1. Post Graduate Induction Day May 2018 Subject Knowledge Workshop
Number
Greater than less than
Neg numbers PV
Decimals
Indices and powers
BODMAS
A few reminders

2. Today’s workshop Today’s workshop Based on the subject audits
Confidence-building
Teachers’ Standard 3: Demonstrate good subject (and curriculum) knowledge

3. Are you sure about these symbols?
Quick check 1
Are you sure about these symbols?
> < =
What could you do to help you visualise? Draw a thermometer.

4. Quick check 2 Multiplying positive and negative numbers
I’m sure I once learned something about that!
If the signs are the same the answer is positive
If the signs are different the answer is negative

5. Negative numbers x and /

6. Negative numbers Addition e.g. Calculate; - 12 + 4
Which number is greater?
Will it be a positive difference or negative difference?
Adding and subtracting are, from one viewpoint, the same thing. Subtracting a number is the same thing as adding the negative of that number. For example, 4 – 12 is the same as 4 + –12 (which, because the order of terms doesn't matter with addition, is the same as –12 + 4). With that in mind, here are the rules for adding with negative and positive numbers:
Here too, you can just count on from -12 to 8.
If both numbers are positive, then the answer is positive.
If both numbers are negative, then the answer is negative.
If the numbers have different signs, the answer takes the sign of the higher number.
Subtracting a negative number is the same as adding the positive of that number. For example, 5 – –4 is the same as
greater than minus 5 because it’s to the right on the number line

7. 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?

8. 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)
– 4 – (– 8)

9. How’s your understanding of place value?
Quick check 3
How’s your understanding of place value?
Draw a PV chart from 1 million to 100 thousandths

10. Place Value chart
etc

11. How many times larger is the red digit than the blue digit?
Quick check
How many times larger is the red digit than the blue digit?

12. Quick check
(10x larger) 8.0 (100 times larger) 80.0 (1000 times larger)

13. Year 4
Year 5
Year 6
count in multiples of 6, 7, 9, 25 and 1 000
(copied from Number and Place Value)
count forwards or backwards in steps of powers of 10 for any given number up to
recall multiplication and division facts for multiplication tables up to 12 × 12
MENTAL CALCULATION
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
multiply and divide numbers mentally drawing upon known facts
perform mental calculations, including with mixed operations and large numbers
recognise and use factor pairs and commutativity in mental calculations (appears also in Properties of Numbers)
multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
associate a fraction with division and calculate decimal fraction equivalents (e.g ) for a simple fraction (e.g. 3/8)
(copied from Fractions Progression Map)
Commutativity: Is the Law that says you can swap numbers around and still get the same answer when you add. Or when you multiply. Examples: You can swap when you add: = You can swap when you multiply: 2 × 4 = 4 × 2
Section of the Multiplication and Division progression map from:

14. 24 = 2 x 2 x 2 x 2 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.
24 = 2 x 2 x 2 x 2

15. Indices and powers
43 x 32 4 x 4 x 4 = 3 x 3 =

16. Indices and powers
53 x 23

17. 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.
‘Of’ = ‘orders‘ (or powers)

18. Here’s why BODMAS matters
What is x 4?
(2 + 3) x 4 =
5 x 4 = 20 or
2 + (3 x 4) =
= 14
Two different answers!
Which one is correct?

19. What is x 4?
(2 + 3) x 4 =
5 x 4 = 20
2 + (3 x 4) =
= 14
Why?
Because in the absence of brackets, multiplication comes first.

20. 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) =
2 x 3 – 2 x 5 =
– 5 x 4 =

21. 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.
For example?

22. Check also…..
1% = 1/100 = % = 1/20 = % = 1/10 = % = 1/8 = 0.125
20% = 1/5 = 0.2
25% = ¼ = 0.25
50% = ½ = 0.5
75% = ¾ = 0.75
Make link to PV chart

23. 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

24. Key Stage 2 SATs