Repeating Patterns and What Comes Next

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What this lesson covers

  • A pattern follows a rule.
  • The part that repeats is called the unit of repeat.
  • 1st, 2nd and 3rd tell you where each thing is in a pattern.
  • You can use the unit of repeat to find a missing part.
Key idea

Patterns are all around

  • Look for patterns on fences, beads, clothes and buildings.
  • Kōwhaiwhai patterns painted in a wharenui repeat along the rafters.
  • A pattern follows a rule, so you can tell what comes next.
Key idea

The unit of repeat

  • red, green, blue, red, green, blue
  • The part that repeats is red, green, blue.
  • That part is called the unit of repeat. This one has 3 things.
Worked example

1st, 2nd, 3rd in a pattern

  • Give each thing a position.
  • The 4th is red again, because the unit starts over.
PositionColour
1stred
2ndgreen
3rdblue
4thred
5thgreen
6thblue
7thred
Worked example

What comes next?

  • Find the unit of repeat.
  • Say the pattern out loud and keep going.
PatternUnit of repeatNext
apple, banana, pear, apple, banana, pear, __apple, banana, pearapple
clap, stamp, jump, clap, stamp, __clap, stamp, jumpjump
1, 2, 3, 1, 2, 3, 1, __1, 2, 32
circle, square, triangle, circle, __circle, square, trianglesquare
Key idea

Try it: what comes next?

Worked example

What is missing?

  • red, green, blue, red, __, blue
  • The unit is red, green, blue. After red comes green.
  • So the missing colour is green.
Key idea

Try it: does it repeat?

Key idea

Make your own

  • Pick 3 things: a shell, a stick and a stone.
  • Lay them out: shell, stick, stone. Then copy that unit again and again.
  • Describe it: the unit of repeat is shell, stick, stone.

Common mistakes

  • red, green, blue, red, green. Next is red.
    The unit has 3 colours. After green comes blue.
  • The unit of repeat in red, green, blue, red, green, blue is red, green.
    The unit is red, green, blue. All 3 come before it starts again.
  • Any row of colours is a pattern.
    A pattern follows a rule. A repeating pattern uses the same unit again and again.
  • The 4th thing in a pattern with 3 things in its unit is something new.
    The 4th thing starts the unit again, so it matches the 1st.

Your turn

1

What comes next? red, green, blue, red, green, __

2

What is missing? apple, banana, pear, apple, __, pear

3

What is the unit of repeat in clap, stamp, jump, clap, stamp, jump?

4

In circle, square, triangle, circle, square, triangle, which shape is 3rd?

5

In 1, 2, 3, 1, 2, 3, what is the 5th number?

Show answer

1. Blue 2. Banana 3. Clap, stamp, jump 4. Triangle 5. 2

Summary

What to take away

  • Find the unit of repeat first.
  • Use it to say what comes next.
  • Use it to fill a gap.
  • 1st, 2nd, 3rd tell you each position.
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More in Algebra

The Equals Sign and Missing NumbersNotesRepeating Patterns and What Comes NextNotes

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