Repeating Cycle Patterns
A pattern that repeats with a fixed period lets you find a far-off term using its position within the cycle (remainder on dividing by the period). Learners use weekday and shape/color cycles, repeating clock times, and number-line intervals. Periodicity plus remainder reasoning answers 'what is the Nth item' without listing all.
grade 2–4 Measurement & dataBase-ten numbersOperations Look for a PatternMake a Systematic List
Progression (6)
g2 1. Weekdays repeat every seven days Base-ten numbers
g4 2. Find the rule of changing clock times OperationsMeasurement & data
g4 3. Find shape and color repeats separately Operations
g4 4. Use the seven-day weekday cycle Operations
g4 5. Find one tick interval, then read the value Base-ten numbers
g4 6. Locate and compare numbers on a number line Base-ten numbers
Bridges to competition (8)
Reasoning problems that extend this idea toward competition:
Finding the day of the week Pattern & rule
Division applications challenge Pattern & rule
Sequences and units-digit cycles Pattern & rule
Weekday of a date from the 7-day cycle Pattern & rule
Find the missing or nth shape in a pattern Pattern & rule
Count digits used over a range Counting
Units-digit pattern of each times table Pattern & rule
Clock chimes and hand cycles Pattern & rule