## Monday, 11 January 2016

Draw out as much information as possible from the 3 sets of numbers.
e.g. characteristics these numbers; relationship
1. 25,  144,  169
2. 121,  3600,  3721
3. 49,  576,  625

1. They are all perfect cubes?

1. How would you test if they are perfect cubes?

2. And they can all be square rooted?

3. They are all perfect squares and also be square rooted.

1. Yes :)
Try to draw a 'connection'/ relationship between "perfect squares" and "square roots"

4. they are whole numbers

1. Yes.
What else?

5. They can be square rooted and there are all perfect square,whole numbers and i think positive integers

1. Yes. So, what relationship/ connection can be draw between "square roots" and "perfect squares"?
Next question: What's the difference between "whole numbers" and "positive integers"?

6. The first number plus the second number equals to the third number

1. Good observation.
Does this exist in coincidence? or if there's any special relationship amongst these 3 numbers (in each set)?

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8. There is an even number between two odd numbers.

1. Interesting observation :)
But is it by coincidence.
There exists a similar relationship for this set of number: 36, 64, 100

What other observations do you have?

9. 1. first 2 numbers summed up is the third. Can be square rooted

1. Good observation for both the summing up of the numbers and the square root.
Let's try generalising the relationship of these 3 numbers :)

10. all of them can be square rooted

1. Yes :)
How else can you connect the three numbers together?

11. The first no. plus second no. equal third no.

1. Yes :)
How else can you connect the three numbers?
Look closer at each number...

2. they are all perfect squares and can be square rooted
the first number plus the second number is the third number

12. Everyone say already if i type then it will be like i copy

1. Then don't read. Do the survey first then read other people's comments. That's what I did and I also found out that all my answers has already been mentioned and I also missed out a few. But as long as you are honest and you did not copy, there is nothing wrong and it is also impossible for everyone to have different answers

2. Well said, Jeffrey :)

Abigail:
It's a good practice to answer the question first before looking at what others have written so that your thoughts will not be clouded by what others said. On the other hand, that's how we learn from different perspectives :)

In addition, if you see my replies, you notice that no one actually had fully explained the relationships of the numbers yet.

13. The third number, when subtracted by the second number, is equal to the first number.

1. Yes.
What has 'caused' this relationship of these numbers?

14. They are perfect squares

1. This is an important observation.
Next step: How are these perfect squares related?

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16. Each set always has one number which is a multiple of 5

1. This is an interesting observation :)
We'll need to find out more to see if it's true after you learn to generalise the relationship of the three numbers.
What other observations can you draw from each set of numbers?

17. 1. They are perfect squares (all of them, set 1, 2 and 3)
2. They are positive numbers.
3. The first number plus the second nnumber equals to the third number.

1. Good - these are clear.
With these observations, try to generalise a relationship amongst the numbers (in each set)

18. Every set has 1 number that's a multiple of 5
Every number is a perfect square and can be square rooted
In every set, the 1st number + 2nd number = 3rd number
In every set, the 2nd number is an even number but the 1st and 3rd number are odd numbers
All numbers are positive integers (numbers above 0) but that's pretty obvious
That's all I could draw out from my calculator :)

1. Your listing is pretty thorough :)
On the other hand
- the position of the odd and even numbers do not matter (after you generalise the relationship amongst the three numbers)
- note it is not necessary that the three numbers would have a mix of odd and even number. There exists a similar relationship for this set of number: 36, 64, 100

So, having drawn out all these observations, the next step is try to generalise the relationship of these 3 numbers in each set.

19. Every set has 1 number that's a multiple of 5
Every number is a perfect square and can be square rooted
In every set, the 1st number + 2nd number = 3rd number
In every set, the 2nd number is an even number but the 1st and 3rd number are odd numbers
All numbers are positive integers (numbers above 0) but that's pretty obvious
That's all I could draw out from my calculator :)

1. This is a repeated post.

20. They are perfect squares and can be square rooted.
The third number is the sum of the first and second number.

1. Good observations.
Can you link the two observations and generalise it?

21. The first and second number add up equals to the third number. They are all perfect squares and can be square rooted to form a whole number.

1. Good observations.
Now, try to link these observations and generalise a relationship :)

22. The sum of all the numbers is an even number(9030) but when you subtract the two biggest number it becomes an odd number.