Mathematics K–6 · Years 5–6

Remainders in context: 50 shared into groups of 6

Number and algebra

PracticalLow risk

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

  1. Share the 50 counters among the 6 plates one at a time. Record how many are on each plate and how many are left.
  2. Write the division and its check: 50 ÷ 6 = 8 remainder 2 and 6 × 8 + 2 = 50.
  3. 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.
  4. Cut the 50 cm strip into 6 equal lengths by measuring, and measure one piece.
  5. Share $50 in $10 notes among 4 people, exchanging the last note for the coins.
  6. 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

Low riskLearners carry it out

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.

  • Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-MR-01MAO-WM-01
  • Australian Curriculum v9AC9M5N07AC9M5A01

Sources

The pages the author read to write this activity.

  1. curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/outcomes
  2. vocabulary.curriculum.edu.au/MRAC/2024/04/LA/MAT/a5d5191d-21a6-4a3c-8219-e1a5234d3ba0
  3. www.mathematicshub.edu.au/planning-tool/5/number/efficient-strategies
  4. amsi.org.au/teacher_modules/multiplication_and_division.html

All Concept Studio activities