Mathematics K–6 · Kindergarten
Under the cup: the parts that make a number up to 10
Number and algebra
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The idea
A collection can be split into two parts in several ways, and knowing one part and the whole tells you the other part.
Safety card
Hazards
- counters are a choking hazard for young children
Controls
- count counters out and back in; supervise
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
What you need
- 10 counters
- an opaque plastic cup
- a part-part-whole mat (a large circle with two smaller circles beneath it) drawn on card
- pencil and a recording strip
- a blank ten-frame mat (2 rows of 5 squares) for the whole of 10
How to do it
- Count out 7 counters together and place them in the whole circle. The child closes their eyes while the adult puts the cup over any number of the counters, from none of them to all 7, and keeps the rest showing, so that the pairs 0 and 7 and 7 and 0 can be found as well as the six pairs between them.
- The child counts the counters showing and says how many are hidden. Lift the cup to check.
- Record the pair on the strip as two numbers, for example 4 and 3. Repeat until the child finds every pair, then ask whether any pair is missing.
- Repeat with 5, 8 and 10 counters. For 10, place the counters on the ten-frame mat before hiding some, so the empty cells show the hidden part.
- Swap roles so the child hides and the adult guesses, and the child checks the answer.
What you should see
For 7 counters there are 8 ordered pairs (0 and 7, 1 and 6, up to 7 and 0); for 10 there are 11. A child who works systematically fills the strip in order and notices when one pair is missing. After several rounds the child names the hidden part without counting the visible part from one, for example seeing 5 and saying 2 for a whole of 7.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- The hidden counters have gone, so the whole is now the number showing.
- There is only one way to break a number into two parts.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMAE-CSQ-01MAE-CSQ-02MAO-WM-01
- Australian Curriculum v9AC9MFN04AC9MFN05
Sources
The pages the author read to write this activity.