Increasing and Decreasing Patterns
Warm-up
Show a staircase pattern with linking cubes: 1, 3, 5, 7. What is the rule? (Add 2 each step.) What comes next? What is the 10th term? Now reverse: 20, 17, 14, 11. Rule? (Subtract 3.) What comes next? What will eventually happen if we keep subtracting?
Explore
Pattern investigation: groups receive a set of linking cubes and must build an increasing pattern using at least 5 terms, record it in a table, describe the rule in words, and predict the 8th term. Then create a decreasing pattern from the same starting point. Compare: when does each sequence reach zero?
Consolidate
Practice
Students create two patterns each (one additive, one multiplicative), record in tables, describe rules, and predict term 10. Exit ticket: write the rule for 80, 72, 64, 56 and find the next term.
Exit ticket
Students create two patterns each (one additive, one multiplicative), record in tables, describe rules, and predict term 10. Exit ticket: write the rule for 80, 72, 64, 56 and find the next term.
Decreasing by 15 each step. Next: 25, 10, -5. This is where the sequence crosses zero and goes negative. Ask: does a decreasing sequence always eventually become negative? Yes, if the rule subtracts a fixed positive amount.
Yes, exactly. Term n = 3n. The times-3 table IS an increasing pattern with rule add 3 each step, starting from 3. Students who see this connection understand why skip-counting generates multiplication tables.