Expression Evaluate

Expression Evaluate practice with teacher guidance, common slips, and next-step routes.

Core · Expression Evaluate · Independent practice · Scalar Entry

Problem number / 2

How many different whole numbers from 10 through 99 appear in exactly five cells of the completed table? Count different qualifying numbers, not cells, and enter one number.

Column 12Column 2n+2Column 3?Column 4?Column 5?Column 6?Column 7?

T(n,1)=2 for every n.T(n,2)=n+2 for every n.T(n,j)=T(n,j-2)+T(n,j-1) for j=3,...,7.97 rows × 7 columnsx in {10,...,99}; exactly 5 cells

Build formulasCount multiplicitiesKeep distinct values

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Print: Ages 13–15 · 15–25 min · Challenge · Recurrence counting · Independent practice · Number entry

Watch: Watch for a response of 30 after the learner identifies six qualifying values. That response is decisive evidence that they counted the five cells for each value instead of counting different values once.

Misread: A response of 5 copies “exactly five cells,” while 90 counts all numbers from 10 through 99. The task asks for the number of different values that satisfy the condition, not the cell count or the size of the range.

Curriculum: Learners generalize an additive row pattern into exact column rules, then count a finite set by multiplicity without duplicates. The scored skill is structural whole-number reasoning and exact cardinality; the variable-based proof makes this an age-11 capstone or supported challenge rather than routine primary practice.