Year 6 Numeracy worksheet focusing on identifying and continuing geometric patterns.

This worksheet is about sequencing patterns — specifically, identifying the rule in each sequence and drawing the next three shapes that follow.

Let’s go through each one step by step.

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1) Triangle → Parallelogram made of 2 triangles

- Pattern: The first shape is 1 triangle. The second is 2 triangles joined to form a parallelogram.
- Rule: Each step adds 1 more triangle, arranged to form a larger parallelogram or trapezoid.
- So:
- Step 3: 3 triangles → a trapezoid (like a row of 3 triangles base-to-base)
- Step 4: 4 triangles → a larger parallelogram
- Step 5: 5 triangles → a longer trapezoid

✔ Next three:
- A trapezoid made of 3 triangles
- A parallelogram made of 4 triangles
- A trapezoid made of 5 triangles

*(Visual tip: Think of adding one triangle to the right side each time, alternating orientation to keep it flat on bottom.)*

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2) House shape → Two houses side-by-side

- Pattern: One house, then two houses.
- Rule: Add one more house each time.
- So:
- Step 3: Three houses
- Step 4: Four houses
- Step 5: Five houses

✔ Next three:
- Three houses in a row
- Four houses in a row
- Five houses in a row

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3) Diamond with 4 points → Two diamonds with 8 points total

- Pattern: First is one diamond (looks like a square rotated 45° with lines from center to corners). Second is two identical diamonds side-by-side.
- Rule: Add one more diamond each time.
- So:
- Step 3: Three diamonds
- Step 4: Four diamonds
- Step 5: Five diamonds

✔ Next three:
- Three diamonds in a row
- Four diamonds in a row
- Five diamonds in a row

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4) “T” shape with crossbar → More complex T with extra lines

- Let’s look closely:
- Shape 1: Vertical line with horizontal crossbar near top — like a capital T.
- Shape 2: Same T, but now with *two* horizontal crossbars — one at top, one at bottom? Or maybe extended arms?
- Actually, looking again: It looks like each step adds a horizontal bar on each side.

Wait — better interpretation:

Actually, this looks like a plus sign (+) growing outward.

Shape 1: A small cross (like +), centered.

Shape 2: The same cross, but with extra lines extending from the ends — making it look like a bigger plus with "arms".

But actually, comparing carefully:

It’s more likely: Each step adds a pair of horizontal bars on the sides.

Alternatively — simpler rule:

> The figure is gaining one horizontal segment on each side per step.

But let’s count segments:

Actually, a clearer pattern:

- Shape 1: A vertical line with one horizontal crossbar in the middle.
- Shape 2: Vertical line with two horizontal crossbars — one above, one below the center.

So perhaps it’s adding one more horizontal bar per step, symmetrically.

Then:

- Step 3: 3 horizontal bars (center, above, below)
- Step 4: 4 horizontal bars
- Step 5: 5 horizontal bars

✔ Next three:
- Vertical line with 3 horizontal bars
- Vertical line with 4 horizontal bars
- Vertical line with 5 horizontal bars

*(Draw them evenly spaced along the vertical line.)*

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5) “T” shape → “L” shape

Wait — this is tricky.

Shape 1: Looks like a capital T — vertical line with horizontal bar on top.

Shape 2: Looks like an L — vertical line with horizontal bar at bottom.

So what’s the pattern?

Possibility: Rotating the horizontal bar down one position each time.

- Step 1: Horizontal bar at top → T
- Step 2: Horizontal bar at bottom → L
- Step 3: Horizontal bar in middle → + (cross)
- Step 4: Back to top? Or continue rotating?

But we only need next three.

Alternative idea: Maybe it’s moving the crossbar down:

- Step 1: Bar at top
- Step 2: Bar at bottom
- Step 3: Bar in middle (centered)
- Step 4: Bar at top again? (cycle)

But that seems inconsistent.

Another possibility: It’s adding a segment each time.

Wait — look again:

Actually, both shapes have 3 segments: 1 vertical, 2 horizontal? No.

Better idea:

> The shape is rotating 90 degrees clockwise each time.

- Step 1: T (horizontal on top)
- Step 2: L (horizontal on right? Wait no — in image, it’s horizontal on bottom — which is 180° rotation?)

Not matching.

Let me reinterpret:

Perhaps it’s changing the position of the horizontal bar:

- Step 1: Horizontal bar at top → T
- Step 2: Horizontal bar at bottom → upside-down T or L

Then:

- Step 3: Horizontal bar in middle → + (cross)
- Step 4: Horizontal bar at top again? Not likely.

Actually, this might be a pattern of removing or moving parts — but that doesn’t fit.

Wait — another thought:

Maybe it’s not about position, but number of endpoints or complexity.

Let’s count lines:

- Shape 1: 3 lines (vertical + 2 horizontal arms) = 3 segments
- Shape 2: Also 3 segments? Vertical + horizontal at bottom — still 3.

Same number.

Perhaps it’s reflection?

