Number busting – number talk (renaming 26)

A thinking mathematically targeted teaching opportunity focussed on investigating part-part whole relationships to reorganise and and rename a collection

Syllabus

Syllabus outcomes and content descriptors from Mathematics K-10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2021

Outcomes

  • MAO-WM-01
  • MA1-RWN-01
  • MA1-RWN-02
  • MA1-CSQ-01

Collect resources

You will need:

  • 26 items (for example, pasta pieces, counters or pencils)

  • pencils or markers

  • your mathematics workbook.


Watch

Watch Number busting: number talk (renaming 26) video (2:00).

Investigate ways to reorganise and describe a collection of 26.

Speaker

Alright mathematicians, are you ready to have a look at number busting?

[On the table there are craft sticks. There are 2 larger bundles of 10 craft sticks and 6 single, separate craft sticks. The presenter picks up the 2 bundles of craft sticks to indicate that there are 10 in each bundle. She then separates the 6 single craft sticks into 2 groups of 3 before pushing them back together.]

So, I've got these bits of equipment, I just have to work out how many I have to start with. I'm pretty confident these are tens, so 2 tens and I can see 2 threes which make 6, so I think that's 26 because it's 2 tens and 6 more, which we would rename as 26. I can check that they're tens because if I fan them out a little bit, Ayesha showed me this strategy. I know that 10 is made up of 2 fives and that inside the 5 is 3 and 2 more so see 3 and 2 there and 3 and 2 there and so I know that's 10 if I measure that I know that's 10.

[The presenter grabs a bundle of 10 craft sticks. She fans them out to show the 2 groups of 5 within the bundle. The presenter then separates the group of 5 craft sticks to show that in the number 5 you can find 2 and 3. After placing the craft sticks down, she writes the ‘26 is …’ at the top of the page. The presenter separates the bundles. On the left she places the 2 bundles of 10 craft sticks. On the right, she places the 6 single craft sticks.]

So, I have 26. So now my goal is to bust it apart and record as many different ways that I can think of to think to rename 26 so I could do 20 and 6 so I could call that 2 tens and 6 ones.

[Underneath the craft sticks, the presenter begins to record her knowledge. She writes ‘2 tens plus 6 ones’. Underneath that she writes ‘1 ten plus 1 ten plus 6 ones.’]

So, 26 is. I could also bust it apart by saying one ten, another 10 and 6 ones, so one 10 plus one ten plus 6 ones. I could also say, oh, I know I could undo this one here and call all of those ones and say I have one ten and 16 ones which is 26.

[The presenter undoes one bundle of 10 craft sticks and groups that bundle with the six separate craft sticks to create 16. She writes a new observation, ‘one 10 and 16 ones’.]

I could also say and bust these all apart further and say what if I had 2 groups of 13 that would also be 26, so 13 plus 13 and I wonder what else you could come up with in ways of number busting 26.

[The presenter removes the elastic from the second bundle of craft sticks so that all of the craft sticks are separate. She divides the group into 2 groups of 13 craft sticks. She writes down a new observation, ’13 plus 13’.]

[End of transcript]

Instructions

  • Get 26 items (for example, pasta pieces, counters or pencils).

  • Organise and describe your collection.

  • Try to reorganise and describe your collection as many times as you can within the next 5 minutes.

  • Draw and record all of your ways of thinking about your collection.

  • Play number busting again.

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