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You will need

• Pen
• Pencil
• Paper
• Eraser
• Ruler

Setting up

Draw a curve

1. Grab your pencil – you’re going to draw a lot of lines, and it’s nice to be able to erase mistakes.
2. Number the marks on the vertical line from the top down. You should also number the intersection like it is a mark.
3. Number the marks on the horizontal line from the left to the right.
4. Take a ruler and rule a line from mark 1 (vertical) to mark 1 (horizontal).
5. Rule a line from mark 2 to mark 2.
6. Keep ruling lines like this until you run out of marks.
7. Look at your picture – can you see a smooth curve?

Extend the curve

You’ve run out of marks, but what happens if you extend the pattern?

1. Using your ruler, mark every centimetre down the rest of the vertical line.
2. Extend the numbering on the vertical line – number the mark under the intersection, then the next one, and so on.
3. There should be matching marks on the horizontal line – so connect them, as before.
4. To see the emerging pattern, you’ll need to draw these lines through the horizontal line, all the way to the edge of the page.
5. When you’ve finished, look at your picture – does the curve continue?

What’s happening?

Ruling these straight lines reveals a shape that looks quite round! The smoothed version of this shape is known as a parabola, and it’s very famous. Parabolas are useful in a range of ways, and can be found in satellite dishes and solar collectors.

This activity also has an important message about maths. You might have thought that you were finished ruling lines when you reached the intersection. But there was a nice way to extend the pattern, and add to the curve!

When you’re learning maths, you might be told that some things are impossible. You can’t divide 3 by 2, or you can’t subtract 5 from 4. As you learn more, you’ll find out how these things are possible – the patterns of division and subtraction can be continued. Dividing 3 by 2 gives a fraction not a whole number: 1 ½, and subtracting 5 from 4 gives a negative answer: – 1.

Extending patterns is one way that new maths is created. You will keep running across examples throughout your studies. What number can you multiply by itself and get a negative number? What number is bigger than all the numbers? And if you decide to become a mathematician, you might come up with your own answers to these types of questions!