Year 6 Numeracy worksheet focusing on sequencing patterns with geometric shapes.

Here are the solutions for the sequencing patterns. The rule for all of these is that each step adds one more shape to the previous group.

1) Triangle, Parallelogram (2 triangles), Trapezoid (3 triangles)
- Next 3: A shape made of 4 triangles, a shape made of 5 triangles, a shape made of 6 triangles.
- *Description:* Draw a row of 4 triangles pointing up/down alternating. Then 5. Then 6.

2) House, Two Houses, Three Houses
- Next 3: Four houses joined together, Five houses joined together, Six houses joined together.

3) Star with circle, Two stars with circles, Three stars with circles
- Next 3: Four stars with circles in a row, Five stars with circles in a row, Six stars with circles in a row.

4) Plus sign with extra lines, Two plus signs connected, Three plus signs connected
- Next 3: A row of 4 connected "plus" shapes, a row of 5, and a row of 6.

5) T-shape, T-shape with base, T-shape with longer base?
- Let's look closer.
- 1st: A vertical line with a horizontal top (like a T).
- 2nd: A T-shape but the bottom has a small square attached to the right? Or is it a T and then a rectangle?
- Actually, looking at the pattern logic from others, it's likely about adding units.
- Let's re-examine 5:
- Image 1: A "T".
- Image 2: A "T" with a small rectangle attached to the bottom right of the stem.
- This one is tricky. Let's look at the others first to confirm the "add one unit" rule.
- 1: 1 triangle -> 2 triangles -> 3 triangles. (Add 1 triangle)
- 2: 1 house -> 2 houses -> 3 houses. (Add 1 house)
- 3: 1 star -> 2 stars -> 3 stars. (Add 1 star)
- 4: 1 cross-unit -> 2 cross-units -> 3 cross-units. (Add 1 cross-unit)
- 6: 1 square with dots -> 2 squares with dots -> 3 squares with dots. (Add 1 square unit)
- 7: 1 arch -> 2 arches -> 3 arches. (Add 1 arch)
- 8: 1 square -> 3 squares (L-shape or pyramid?) -> Wait.
- Image 1: One square.
- Image 2: Three squares (one on top of two). This is +2 squares? Or is it a pyramid of height 2?
- If it's pyramids: Height 1 (1 block), Height 2 (3 blocks). Next would be Height 3 (6 blocks)?
- Let's re-read the instruction: "Complete the next three patterns". It doesn't say "next three items in the sequence". It says "Complete the next three patterns". This usually means fill in the blanks for the sequence shown. But there are no blanks drawn. The lines are empty. So I need to draw the next 3 items in the sequence for each number.

Let's re-evaluate #5 and #8 based on the "add one unit" vs other rules.

Re-evaluating #5:
- Shape 1: A T.
- Shape 2: A T with a box attached to the right side of the stem.
- This looks like it might be building a letter or a specific structure.
- Alternative interpretation: It's constructing a "Fence" or "Gate"?
- Let's look at the components.
- Step 1: Top bar, middle stem.
- Step 2: Top bar, middle stem, right lower block.
- Maybe Step 3 is adding a left lower block? Making a U shape with a top?
- Or maybe it's adding to the right?
- Let's look at #8 again.
- Step 1: 1 square.
- Step 2: 3 squares (pyramid base 2, height 2).
- If the pattern is "Pyramids", Step 3 is Pyramid base 3, height 3 (6 squares). Step 4 is Base 4, height 4 (10 squares).
- If the pattern is just "adding squares", 1 -> 3 is +2. Next might be +3? (6 squares). Next +4? (10 squares). This fits the triangular numbers sequence (1, 3, 6, 10...).

Let's look at #5 again with a fresh eye.
- Item 1: `T`
- Item 2: `T` with a square on the bottom right.
- Is it possible Item 3 is `T` with squares on bottom right AND bottom left? That would make a `U` shape with a lid? Or a `H` shape missing the top right?
- Let's look at similar worksheets online. Often these are "growing patterns".
- Pattern 5 could be:
1. Vertical line with top hat.
2. Add a block to the right.
3. Add a block to the left?
4. Add a block on top?
This seems inconsistent.

Let's try another angle for #5.
Maybe it's not "T". Maybe it's a "post".
1. Post.
2. Post with a brace.
3. Post with two braces?

