Submarine maths quest: patterns

Quick answer

You can use patterns to help a submarine navigate through the ocean by following repeating sequences of depths, pressure readings, and hidden coordinates.

Learning outcome

By the end of this page, you will be able to find and continue repeating patterns in numbers, shapes, or objects using clues from real-life situations like a submarine's journey through the ocean.

• You can spot a pattern in a sequence of numbers or shapes
• You can continue a pattern by one more step
• You can explain what the pattern means in a real-life situation
• You can create your own simple pattern using objects or drawings

Why this matters

Patterns help us understand how things work and make predictions. In real life, patterns help scientists and engineers understand the ocean, build better submarines, and even help us find treasure! When you see a pattern, you can guess what comes next. This is useful for everything from solving puzzles to understanding how nature works. In the ocean, submarines use patterns to stay safe and find their way through deep water.

How it works

Patterns are repeated sequences that follow a rule. A pattern can be:

1. Numbers like 2, 4, 6, 8, 10
2. Shapes like circle, square, triangle, circle, square, triangle
3. Actions like clap, snap, jump, clap, snap, jump
4. Things in nature like leaves on a tree or stars in the sky

Patterns always follow a rule. For example, if you see 2, 4, 6, 8, the rule might be "add 2 each time". To continue a pattern, you need to:

1. Look at what comes before
2. Find the rule
3. Apply the rule to find the next item

Patterns can be simple or complex. The more you look for patterns, the better you get at finding them!

Examples you can see

Let's imagine you are on a submarine adventure. The submarine's computer shows a pattern of depths it needs to go down:

What is the pattern here? The depth increases by 10 each time. So, the 5th step is 50 metres.

Another example: The submarine's pressure readings show this pattern:

• First reading: 100
• Second reading: 150
• Third reading: 200
• Fourth reading: 250
• Fifth reading: ?

The rule is to add 50 each time. So, the fifth reading is 300.

Here's a shape pattern:

• Circle
• Square
• Triangle
• Circle
• Square
• Triangle
• Circle
• ?

What comes next? A Square! The pattern repeats every three shapes.

Let's look at a growing pattern:

• Step 1: 1 block
• Step 2: 3 blocks
• Step 3: 5 blocks
• Step 4: 7 blocks
• Step 5: ? blocks

The pattern adds 2 blocks each time. So, Step 5 has 9 blocks.

Try it as a mini adventure

Imagine you are a young scientist on a submarine mission. The submarine's computer is giving you clues to find a hidden treasure in the ocean. You must solve the pattern to find where to go next.

Here's your first clue:

1. Step 1: 500 metres deep
2. Step 2: 450 metres deep
3. Step 3: 400 metres deep
4. Step 4: 350 metres deep
5. Step 5: ? metres deep

What is the pattern? How deep should the submarine go on Step 5?

Answer: The submarine goes down 50 metres each time. So, Step 5 is 300 metres deep.

Your next clue is a pressure pattern:

1. Reading 1: 1000 units
2. Reading 2: 1200 units
3. Reading 3: 1400 units
4. Reading 4: 1600 units
5. Reading 5: ? units

What is the next pressure reading?

Answer: The pressure increases by 200 units each time. So, Reading 5 is 1800 units.

Finally, you see a pattern in the submarine's coordinates:

• Point A: (2, 3)
• Point B: (4, 6)
• Point C: (6, 9)
• Point D: (8, 12)
• Point E: (?, ?)

What are the coordinates for Point E?

Answer: The x-coordinate goes up by 2, and the y-coordinate goes up by 3 each time. So, Point E is (10, 15).

Common mistakes

• Mistake: Thinking the pattern is just "add 10" when it's really "add 50" or "add 2".
  Why it happens: Children might rush to add the first two numbers without checking the pattern.
  Fix: Always check the difference between the first few numbers to find the rule.
• Mistake: Not noticing that a pattern can be both numbers and shapes at the same time.
  Why it happens: Children often focus on one part of the pattern and miss the other.
  Fix: Look at all parts of the pattern together, not just one type of item.
• Mistake: Thinking that the pattern always goes up, not down or repeats.
  Why it happens: Children are used to seeing numbers going up, not down or repeating.
  Fix: Practice with patterns that go up, down, and repeat to understand all types.

Parent and carer guide

As a parent or carer, you can help your child practice patterns by:

1. Looking for patterns in daily life, like the tiles on the floor or the rhythm in songs
2. Using objects like blocks, buttons, or toys to make and continue patterns
3. Playing pattern games together, like "What comes next?"
4. Encouraging your child to explain the rule they see in a pattern
5. Letting them create their own patterns for you to guess

Try asking questions like:

• "What do you notice about these numbers?"
• "Can you see what comes next?"
• "How do you know that's the right answer?"

Don't worry if your child makes mistakes – they're learning! The key is to help them find the rule and apply it correctly.

Practice questions

1. What comes next in this pattern: 5, 10, 15, 20, ?
   Answer: 25
2. Complete the shape pattern: Circle, Square, Triangle, Circle, Square, ?
   Answer: Triangle
3. What is the next number in this pattern: 100, 200, 300, 400, ?
   Answer: 500
4. What comes next in this pattern: 1, 3, 5, 7, ?
   Answer: 9
5. What is the next pair of coordinates: (1, 2), (3, 4), (5, 6), ?
   Answer: (7, 8)

FAQ

What is a pattern in maths?

A pattern is a sequence of numbers, shapes, or objects that follows a rule. The rule tells you how the pattern repeats or changes.

How do I find a pattern?

Look at the first few items in the sequence. Then, figure out how they change from one to the next. This change is the rule.

Can patterns go backwards?

Yes! Patterns can go up, down, or repeat. For example, 100, 80, 60, 40 is a pattern that goes down by 20 each time.

Why are patterns important?

Patterns help us predict what comes next and understand how things work. They are used in science, art, music, and even in nature!

How can I practice patterns at home?

You can make patterns with toys, draw shapes, count objects, or listen to music with a rhythm. Try to find patterns in your daily life, like the days of the week or the hours on a clock.