Increasing and Decreasing Patterns
Grade 3 patterns now include both increasing (growing) and decreasing (shrinking) sequences. A decreasing pattern like 100, 90, 80, 70 subtracts the same amount each step. Doubling sequences (1, 2, 4, 8, 16) increase by a multiplicative rule rather than an additive one. The key competency is describing the pattern rule in words and numbers: not just what comes next, but WHY it comes next and what general rule generates every term.
Additive vs. multiplicative rules
Additive increasing: 5, 8, 11, 14 (add 3 each time). Multiplicative increasing: 2, 4, 8, 16 (double each time). Both are increasing patterns, but the multiplicative one grows much faster. Decreasing patterns can also be additive (100, 93, 86, 79: subtract 7) or multiplicative (64, 32, 16, 8: halve each time). The rule type (additive or multiplicative) is more important than whether the pattern grows or shrinks.
Multiple representations
The pattern 3, 6, 9, 12 can be shown as: a table of values (input 1,2,3,4; output 3,6,9,12), a concrete pattern (1 triangle, 2 triangles, 3 triangles...), a pictorial drawing, or a verbal rule (multiply by 3). Each representation reveals different aspects of the same pattern. The table of values is the most algebraically powerful: it shows the input-output relationship that will become the function concept in later grades.
First Peoples art and natural patterns
The BC curriculum asks teachers to share examples of local First Peoples art and ask students to notice patterns. Basket weaving often uses increasing or decreasing patterns (the weave changes as the shape widens or narrows). Natural patterns (pinecone spirals, plant branching) often follow multiplicative rules. Song rhythms and drum patterns use increasing and decreasing structures. These contexts show that mathematical pattern recognition is a human universal.