Two handfuls 2

Watch the video to see how to play

(Adapted from Ann Gervasoni, Monash University. reSolve - Counting handfuls)

Transcript

OK so I have my 36 pieces of pasta and what I'm interested in this time is thinking about those same ideas of how I can work out how many I have. But in this case, I know so we're working backwards.

Now with my 36 pieces, I can think about how I can arrange them into a particular form of structure that we call an array. So it'll form a rectangle where it will have equal rows and equal columns.

So, I could use what I know about 36 already to form an array. Or I could use some trial and error. I know that 36 is a square number and so to make 36 I can make 6 sixes and so I might start by making that rectangular array, which also happens to be a square.

OK, and so now I can see I have my collection of 36 and I can see that it's formed into 6 rows with six in each row. So there's one row, the next row, the third row, the fourth row, the fifth row and the 6th row. And in fact each of my columns also has six. So I can record 36 over here as 36 is 6 sixes.

And that describes my array.But what I wonder is, is there another way to organise my structure? So, I could try arranging them by fives now because I know I have five in each row and if I make another row down here... I can't quite make it when there's one left over so that way won't work for me. But I could maybe try with threes, because six and three 3 is half of 6.

OK, and now I've got a bit wonky, but I can still see that I have three in each row, so that means I can also say that 36 is 12 threes.

I wonder how many other ways you can find to organise 36.

Collect resources

You will need:

  • pencils/ markers

  • your mathematics workbook

  • pasta, counters, marbles or dried beans.

Instructions

  • Take 36 objects.

  • Form them into a rectangular structure so that you have equal rows and columns. We call this an array. Draw and describe your array using words and symbols.

  • Re-organise your pasta pieces so it forms a different rectangle. Draw and describe your array using words and symbols.

  • Keep re-organising your pasta pieces until there are no more arrays you can make. Draw and record all of your arrays.

  • Pick your favourite array and describe it using both multiplication and division. Record your thinking in your notebook.

  • Post the pictures of your arrays and share your thinking on our digital platform.

Share/submit

Share your work with your class on your digital platform.

  • Post your pictures or drawings.

  • Comment on the arrangements of others.