Patterns and Relations: Rules, Tables, and Equations
What you must understand
Grade 3 pattern work has two strands. Repeating patterns use a core that repeats, such as circle, square, square, circle, square, square; you must identify the core and predict any term. Growing patterns change by a constant amount, such as 3, 6, 9, 12, and you should state the rule ("add 3") and continue or extend the pattern. Relations connect two quantities in a table, and you should describe the relationship in words and, where appropriate, as a simple equation with a missing number, such as 4 × □ = 20.
Traps to watch for
- Wrong core: in A A B A A B, the core is A A B, not A A. Counting the core incorrectly throws off every later term.
- Alternating rules: some sequences add 2, then add 3, then add 2; check two or three differences before naming a rule.
- Starting value ignored: in a table where the output is 2 more than the input, the rule is "add 2", not "multiply by 2".
- Term versus position: the 5th term is not the same as a pattern whose rule adds 5.
- Missing-number placement: in □ + 7 = 15, the box is 8; students often answer 22 by adding instead of subtracting.
Worked example
A table shows 1 pencil costs 4 cents, 2 pencils cost 8 cents, 3 pencils cost 12 cents. The rule is "multiply the number of pencils by 4". For 7 pencils: 7 × 4 = 28 cents. To check, note the outputs increase by 4 each time, which matches the rule.
Rule of thumb
For any pattern, first find the change between terms. Constant change means an addition or subtraction rule; constant ratio between outputs and inputs means a multiplication rule.