1. Something to be getting on with…
Four expressions of the form ax + b are added together in pairs.
All of the possible outcomes are
3x x x + 3
6x x x + 4
What are the four expressions?
One answer to the problem is on the final PowerPoint slide. You may wish to give your groups a clue such as a and b are both positive integers.

3. Fiona Allan fiona.allan@ncetm.org.uk

4. 10.30 – Who we are etc – Exploring Questioning – Sharing resources (continued during lunch) – The Challenges you have faced this year – Working with vocational learners and teachers – Useful things – Evaluations

5. Introductions Who we are Where we teach Who we teach How much we teach
Draw a picture of yourself and name it and put it in the gallery (opposite a number)
On a map of England, put a coloured dot where you teach, with your number on the dot.
Each person takes a post-it and sticks it on a bar chart to show the number of hours a week they teach.
On a bar chart with possible courses along the bottom, they stick on post-its to make a bar chart against these possible courses and add any other as needed.

6. Session 1 – Exploring questions
This session aims to support you in considering
What makes a good question?
Why might we ask different types of question?

7. Standpoint activity
Work in pairs
Choose one person to be A and one person to be B
Person A is going to argue against the following statement
Person B is going to argue for the following statement.
Ignore your personal beliefs and opinions for this activity!
The great thing about questions in maths lessons is that they’re black and white. An answer is either right or wrong. There’s no middle ground.

8. If a + b = 8, what might be the values of a and b?
Why ask questions?
What’s the same and what’s different about these two questions? What information might you gather from a learner’s response?
If a = 2 and b = 6, what is a + b?
If a + b = 8, what might be the values of a and b?

9. If a + b = 8, what might be the values of a and b?
What do the questions question?
The aims of the new Key Stage 4 Programme of Study are stated as ensuring that all learners:
become fluent in the fundamentals of mathematics
reason mathematically
can solve problems
Which of these aims do these two questions address? Do they fit neatly into one category?
If a + b = 8, what might be the values of a and b?
If a = 2 and b = 6, what is a + b?

10. If a + b = 8, what might be the values of a and b?
Why ask questions?
What’s the same and what’s different about these two questions? What information might you gather from a learner’s response?
If a = 2 and b = 6, what is a + b?
If a + b = 8, what might be the values of a and b?

11. What do the questions question?
Become fluent in the fundamentals of mathematics
Reason mathematically
Can solve problems
Place the questions from Resource Sheet 2 in this Venn Diagram
Is there a question in every intersection?
If not write a question (or questions) that will fill the gaps

12. Finding out by questioning
Work in pairs on Calculator Mistakes How did the learners arrive at their answers?

13. Tops tips
Write a Top Tips poster for learners on Using a calculator

14. Ofsted ‘Made to Measure’ (May 2012)
51. In the very best [institutions], all lessons had a clear focus on thinking and understanding... Teachers’ explanations were kept suitably brief and focused on the underlying concepts, how the work linked with previous learning and other topics and, where appropriate, an efficient standard method. Their questions were designed to encourage [learners] to give reasoned answers.

15. Ofsted ‘Made to Measure’ (May 2012)
A common feature of the satisfactory teaching observed was …. teachers typically demonstrated a standard method, giving tips to [learners] on how to avoid making mistakes and, sometimes, ‘rules’ and mnemonics to help them commit the methods to memory. Many of their questions concerned factual recall so that [learners]’ ‘explanations’ often consisted of restating the method rather than justifying their answers.

16. Ofsted ‘Made to Measure’ (May 2012)
81. The best questioning probed [the learners’] knowledge and understanding, with follow-up questions that helped pupils to explain their thinking in depth and refine initial ideas.

17. Ofsted ‘Made to Measure’ (May 2012)
204. Where satisfactory teaching dominated, [the learners] … relied on memorising methods, because teachers emphasised emulating the worked examples rather than why the methods work. Most of the teacher’s questions required factual answers only.

18. Ofsted ‘Made to Measure’ (May 2012)
225. Prime practice ‘Why?’, ‘How?’, ‘What if?’ questions ensured that [the learners] thought deeply about what they were learning

19. Effective questioning
‘Questions and Prompts for Mathematical Thinking’ Anne Watson and John Mason. Published by ATM. ISBN X.

20. Change one aspect of … so that …
Change one aspect of the equations
so that the lines do not cross in the first quadrant.

21. Give me an example of … now give me another example…
Give me an example of … now give me another example…. Now give me a general example ….
Give me an example of a line which passes through the point (3,-5)
Give me an example….a peculiar example…a general example

22. Is it always, sometimes, or never true.…?
Is it always, sometimes, or never true that the product of the x-axis intercepts of a quadratic curve is equal to the y-axis intercept?
Now use the two way table.

23. Tell me a property that … must have so that …
Tell me a property that a and b must have so that the line does not pass through the fourth quadrant

24. What is the same and what is different about …?
What is the same and what is different about and ?

25. This is the third picture in a sequence
This is the third picture in a sequence. What might the fifth picture look like?

26. This is the second picture in a sequence…

27. Make up an easy example… now make up a hard one.
Changing the subject of a formula…
Make x the subject of
Solving quadratic equations?

28. Inverse processes
The line in the box passes through the points in the circles adjacent to it

29. How could this question have been made harder?
On the grid, A is the point (0,1).
The midpoint, M, of AB is (2,7).
The gradient of AB is 3.
C is on the y-axis and CB is parallel to the x-axis.
(a) Find the coordinates of point B
(b) Work out the equation of the line through C that is parallel to AB.
Based on question 16
What could part (c) of the question be?

30. Probing questions Probing questions can expose misconceptions
Use the question stems on the sheet to write some probing questions for a lesson or topic that you’re teaching next week

31. Sharing Resources

32. Lunch and networking

33. Challenges
List on Post-It’s the challenges you have faced this year. Divide them into two piles – those challenges that you feel you overcame and those you didn’t
The ones that they overcame, can be put onto a poster.
The others should be collected and sorted into types.
Go through the pile asking the group to respond to the challenges – what would they have done? OR divide the group into new small groups and give each group some of the challenges to respond to.

34. Working with vocational learners
Stick the photograph in the middle of the flipchart paper. Around the photo write all the tasks that a vocational learner might link with the photograph

35. Working with vocational learners
Now using a different coloured pen, write down underneath each task any maths that they will need to complete the task.

36. How much shampoo does a hairdressing salon use in a year?

37. You are responsible for the Meals-on-Wheels deliveries in your local area. How many drivers do you need?
Choose either 34 or 35

38. Plenary What mathematical topics were explored here?
What did you like about this Activity?
How does this Activity allow for differentiation?
How might you adapt this activities for use with a group of learners / individuals?

39. Useful videos for the start of a topic
Explore the Maths at Work videos

40. A new landing page!
FE and Skills sector landing page accessed from
Explore new site with them

41. Anything you can share/suggest?
Please upload any resources and post ideas to ETF Maths Incentive –Graduates Community

42. Please complete your evaluations
Thank you
Please complete your evaluations
Is the solution unique?
5x+1
x+5
2x+3 2x
The answer to the first puzzle of the day is…