seegongsik
Grade 3 (age 8-9)

grade 3 Finding Patterns

Look carefully at a row of numbers and you can often find a hidden rule. 2, 5, 8, 11 grows by 3 each time, so you know the next number is 14 without counting. When blocks are stacked into stairs or squares, writing down the number of blocks, such as 1, 3, 6 or 1, 4, 9, turns a growing shape into a number pattern. Change the starting number and the amount added to make a number pattern, then pick a block shape with the buttons and count how many blocks each stage adds.

Rules Hidden in Numbers

🔢 The Rule Between Numbers
①In 2, 5, 8, 11, each number is 3 more than the one before
②So 3 more than 11, which is 14, comes next
③Add 3 once to the starting number to get the second number, and twice to get the third
④The sixth number is the start, 2, with 3 added five times: 2 + 3 × 5 = 17

Adding the Same Amount

2
3
6

Patterns in Block Shapes

🧱 Finding Rules in Block Shapes
①Count how many blocks are added each time you go up a stage
②The stairs use 1, 3, 6, 10, 15 blocks, and the number added grows by one each time: 2, 3, 4, 5
③The squares use 1, 4, 9, 16, 25 blocks; stage 3 is 3 × 3 = 9, the number of blocks on one side times itself
④The triangles use the same numbers of blocks as the stairs; only the rows are centered instead of lined up on the left

Summary

Adding the Same Amount
Next number = number before + amount added
Keep adding the same amount to get each next number
Finding Any Number in the Pattern
nth number = start + amount added × (n − 1)
The nth number is the start with the amount added n − 1 times
Blocks in the Squares
1, 4, 9, 16, 25, …
The block counts when each side has 1, 2, 3, 4 or 5 blocks
🎯 Summary
①A pattern is a steady way that numbers or shapes change
②Finding the difference between neighboring numbers makes the rule easy to spot
③Once you know the rule, you can find the next number or any later number
④Counting the blocks in a shape turns it into a number pattern you can read
⑤The stairs and the triangles use the same numbers of blocks; only their shapes differ

Examples and Unit Test

Example 1
What number comes next in 2, 5, 8, 11, …?
1
Find the differences: 5 − 2 = 3, 8 − 5 = 3, 11 − 8 = 3, so the rule is add 3.
2
11 + 3 = 14.
▸ 14
When a pattern adds the same amount each time, adding it once more gives the next number.
Example 2
A pattern starts at 4 and adds 5 each time. What is the 6th number?
1
The 6th number is the start, 4, with 5 added 6 − 1 = 5 times.
2
4 + 5 × (6 − 1) = 4 + 25 = 29.
▸ 29
For any position, add the amount to the start one fewer time than the position number.
Unit Test
What comes next in 1, 4, 9, 16, …?
①20
②25
③24
④32
▸ ② 25
1
1 = 1 × 1, 4 = 2 × 2, 9 = 3 × 3, 16 = 4 × 4.
2
Next is 5 × 5 = 25.
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