Early maths
Patterns Are Maths: Why "What Comes Next?" Is a Serious Question
Red, blue, red, blue. It looks like a game with beads, and it is the start of algebra. How pattern play grows, and ways to do it at home.
A child threading beads, red, blue, red, blue, does not look as if they are doing mathematics. There are no numbers anywhere. But noticing what repeats, and using it to say what comes next, is one of the central habits of mathematical thinking.
Why patterns count as maths
Mathematics is largely the study of patterns. Even numbers are every second one. The five times table ends in five, nought, five, nought. Days of the week come round in sevens.
A child who is used to asking "what is the rule here?" has a way into all of these. When they later meet a sequence like 2, 4, 6, 8, they do not see four separate facts to remember. They see one rule.
That is why early years teachers spend time on beads and bricks. The skill is finding the rule, and it carries a long way.
Four kinds of repeating pattern
Our game What Comes Next uses four patterns. They are a good map of how the idea develops.
A B A B. Circle, triangle, circle, triangle. Two things taking turns. This is where everyone starts.
A A B. Circle, circle, triangle, circle, circle, triangle. One item is doubled.
A B B. Circle, triangle, triangle. The same idea with the double in a different place. Children often find this harder than A A B, because the pattern does not announce itself at the beginning.
A B C. Circle, triangle, square. Three different items.
In the game, each shape always has its own colour. So a child can follow the pattern by shape, by colour, or both.
The part that is hard
Copying a pattern is easy. Continuing one is harder. Hardest of all is finding the unit of repeat: the chunk that keeps coming round.
Take circle, circle, triangle, circle, circle, triangle. The unit is "circle, circle, triangle". A child who sees that can answer any question about the pattern. A child who only looks at the last shape will guess.
You can help by saying the pattern aloud in a rhythm, with a pause after each unit: "circle circle triangle... circle circle triangle...". The voice does the grouping.
A common mistake
When a pattern ends partway through the unit, children often go back to the start. Shown circle, circle, triangle, circle, circle, and asked what comes next, they say "circle", because the pattern "starts with circle".
If this happens, cover the row and uncover it one shape at a time, saying each aloud. The rhythm usually sorts it out.
Pattern play at home
Things in a row. Spoons and forks. Socks. Toy cars. Start a pattern and ask your child to carry it on. Then swap, and let them set one for you.
Sounds. Clap, clap, stamp. Clap, clap, stamp. Patterns do not have to be seen.
Movement. Jump, jump, turn. This is good for children who will not sit still.
Food. Grape, cheese, grape, cheese on a stick. A pattern you can eat is very motivating.
Break it. Make a pattern with one mistake in it. "Something is wrong. Can you find it?" Spotting an error needs real understanding.
Name it. Use letters or sounds for the pattern: "This is an A-B-B pattern." Then make the same pattern with different things. Seeing that clap-stamp-stamp and red-blue-blue are the same pattern is a big step.
Patterns in the world
Point them out when you see them.
- Stripes on a jumper.
- Paving stones and brick walls.
- The days of the week.
- Verses and chorus in a song.
- Traffic lights.
A child who starts noticing patterns on their own, and telling you about them, has caught the habit.
Where it leads
From repeating patterns, children move on to growing patterns: one, two, three bricks in a tower, then four. That leads to counting in steps, which is what Count in Steps practises with twos, fives and tens. Counting in steps leads to times tables.
Much later, the same thinking turns into algebra, where the rule is written down with letters. The line from beads on a string to that is a direct one.
A few minutes of practice
What Comes Next is eight questions and takes two or three minutes. If your child gets one wrong, the choice fades and they can try again. Nothing is lost.
After a round, ask your child to explain one of the patterns to you. "How did you know it was a triangle?" Putting the rule into words is harder than choosing the answer, and worth more.
Then make a pattern with whatever is on the table. HTML5 games are handy for a quick go. The fruit bowl is better.