Square Numbers in Numberblocks: Why 1, 4, 9, 16, and 25 Belong Together
See why 1, 4, 9, 16, and 25 are square numbers, build them in equal rows, and try a simple Square Club challenge.
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Why do 4, 9, 16, and 25 belong to Numberblocks' Square Club? Make four dots in two rows of two. Make nine dots in three rows of three. Each group forms a square because its rows and columns are the same length.
One belongs too: a single dot makes a 1-by-1 square. You can visit each number in Numberblocks Generator, then use dots, coins, or paper squares to build the shape yourself.
Build the first five squares
Start small. Draw the first two arrangements, then build up to 25 if you have enough objects handy.
| Number | Equal rows | Multiplication |
|---|---|---|
| 1 | 1 row of 1 | 1 × 1 |
| 4 | 2 rows of 2 | 2 × 2 |
| 9 | 3 rows of 3 | 3 × 3 |
| 16 | 4 rows of 4 | 4 × 4 |
| 25 | 5 rows of 5 | 5 × 5 |
Now try 12 objects. Three rows of four make a rectangle, but not a square. Four rows of three don't help either. The two sides have different lengths. The Oak National Academy lesson on square numbers explains the same idea with rows of objects.
Try a Square Club hunt in the generator
Load the main game and choose 1, 4, 9, 16, and 25 in turn. Before changing the number, predict how many rows the new square needs. Draw it and check the total. Open CLUBS to browse the game's number groups; the control guide shows where to find the menu.
Then test 10 and 15. Neither makes a square with equal rows and columns. What rectangles can you make instead? Ten can be 2 by 5; fifteen can be 3 by 5. Those shapes give you something concrete to compare with 3 by 3 and 4 by 4.
Find the next square without memorizing it
The next square after 25 is 36: six rows of six. Look at how many dots you add as the squares grow:
- 1 to 4 adds 3.
- 4 to 9 adds 5.
- 9 to 16 adds 7.
- 16 to 25 adds 9.
The additions are consecutive odd numbers. If you build a 4-by-4 square around a 3-by-3 square, the new edge has seven dots. It's a neat way to predict the next square, though equal rows and columns are still the simplest way to check one.
A two-minute challenge
Put 4, 9, 12, 16, 20, and 25 on paper. Circle the numbers you think are square, then build or draw each one to check. For 16, say the rows aloud: “Four rows of four.” For 20, try four rows of five and see what's different.
The hand2mind Square Club activity uses 25 as five groups of five if you'd like another arrangement to try.