Patterns & rules
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Learning Objectives
- 1Identify the rule that creates a number pattern by examining the change between terms
- 2Extend a number pattern by applying its rule to the last known term
- 3Match a function rule to a table of input-output pairs
- 4Generate the next two terms of a pattern given the rule and first term
Mini Lesson
A number pattern is a list of numbers that follow the same rule from one term to the next. The rule tells you exactly what to do to get from one term to the next term. Once you know the rule, you can extend the pattern as far as you like.
Finding the Rule
- Look at the first two terms and ask: what was done to the first term to get the second term?
- Check the same change holds between every pair of neighbors.
- Common rules: add a number, subtract a number, multiply by a number, or divide by a number.
- Some rules combine steps, like multiply by 2 then add 1.
Extending a Pattern
- Apply the rule to the last term to get the next term.
- Repeat the rule to get the term after that.
- Example: 5, 10, 15, 20, ___ — rule is add 5, so the next term is 25.
- Example: 2, 6, 18, 54, ___ — rule is multiply by 3, so the next term is 162.
Function Rules and T-Tables
- A function rule pairs every input with one output. Example rule: input times 2 plus 1.
- A T-table lists inputs on the left and outputs on the right.
- Test a rule by checking that it works for every row in the table.
- If even one row fails, the rule does not fit and you must try another.
Tip: write the difference (or quotient) between each pair of neighbors above the arrows. If the same value appears every time, you have found the rule.
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