Split an Array Without Losing Dots
Find an array total by adding totals from two smaller arrays.
Supplied materials
- Paper and pencil, or spoken reasoning with an adult.
- Supplied array: four rows of five dots; split it after two rows.
Learn the idea
A large array can be split into smaller arrays. Each dot must belong to exactly one part: do not skip a row or count it in both parts. The total of the two parts equals the total of the original array.
Four rows of five can be split into two rows and two rows. Each smaller array has 5 + 5 dots. Adding the two smaller totals counts every dot once. A split after the first row also works, but creates unequal-sized parts.
- Draw four rows of five dots.
- Draw a line between the second and third rows and count ten dots on each side.
- Add 10 + 10; then redraw three rows of four and split after the first row.
See the method in action
Four rows of five contain (5 + 5) + (5 + 5) = 10 + 10 = 20 dots. Three rows of four can be split as 4 + (4 + 4) = 4 + 8 = 12.
Check your reasoning
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See the answer and explanation
6 + 9
Two rows give 3 + 3 = 6 dots. Three rows give 3 + 3 + 3 = 9. Adding 6 + 9 gives all 15 dots.
Take it further
Split the same five-row array into one row and four rows. Add 3 + 12 = 15. The split changed, but every dot is still counted once.
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