Increasing and Decreasing Patterns with Tables and Charts
Grade 4 patterning formalizes the connection between patterns and data: a table of values is both a pattern description and a data display. Fish stock changes over time (BC curriculum context) produce a decreasing pattern that students can represent in a table, graph on a number line, and use to predict future values. This is the beginning of mathematical modelling: using a pattern rule to describe and predict real-world change.
Tables and charts as pattern tools
A table of values records a pattern systematically: term number in one column, term value in the other. From this table, the rule is visible: the difference between consecutive terms is constant (additive rule) or the ratio is constant (multiplicative rule). Tables allow prediction: given any term number, apply the rule to find the value.
Patterns in real-world data
Fish stocks in a lake over 5 years: 8,400 / 7,200 / 6,000 / 4,800 / 3,600. The pattern: decrease by 1,200 per year. Rule: start at 8,400, subtract 1,200 each year. Prediction for year 6: 3,600 - 1,200 = 2,400. This is mathematical modelling at Grade 4 level: using a pattern to predict a real outcome.
Connecting to multiplication and division
The sequence 6, 12, 18, 24, 30 follows rule add 6. It is also the multiples of 6. Term n = 6n. This connection shows that multiplication tables ARE increasing patterns with a constant additive rule equal to the multiplier. Division appears in decreasing patterns: 60, 50, 40, 30 decreases by 10 per step, or equivalently, divides each term by a related factor.