lessons)
Begin by looking at an OHP of a calculator and in
groups identifying what keys do. After feedback
this may be useful in assessment for learning (which
areas to address).
Use the power keys efficiently and model their use.
Use this to establish the order of priorities with
a4 2
powers. E.g. (a2 - 2a3 +
) might be worth
2
discussing or evaluating each term in the expression
for various values of a.
Notes
Key Vocab.
Index
Power
Reciprocal
Trial and
improvement
Term
Exponent
Discuss outcomes.
Discuss use of a
calculator.
Objective H
How can I get 0.3333
going on forever from a
calculation? Develop to
other recurring decimals.
What do they have in
common?
Stress that as vulgar
fractions they are exact
values.
A collection of questions to be done in groups or
pairs followed by feedback on methods used is a
useful strategy. Some groups can be restricted e.g.
no memory used, no power key, no brackets.
These could be in a pack of cards drawn at random
for each question.
Discussion should centre on efficiency estimation
and communicating the methods used.
Extend to worded questions perhaps drawn from
SAT data base or framework.
Challenge students to solve
questions with the smallest number
of key presses.
Establish understanding of priorities
of powers.
Assess knowledge of key use on
calculator.
Challenge students to estimate
answers to questions – invite
students to model solutions.
You may want to use trial and improvement to
calculate roots before using the root function keys.
Reinforce the use of brackets, the order of priorities
of a calculator, the change of sign key and insist on
estimates as ways of checking answers.
Much of this will be revision from Y8 work.
Plenary
Model some SAT questions.
Model questions from real life.
Check key language.
SHEETNUMB2-1
For examples