Shape and space · Ages 9–10

Drawing in one stroke worksheet

Part of: Quadrilaterals, tiling and the eight directions

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Shape and space · Ages 9–10

Numsprite
numsprite.com

Name:Date:Score:／34

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

1.How many odd points (points with an odd number of lines) are in the drawing?
Answer:
2.At least how many lines (each joining two points) must be added so the drawing can be done in one stroke?
Answer:

3.This drawing can be done in one stroke (pen never lifted, each line drawn once).
True or false?
Answer:
4.To draw this in one stroke, which point should you start from?
- A. Point 4
- B. Point 3
- C. Point 1
- D. Point 2
Choose the right answer
Answer:
5.Which drawing can be done in one stroke?
- A
- B
- C
- D
Choose the right picture
Answer:

6.The park's paths are shown; each point is a junction. How many junctions have an odd number of paths?
Working:
Answer:
7.The park's paths are shown. Tsz-ching can start at a junction, walk every path exactly once and end back where Tsz-ching began.
True or false?
Working:
Answer:
8.The park's paths are shown. Ming wants to walk every path exactly once. Which junction should Ming start from?
- A. Junction 2
- B. Junction 3
- C. Junction 1
- D. Junction 4
Choose the right answer
Working:
Answer:
9.The park's paths are shown. Tsz-hin wants to walk every path exactly once. Which junction should Tsz-hin start from?
- A. Junction 2
- B. Junction 1
- C. Junction 4
- D. Junction 3
Choose the right answer
Working:
Answer:
10.The park's paths are shown. Tsz-hin can start at a junction, walk every path exactly once and end back where Tsz-hin began.
True or false?
Working:
Answer:
11.The park's paths are shown. Ming can start at a junction, walk every path exactly once and end back where Ming began.
True or false?
Working:
Answer:

Show the answers and working

Drawing in one stroke worksheet: Answers and working

1. 4 points
Go point by point and write down how many lines meet there, then pick out the odd numbers.
Count the lines at each point: 4 have an odd number.
2. 1 line
First count the odd points. Then think what one new line joining two odd points does to them.
There are 4 odd points; each line joining two of them removes 2, until 2 or fewer remain: 1.

3. True
Count the lines at each point first, and see how many odd points there are.
Count the odd points: 0. Only 0 or 2 can be drawn in one stroke.
4. C. Point 1
Count the lines at each point and find the odd points.
There are two odd points: start at one and finish at the other. Point 1 is odd.
5. B
For each drawing, count how many odd points it has.
Only a drawing with 0 or 2 odd points can be done in one stroke.

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

6. 4 junctions
Go junction by junction, write down how many paths meet there, then pick out the odd numbers.
Count the paths at each junction: 4 have an odd number.
7. True
To end back where you began, how many odd junctions can there be? Count the paths at each junction first.
To end where you began there must be 0 odd junctions; here there are 0.
8. A. Junction 2
Count the paths at each junction and find the odd junctions.
With two odd junctions, start at one of them: junction 2.
9. A. Junction 2
Count the paths at each junction and find the odd junctions.
With two odd junctions, start at one of them: junction 2.
10. True
To end back where you began, how many odd junctions can there be? Count the paths at each junction first.
To end where you began there must be 0 odd junctions; here there are 0.
11. True
To end back where you began, how many odd junctions can there be? Count the paths at each junction first.
To end where you began there must be 0 odd junctions; here there are 0.

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