Combinatorial problems: listing, the tree and the product rule
Find all the ways to place three girls on floors, grow a tree of options and find out why the number of ways is found by multiplying.
- Germany: grade 4
- Ukraine: grade 5
Guide
This follows the Ukrainian Year 5 book: section 3, item 24 "Combinatorial problems". Problems where you must look at and count all possible cases (combinations) are called combinatorial. Children first list the options (a list, table or tree) and then learn that their number can be found by multiplying.
The product rule: if the first choice can be made in m ways and after it the second in n ways, there are m · n ways altogether. For three choices multiply all three numbers. A choice where items cannot repeat (three girls on three floors) gives 3 · 2 · 1 = 6.
The child taps + to grow the tree and then types the number of ways. Some problems are solved without a picture.