A few years back I took the workshop Mathematics in the PYP in The Netherlands. One of the learning experiences I took away and still use today was turning the multiplication tables into spirolaterals.
By doing this the students can:
-practice and learn their times tables
-see patterns in their times tables
-inquire into why some times table spirolaterals look similar to others
-predict how other times table spirolaterals will look based on the tables they have already done
I will share with you the process as well as some student samples.
I will use the 3 times table.
First list out the times table on paper.
Now we are only looking for single digit numbers, so any two digit numbers that appear, you need to add together until you get a single digit. Keep going until you see a repeated pattern.
12 = 1+2= 3
15 = 1+5=6
I can stop for now I see the pattern is 3, 6, 9
Now I take my number pattern to the graph paper.
Pick your starting spot and then draw a line 3 units right
Then 6 units down.
Then 9 units left.
Then 3 units up.
Then 6 units right
Then 9 units down
And so on and so on , UNTIL you get back to your original starting point.
This image created is your 3 times table spirolateral.
You can add color to it as well.
As the students continue they begin to see similarities between certain times tables and you can have them inquire into why that might be.
They also begin to think about larger times tables like the 27 times table, and predict based on what they know, what the spirolateral will look like.
Through this learning experience, students are:
-constructing their own meaning
-transferring meaning (into symbols)
-understanding and applying their knowledge
I have done this with grades 3, 4, and 5. Each time the students truly enjoy the experience and are engaged in their thinking and learning.
What do you think the 9 times table would look like? Have a go!