K–2AlgebraPlanned
Patterns
Repeating and growing patterns with shapes, sounds, movements and numbers: finding the unit that repeats, predicting what comes next and describing the rule.
math.algebra.patterns
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 2
You will learn to
- Copy, extend and create repeating patterns such as red, blue, red, blue, … and identify the unit that repeats.
- Extend simple growing patterns such as 2, 4, 6, 8, … and describe the rule in words.
- Predict an item further along a repeating pattern without drawing every step.
Definition
- A repeating pattern is made by repeating the same unit again and again.
- A growing pattern changes by the same rule at each step, such as 'add 2'.
Theorem
- In a repeating pattern whose unit has k items, the item k places further on is always the same.
- The first few items do not always decide a pattern: 1, 2, 4 could continue with 8 (doubling) or with 7 (add 1, then 2, then 3), so the rule must be stated.
Common misconceptions
- Thinking a pattern must continue the way you first guessed.
- Confusing the repeating unit with a single item of the pattern.
Optional discoveries
- Clock arithmetic: remainders and modular arithmetic Which colour is the 100th bead in a red–blue–green pattern? The answer depends only on the remainder when 100 is divided by 3.
- Expressions, unknowns and rules Growing patterns lead to rules such as 'the n-th term is 2 × n', the first algebraic expressions.