Combinatorics Counting List
Combinatorics Counting List practice with teacher guidance, common slips, and next-step routes.
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Print: Ages 10–11 · 4–5 min · Challenge · Systematic Counting · Independent Practice · Count Entry
Watch: Watch for 140: it shows the learner found all three cases but counted 122 and 322 twice. A response of 138 is decisive evidence that the overlaps were removed once.
Misread: A response of 100 suggests the learner counted only the 200s block; 38 suggests they counted only the two outside bands. These are case-coverage errors, not a request to count how many digit 2s are written.
Curriculum: This task uses base-ten place value to organize an exhaustive count, then applies inclusion–exclusion to two overlapping digit-position cases. The scored skill is entering the exact cardinality of a finite set.