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

Let’s go through each pattern one by one. We’re looking for how the shape or number of shapes changes from step 1 to step 2, and then we’ll continue that same rule to find the next three steps.

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Pattern 1:
Step 1: One triangle
Step 2: Two triangles joined together (like a diamond made of two triangles)
→ So it looks like we’re adding one more triangle each time, but connecting them side-by-side.
Actually, looking closer — Step 1 is 1 triangle. Step 2 is 2 triangles sharing a side.
So maybe Step 3 = 3 triangles in a row? But wait — let’s think differently.

Wait — actually, this might be about *adding* a triangle each time, attached to the previous shape.

But let’s look at all patterns first — maybe there’s a simpler rule.

Actually, let’s re-express:

Pattern 1:
- Figure 1: △
- Figure 2: △△ (but connected as a parallelogram)

Hmm — perhaps it’s not about counting, but about building up.

Wait — let’s try another approach. Maybe each pattern shows a sequence where you add one unit each time.

Let me check Pattern 8 — it’s easy:

Pattern 8:
Step 1: 1 square
Step 2: 3 squares (one on top of two) → like a small pyramid

So Step 3 would be: 6 squares? No — probably not. Wait — maybe it’s layers?

Actually, let’s do them one by one carefully.

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Pattern 1:
Figure 1: 1 triangle
Figure 2: 2 triangles forming a diamond (or rhombus)
→ So likely, Figure 3: 3 triangles in a row? Or maybe a bigger shape?

Wait — actually, if you look at Figure 2, it’s two triangles sharing a side — so it’s like a “double triangle”.

Maybe the pattern is: each time, add one more triangle to the right?

So:
Figure 1: △
Figure 2: △△ (connected)
Figure 3: △△△ (three in a row, connected)
Figure 4: four in a row
Figure 5: five in a row

But the question says “complete the next three patterns” — meaning after the two shown, draw the next three.

So for Pattern 1:
After [△] and [△△], next three are:
→ Three triangles in a row (connected)
→ Four triangles in a row
→ Five triangles in a row

But let’s confirm with other patterns.

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Pattern 2:
Figure 1: one house (square + triangle roof)
Figure 2: two houses side by side
→ So clearly, adding one house each time.

So next three:
→ Three houses in a row
→ Four houses
→ Five houses

That makes sense.

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Pattern 3:
Figure 1: one star-like shape (a square with triangles on each side — like a compass rose)
Figure 2: two of those stars side by side
→ Again, adding one per step.

Next three:
→ Three stars
→ Four stars
→ Five stars

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Pattern 4:
Figure 1: a cross made of 4 lines (up, down, left, right from center) — but drawn as a plus sign with extra bits? Actually, it looks like a “plus” with short arms.

Wait — Figure 1: looks like a vertical line with a horizontal line crossing it near the top — like a “T” but with a little tail? Actually, let’s describe:

Figure 1: A vertical line, with a horizontal line crossing it near the top, and a small horizontal line at the bottom? Hmm.

Actually, looking again — it might be better to count segments.

Alternatively — perhaps it’s about symmetry or adding parts.

Wait — Figure 1: looks like a “cross” but incomplete? Actually, let’s compare to Figure 2.

Figure 2: It has two of those shapes side by side? Or is it one big shape?

Actually, Figure 2 looks like two copies of Figure 1 placed side by side, sharing the middle vertical line? Not exactly.

Wait — maybe it’s about doubling?

No — let’s think differently.

Actually, Pattern 4 might be tricky. Let’s skip and come back.

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Pattern 5:
Figure 1: letter T
Figure 2: T with an extra vertical line on the right, making it look like a gate or something.

Wait — Figure 1: T
Figure 2: T with a vertical line extending down from the right end of the top bar — so now it’s like a “T” with a leg on the right.

So what’s the pattern? Adding a vertical line on the right each time?

Then Figure 3: Add another vertical line on the right? But where?

Actually, maybe it’s mirroring or expanding.

Wait — perhaps it’s about adding a mirror image.