Shape 1: T

Shape 2: Mirror image? No — if you flip T vertically, you get upside-down T, which is what shape 2 looks like.

So:

- Step 1: T (normal)
- Step 2: Upside-down T (inverted)
- Step 3: Normal T again?
- Step 4: Inverted T

That would be alternating.

✔ So next three:
- Step 3: Normal T (same as step 1)
- Step 4: Inverted T (same as step 2)
- Step 5: Normal T

*(Alternate between normal T and inverted T.)*

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6) Square with dots → Rectangle with more dots

- Shape 1: A square with 4 dots — one on each side (center of each edge).
- Shape 2: A rectangle (2 squares wide) with 6 dots — 2 on top, 2 on bottom, 1 on left, 1 on right? Or 3 on top, 3 on bottom?

Looking closely: It’s a rectangle made of two squares side-by-side, with dots at the midpoints of all outer edges.

- Shape 1 (square): 4 dots (top, bottom, left, right)
- Shape 2 (2x1 rectangle): 6 dots — top has 2 (one per square), bottom has 2, left has 1, right has 1 → total 6

So rule: Add one square to the right each time, and add dots at midpoints of new exposed edges.

When you add a square:

- You add 2 new dots (top and bottom of new square) — because left edge is covered by previous square, right edge becomes new.

Wait — for shape 2 (2 squares):

- Top: 2 dots (midpoint of each square’s top)
- Bottom: 2 dots
- Left: 1 dot (leftmost edge)
- Right: 1 dot (rightmost edge)
→ Total 6

For shape 3 (3 squares):

- Top: 3 dots
- Bottom: 3 dots
- Left: 1 dot
- Right: 1 dot
→ Total 8

Shape 4: 4 squares → top 4, bottom 4, left 1, right 1 → 10 dots

Shape 5: 5 squares → 12 dots

✔ Next three:
- 3 squares with 8 dots (3 top, 3 bottom, 1 left, 1 right)
- 4 squares with 10 dots
- 5 squares with 12 dots

*(Draw the rectangle made of 3, then 4, then 5 squares, with dots at midpoints of all outer edges.)*

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7) Single arch → Double arch

- Shape 1: One curved arch (like a rainbow or ∩)
- Shape 2: Two arches side-by-side

Rule: Add one more arch each time.

✔ Next three:
- Three arches in a row
- Four arches in a row
- Five arches in a row

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8) Single square → Two squares stacked (bottom) + one on top

- Shape 1: One square
- Shape 2: Three squares — two on bottom row, one centered on top → like a small pyramid or “Tetris” block

Rule: Each step adds a layer or grows the structure.

What’s the growth?

From 1 square to 3 squares — added 2.

Perhaps next is 5 squares? Like a bigger pyramid?

Standard pattern: Triangular numbers or centered stacking.

Actually, common pattern:

- Step 1: 1 square (level 1)
- Step 2: 3 squares (level 2: 2 on bottom, 1 on top)
- Step 3: 6 squares (level 3: 3 on bottom, 2 above, 1 on top) — triangular arrangement
- Step 4: 10 squares (4+3+2+1)
- Step 5: 15 squares

But that might be too advanced for Year 6.

Alternative: Maybe it’s adding a row below?

No — shape 2 has 2 on bottom, 1 on top.

Perhaps it’s always having a base of n squares, and stacking up.

Wait — another idea:

> Each step adds a complete row of squares at the bottom, and centers the previous structure on top.

But shape 1: 1 square

Shape 2: 2 on bottom, 1 on top — total 3

Then:

- Step 3: 3 on bottom, 2 on top, 1 on top → total 6
- Step 4: 4+3+2+1 = 10
- Step 5: 15

This is the triangular number pattern.

✔ Next three:
- 6 squares: 3 on bottom, 2 above, 1 on top
- 10 squares: 4 on bottom, 3 above, 2 above, 1 on top
- 15 squares: 5+4+3+2+1

*(Draw the triangular stack: each row has one less square than the row below, centered.)*

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## ✔ Final Answers (What to Draw):

1. Three triangles → four → five (forming trapezoids/parallelograms)
2. Three houses → four → five (in a row)
3. Three diamonds → four → five (in a row)
4. Vertical line with 3 horizontal bars → 4 → 5 (evenly spaced)
5. Normal T → inverted T → normal T (alternating)
6. Rectangle of 3 squares with 8 dots → 4 squares with 10 dots → 5 squares with 12 dots
7. Three arches → four → five (side by side)
8. Triangular stack: 6 squares (3-2-1) → 10 squares (4-3-2-1) → 15 squares (5-4-3-2-1)

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## 📝 Note for Student:
Since this is a worksheet, you should draw these shapes neatly on the lines provided. Use a ruler if needed for straight lines. For the dot patterns, place dots at the center of each outer edge.

The score box says “8” — that might be the student’s score or just an example. Don’t worry about that — focus on completing the patterns correctly!

Good luck! 😊