1. Developing Reasoning, Explanation and Fluency St Helens Teaching Alliance
Tara Loughran

3. Made to Measure – Ofsted 2012
Develop the expertise of staff
in understanding the progression in strands of mathematics over time, so that they know the key knowledge and skills that underpin each stage of learning

4. Schools should: increase the emphasis on problem solving across the mathematics curriculum Ofsted, 2012 Potential heavy users of mathematics should experience a deep, rich, rigorous and challenging mathematics education, rather than being accelerated through the school curriculum. A.C.M.E 2012

5. fosters mathematical understanding of new concepts and methods – this includes teachers’ explanations and the way they require pupils to think and reason for themselves
helps pupils to apply the mathematical knowledge and skills they have been taught, by solving a variety of mathematical problems
how well pupils apply their mathematical skills across the curriculum.

6. Review Plan Model the mathematics Practise the model Practise Games
Missing numbers
Word problems
Reasoning
Investigations
Decision making

7. Explanations in Calcualtion
Check my answers
Explain my diagram
Make the calculations from my numbers
Make the calculations from my digits
Decision making
Missing numbers in calculation
Which calculation if this is the answer?

8. Addition of 3 numbers

10.
7.05
10.02
11.91
11.82
13.44
What is the biggest total you can make?
What is the smallest total you can make?

11. What Calculation?

12. Use all my numbers

13. Replace my missing numbers
4 □ 5
○ ■ 9
7 8 ▲
2 □ 8
3 ■ 6
6 4 4
8 □ 7
● ■ 9
○ ■ ▲ 6

14. Are all my answers correct?
174 – 19 = 153
= 185
256 75
200
110 11
321

15. TU + TU TU – TU
What does this diagram show? 66 70 82

16. □ □ □ □ □ Largest total Smallest sum Answer that is a multiple of 10
□ □ □ □ □
Largest total
Smallest sum
Answer that is a multiple of 10
Answer that is a multiple of 3
Odd answer
Largest subtraction answer
Answer that is a multiple of 10 using subtraction

18. 21 16 28 23 40

21. 21

22. 13, 16, 19, 22, __, __ ___ , ___, 29, 34, ___ Something like this?
13, 16, 19, 22, __, __
___ , ___, 29, 34, ___
What’s my rule?

23. Understanding the score
Under features of good teaching it says:
When offering answers or accounts, the teacher expects pupils to give explanations of their reasoning as well as their methods. Pupils are challenged if their explanations do not reflect their ability.
Under features of satisfactory teaching it says:
Questioning is clear and accurate but does not require explanation or reasoning; pupils describe the steps in their method accurately but do not explain why it works.

24. Made to Measure
The best questioning probed pupils’ knowledge and understanding, with follow-up questions that helped pupils to explain their thinking in depth and refine initial ideas.

25. …. 23, 27, 31, 35 …. Sequences Here are some numbers in a sequence:
Will the following numbers be in the sequence: 3, 16, 21, 58?
Explain how you know.

26. Number boards

27. Questioning Whole class sessions Group sessions Playing games
Written questions
Marking
Children questioning

28. Questioning starts What would happen if….. What do you notice or see?
Why do we……
What is the same? What is different?
If you know …how could you find out…
How might you record that for someone else?
How can you be sure…..

29. Questioning Range of questions Always, sometimes, never true?
What can the answer be? not be ?
Why is this the odd one out?
If we know this, what else do we know?
Give me . . .tell me . . .show me draw me…
The answer is . . .what is the question?
Give me a silly answer for . . .?
Why is that a good mistake?

30. If you double the area of a rectangle, you double the perimeter.
If you add two whole numbers that end in 6 and/or 8, the answer will end in 2.
You can pay for a lolly that costs 15p using just 2p coins
The sum of two consecutive triangular numbers is a square number
When you double a number you get an even answer.
The product of two numbers is greater than either of the two starting numbers.

31. 3 4 5 7 10 12 16 17 60 64 96
120

32. Decision making
Modelling
Assessment
Application
Talk