📊 Part 1: Pattern Recognition and Tables

1. Complete the table below by calculating the missing triangular, square, and cube numbers:

n	Triangular Number	Square Number	Cube Number
1	1	1	1
2	3	____	8
3	____	9	____
4	10	____	64
5	____	25	____
6	____	____	____

2. Which pattern grows the fastest? Circle your answer:

Triangular Numbers

Square Numbers

Cube Numbers

3. Write the next three numbers in each pattern:

Triangular: 1, 3, 6, 10, 15, 21, ____, ____, ____

Square: 1, 4, 9, 16, 25, 36, ____, ____, ____

Cube: 1, 8, 27, 64, 125, 216, ____, ____, ____

📈 Part 2: Coordinate Plotting and Formulas

4. Plot the ordered pairs (n, value) for each pattern on the coordinate plane below. Use different colours or symbols for each pattern.

Coordinate Plane

Plot points for n = 1 to 6

x-axis: n values, y-axis: pattern values

5. Match each pattern to its correct formula by drawing lines:

Triangular Numbers

Square Numbers

Cube Numbers

n³

n(n+1)/2

n²

6. Using the formula n(n+1)/2, calculate the 8th triangular number. Show your working:

7. Describe how the three patterns are different when you look at their graphs. Use mathematical vocabulary in your answer:

8. Explain in your own words what a triangular number represents. Give an example:

9. If you were to continue plotting these patterns beyond n = 6, which pattern would reach a value of 1000 first? Explain your reasoning: