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Patterns in the world

Patterns and sequences · level 1, lesson 6 of 6

A question to start

Today is Monday. What day will it be in 7 days? What day will it be in 70 days?

The first one many people know: in 7 days it is Monday again. The second one sounds very hard. Seventy days is more than two months! But it is not hard at all, once you see that the days of the week are a repeating pattern. By the end of this lesson you will be able to answer it in your head.

The idea

The world is full of patterns

Patterns are not only on worksheets. Once you start looking, you see them everywhere: in time, in sounds, on floors and walls, on clothes, in plants and animals. In this lesson we go on a pattern hunt, and for each pattern we ask the two big questions from this level:

  1. Does it repeat? If so, what is the core, and how long is it?
  2. Does it grow? If so, where does it start, and how does it grow?

Patterns in time

Day and night. Day, night, day, night, day, night. The core is day, night: an AB pattern. It is the oldest pattern people know. It happens because the Earth spins round, so your side of the Earth turns towards the Sun (day) and then away from it (night), again and again.

On Mars, day and night repeat too, because Mars spins as well. A day on Mars is called a sol, and it is a little longer than a day on Earth: about 40 minutes longer.

The days of the week. Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, and then Monday again. The core is 7 days long. It is easier to see as a circle, because after Sunday you go back round to Monday.

Mon Tue Wed Thu Fri Sat Sun spring summer autumn winter

The seasons. Spring, summer, autumn, winter, and then spring again. The core is 4 seasons long. (In some places near the middle of the Earth there are only a wet season and a dry season: an AB pattern!)

The months. January, February, ..., December, then January again. The core is 12 months long.

Each of these is a repeating pattern drawn as a circle. A circle is a good picture for a repeating pattern, because when you get to the end, you are back at the start.

Going round the week

Now the puzzle. Today is Monday. Going round the week circle once takes 7 days, and brings you back to Monday.

  • In 7 days: one time round. Monday.
  • In 14 days: two times round. Monday.
  • In 21 days: three times round. Monday.

The days when it is Monday again are 7, 14, 21, 28, ... days away: the count by 7s. Ten times round the circle is 70 days. So in 70 days it is Monday again!

What about 8 days? That is one time round (7 days), and then 1 more day. One more day after Monday is Tuesday. In 15 days: two times round (14 days), and 1 more: Tuesday again.

This is the same trick as in lesson 1: find the length of the core, and count round by it.

The clock

1 2 3 4 5 6 7 8 9 10 11 12

A clock has the numbers 1 to 12 round its edge. The short hand goes round, and the hours go 1, 2, 3, ..., 11, 12, and then 1 again, not 13. The core is 12 hours long.

That is why clock adding can be surprising. If it is 11 o'clock and you wait 3 hours, it is not 14 o'clock. Count on round the circle: 12, 1, 2. It is 2 o'clock.

The clock goes round twice in one day: 12 hours of morning and 12 hours of afternoon and night.

Patterns you can see: stripes and tiles

On the left is a striped cloth: orange, blue, green, orange, blue, green. A repeating ABC pattern that goes across.

On the right is a brick wall. Every row of bricks is the same, but each row is moved along by half a brick from the row below. That is a pattern too: row moved left, row moved right, row moved left... Builders do this on purpose, because it makes the wall stronger. If the gaps lined up, the wall could crack straight down along them.

Look around you for more: floor tiles, a zebra's stripes, a fence (post, gap, post, gap), a pine cone, the keys on a piano (the black keys come in groups of 2, 3, 2, 3...).

Patterns that grow

Not every pattern in the world repeats. Some grow.

Your birthdays. Each year you have one more candle on your cake.

age 1 age 2 age 3 age 4 age 5 age 6

It starts at 1 and grows by 1 each year: a growing pattern, exactly like the towers in lesson 5. At age 10 you have 10 candles.

Counting the days of school. Day 1, day 2, day 3 ... a growing pattern, one more each day.

