Post Graduate Induction Day
June 2017
Subject Knowledge Workshop
Number
1
Today’s
Today’sworkshop
workshop
• Based on the subject audits
• Confidence-building
• Teachers’ Standard 3: Demonstrate good
subject (and curriculum) knowledge
2
Quick check
Are you sure about these symbols?
>
<
=
3
Quick check
Are you sure about these symbols?
>
-10
<
=
-3
4
Negative numbers
‘Take away’ or ‘find the difference between’
e.g. Calculate; 3 - – 5 =
Which number is greater?
Will it be a positive difference or negative
difference?
5
Negative numbers
a) The minimum temperature recorded over
night was minus 6 degrees Celsius, if the
temperature rises by 10 degrees what
temperature will it read?
b) 7 - – 3
c) –4 - – 8
6
Quick check
How’s your understanding of
place value?
386.712
7
Quick check
How many times larger is the red
digit than the blue digit?
386.782
8
Quick check
386.782
0.8 (10x larger)
8.0 (100 times larger)
80.0 (1000 times larger)
9
Year 4
count in multiples of 6, 7, 9, 25
and 1 000
(copied from Number and Place
Value)
Year 5
Year 6
count forwards or backwards in
steps of powers of 10 for any given
number up to
1 000 000
(copied from Number and Place
Value)
recall multiplication and division
facts for multiplication tables up
to 12 × 12
MENTAL CALCULATION
multiply and divide numbers
perform mental calculations,
mentally drawing upon known facts including with mixed operations and
large numbers
use place value, known and
derived facts to multiply and
divide mentally, including:
multiplying by 0 and 1; dividing by
1; multiplying together three
numbers
recognise and use factor pairs and multiply and divide whole numbers
commutativity in mental
and those involving decimals by 10,
calculations (appears also in
100 and 1000
Properties of Numbers)
associate a fraction with division and
calculate decimal fraction equivalents
(e.g. 0.375) for a simple fraction (e.g.
3/ )
8
(copied from Fractions Progression Map)
Section of the Multiplication and Division progression map from:
https://www.ncetm.org.uk/resources/42990
10
Indices and powers
An index, or a power, is the small floating
number that goes next to a number or letter.
(The plural of index is indices.) Indices show how
many times a number or letter has been
multiplied by itself.
4
2
=2x2x2x2
11
Indices and powers
3
4
x
2
3
4x4x4=
3x3=
12
Indices and powers
3
5
3
2
x
5
2
3 +4
13
Negative indices
-4
2
= 1/(2x2x2x2)
=1/16
=0.0625
14
Negative indices
306.45 x
-3
2
15
Negative indices
306.45 x
1 / 2x2x2
=1/8
= 0.125
-3
2
1/8 306 divided by 8
306.45 x 0.125= 38.30625
38.25
16
BODMAS
Order of operations
BODMAS stands for 'brackets', 'of',
'division', 'multiplication',
'addition' and 'subtraction'. The
order in which a calculation is
carried out is important.
17
Here’s why BODMAS matters
What is 2 + 3 x 4?
(2 + 3) x 4 =
5 x 4 = 20
2 + (3 x 4) =
2 + 12 = 14
Two different answers!
Which one is correct?
18
What is 2 + 3 x 4?
(2 + 3) x 4 =
5 x 4 = 20
2 + (3 x 4) =
2 + 12 = 14
Why?
Because in the absence of brackets,
multiplication comes first.
19
Here’s why BODMAS matters
BODMAS stands for 'brackets', 'of',
'division', 'multiplication', 'addition' and
'subtraction'. The order in which a
calculation is carried out is important.
3 x (7 – 3) =
2x3–2x5=
50
2–5x4=
20
Don’t forget to check:
Prime numbers can only be divided by themselves and 1
What are the first ten prime numbers?
Factors of a number are the numbers that divide into it exactly
What are the factors of 12?
The multiples of a number are the numbers that belong to the
number’s times table.
What are the first five multiples of 3?
A square number is the product of the number multiplied by
itself.
21
For example?
Check also…..
1% = 1/100 = 0.01
5% = 1/20 = 0.05
20% = 1/5 = 0.2
25% = ¼ = 0.25
50% = ½ = 0.5
10% = 1/10 = 0.1
75% = ¾ = 0.75
12.5% = 1/8 = 0.125
22
What next?
You will be able to repeat your maths audit,
but do prepare.
Remember this is to give you confidence in
the classroom.
Teachers’ Standard 3: Demonstrate good
subject (and curriculum) knowledge
23