Repeating Patterns with Multiple Elements
Warm-up
Clap-snap-stomp-stomp, clap-snap-stomp-stomp, clap-snap... What is the pattern? How many sounds in the core? What letter code would you use? (ABCC.) What comes after the 10th element? Discuss in pairs before sharing.
Explore
Groups create a bead pattern (3+ colours) on a string. They must: plan their core before threading; record the pattern in three representations (beads, drawing, letter code); predict the 20th bead without extending the whole sequence.
Formalize
Focus on prediction. In the pattern ABCABC, what is the 13th element? Share strategies: I extended the pattern versus I know the core has 3 elements, 13 divided by 3 is 4 remainder 1, so the 13th is the 1st element: A. Both strategies are valid; the second is more powerful.
Repeating Patterns with Multiple Elements
Connect to numerical patterns. On the hundred chart, what is the 15th number when skip-counting by 5? (75.) What pattern rule tells you that? Students begin to see that numerical sequences have structural patterns just like bead sequences.
Practice
Students complete a pattern translation activity (given in one representation, draw it in two others and write the letter code) plus one prediction problem. Exit ticket: teacher shows ABCABC and asks what is the 10th element.
Exit ticket
Students complete a pattern translation activity (given in one representation, draw it in two others and write the letter code) plus one prediction problem. Exit ticket: teacher shows ABCABC and asks what is the 10th element.
Step 1: Read the pattern aloud with rhythm: "red, red, blue, blue, green, green, red, red…" The voice naturally chunks it.
Step 2: Find the core — the shortest chunk that repeats. Physically pick up one copy: A-A-B-B-C-C (six elements). Test it: does laying this chunk down again and again rebuild the whole pattern? Yes → it's the core.
Step 3: Common error: a student says the core is A-B-C "because there are three colours." Test THEIR core honestly: A-B-C laid twice gives A-B-C-A-B-C — which does not match A-A-B-B-C-C. The pattern itself referees the disagreement, not the teacher.
Step 4: Extend by laying the core again: after …C-C comes A-A. Students should extend by placing the whole core chunk, not by guessing one element at a time.
Step 1: The core A-B-C-D-E has 5 elements, so the pattern restarts every 5: positions 1–5 are the first copy, 6–10 the second, 11–15 the third, 16–20 the fourth.
Step 2: Count by 5s toward 19: 5, 10, 15 — three full copies used up, landing at position 15 on an E.
Step 3: Walk the remainder: position 16 → A, 17 → B, 18 → C, 19 → D.
Step 4: The answer is D — found WITHOUT writing out nineteen letters. Name the strategy out loud: "use the size of the core to leap, then step the leftovers." This leap-then-step idea is the seed of division with remainders.
Step 1: Build an A-B-B pattern with cubes: red, blue, blue, red, blue, blue.
Step 2: Ask students to make the SAME pattern with sounds instead: clap, tap, tap, clap, tap, tap. Then with shapes: circle, square, square…
Step 3: Ask what stayed the same when everything changed. (The STRUCTURE — one of something, then two of something else.) The letters A-B-B are how we write that structure down without caring what the somethings are.
Step 4: Now flip it: write A-B-B on the board and let students invent their own version (hop, blink, blink…). If a student produces red, red, blue — that's A-A-B — hold both patterns up and have the class find the difference.
Seeing one structure in many disguises is the whole point of pattern work — it is abstraction, done at age six.