2. Aims of the Session
To build understanding of mathematics and it’s development throughout KS2
To have a stronger awareness of when and how to progress from non-formal to formal methods at the appropriate stage for your pupils (and the pitfalls of formal methods)
To enhance subject knowledge of the pedagogical approaches to teaching mathematics

3. What comes first? Fractional Understanding? Equal parts
Larger denominators means smaller parts
Year 3
recognise that tenths arise from dividing an object into 10 equal parts and in dividing one – digit numbers or quantities by 10.

4. What comes first? Place Value and scaling? Dienes Place Value Counters
Bead bars and beadstrings
Money (problem solving)
Counting
Other ideas?
3 times
as tall

5. The Decimals & Percentages Journey
Visual Appreciation
Formal Operations
Informal Operations
Rounding Decimals
Equivalence between Fractions, Decimals & Percentages
Percentages
Try to have consistent approaches across year groups.

6. Count spaces or lines? What's the difference?
Appreciation of Decimals
Year 3
Pupils connect tenths to place value, decimal measures - Sort place value first –
Make early links
Use Dienes Creatively
Count in tenths: Prepare for misconceptions when bridging units… U
1 10
Need to use the lines when counting in decimals – so that there are values between the points
Count spaces or lines? What's the difference?

7. Possible misconception
Appreciation of Decimals
Year 4
Recognise and write decimal equivalents of any number of tenths or hundredths - Count in tenths
Count up and down in hundredths and be able to compare (differentiation opportunity)
Plan for misconceptions when bridging units & tenths! 
Possible misconception

8. Appreciation of Decimals
Year 5
And on to thousandths… providing pupils have understood the build up in year 3 and year 4, this will be a natural progression.
But, if pupils have had difficulty, differentiation is needed – some might need to be more “hands on” with kinaesthetic resources, others will appreciate visually on a number line.

9. Comparing & Ordering Decimals
Year 5
Read, write, order and compare numbers with up to 3 decimal places
Just add zeros and make the numbers all the same length????
Good diagnostic question: “Which is bigger: 0.2 or 0.20?”
“Which is bigger: 0.47 or 0.470?” U T H
1 10
1 100

10. Formal Operations Year 4
Multiplication and division by 10, 100 and 1000 (starting with a one or 2 digit no.)
Year 6
Multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 dp
How many places does the decimal point move??
Sliders - let them see and do it!!
Try the following on your sliders - What misconceptions or problems could arise?
With Slider: a) 2.3 x 100 b) 1.2 ÷ 10 c) 1.8 ÷ 100 d) 6060 ÷ 1000
Without Slider: e) x 100 f) 3 ÷ 100 U T H
1 10
1 100
Top Marks
Moving Digits

11. Addition & Subtraction
Year 5
Practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places
Why does the column method work??
e.g U
1 10
1 100
Physical – Visual – Dual - Formal Written

12. Addition & Subtraction
Year 5
Practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places
Why does the column method work??
e.g U
1 10
1 100
Physical – Visual – Dual - Formal Written

13. Multiplication & Division
Year 6
Multiply one-digit numbers with up to 2 decimal places by whole numbers
Why do the written methods work??
e.g 1.25 x 3 1
0.2
0.05 3
1 10
1 100 U 1
0.1
0.1
0.01
0.01
0.01
0.01
0.01 1
0.1
0.1
0.01
0.01
0.01
0.01
0.01
Column method – multiply the whole numbers and putting decimal point back in - do they realise that it is scaling up and down 1
0.1
0.1
0.01
0.01
0.01
0.01
0.01
Physical – Visual – Dual - Formal Written

14. 3 7 . 8 6 Multiplication & Division Year 6
Use written division methods where the answer has up to 2 decimal places
Why does the bus stop method work??
e.g 7.86 ÷ 3
1 10
1 100 U 1
0.1
0.01 1
0.1
0.01 1
0.1
0.01 1
0.1
0.01 1
0.1
0.01
What about 121 ÷ 4 1
0.1
0.01 1
0.1
0.1
Physical – Visual – Dual - Formal Written

15. Informal Operations Year 4 Solve simple measure and money problems
Mentally add and subtract decimals and whole numbers and decimals.
Work with complements of 1 (eg: =1).
Use real money first! Can we use scales?
Progression of examples with money - in what order would you do these??
£7 - £4 £ £ £ £3.53
£ £0.30 £ £ £ £3.43
£ £ £1 + £2 £4 - £ £10 - £3.27
Number bonds to 10 and 100 are key!!

16. Rounding Decimals
This journey should have started in Year 3 and 4 as you build up to be able to round any whole number to the nearest 10, 100, 1000
Round 185 to the nearest 10, 100, 1000
NB – which ten is “closest” to 185

17. Rounding Decimals Year 4
Round decimals with 1 decimal place to the nearest whole number
e.g. 1.7 to the nearest whole number:
Year 5
Round decimals with 2 decimal places to the nearest whole number and to 1 dp
e.g to the nearest whole number and to 1 d.p.
e.g to the nearest whole number and to 1 d.p. (Misconception opportunity?)
Extension: Round 9.99 to the nearest whole number and to 1 d.p.
Year 6
Solve problems which require answers to be rounded to specified degrees of accuracy.
e.g. Two-stage problems – 1st stage = calculation, 2nd stage = round appropriately.

18. Equivalence between FDP
Year 4
Recognise and write decimal equivalents to 1/4, 1/2, 3/4
Year 5
Understand what percent means
Know percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5
Percent - What does it mean?
What can the pupils relate it to in their prior learning?
How can we use this to find simple equivalents?

19. Equivalence between FDP
Year 5
Write percentages as fractions
Year 6
Associate a fraction with division and calculate fraction equivalents
Recall and use equivalences between fractions, decimals and percentages
%  Fractions 17% = 78% = 48% = 3.5% =
Fractions  % = = = =
Decimals  % = = = =
%  Decimals 70% = 7% = 0.7% =
Fractions  Decimals = = = =
FDP National Strategy
Interactive FDP and compliments
Starters: Equivalent Fractions and x & ÷ by 100
Allow pupils the chance to explore

20. Percentages of an Amount
Year 6
Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360]
50, 75, 25

21. Percentages of an Amount
Year 6
Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360]
Based on 10
Percentage strips

22. Aims of the Session
To build understanding of mathematics and it’s development throughout KS2
To have a stronger awareness of when and how to progress from non-formal to formal methods at the appropriate stage for your pupils (and the pitfalls of formal methods)
To enhance subject knowledge of the pedagogical approaches to teaching mathematics

23. Where now? I am going to trial/action... * Where next?
Disseminate amongst colleagues