Patterns with numbers
Numbers love patterns. Some always end in 0, 2, 4, 6, 8 , these are even. Some end in 1, 3, 5, 7, 9 , these are odd. Some come from squares of other numbers , these are square numbers. Each pattern has its own personality.
What is this?
Even numbers are multiples of 2. They can be split into two equal halves. 2, 4, 6, 8, 10, … Every even number ends in 0, 2, 4, 6, or 8.
Odd numbers are not multiples of 2. They cannot be split into two equal whole-number halves. 1, 3, 5, 7, 9, 11, … Every odd number ends in 1, 3, 5, 7, or 9.
Rules:
- even + even = even (e.g., 4 + 6 = 10).
- odd + odd = even (e.g., 3 + 5 = 8).
- even + odd = odd (e.g., 4 + 3 = 7).
- even × any = even.
- odd × odd = odd.
Square numbers are numbers that come from squaring (multiplying a number by itself). 1, 4, 9, 16, 25, 36, … For example, 4 = 2 × 2, 9 = 3 × 3. Why "square"? Because 4 dots form a 2 × 2 square, 9 dots a 3 × 3 square.
Triangular numbers come from adding 1, 2, 3, 4 in a row. 1, 3, 6, 10, 15, … These dots arrange in a triangle.
There are also patterns inside multiplication tables. The 9 × table has a neat pattern: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. The digits add up to 9 each time. 1 + 8 = 9, 2 + 7 = 9, 3 + 6 = 9 …
Hunting for patterns is the heart of mathematics. The more patterns you spot, the more you start to see numbers, not just compute with them.
Worked examples
Example 1. Is 56 even or odd?
- Ends in 6 → even.
Example 2. Is 25 a square number?
- 5 × 5 = 25. Yes.
Example 3. Find the next two triangular numbers after 15.
- 1, 3, 6, 10, 15, …
- Next: 15 + 6 = 21. Then 21 + 7 = 28.
- Next two: 21, 28.
Try it
- Is 89 even or odd?
- List the first 5 square numbers.
- Is 49 a square number?
- What comes next in the pattern 1, 4, 9, 16, ___?
- Add: 17 + 23. Is the answer even or odd? Why?
Hands-on
Even-odd sort. Take 20 pebbles. Pick up any number and try to split them into two equal groups. If you can, that number is even. If you can't, it's odd. Test 7, 10, 11, 12 this way.
Square art. On grid paper, draw a 1×1 square, then a 2×2, then 3×3, then 4×4. Count the small squares each time. You get the square numbers 1, 4, 9, 16. Add a 5×5 , how many squares?