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 Measurement & dataBase-ten numbersFractionsOperations Look for a PatternEvaluate Finite Differences
Progression (12)
g4 1. Find the constant skip-count step Base-ten numbers
g3 2. Complete addition and multiplication tables Operations
g4 3. Find the rule of a growing block stack Operations
g3 4. Multiplication table folds to equal cells Operations
g4 5. Perimeter of the nth figure by rule OperationsMeasurement & data
g3 6. Write a growing pattern as an expression Operations
g3 7. Find the rule in a fraction sequence OperationsFractions
g4 8. Sum-and-difference rules in a number grid Operations
g4 9. Use neighbor differences to find rule Operations
g4 10. Pattern in equations predicts the answer Operations
g4 11. Find shape and number rule together Operations
g4 12. Find patterns in mixed-number sequences and sum FractionsOperations
Bridges to competition (13)
Reasoning problems that extend this idea toward competition:
Shrinking self-similar shapes Pattern & rule
Find a fraction in a patterned sequence Pattern & rule
Finding the hidden rule Pattern & rule
Find the rule in a fraction sequence Pattern & rule
Sum of consecutive odds and evens Pattern & rule
Divide a circle into min or max regions Optimization
Segments joining points on a circle Counting
Represent numbers by figure rule Pattern & rule
Find missing numbers in a skip-count rule Pattern & rule
Count stones at a given step of a growing pattern Pattern & rule
Find numbers placed by an arrangement rule Pattern & rule
Find the rule for a growing figure Pattern & rule
Lengths in an Arithmetic Progression Pattern & rule