Figure 1: T
Figure 2: T plus a reflected version on the right? But not quite.

Another idea: Figure 1 has 2 lines (vertical stem, horizontal top).
Figure 2 has 3 lines? Vertical stem, horizontal top, and a new vertical on the right.

So adding one line each time? Then Figure 3: add another line — maybe on the left? Or extend?

This is confusing. Let’s look at Pattern 6.

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Pattern 6:
Figure 1: a rectangle with 4 dots — one on each side (top, bottom, left, right)
Figure 2: two rectangles side by side, each with 4 dots — but shared side? Actually, total dots: 6? Because middle dots are shared?

Wait — Figure 1: 4 dots
Figure 2: 6 dots (because when you put two rectangles together, the inner sides share dots? Or not?)

Actually, looking at the drawing:
Figure 1: rectangle with dot above, below, left, right → 4 dots
Figure 2: two rectangles side by side — so now, left rectangle has left, top, bottom; right rectangle has right, top, bottom; and between them, no dot? Or shared?

In the image, Figure 2 shows 6 dots: top-left, top-right, bottom-left, bottom-right, and one on the far left, one on the far right? Wait no.

Actually, standard interpretation: when you have two adjacent rectangles, the dots on the shared side are not duplicated. So:

Each rectangle normally has 4 dots. When joined, the two inner dots (on the shared side) become one? Or disappear?

In Figure 2, it shows 6 dots: so probably, for n rectangles in a row, number of dots = 2n + 2? For n=1: 4 dots → 2(1)+2=4 ✓
For n=2: 2(2)+2=6 ✓
So for n=3: 8 dots
n=4: 10 dots
n=5: 12 dots

And the shape is just more rectangles added to the right.

So Pattern 6 next three:
→ Three rectangles in a row with 8 dots
→ Four rectangles with 10 dots
→ Five rectangles with 12 dots

Good.

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Pattern 7:
Figure 1: one "mountain" shape (like a V with flat top? Or a chevron) — actually, it's a single peak: /\ but with flat base? Looks like a tent.

Figure 2: two such peaks side by side — like /\/\

So clearly, adding one peak each time.

Next three:
→ Three peaks: /\/\/\
→ Four peaks
→ Five peaks

Easy.

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Pattern 8:
Figure 1: one square
Figure 2: three squares — one on top of two (like a small pyramid)

So this is different — not linear addition.

What’s the pattern?
Step 1: 1 square
Step 2: 3 squares (row of 2, with 1 on top centered)

This looks like triangular numbers or stacking.

Step 3: probably row of 3 on bottom, then 2 on top, then 1 on top → total 6 squares?
But let’s see the growth:

From Step 1 to Step 2: added 2 squares.

If Step 3 adds 3 more? Total 6?
Or maybe it’s layering: each step adds a new row at the bottom.

Standard pyramid:
Level 1: 1
Level 2: 1+2=3
Level 3: 1+2+3=6
Level 4: 10
etc.

But in the figure, Step 2 is already 3, which is level 2.

So Step 3 should be level 3: 6 squares (bottom row 3, middle row 2, top row 1)

Step 4: 10 squares
Step 5: 15 squares

But the problem says “complete the next three patterns” — so after Step 2, we need Step 3, 4, 5.

So:
Step 3: pyramid with 3 rows (6 squares)
Step 4: 4 rows (10 squares)
Step 5: 5 rows (15 squares)

Yes.

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Now back to Pattern 4 and Pattern 5, which were tricky.

Pattern 4:
Figure 1: looks like a vertical line with a horizontal line crossing it near the top, and a small horizontal line at the bottom? Actually, upon close inspection, it might be a “plus” sign but with only three arms? Or perhaps it’s a symbol for “add” or something.

Wait — another idea: maybe it’s about the number of endpoints or something.

Let’s count the line segments.

Figure 1: appears to have 3 line segments: one vertical, one horizontal crossing it (so two halves?), but actually, it’s drawn as:

- A vertical line
- A horizontal line intersecting it near the top (so forming a T-shape but with the horizontal centered)
- And a small horizontal line at the bottom of the vertical? Or is that part of the same?

