Grade 3 (age 8-9)

Finding Patterns

A list of numbers often hides a rule you can find. Since 2, 5, 8, 11 grows by 3, you can predict the next number by adding the same step. Growing shapes like stairs or squares become numbers such as 1, 4, 9. Slide the start and step to build a sequence, then tap a button to grow the shapes.

Let's Find Number Patterns

🔢 Hidden Rules in Numbers

①2, 5, 8, 11... → +3 each!

②Find rule → predict next number

③Look at difference between consecutive numbers

Arithmetic Sequence

Start2

Step3

Count6

Patterns in Shapes

🧱 Patterns in Shapes

①Count how many blocks added each stage

②Stair: 1, 3, 6, 10 → adds 2, 3, 4

③Square: 1, 4, 9, 16 → 1×1, 2×2, 3×3, 4×4

Summary

Arithmetic Rule

next = previous + step

Add the same amount repeatedly

nth Term

nth = start + step × (n − 1)

Find any term using the rule

Shape Pattern

Square numbers: 1, 4, 9, 16, 25, ...

Side length 1, 2, 3, 4, 5 → block count

🎯 Key Points

①Pattern = numbers/shapes changing regularly

②Compute difference to find the rule

③Find rule → predict next

④Shape patterns convert to numbers

⑤Times-tables have many hidden patterns

Examples and Unit Test

Example 1

In the rule 2, 5, 8, 11, ..., what number comes next?

Look at the differences: 5 − 2 = 3, 8 − 5 = 3. The rule grows by 3.

11 + 3 = 14.

▸ 14

In an arithmetic rule, keep adding the same difference for the next term.

Example 2

For an arithmetic rule with start 4 and step 5, what is the 6th term?

Use nth term = start + step × (n − 1).

4 + 5 × (6 − 1) = 4 + 25 = 29.

▸ 29

Knowing the rule lets you find any term directly with the formula.

Unit Test

In the square numbers 1, 4, 9, 16, ..., what comes next?

①20

②25

③24

④32

▸ ② 25

Square numbers are 1×1, 2×2, 3×3, 4×4.

The next is 5×5 = 25.

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