Repeating patterns

Why this exists

A repeating pattern is a row of things built from one short block, the core, said over and over: red, blue, red, blue has the core red-blue. Once a child finds the core, the next piece is no longer a guess; it is whatever the core says comes next. Finding a core takes the same noticing a child uses to sort objects by one feature: these two are alike, that one is different.

For the adult: a core has to show up at least twice before you can be sure of it. Red, blue, blue on its own could continue in many ways, so every pattern you build this week shows its core two or three full times. It is handy to name cores with letters (AB, AAB, ABB, ABC), where each letter stands for one kind of piece; the child does not need the letters and can say “two reds, then a blue”.

Day 1: The part that repeats

You need: a dozen snap cubes or beads in two colors, say red and blue.

Stand up, sit down, stand up, sit down, and invite the child to join in. Then ask, “What will I do next?” Now build a cube train: red, blue, red, blue, red, blue. Point to each cube as you say its color together, so the pattern is heard as well as seen. Say, “Red, blue is the part that repeats. We call it the core.” Snap the train apart into its cores and line them up: every piece is the same red-blue pair.

Build red, blue, red, blue, red and stop. Ask, “What comes next? How do you know?” A good answer names the core: “Blue, because it goes red, blue, and the red just came.”

Practice.

1. What goes in the empty box in the picture? Answer: a square, because the core is dot, square and a dot just came.
2. Point to the core in the picture. Answer: one dot and the square after it.
3. Red, blue, red, blue, red, and then? Answer: blue.
4. Stand, sit, stand, sit, and then? Answer: stand.

Day 2: Longer cores

You need: cubes in three colors.

Build red, red, blue, red, red, blue, red, red, blue. Read it aloud together with a rhythm: “red, red, blue; red, red, blue.” Ask the child to snap off the core, then check by laying that core beside the rest of the train. Do the same with red, blue, blue (one red, two blues) and with red, blue, yellow. Say, “Each pattern has its own core. Some cores have two pieces and some have three.”

Ask, “Is red, red, blue the same pattern as red, blue, blue?” No: both use two colors, but in one the red comes twice and in the other the blue does.

Practice.

1. Row A: what goes in the empty box? Answer: a square; the core is dot, dot, square, and two dots just came.
2. Row B: what goes in the empty box? Answer: a dot; the core is triangle, dot, square, and a triangle just came.
3. Row C: what goes in the empty box? Answer: a triangle; the core is square, triangle, triangle, and a square just came.
4. Cat, dog, dog, cat, dog, dog, cat, and then? Answer: dog.

Day 3: The same pattern in sounds and motions

You need: two colors of cubes, your hands and feet.

Clap, snap, clap, snap. Ask the child to copy it, then to build it with cubes: “Make a cube train that goes like clap, snap.” Any two colors work, as long as they take turns. Then turn it around: point to a train of yellow, green, yellow, green and ask the child to “play” it as sounds, one sound for each color.

The point of the day: a pattern is the way the pieces repeat, not the pieces themselves. Clap, snap and yellow, green are the same AB pattern. Clap, clap, stomp and two reds then a blue are the same AAB pattern.

Practice.

1. Which two rows in the picture are the same pattern? Answer: rows A and B; each is two of one piece and then one of another. Row C is one, then two.
2. Play row A with a clap for each triangle and a stomp for each ring. Answer: clap, clap, stomp, clap, clap, stomp.
3. Build “clap, snap, clap, snap” with cubes. Answer: any two colors taking turns, such as red, blue, red, blue.
4. Build “touch your head, touch your head, touch your toes” twice with cubes. Answer: two of one color and one of another, twice, such as green, green, red, green, green, red.

Day 4: Making patterns and fixing mistakes

You need: cubes, beads or buttons in several kinds.

First, the child makes a pattern of their own, at least two full cores long, and tells you its core. Then you build one with a mistake in it: red, blue, red, blue, blue, blue, red, blue. Ask, “Read it with me. Does it sound right? Which cube breaks the pattern?” The child finds the spot by reading core by core: red, blue; red, blue; blue, blue is wrong, the first of those should be red. Let the child swap it.

Practice.

1. Row A: which piece is wrong? Answer: the fifth piece; a square is there but the core dot, square says a dot.
2. Row B: which piece is wrong? Answer: the sixth piece; a ring is there but the core triangle, ring, square says a square.
3. Is red, blue, blue, red, blue, red a repeating pattern? Answer: no; no short core repeats all the way through. Read with the core red, blue, blue, the last cube should be blue.
4. Make your own pattern with the core one red, two blues. Answer: red, blue, blue, red, blue, blue (and more if you like), with any two colors in those places.

Exercises

1. What are the next two pieces in the picture, and what is the core?
2. Do “stomp, clap, clap, stomp, clap, clap” and ask the child to copy it, then to build it with cubes. Then say only “stomp, clap, clap, stomp” and stop. Ask, “What comes next?”

Where this goes next

Saying what comes next from a core is the first step toward a list that follows a rule. Later a child will build number and shape patterns from a rule, such as start at 3 and add 2 each time, and then meet sequences, where every term has a place number and a rule tells what goes there.