Actually, looking at common worksheets, this might be a “cross” that grows.

Figure 2: has two of these? Or a larger version?

Upon second thought, I recall that in some pattern worksheets, this represents a “grid” or “window pane” growing.

Figure 1: might be a single cell with borders — but simplified.

Alternative approach: perhaps each figure is made by adding a copy to the right.

Figure 1: basic unit
Figure 2: two units side by side, sharing the middle vertical line.

So for Pattern 4:
Figure 1: one “cell”
Figure 2: two cells side by side
Then Figure 3: three cells
Figure 4: four cells
Figure 5: five cells

And the shape is a row of rectangles or windows.

In the drawing, Figure 2 looks like two squares side by side with internal lines — yes, like a window with two panes.

So Pattern 4 is similar to Pattern 2 and 3 — adding one unit each time.

So next three:
→ Three panes in a row
→ Four panes
→ Five panes

Similarly for Pattern 5:

Figure 1: T shape
Figure 2: T with an additional vertical line on the right side, extending down — so now it’s like a “gate” with two posts.

So perhaps each time, we add a vertical post on the right.

Figure 1: one vertical post (the stem of T), and a top bar.

Figure 2: two vertical posts (left and right), with the top bar spanning both.

So Figure 3: three vertical posts, with top bar spanning all three.

Figure 4: four posts
Figure 5: five posts

Yes, that makes sense.

So summarizing all:

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Final Answers for Each Pattern (next three figures):

1) Three triangles in a row (connected), then four, then five.
→ Draw: △△△ , then △△△△ , then △△△△△

2) Three houses, then four, then five.
→ Draw: 🏠🏠 , then four houses, then five.

3) Three star-shapes, then four, then five.
→ Draw: ⭐⭐⭐ , etc. (but as drawn — square with triangles on sides)

4) Three window panes in a row, then four, then five.
→ Like Figure 2 but with 3,4,5 sections.

5) T-shape with three vertical posts (top bar spanning three), then four posts, then five.
→ Like a fence with increasing posts.

6) Three rectangles in a row with 8 dots, then four rectangles with 10 dots, then five with 12 dots.
→ Dots: for n rectangles, dots = 2n + 2

7) Three mountain peaks (/\/\/\), then four, then five.

8) Pyramid with 3 rows (6 squares), then 4 rows (10 squares), then 5 rows (15 squares).

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Since the student needs to draw them, I’ll describe what to draw for each.

But since this is text, I’ll write the description clearly.

Final Answer:

For each pattern, draw the next three figures based on continuing the observed pattern:

1) Add one triangle each time, connected in a row:
- Third figure: three triangles in a row
- Fourth: four triangles
- Fifth: five triangles

2) Add one house each time:
- Third: three houses side by side
- Fourth: four houses
- Fifth: five houses

3) Add one star-shape each time:
- Third: three star-shapes in a row
- Fourth: four
- Fifth: five

4) Add one window pane each time (each pane is a rectangle with crossbars):
- Third: three panes in a row
- Fourth: four panes
- Fifth: five panes

5) Add one vertical post each time under the top bar:
- Third: three vertical posts with one top bar spanning all
- Fourth: four posts
- Fifth: five posts

6) Add one rectangle each time; dots increase by 2 each time (starting from 4):
- Third: three rectangles with 8 dots
- Fourth: four rectangles with 10 dots
- Fifth: five rectangles with 12 dots

7) Add one mountain peak each time:
- Third: three peaks (/\/\/\)
- Fourth: four peaks
- Fifth: five peaks

8) Build a pyramid: each step adds a new bottom row with one more square than the previous bottom row:
- Third: bottom row 3 squares, middle row 2, top row 1 (total 6)
- Fourth: bottom row 4, then 3, then 2, then 1 (total 10)
- Fifth: bottom row 5, then 4,3,2,1 (total 15)