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Class 6 Patterns in Mathematics: cheat sheet
CBSE Mathematics. Number sequences and the shapes behind them: odd, triangular, square and cube numbers, and counting matchsticks in growing patterns.
Key ideas
- Odd numbers: 1, 3, 5, 7, … Even numbers: 2, 4, 6, 8, …
- Triangular numbers: 1, 3, 6, 10, 15, … Each adds one more than the last addition.
- Square numbers: 1, 4, 9, 16, 25, … They can be drawn as dots in a square.
- Adding the odd numbers in order gives the square numbers: 1 + 3 + 5 + 7 = 16.
- Two triangular numbers in a row add up to a square number: 6 + 10 = 16.
- In a growing pattern, count what the first shape needs and what each new shape adds.
Remember
| Sum of the first n odd numbers | n × n |
| nth triangular number | n × (n + 1) ÷ 2 |
| Row of n squares (matchsticks) | 4 for the first + 3 for each more = 3n + 1 |
| Row of n hexagons (matchsticks) | 6 for the first + 5 for each more = 5n + 1 |
Watch out
- Counting the shared stick twice in matchstick patterns.
- Mixing up triangular numbers (1, 3, 6, 10) and square numbers (1, 4, 9, 16).
- Multiplying by n instead of n − 1 for the shapes after the first.
Worked example
Matchsticks make a row of hexagons, each sharing a side with the next. How many matchsticks are needed for 36 hexagons?
Working: 6 for the first, then 5 more for each: 6 + 5 × 35 = 181
Answer: 181
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