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Extend a Repeating Pattern

with Lumi

Lumi the glowing guide sits cross-legged on a sunny playground, carefully laying out a long line of colorful beads — round red ones and flat blue ones — on a wooden tray, peering ahead with a big curious smile as if wondering what bead should come next.

Identify the repeating unit in a simple pattern.
Predict the next item in a repeating pattern by finding the unit.
Extend a pattern by placing at least two more items correctly.
Recognize a distractor that does not belong in the pattern.

Key terms

pattern: A sequence where the same part repeats over and over.
unit: The smallest part of a pattern that repeats.
extend: To keep a pattern going by adding the next items.
predict: To use the unit to tell what comes next.

Finding the Pattern Unit

Every repeating pattern is built from one little chunk that keeps coming back, and that chunk is called the unit. To find it, start at the first item and name each one until the pattern is about to start over from the beginning. The pieces you named before it repeats are the unit. The unit is always the smallest complete chunk that repeats.

Using the Unit to Predict

Once you know the unit, you can extend the pattern forever. Find where you are inside the unit, then say the next piece the unit calls for. If you reach the end of the unit, it simply starts over from its first item. This is why knowing the unit lets you predict the next item every single time, even far down the line.

Worked examples

Find the next item in triangle, circle, triangle, circle, triangle, ___.

Find the unit: triangle, circle.
The last item shown is triangle.
Inside the unit, circle always comes after triangle.

Answer: circle

Continue the pattern red, red, blue, red, red, ___.

Find the unit: red, red, blue.
Two reds have just been placed.
After two reds, the unit calls for blue.

Answer: blue

Hi there! I am Lumi, and I love patterns! Look at this line of beads: a round red bead, then a flat blue bead, then a round red bead, then a flat blue bead. Do you see it? The same thing keeps happening over and over! The part that repeats is called the **unit**. In this pattern, the unit is: round red, flat blue. Then it starts again: round red, flat blue. Then again! Here is how to find the unit. Start at the very first piece. Keep naming pieces until you notice the pattern is about to start over from the beginning. Everything you named — that is the unit! With our beads: we say 'round red' — has the pattern started over? Not yet. We say 'flat blue' — now round red is coming again! The unit is round red, flat blue. When you know the unit, you can always tell what comes next. After round red, flat blue, round red, flat blue... what comes next? Round red! Because the unit starts over. Patterns can use shapes, colors, sounds, or even claps — they all share the same secret: a unit that repeats. If you ever feel stuck, go back to the very beginning, say each piece out loud one by one, and listen for when the pattern wants to start over again. That is your rescue move! Now you try. Find the unit. Say it out loud. Then tell me what comes next!

Activity

Each row on the mat shows a repeating pattern with one piece missing. Drag the correct shape to fill in the blank and keep the pattern going.

Practice

Tell the next two items in: clap, stomp, clap, stomp, clap.

Name the repeating unit in: square, square, star, square, square, star.

Common mistakes to avoid

The unit is just one itemThe unit includes every piece that repeats together, which can be two or more items, not only one.
Any familiar item can come nextThe next item must follow the unit, so an item that never appeared in the pattern cannot come next.

Check your understanding

Look at this pattern: triangle, circle, triangle, circle, triangle, ___. What comes next?

Lumi's bead pattern is: red, red, blue, red, red, blue, red, red, ___. What comes next?

What is the repeating unit in this pattern: star, heart, star, heart, star, heart?

Recap

A repeating pattern is built from a unit, the smallest part that repeats over and over. Find the unit by naming pieces until the pattern starts over, then use the unit to predict and extend what comes next.

Reflect

What repeating patterns can you spot in your room, on your clothes, or in a song?