Saving coins. If you put 2 coins in a jar every day, the jar has 2, 4, 6, 8, ... coins: it grows by 2 each day.

Some things grow, but not by a rule

You get taller as you grow up. But this is not a pattern like the towers: you do not grow by the same amount every year, and nobody can say exactly how tall you will be next year. A pattern needs a rule that tells you what comes next. Your height has no exact rule. It is growing, but it is not a growing pattern in the math sense.

The same is true of the weather. Some days are sunny, some are rainy, but there is no core that repeats exactly. It is not a pattern you can continue for sure.

So, part of being good at patterns is knowing when something is not a pattern.

Worked examples

Example 1. Repeating or growing? Sort these: the seasons, the number of candles on your cake each birthday, a zebra's stripes, a clock's hours.

  1. Seasons: spring, summer, autumn, winter, spring... comes back. Repeating, core 4 long.
  2. Candles: 1, 2, 3, 4... more each year. Growing, by 1 each time.
  3. Zebra's stripes: black, white, black, white... Repeating (roughly; real zebras are not perfectly neat!).
  4. Clock's hours: 1 to 12 and back to 1. Repeating, core 12 long.

Example 2. Days of the week. Today is Wednesday. What day is it in 9 days?

  1. 7 days is once round the week: Wednesday again.
  2. 9 days is 7 days and 2 more.
  3. Two days after Wednesday: Thursday, Friday.

Example 3. The clock. It is 10 o'clock. What time will it be in 4 hours?

  1. Count on round the clock: 11, 12, 1, 2.
  2. It will be 2 o'clock.

Example 4. A fence. A fence goes post, rail, rail, post, rail, rail, post... The 1st thing is a post. Is the 10th thing a post or a rail?

  1. The core is post, rail, rail, 3 long.
  2. The posts are at the start of each core: 1, 4, 7, 10, ... (start at 1 and add 3 each time).
  3. 10 is on that list, so the 10th thing is a post.

Try it

  1. What is the core of the pattern day, night, day, night? How long is it?
  2. Today is Saturday. What day is it tomorrow? What day was it yesterday?
  3. Today is Friday. What day will it be in 7 days? In 14 days?
  4. Today is Sunday. What day will it be in 10 days?
  5. It is 9 o'clock. What time is it in 5 hours?
  6. Sort into repeating, growing, or not a pattern: the months of the year; how many people are in the park; the number of pages you have read if you read 3 pages every night; the colours of a traffic light.
  7. The black keys on a piano come in groups: 2, 3, 2, 3, 2, 3... Is this repeating or growing? What is the core?
  8. On Mars, day and night repeat too. Why is that a repeating pattern, and how is a Mars day different from an Earth day?
Answers
  1. The core is day, night. It is 2 long (an AB pattern).
  2. Tomorrow is Sunday. Yesterday was Friday.
  3. Friday both times. 7 days is once round the week, 14 days is twice round.
  4. 7 days is once round (Sunday again), then 3 more: Monday, Tuesday, Wednesday.
  5. Count on: 10, 11, 12, 1, 2 o'clock.
  6. Months: repeating (core 12 long). People in the park: not a pattern (it changes, but with no rule). Pages read: growing (3, 6, 9, 12 ... grows by 3 each night). Traffic light: repeating (green, yellow, red, then green again; core 3 long).
  7. Repeating. The core is a group of 2, a group of 3. (On a real piano the pattern of white and black keys repeats every 12 keys.)
  8. Mars spins round like the Earth, so each part of Mars turns to the Sun and away again and again: day, night, day, night. A Mars day, called a sol, is about 40 minutes longer than an Earth day.

Common mistake

Thinking anything that changes is a pattern. The weather, how tall you are, and how many people are in the park all change, but there is no rule that tells you exactly what comes next. A pattern needs a rule.

Counting the starting day. "In 2 days" from Monday is Wednesday, not Tuesday. Count the days after today: Tuesday is 1, Wednesday is 2. Do not count today itself.

Where it leads