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.
Consolidate
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.
Ask: If the core is AB, show me where it repeats. Working through the sequence: A, A, B, B, C, C. After element 2 the third element is B, not A. The repeat has not started. The true core is AABBCC: all 6 elements. Finding the actual repeat is the key skill.
Core length = 5. 19 divided by 5 = 3 remainder 4. The 19th element is the 4th element of the core = D. Check: 1=A, 2=B, 3=C, 4=D, 5=E, 6=A, ... 19=D.