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Mathematics
Multiplication and division — Arrays and equal groups
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Arrange equal rows, share equally and form groups using whole counters.
Change the rows or drag a blue handle. How does the total change?
3 rows with 4 objects each
Total objects
12
4 + 4 + 4 = 12
4 × 3 = 12
Objects per row × rows
3 rows with 4 objects each. 12 objects
Loading resourceModel notes
- Each counter represents one whole object and cannot be split. The limit of 100 objects keeps the scene readable; it is not a mathematical limit on multiplication or division.
- This resource writes objects per row × number of rows. Transposing preserves the total while exchanging the factors' roles in the array.
- Equal sharing: the divisor counts groups and the quotient counts objects per group. Grouping: the divisor counts objects per group and the quotient counts full groups. The divisor is always positive.
- Unallocated objects are not yet the remainder. Once no complete step is possible, the remainder is smaller than the divisor; total equals divisor times quotient plus remainder.
- Motion illustrates arranging objects, not gravity or physical time. Reopening the page starts from the defaults.