Generalize a Growing Pattern into a Rule
A figure or sequence that grows by a fixed amount each step is captured by a rule (often multiplication plus a constant) that predicts any term, including table symmetries and neighbor-difference rules. Learners move from skip-count steps and block stacks to perimeter-of-nth-figure and fraction-sequence rules. Generalizing from a few cases to a formula is core algebraic reasoning.
grade 2–4 MDNBTNFOA Look for a PatternEvaluate Finite Differences
Progression (12)
2-2 1. Find the constant skip-count step 4.NBT.A.2
2-2 2. Complete addition and multiplication tables 3.OA.D.9
2-2 3. Find the rule of a growing block stack 4.OA.C.54.OA.A.3
2-2 4. Multiplication table folds to equal cells 3.OA.B.53.OA.D.9
3-1 5. Perimeter of the nth figure by rule 4.OA.C.53.MD.D.83.OA.D.9
3-1 6. Write a growing pattern as an expression 3.OA.D.93.OA.D.8
3-2 7. Find the rule in a fraction sequence 3.OA.D.93.NF.A.1
4-1 8. Sum-and-difference rules in a number grid 4.OA.C.53.OA.D.9
4-1 9. Use neighbor differences to find rule 4.OA.C.5
4-1 10. Pattern in equations predicts the answer 4.OA.C.53.OA.D.9
4-1 11. Find shape and number rule together 4.OA.C.5
4-2 12. Find patterns in mixed-number sequences and sum 4.NF.B.34.OA.C.5