Mathematics K–6 · Kindergarten
Sorting our shoes: a graph made of real objects
Statistics and probability
The idea
When objects are sorted into rows that start on the same line and each object takes one equal space, the longest row shows the most common group without counting.
Safety card
Hazards
- shoes on the floor are a trip hazard
Controls
- keep the graph area clear of walkways and put shoes back on at the end
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
- one shoe from each child in the group
- masking tape on the floor marking a baseline and, for each category, a row of equal squares big enough to hold one shoe (about 25 cm)
- category cards written by the group (for example laces, velcro, slip-on)
How to do it
- Decide a question: which kind of shoe fastening is most common in our group today.
- Each child places one shoe in the next empty square of the row for its category, starting from the square on the baseline, one shoe to a square.
- Look before counting: which row is longest, which is shortest, are any rows the same.
- Count each row and write the number on its card. Check that the numbers add up to the number of children.
- Answer the question in a sentence, then ask a new question (which colour is most common) and rebuild the graph.
What you should see
The rows start level and every shoe takes one equal square, so the longest row is visibly the most common category before anyone counts, even though the shoes are different lengths. The row counts add up to the number of children in the group, one shoe each. Children can say how many more shoes are in the longest row than the shortest by matching shoes one to one.
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.
- A row that is spread out has more shoes than a row that is packed together.
- The row that is nearest to me is the biggest.
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-DATA-01MAO-WM-01
- Australian Curriculum v9AC9MFST01
Sources
The pages the author read to write this activity.