Actually, let's look at the visual similarity to #4.
#4 is clearly linear addition.
#6 is clearly linear addition.
#7 is clearly linear addition.
#1, #2, #3 are clearly linear addition.

Why would #5 and #8 be different?
#8: 1 square. Then 3 squares arranged in a pyramid.
If we assume linear addition doesn't apply to #8, what does?
Triangular numbers: 1, 3, 6, 10.
Shape 3: A pyramid of 6 squares (base 3).
Shape 4: A pyramid of 10 squares (base 4).
Shape 5: A pyramid of 15 squares (base 5).

Now back to #5.
If #8 is triangular/pyramidal growth, is #5 also structural growth?
1. `|-` (Top and stem)
2. `|-` plus `_` on right.
3. Maybe it completes a square? Or makes a `P` shape?

Let's look really closely at #5 in the crop.
Image 1: A vertical line with a horizontal line on top centered. (A T).
Image 2: The same T, but with a small square attached to the right side of the vertical stem, at the bottom.

Hypothesis: It is building a "B" or "R" or "P"?
If it builds clockwise:
3. Add a square to the top right? (Making a P shape with a thick stem?)
4. Add a square to the bottom left?

Alternative Hypothesis for #5: It's a "Tree" growing branches?
1. Trunk and top.
2. Right branch.
3. Left branch?
4. Another layer?

Let's reconsider the "Linear Addition" rule because it applies to 6 out of 8 questions perfectly. It is highly likely #5 and #8 follow a slightly different but standard mathematical progression taught in Year 6.

For #8, the jump from 1 to 3 is distinct. The arrangement is a pyramid. The next logical step in a pyramid sequence is a larger pyramid.
Sequence: 1, 3, 6, 10.
Answer for 8:
- 3rd item: Pyramid of 6 blocks (row of 3, row of 2, row of 1).
- 4th item: Pyramid of 10 blocks (row of 4, 3, 2, 1).
- 5th item: Pyramid of 15 blocks (row of 5, 4, 3, 2, 1).

For #5, let's look for a numerical pattern in the "lines" or "segments".
Shape 1: 3 segments (top, stem-top, stem-bottom? No, usually drawn as 2 lines or 3). Let's count endpoints or boxes.
It looks like "Matchstick patterns".
Shape 1: 3 matchsticks? (Top-left, Top-right, Stem). Or just a T.
Shape 2: Adds a square (3 matchsticks if sharing one side?).

Let's try counting "squares/units":
Shape 1: 0 squares? Just lines.
Shape 2: 1 square.
This doesn't help much.

Let's try counting "ends":
Shape 1: 3 ends.
Shape 2: 3 ends (the square closes off some, but opens new ones?).

Let's go with the most common pattern for this specific worksheet type (Primary Leap Year 6).
Usually, if the first two steps are shown, you continue the trend.
Trend in #5:
Step 1: Central vertical axis with top cap.
Step 2: Added a block to the right.
Step 3: Likely adds a block to the LEFT to balance it? Or adds a block to the TOP?
If it balances: Step 3 is a T with a block on bottom-left and bottom-right. (Looks like a mushroom or a gate).
Step 4: Adds a block on top of the right one?

However, there is a simpler interpretation. Look at the negative space.
No.

Let's look at #5 again. Is it possible it's the letter 'F'?
1. Top bar and stem.
2. Middle bar added? No, the box is at the bottom.

Let's assume the question implies linear growth for all, and I am misinterpreting the drawing of #5.
Could #5 be:
1. One "T" unit.
2. Two "T" units? No, they are merged.

Let's look at #8 again.
1. One square.
2. Three squares.
If this was linear addition of 1, it would be 1, 2, 3. It is not.
If it is linear addition of 2, it would be 1, 3, 5. But the shape is a pyramid. A pyramid of 5 squares doesn't make a neat symmetric shape (Base 2, Height 2 is 3. Base 3, Height 1 is 3. Base 2, Height 2 with one on top is 4?).
The shape shown is definitely a pyramid of 3.
Therefore, #8 is Triangular Numbers.

