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Mathematics K–12

Sam and Holly's problem

A thinking mathematically context for practise opportunity, focussed on using reasoning and additive thinking to work out hidden quantities

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, 2023

Outcomes

  • MAO-WM-01
  • MA1-CSQ-01

Collect resources

You will need:

  • something to write on
  • something to write with
  • 2 cups (optional)
  • 10 blocks or counters (optional).

Read about Sam and Holly playing a game

Sam and Holly were playing with combinations of numbers that make 10. They started by getting out 10 blocks.

2 rows of 5 blocks 2 rows of 5 blocks
Image: 2 rows of 5 blocks

Then, Sam covered some of the blocks and Holly had to work out how many were missing.

An upside down cup and random 7 blocks on the side An upside down cup and random 7 blocks on the side
Image: An upside down cup and random 7 blocks on the side

Holly decided she to organise what she could see to help her work out what was missing.

An upside down cup and a row of 5 blocks and a row of 2 blocks below it An upside down cup and a row of 5 blocks and a row of 2 blocks below it
Image: An upside down cup and a row of 5 blocks and a row of 2 blocks below it

She imaged a ten-frame in her head and organised the blocks. This helped her see she needed 3 more to make 10.

Holly and Sam kept taking turns like this until Holly asked Sam if they could make it more challenging for them.

Watch

Watch Sam and Holly's problem video (1:06).

Make a game involving hidden numbers more challenging.

[On a grey carpet, 10 small green cubes are arranged in 2 columns of 5 each. On the right, 2 white coffee mugs are turned down on the carpet.]

Sam

Hi, Holly.

Holly

Hi!

Sam

Do you want to play a game?

Holly

Yeah.

Sam

Sure. So we're gonna start off. Can you just tell me how many are here?

Holly

10.

Sam

Alright. So I'm going to take some, put it under a cup, OK?

Holly

Is there a way you can make it a bit more harder for my brain?

Sam

Sure. Alright, so I'll do this. Alright. So close your eyes, OK? So don't peek. Close your eyes. Alright.

[A hand reaches over and takes 7 of the green cubes to put under the 2 mugs.]

Sam

So... So how many do you think is left? How many do you think are in here?

[Can you help solve Holly’s problem?’ In the bottom right, a white NSW Government ‘waratah’ logo.]

[Black text on white reads ‘How many cubes are hidden?’ and ‘How many cubes might be under each cup?’ Below, a colour image of the 2 white coffee mugs turned down and 3 green cubes to the left.]

[White text on blue reads ‘Over to you!’]

[The NSW Government waratah logo turns briefly in the middle of various circles coloured blue, red, white and black. A copyright symbol and small blue text below it reads ‘State of New South Wales (Department of Education), 2021.’]

[End of transcript]

A problem for Holly

Sam made this for Holly to think about.

2 upside down cup and 3 blocks on the side 2 upside down cup and 3 blocks on the side
Image: 2 upside down cup and 3 blocks on the side

Instructions

  • Can you help Holly work out how many blocks are hidden?

  • Can you help her work out how many of the hidden blocks might be underneath each cup?

  • What are all the possibilities? Record your thinking.

Discuss

  • What possibilities did you find?
  • Could you work out exactly what Sam put under each cup for Holly?
    • Why?
    • Why not?

Share and submit

Share your work with your class on your digital platform. You may like to:​

  • write comments​

  • share pictures of your work​

  • comment on the work of others.

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