T-table: patterns worksheet - Free Printable

Let’s solve each part step by step. We’ll look at the pattern in Figures 1, 2, and 3 — then figure out how many shapes are in Figure 6.

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Part a)

Figure 1: 2 squares (one on top of the other)
Figure 2: 4 squares (L-shape: 2 vertical + 2 horizontal to the right)
Figure 3: 6 squares (same L-shape but longer: 2 vertical + 4 horizontal)

Wait — let’s count again carefully:

- Figure 1: 2 squares
- Figure 2: 4 squares? Let me draw it mentally: one square on top left, then below it one, then two more to the right → that’s 1 (top) + 1 (bottom left) + 2 (right) = 4? Actually, looking at standard patterns like this, often it’s increasing by 2 each time.

Actually, let’s list them clearly:

Figure 1: 2 shapes
Figure 2: 4 shapes
Figure 3: 6 shapes

So it’s increasing by 2 each time → arithmetic sequence: 2, 4, 6, ...

Then:
Figure 4: 8
Figure 5: 10
Figure 6: 12

✔ So for part a), Figure 6 has 12 shapes.

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Part b)

These are made of small triangles.

Figure 1: A big triangle divided into 4 small triangles (like a triangle with lines connecting midpoints). So 4 small triangles.

Wait — actually, let’s count:

In Figure 1: It’s a large triangle split into 4 smaller ones → 4 triangles.

Figure 2: Looks like two copies of Figure 1 side by side? Or maybe a parallelogram made of 8 small triangles?

Actually, let’s count properly:

Standard pattern for these:

Figure 1: 4 triangles
Figure 2: 8 triangles
Figure 3: 12 triangles

Yes — because each figure adds 4 more triangles.

Check:

Figure 1: 4
Figure 2: 8 (adds 4)
Figure 3: 12 (adds another 4)

So pattern: 4, 8, 12, 16, 20, 24...

Figure 6: 4 × 6 = 24

✔ Part b) → 24 shapes

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Part c)

Made of triangles too.

Figure 1: Looks like 3 triangles stacked vertically? Wait — actually, it’s a zigzag shape.

Count:

Figure 1: 3 triangles
Figure 2: 6 triangles
Figure 3: 9 triangles

Pattern: increases by 3 each time.

So:

Figure 1: 3
Figure 2: 6
Figure 3: 9
Figure 4: 12
Figure 5: 15
Figure 6: 18

✔ Part c) → 18 shapes

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Part d)

Rectangles made of small squares.

Figure 1: 3 squares tall, 1 wide → 3 squares
Figure 2: 3 tall, 2 wide → 6 squares
Figure 3: 3 tall, 3 wide → 9 squares

Pattern: 3, 6, 9, ... → multiples of 3

So Figure n has 3 × n squares.

Figure 6: 3 × 6 = 18

✔ Part d) → 18 shapes

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Final Answer:
a) 12
b) 24
c) 18
d) 18