If #8 is Triangular, #5 is likely a different structural pattern.
Common pattern: "Growing Crosses" or "Growing Frames".
Shape 1: T.
Shape 2: T with right foot.
Shape 3: T with right foot and left foot? (Symmetry).
Shape 4: T with feet and a head? (Closing the loop).

Let's provide the answer based on Symmetry/Balancing for #5 and Triangular Pyramids for #8, as these are the standard non-linear patterns in this curriculum.

Refined Plan for #5:
- Pattern: Building a symmetrical object around a central stem.
- Step 1: Stem + Top.
- Step 2: Add Right Bottom.
- Step 3: Add Left Bottom (Completes the base).
- Step 4: Add Right Top (Starts filling the upper arms).
- Step 5: Add Left Top.
- *Self-Correction*: This is getting complex. Is there a simpler one?
What if it's just adding a square in a spiral?
1. (No square)
2. Square at SE.
3. Square at NE.
4. Square at NW.
5. Square at SW.
This creates a box around the stem. This is a very common "spiral growth" pattern.

Refined Plan for #8:
- Pattern: Stacking squares in a pyramid.
- Step 1: 1 high.
- Step 2: 2 high.
- Step 3: 3 high.
- Step 4: 4 high.
- Step 5: 5 high.

Final Answer Formulation:
I will describe the shapes to be drawn for the next three steps (steps 3, 4, and 5) for each problem.

1) Triangles: Row of 4, Row of 5, Row of 6.
2) Houses: Row of 4, Row of 5, Row of 6.
3) Stars: Row of 4, Row of 5, Row of 6.
4) Crosses: Row of 4, Row of 5, Row of 6.
5) T-Shape Spiral:
- 3rd: T-shape with a square on the bottom-left (balancing the right one).
- 4th: T-shape with squares on bottom-left, bottom-right, and top-right.
- 5th: T-shape with squares on bottom-left, bottom-right, top-right, and top-left (forming a square frame around the stem).
6) Dotted Squares: Row of 4, Row of 5, Row of 6.
7) Arches: Row of 4, Row of 5, Row of 6.
8) Square Pyramids:
- 3rd: Pyramid of 6 squares (Base 3).
- 4th: Pyramid of 10 squares (Base 4).
- 5th: Pyramid of 15 squares (Base 5).

Wait, looking at #5 again. Is it possible it's simpler?
What if #5 is just "Adding a segment to the right"?
1. T
2. T with box on right.
3. T with box on right and... another box on right? (Extending the arm?)
If it extends the arm, it becomes a long L shape with a hat.
But the box in #2 is attached to the *stem*, not the *arm*.
So extending right would mean attaching to the first box.
Let's stick to the Spiral/Symmetry idea, it's more robust for "patterns". However, for a Year 6 student, "Symmetry" is a key topic. Completing the pair (Left and Right) is the most logical step after adding one side.

Let's double check #8.
Is it possible #8 is just "Odd numbers"? 1, 3, 5, 7?
Shape for 5: An L shape? Or a cross?
Usually, geometric sequences preserve the shape type. The "Pyramid" shape is preserved in the triangular number sequence. A random cluster of 5 squares doesn't have a clear "next step" logic compared to a pyramid. I will stick with Pyramids.

One final check on #5.
Could it be constructing the letter 'E'?
1. Top and spine.
2. Middle bar? No, it's at the bottom.
Could it be constructing 'F'?
1. Top and spine.
2. Middle bar? No.
Could it be 'R'?
1. Spine and top loop start?
No, the T is distinct.

I will provide the solution assuming the "Spiral/Box completion" for #5 and "Pyramid" for #8.

Final Answer Construction:
1) Draw a row of 4 triangles, then 5, then 6.
2) Draw a row of 4 houses, then 5, then 6.
3) Draw a row of 4 stars, then 5, then 6.
4) Draw a row of 4 cross-shapes, then 5, then 6.
5)
- Next: Add a square to the bottom-left of the stem.
- Next: Add a square to the top-right of the stem.
- Next: Add a square to the top-left of the stem (completing a box around the center).
6) Draw a row of 4 dotted squares, then 5, then 6.
7) Draw a row of 4 arches, then 5, then 6.
8)
- Next: A pyramid with a base of 3 squares (total 6 squares).
- Next: A pyramid with a base of 4 squares (total 10 squares).
- Next: A pyramid with a base of 5 squares (total 15 squares).