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 (9)
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
g6 7. Events coincide at common multiples of intervals Number systemOperations
g6 8. Meshing gears realign at LCM of teeth Number system
g6 9. Blinking lights coincide at the LCM Number system
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