A Project on Critical Thinking in Mathemtics

1. Critical Thinking Project
by Chris Hook

2. 1 2 3 4 5
Before you give me an answer, think for a few minutes.
Write the number on your white board.
Which is the odd one out and why?

3. 1 2 3 4 5
Who thought it was the last one that was different?
Did anyone have a different opinion?
Which one did you think was the odd one out?
Why did you think that?
Is there anyone who had another one that they thought
was the odd one out?
Which is the odd one out and why?

4. A set of 5 numbers has a
Mode of 24
Median of 21
Mean of 20
What could these 5 numbers be?

5. A set of 5 numbers has a
Mode of 24
Median of 21
Mean of 20
 What could the numbers be?
 How could you start?
 What could you write down first from this information?
 What other numbers can you put place from this
information?
 Can you work out what the numbers are?

6. Is 40% of 90 the same as 90% of 40?
Quick answer yes or no
Why do you think that?

7. Is 40% of 90 the same as 90% of 40?
?
 Have a go and check it out – were you correct?
 Prove to me that it is/isn’t the same.
 Will it work with other percentages?
 Try to work out a few other percentages –
 Did they work?
 Can you give a reason why/why not? (justify!)

8. Is 40% of 90 the same as 90% of 40?
Continued.
 Will this work for all percentages like this?
 If so why? If not why not?
 Explain
 Does it work for any numbers?
 Did you try any fractions or decimals?

9. Can you solve this without a calculator?
36 x 175 ÷ 63

10. Can you solve this without a calculator?
36 x 175 ÷ 63
 Did you notice any connection between 36 and 63?
 What do you know about multiples of 3?
 How might this help you?
 Would it help to write it as a fraction like this?
 36 x 175
 63
 Or would it help to factorise each of the numbers

11. What number when multiplied by itself
is equal to 27 x 147?
 What type of number are you trying to find?
 What is the name for this type of number?
 How would you do this?
 What method would you use?
 Is there a way that might make this easier to
solve?
 What will the last digit be? why?
 Did you do it differently to check your answer?
 Is it going to be a big number or a small number?

12. What number when multiplied by itself
is equal to 27 x 147?
 Would factorising these numbers help you?
 How could we work this out without a calculator?
 Estimation?
 Prime decomposition?
 When you think you have found an answer:
 You are allowed to check your answer with a calculator.

13. I have written a whole variety of questions
of varied topics for three different levels
Foundation, Intermediate and Higher -and
am still writing them and possible teacher
prompts.
Here are a few others

14. What can you see in this diagram?

15. What can you see in this diagram?
 Can you name the shapes?
 What do you know about the properties of these
shapes?
 Interior/ exterior angles?
 Can you work out the size of the interior angles of
each of them?
 Looking at the labelling - what do you think the
question might be asking you to do?
 Is there a reason that only a few letters have been
used on the diagram?
 When might we only use letters like this?

16. The question actually asks you to find the angle KLM
Did you guess that?
How could you find that?
Talk about it in your group and see if you can come
up with an answer.
Show your workings and explain what you are doing
in a concise way.

17. The Perimeter of this triangle is 20cm
One side is 4cm and another is 7cm.
Is it a right angled triangle?

18. Write a GCSE question for this diagram
40°
8cm

19. The area of the shape is 48 units. Work out
possible coordinates of the vertices.
8 P Q
0
R S
>
>