Playing with numbers

Every now and then, Tiger and I get slightly bored by how maths is done at home and both of us want to make changes to how we do maths.  It seems that we have come to a point where I am comfortable with Tiger's grasp of the fundamental concepts in elementary maths that we can afford to be more adventurous in taking detours from our usual maths routine.

Rather than playing random maths games (nothing wrong with that), I am inclined to take a thematic route in this area.

We started with the topic of "numbers".  The first activity we did was to make a number chart puzzles.  This was intended to help cement the concept of consecutive whole numbers.

First I printed off a number chart of whole numbers from 1 to 100, and had Tiger block out different sections with coloured pencils (to be cut out later) to make the puzzle.

The first one with consecutive whole numbers was too easy, so we did another in multiples of 10.

That was just warm-up.  Next, we played all the games found on this page.  These games were fun refreshers for Tiger in the concepts of multiples and odd and even.  His favourite game was Read My Mind.

Tiger and I found more challenges and satisfaction at solving maths puzzles that require a combination of different skills, which involve mathematical thinking as well as visualisation skills.  The four puzzles we worked through together were:

1. Make 37 (main concept: odd and even numbers)

2. Mystery Matrix (main concept: multiplication)

3. Consecutive Numbers (main concept: addition and subtraction)

4. Magic Vs (main concept: odd and even numbers)

We love these maths games!  They tend towards the abstract side of mathematics, which helps if you have strong maths foundation and visualisation skills.  Manipulatives don't work so well to solve such puzzles.  Additionally, it is also a very involved process for parent and child in that we would discuss, debate, and argue about how we would approach the problem, before solving it together.  Discussion is a big part of the learning process for such puzzles (at least in our case), so I don't think these puzzles will be as effective without parental involvement.  We find the process to be very interesting and mutually beneficial in that Tiger can apply his intuitive problem-solving skills while I can observe and learn more about the way he thinks, which is very different from my thinking process.

Tiger can pretty much hold his own in our maths discussions now due to his strong intuitive and visualisation skills in solving maths problems, while I bring logic and methodology to the table.  So far, this has worked very well for us.

Another number game that Tiger has taken an interest in is Sudoku.  He takes the book with him and solves a few puzzle on the go each time we are out and about.

This post is linked up to:
1) All Year Round Blog Carnival: Winter 
2) Hearts for Home Blog Hop #5
3) Homeschool Mother's Journal: February 22, 2013
4) Hobbies and Handicrafts - Feb 22
5) Collage Friday - Family, History, and More
6) TGIF Linky Party #64
7) It's a Wrap
8) Weekly Wrap-Up: The One with the Busy Break Week
9) Share it Saturday - Feb 23
10) The Sunday Showcase - 2/23/13
11) Math Monday Blog Hop #88
12) Hip Homeschool Hop - 2/26/13

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