Chapter 3: Pattern Around Us

A rangoli, a checked shirt, the chirping of a koel , patterns are music for the eyes and ears. Let's find the rules behind them!

What we'll learn

• Spot patterns in shapes, colours and numbers.
• Find the rule of a pattern.
• Make our own growing patterns.
• Use patterns to predict what comes next.

The big idea

A pattern is anything that follows a rule. The rule may be "add 2 each time" or "red, blue, red, blue". Once we know the rule, we can guess what comes next without thinking too hard.

Look at this: 2, 4, 6, 8, ___. The rule is "add 2". So the next number is 10.

Patterns can grow too. Look at: 1, 4, 9, 16, ... These are 1×1, 2×2, 3×3, 4×4. The next one will be 5×5 = 25. Squares grow!

Shapes can form patterns too. Floor tiles, sarees with borders and even the petals of a marigold follow patterns. A rangoli starts with one dot in the centre and grows outward in beautiful rings.

Patterns help us think ahead. If the milkman comes every 3 days starting Monday, when will he come next? Monday, Thursday, Sunday... we don't have to write a calendar. The rule does the work.

Some patterns repeat exactly. Others grow , they get bigger or longer each time. A staircase is a growing pattern: 1 step, then 2, then 3...

Explore with examples

1. Find the next number: 5, 10, 15, 20, ___.

The rule is "add 5". Next number = 20 + 5 = 25.

2. What comes next? Circle, square, triangle, circle, square, triangle, ___.

The rule is the trio repeats. Next shape = circle.

3. Look at: 1, 3, 6, 10, 15, ___.

Differences: 2, 3, 4, 5. So next difference is 6. Next term = 15 + 6 = 21. These are triangle numbers!

4. Make a pattern using clap and stamp.

Clap, stamp, clap, clap, stamp, clap, clap, clap, stamp... Each time the number of claps grows by one before the stamp.

Hands-on activities

Rangoli Rules

On grid paper, draw a small flower in the centre. Add 4 more flowers around it. Then add 8 in the next ring. Note the rule: each ring doubles. Continue if you can!

Border Designer

Make a 2 cm strip of paper. Use two colours of beads or sticker dots to create your own repeating border. Show it to a friend , can they say what comes next?

Number Staircase

Stack matchboxes into a staircase: 1 box on step 1, 2 on step 2, 3 on step 3, up to 5. Count the total. Then guess the total for steps up to 6.

Try it yourself

1. Continue: 100, 95, 90, 85, ___, ___.
2. Continue: 1, 2, 4, 8, ___, ___.
3. What comes next: ▲ ● ▲ ● ▲ ___.
4. Write the rule for: 3, 6, 9, 12, 15.
5. Look at this: 11, 22, 33, 44. What is the 7th term?
6. Make a 4-step pattern using "hop, jump, jump".
7. Look at the petals of a daisy. Count them. Now look at a sunflower's spirals , does it follow a pattern?

Recap

• A pattern follows a rule.
• Some patterns repeat, others grow in size.
• The rule helps us predict the next term without guessing.
• Patterns are in nature, music, art and numbers.