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Published 2011
I liked it because the problem made me think harder than I have in a Maths lesson this year!
It's something different to just writing out sums in books.
I liked it because it was hard.
I enjoyed doing a problem that was impossible.
I like the problem because it was very challenging.
I liked it because you get 36 or 38 so you get determined to get 37.
Yes, as soon as I started I knew I wanted to finish it. I liked thinking about it.
The maths problem was very frustrating and I enjoyed it. It was fun because you learnt how odd and even numbers work.
Working in silence; having longer thinking time at the beginning.
Talking to more than one person.
A number line.
A calculator.
Think about odd numbers and even numbers.
Think of what happens if you add 2 odd numbers together.
Think and see if you can get up to thirty with seven numbers.
I was more trying to add together than looking at the numbers?
I don't really like doing maths problems and it was impossible to do which made it worse.
Being an impossible problem there is no point in doing it because it is pointless sitting there for ages stuck.
Was quite annoying when you found out it was impossible.
I love maths and enjoy it very much u gave me that problem to work out and I could't so I was enoyed, but then u tell me its impossible its such a waste of time and effort and Im very enoyed. (sic)
A clue to point in the direction of impossibility.
There is no answer.
Don't think it can definitely be done.
U can't do it.
Telling me it was impossible might!!
odd + odd = even
Spend a few minutes "playing with the problem", trying different numbers.
Have you kept a record of the totals "made"?
What do you notice about your totals?
What can you say about these types of numbers?
Can you make 37 with a different number of numbers? How many?
Can you explain why?
If we imagine learners and mathematics as separated by a gap, and the teacher's job as bringing the two together, then we are talking about the difference between adapting the mathematics so that it can be more easily taken into the world of the learner, and adapting the habits of the learner and classroom so that the learner may be taken more easily into the world of mathematics.
Don't expect to know what to do immediately,
Try the problem, get your hands dirty... work in rough... talk to someone...
Would making a sketch, a drawing, a table, some notes help?
All the time think, explore... do you notice anything?... any patterns?
Then, step back from the problem...
Really stuck? There are hints available...
Talk to others about what you have done and found out.
Fibonacci Factors
In the Fibonnaci sequence each term is the sum of the two terms before it:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
Where do the even numbers come in the sequence?
Is there a pattern? Why?
You can discuss how you are getting on with the problems, and give each other hints, BUT DON'T GIVE AWAY THE ANSWERS!
If you want to check your solution agrees with someone else, you can post it in white "ink". That way, people still working on the problem won't see it, but those who want to can see it by selecting that bit of text.