Halloween: Investigations

Do you know how the festival of Halloween came about?  It has an interesting historical beginning going all the way back to the pagan rituals of the Celts, which were adopted by the Christian church, followed by its development into a major festival in America:

Following the historical investigation into the origins of Halloween, we undertook a Halloween-themed mathematical investigation.  The maths problem looks deceptively simple, but it is a good training for logical, systematic thinking, and is the beginning of the concept of combinations and permutations.

Mathematics at the elementary school stage is a lot about common sense, so Tiger has no problem visualising what the solution is.  In fact, he could work out in his mind (some call it intuition) and tell me the answers to the different parts of the problems - and they were correct answers when we checked later using the spreadsheet.  When I asked him to explain how he got the answers, he couldn't tell me why.  This was not a new phenomenom and I used to let that pass.  I was happy as long as he consistently arrived at the correct answer.  However, as Tiger grows older, I think it is important for him to develop different ways to communicate his solution.

With me acting as his scribe, Tiger started to narrate how he would go about solving the problem.  The process soon became a discussion as we determined together the best way to represent his solution.  We started with working out the solution on paper, but soon realised that if we were to answer all the questions in the problem, we would have to find a more efficient way to work it out.

As Tiger has been playing around with Excel spreadsheet on his own for a while, he has some idea that the spreadsheet can be used to represent and solve maths problems.   We then spent an hour or so on Excel, with Tiger learning software user skills that include:

• how to represent data in a table
• how to format tables
• how to cut and paste
• how to use simple spreadsheet formulae as short cuts to represent the logic of the solution

Tiger was fascinated by the spreadsheet's ability to represent his solution visually, so he did not mind spending an hour to work out the answers on the computer when he could have given the same answers in a few minutes in his mind.  I am also not convinced that it is necessary to show step-by-step procedures to every maths question therefore we will only do so for the following reasons:

• to train Tiger's communication skills
• to learn a new skill, e.g. how to use spreadsheets

This post is linked up to:
1) Math Monday Blog Hop #71
2) Hip Homeschool Hop - 10/23/12
3) All Year Round Blog Carnival: Autumn
4) Enchanted Thursdays Blog Hop #36
5) History and Geography Meme #47
6) Homeschool Mother's Journal: October 26, 2012
7) Collage Friday
8) Favourite Resources: October 26, 2012
9) TGIF Linky Party #53
10) It's a Wrap
11) Weekly Wrap-Up