Shape and space · Ages 8–9

Folding paper, cutting and punching holes worksheet

Part of: Symmetry

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Shape and space · Ages 8–9

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A sheet of paper is folded in half once and 5 holes are punched through it. Opened out, how many holes are there?
Answer:
2.A square of paper is folded in half and holes are punched in it as shown (the dashed line is the crease). Opened out, how many holes does it have?
Answer:
3.A sheet of paper is folded in half once and 6 holes are punched through it. Opened out, how many holes are there?
Answer:
4.A square of paper is folded in half and in half again, then punched as shown (the dashed lines are creases). Opened out, how many holes does it have?
Answer:
5.A sheet of paper is folded in half once and 1 holes are punched through it. Opened out, how many holes are there?
Answer:
6.A sheet of paper is folded in half once and 4 holes are punched through it. Opened out, how many holes are there?
Answer:
7.A sheet of paper is folded in half once and 3 holes are punched through it. Opened out, how many holes are there?
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8.A sheet of paper is folded in half once and 2 holes are punched through it. Opened out, how many holes are there?
Answer:

9.A piece of paper is folded and the shaded part is cut off along the crease, as shown (the dashed line is the crease). Opened out, what shape is the piece?
- A. A right-angled triangle
- B. A rectangle
- C. A trapezium
- D. An isosceles triangle
Choose the right answer
Answer:
10.The paper is folded and punched as shown (the dashed lines are creases). Which picture shows it opened right out?
- A
- B
- C
- D
Choose the right picture
Answer:
11.This paper could be the result of folding once along the dashed line, punching, and opening it out.
True or false?
Answer:

12.Ming folds a long strip of paper back and forth 7 times like a fan, draws a figure on the top layer with its hands touching both creases, and cuts it out. Opened out, how many figures holding hands are there?
Working:
Answer:
13.Ka-yee folds a sheet of paper once, punches 1 holes in the middle of it and 3 holes right on the crease (each only half a hole). Opened out, how many holes are there?
Working:
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14.Ming is making a Lunar New Year paper cutting: a red sheet is folded in half 1 times, then 4 small holes are cut, each through every layer. Opened out, how many holes are there?
Working:
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15.May is making a Lunar New Year paper cutting: a red sheet is folded in half 1 times, then 6 small holes are cut, each through every layer. Opened out, how many holes are there?
Working:
Answer:
16.Ming folds a long strip of paper back and forth 9 times like a fan, draws a figure on the top layer with its hands touching both creases, and cuts it out. Opened out, how many figures holding hands are there?
Working:
Answer:
17.May folds a sheet of paper once, punches 2 holes in the middle of it and 1 holes right on the crease (each only half a hole). Opened out, how many holes are there?
Working:
Answer:

Show the answers and working

Folding paper, cutting and punching holes worksheet: Answers and working

1. 10 holes
How many layers does folding once make? Each hole goes through every layer.
Folded once the paper has 2 layers, and each hole goes through both: 5 × 2 = 10 holes.
2. 4 holes
How many layers does folding once make? Each hole goes through every layer. Then count the holes punched.
Folded once, the paper has 2 layers and each hole goes through both: 2 × 2 = 4.
3. 12 holes
How many layers does folding once make? Each hole goes through every layer.
Folded once the paper has 2 layers, and each hole goes through both: 6 × 2 = 12 holes.
4. 8 holes
How many layers after one fold? What does a second fold do to that? Then count the holes punched.
Folded twice, the paper has 4 layers and each hole goes through all 4: 2 × 4 = 8.
5. 2 holes
How many layers does folding once make? Each hole goes through every layer.
Folded once the paper has 2 layers, and each hole goes through both: 1 × 2 = 2 holes.
6. 8 holes
How many layers does folding once make? Each hole goes through every layer.
Folded once the paper has 2 layers, and each hole goes through both: 4 × 2 = 8 holes.
7. 6 holes
How many layers does folding once make? Each hole goes through every layer.
Folded once the paper has 2 layers, and each hole goes through both: 3 × 2 = 6 holes.
8. 4 holes
How many layers does folding once make? Each hole goes through every layer.
Folded once the paper has 2 layers, and each hole goes through both: 2 × 2 = 4 holes.

9. D. An isosceles triangle
The crease becomes the shape's line of symmetry. Imagine flipping the cut half over the crease: what do the two halves make?
The crease becomes the shape's line of symmetry: flip the half you cut over the crease, and the two halves together make the whole shape.
10. D
Find the dashed creases first, then flip each hole across them, one fold at a time.
Open it one fold at a time: each hole flips across the crease like a mirror image, just as far from it.
11. True
The crease is the opened pattern's line of symmetry. Folded on the dashed line, does every hole land on another hole?
The crease is the opened pattern's line of symmetry: folded on the dashed line, every hole must land on another hole.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

12. 8 figures
How many creases do 7 folds make, and how many layers? Each layer gives one figure.
7 folds make 7 creases and 8 layers, a figure on each: 7 + 1 = 8.
13. 5 holes
Think of two kinds: the 1 middle holes go through two layers; each half hole on the crease opens into one whole hole.
The middle holes go through 2 layers, making 2; each half hole on the crease opens into 1: 2 + 3 = 5.
14. 8 holes
Each fold doubles the layers. Work out how many layers 1 folds make first.
Each fold doubles the layers: 1 folds make 2, so 4 × 2 = 8.
15. 12 holes
Each fold doubles the layers. Work out how many layers 1 folds make first.
Each fold doubles the layers: 1 folds make 2, so 6 × 2 = 12.
16. 10 figures
How many creases do 9 folds make, and how many layers? Each layer gives one figure.
9 folds make 9 creases and 10 layers, a figure on each: 9 + 1 = 10.
17. 5 holes
Think of two kinds: the 2 middle holes go through two layers; each half hole on the crease opens into one whole hole.
The middle holes go through 2 layers, making 4; each half hole on the crease opens into 1: 4 + 1 = 5.

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