Mathematics K–6 · Years 5–6
Remainders in context: 50 shared into groups of 6
Number and algebra
The idea
The same division, 50 ÷ 6, has different answers in different situations: round up when everyone needs a place, drop the remainder when only full groups count, and split it into a fraction or decimal when the quantity can be cut.
What you need
- 50 counters and 6 paper plates per group
- a 50 cm strip of paper, a ruler marked in millimetres and scissors
- paper replicas of five $10 notes, and replica coins for one exchange: 4 × $2 and 4 × 50c
How to do it
- Share the 50 counters among the 6 plates one at a time. Record how many are on each plate and how many are left.
- Write the division and its check: 50 ÷ 6 = 8 remainder 2 and 6 × 8 + 2 = 50.
- Decide what the remainder means in three situations: 50 guests sit at tables of 6; 50 stickers are shared among 6 learners; a 50 cm strip is cut into 6 equal lengths.
- Cut the 50 cm strip into 6 equal lengths by measuring, and measure one piece.
- Share $50 in $10 notes among 4 people, exchanging the last note for the coins.
- Arrange 48 counters as 6 rows of 8 and write the four related facts for the array.
What you should see
Each plate gets 8 counters and 2 are left over. The guests need 9 tables, because 8 tables leave 2 people standing. Each learner gets 8 stickers and 2 are left. Each piece of the strip is 8 1/3 cm, which measures 83 mm to the nearest millimetre, so six pieces cut at 83 mm come to 498 mm and fall 2 mm short of the 50 cm strip, a third of a millimetre lost on each piece. $50 shared among 4 is $12.50 each: one $10 note each, and the last note exchanged for 4 × $2 and 4 × 50c gives each person another $2.50. The array shows 6 × 8 = 48, 8 × 6 = 48, 48 ÷ 6 = 8 and 48 ÷ 8 = 6.
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.
- 50 ÷ 6 = 8 remainder 2 means the answer is 8.2.
- A remainder is always written the same way whatever the situation.
Safety card
Hazards
- scissors
Controls
- cut seated at a table
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.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.