In this topic you will

• Draw and measure lines using centimetres ($\text{cm}$).
• Use a ruler and a metre ruler as a number line.

In this section you will use what you know about measuring with centimetres. It is important to remember how to use your ruler when drawing and measuring.

EXERCISES

1. Which line is longer?

I think the __________________________ line is longer.

Which line is shorter?

I think the __________________________ line is shorter.

👀 Show answer

The green line is longer.

The blue line is shorter.

2. You will make strips of paper of different lengths and widths.

You will need an A$4$ piece of paper. Use your ruler and draw a line $5$ centimetres below the longest edge of your paper (see the bottom line in strip $1$ in the picture below).

Measure the length of this line and draw the next strip $5$ centimetres shorter and $1$ centimetre narrower.

Keep measuring $5$ centimetres shorter and $1$ centimetre narrower for each new strip, until you have drawn $4$ strips.

Cut along the lines you have drawn.

You now have $4$ strips of paper.

Bend them round and stick the edges together.

You now have $4$ rings.

Can they fit inside each other?

Now you are ready to decorate them.

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Yes. The strip with the greatest length makes the largest ring, and the shorter strips make smaller rings, so the smaller rings can fit inside the larger ones.

Because each new strip is $5$ centimetres shorter than the previous one, each new ring has a smaller circumference, so the ring sizes go from largest (strip $1$) to smallest (strip $4$).

3. Let’s make a ruler!

Make a rod of $15$ or more centimetre cubes.

Cut a strip of paper.

Lay the cubes on top of your paper.

Make sure you put the edge of a cube at the left edge of the paper.

This left edge will be $0$. (There is no space to write $0$ on your ruler.)

Where $2$ cubes meet, draw a line on your paper.

Keep on adding cubes. Keep on drawing lines until you reach the end of your paper.

Write numbers on your ruler. Write ‘centimetres’ on your ruler.

Use your ruler to measure lots of different things at home and at school.

👀 Show answer

You make the ruler by using the cubes as equal $1$-centimetre units: line up the first cube edge with the left edge of the paper (this is $0$), then draw a mark at every place where two cubes meet.

After marking all the cube boundaries, write the numbers $1$, $2$, $3$, … at the marks (and write “centimetres”) so each space between marks represents $1$ centimetre.

Think like a Mathematician

Question: How does your height compare with your arm span?

Method:

1. Stand up straight and measure your height (from the floor to the top of your head).
2. Stretch your arms out to the sides and measure your arm span (from fingertip to fingertip).
3. Compare the two lengths.

If the length of your arm span is smaller than your height, you are a wide rectangle.

If the length of your arm span is the same as your height, you are a square.

If the length of your arm span is larger than your height, you are a tall rectangle.

Continued:

If the length of your arm span is the larger than your height, you are a wide rectangle.

Conclusion: I am ____________________.