Repeating Patterns: What Comes Next?

A part that keeps coming back

Look at a striped shirt, a brick wall, or the beads on a bracelet. You will notice the same small group of colors or shapes appearing again and again. That little group is called the pattern unit, and it is the heart of every repeating pattern. In the simplest pattern, circle, square, circle, square, the pattern unit is just two shapes long: circle, square. Once you spot the unit, you can predict every shape that follows, no matter how far the pattern stretches.

Repeating patterns are often the first algebra children meet, even though nobody calls them that. Algebra is about finding the rule that makes a sequence work. When a child looks at red, blue, blue, red, blue, blue and announces, "Blue comes twice each time!" they are doing real mathematical thinking. They found the unit (red, blue, blue) and used it to predict the future of the sequence. The fancy word for that skill is generalization, and it powers everything from skip counting to multiplication tables to the patterns in calendars.

On this page the pattern unit is made of shapes. An AB pattern uses two different shapes, like circle then square. An ABB pattern uses three shapes in its unit, with the second shape repeated: circle, square, square. An AAB pattern repeats the first shape twice: circle, circle, square. A pattern with three shapes, like circle, square, triangle, is sometimes called an ABC pattern. In every case the same question applies: what is the smallest group that repeats?

Learning to spot the unit helps children in surprising places. When they learn to count by twos, they are following the pattern 2, 4, 6, 8. When they read a calendar and predict that the seventh day of next month will fall on a certain weekday, they are using repeating patterns. Even music is a repeating pattern of beats and notes. The skill of finding "what repeats" is one of the most useful thinking tools a young mathematician can carry.

• A pattern unit is the smallest group that repeats over and over.
• AB means two shapes in the unit; ABB means the second shape repeats.
• To predict the next shape, find the unit and count through it.
• Patterns appear in clothes, tiles, calendars, music, and counting.

Stretch the pattern one slot at a time

Five shapes are already filled in at the start of the row. Your job is to fill the three empty slots by predicting what comes next. Start by naming the shapes out loud in order: "Circle, square, circle, square, circle…" Saying them out loud makes the repeating part jump out. Then ask: what should come after circle? A square!

Tap the colored shape icon that belongs in the next slot. A correct choice plays its sound, slides into place, and asks for the following shape. A wrong choice plays the wrong-answer sound but does not change the row, so you can inspect the repeating unit and try again. The readout shows how many of the three empty slots you have completed.

Filling all three slots triggers the celebration and leaves the finished pattern visible. Press New pattern for another challenge. The board chooses a different unit — sometimes two shapes, sometimes three, and sometimes a unit where one shape repeats twice. Try to say the whole unit before making the first choice.

Make patterns with your body

Stand up and try a movement pattern: clap, stomp, clap, stomp. Then make it trickier: clap, clap, stomp. Can your child copy it? Can they extend it when you stop mid-pattern? Movement patterns use the exact same brain machinery as shape patterns, and they are wonderful for wiggly learners who find sitting still hard.

• Snack patterns — arrange crackers and raisins in an AB pattern and let your child continue it.
• Laundry patterns — sort socks into a red, blue, blue line before folding.
• Sound patterns — tap a drum or a table in a rhythm and ask, "What comes next?"
• Shape hunts — find repeating patterns at home: floor tiles, wallpaper, the rim of a plate.

When your child can both copy a pattern and continue it, try asking them to invent one. Making up a new pattern is the strongest proof that they understand what a pattern is. Let them be the boss and you be the guesser — the role swap is half the fun.