Chapter 1 of 8

All 8 chapters
  1. 1Straight lines and parallel lines, readunderstood
  2. 2Polygons, readunderstood
  3. 3Right angles and turns, readunderstood
  4. 4Measuring angles in degrees, readunderstood
  5. 5Triangles and four sided shapes, readunderstood
  6. 6Lines of symmetry, readunderstood
  7. 7Solid shapes and nets, readunderstood
  8. 8Grids and directions, readunderstood

M2.5.1 Chapter 1

Straight lines and parallel lines

How do I draw a line that is exactly 6 cm long?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Draw a straight line of a given length with a ruler
  • Find parallel lines around you, like the two sides of a door

A straight line does not bend. You draw one along the edge of a ruler.

The length of a line is how long it is. A ruler shows length in centimetres, written cm.

Draw it first

Draw a line 6 cm long

  1. A ruler marked from 0 to 8 with the word cm. Step 1 puts a cross above the 0 mark, labelled start. Step 2 puts a second cross above the 6 mark, labelled 6 cm. Step 3 draws a straight line from one cross to the other.012345678cmstart

    1 Make a small cross where the line starts. Put the 0 mark of the ruler under it.

  2. A ruler marked from 0 to 8 with the word cm. Step 1 puts a cross above the 0 mark, labelled start. Step 2 puts a second cross above the 6 mark, labelled 6 cm. Step 3 draws a straight line from one cross to the other.012345678cmstart6 cm

    2 Find 6 on the ruler. Make a second cross above it.

  3. A ruler marked from 0 to 8 with the word cm. Step 1 puts a cross above the 0 mark, labelled start. Step 2 puts a second cross above the 6 mark, labelled 6 cm. Step 3 draws a straight line from one cross to the other.012345678cmstart6 cm

    3 Hold the ruler still. Draw from cross to cross.

Do not start at the end of the ruler. Many rulers have a small gap before the 0 mark.

A ruler marked from 0 to 8 with the word cm. A cross labelled edge sits at the left end of the ruler, before the 0 mark. A line runs from that cross to the 6 mark.012345678cmedge
This line starts at the edge, not at 0. It is longer than 6 cm.

Look at a door. Its two long sides are parallel. Parallel lines always stay the same distance apart. They never meet.

Two pairs of lines. On the left, two lines slope the same way and are the same distance apart. Two short dashed lines of equal length join them. It is labelled parallel. On the right, two lines get closer. Dashed lines carry them on until they cross at a cross, labelled they meet. It is labelled not parallel.parallelthey meetnot parallel
The left pair stay the same distance apart. The right pair get closer, so they will meet.

Parallel lines can be different lengths. They can point across, up or slanted.

See it three ways

With things

Lay two sticks on the ground. Make the gap the same at both ends.

As a picture

Two straight lines, one above the other, with two dashed lines of equal length between them. Both gaps are labelled same gap.same gapsame gap

In symbols

The gap at one end = the gap at the other end. So the lines are parallel.

Try it

Draw two parallel lines

You need: a sheet of paper, a pencil, a ruler, or a book with straight sides.

  1. Draw a line 6 cm long. Put the 0 mark at the start.
  2. Measure 2 cm straight down from each end. Make a dot each time.
  3. Join the two dots with the ruler.
  4. Measure the gap in the middle. It is 2 cm too.
  5. No ruler? Draw round a book. Its two long sides are parallel.
  6. Now look around. Find parallel lines in the room.

What you will see: The gap is 2 cm at both ends and in the middle. So the lines are parallel.

If you cannot try it, this is what happens.
Two straight lines, one above the other, each 6 cm long. Dashed lines join their ends. Each dashed line is labelled 2 cm. The top line is labelled 6 cm.6 cm2 cm2 cm

A wrong idea many people have

Two lines that do not touch on the page are parallel.

Why it feels right: On a small drawing, two lines can seem to never meet.

The test that breaks it: Draw both lines longer with a ruler. If they get closer, they will meet. Then they are not parallel.

What is true: Parallel lines stay the same distance apart, however long you draw them.

Key words

straight line
a line that does not bend.
length
how long a line is.
parallel
lines that stay the same distance apart and never meet.

Back to your guess

The answer is B: Put the 0 mark on the start of the line. Stop at 6.

Length starts at the 0 mark. Many rulers have a small gap before 0. The end of the ruler is not the start.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. You draw a line 8 cm long. Where do you put the 0 mark of the ruler?

    Tap your answer.

    1. Yes, that is right. Length starts at the 0 mark. Put it on the start of the line and stop at 8.

    2. Not this one. Many rulers have a gap before 0. The end of the ruler is not the start of length. Try another.

    3. Not this one. Then you would count from 1. A line from 1 to 8 is only 7 cm long. Try another.

    See the answer

    On the start of the line

    Length starts at the 0 mark. Put it on the start of the line and stop at 8.

    • If you chose B: Many rulers have a gap before 0. The end of the ruler is not the start of length.
    • If you chose C: Then you would count from 1. A line from 1 to 8 is only 7 cm long.

  2. Mei wants a line 6 cm long. She starts at the 1 mark and stops at the 6 mark. How long is her line, in cm?

    See the answer

    5 cm

    From 1 to 6 is 6 − 1 = 5 cm. She should have started at 0.

  3. Which pair of lines is parallel?

    Three pairs of lines. Pair A has two lines that slope the same way with a gap that stays the same. Pair B has two lines that do not touch but get closer. Pair C has two lines that cross.ABC
    Tap your answer.

    1. Yes, that is right. Both lines in A slope the same way. The gap stays the same.

    2. Not this one. The lines do not touch here, but they get closer. Draw them longer and they meet. Try another.

    3. Not this one. These lines cross, so they meet. Parallel lines never meet. Try another.

    See the answer

    Pair A

    Both lines in A slope the same way. The gap stays the same.

    • If you chose B: The lines do not touch here, but they get closer. Draw them longer and they meet.
    • If you chose C: These lines cross, so they meet. Parallel lines never meet.

  4. How long is the line on the ruler, in cm?

    A ruler marked from 0 to 8 with the word cm. A line runs from a cross above the 2 mark to a cross above the 8 mark.012345678cm
    See the answer

    6 cm

    The line starts at 2, not at 0. From 2 to 8 is 8 − 2 = 6 cm.

  5. Name two pairs of parallel lines you can see around you.

    See the answer

    The long sides of a door. The lines on a page.

    Each pair stays the same distance apart and never meets.

  6. A line starts at the 3 mark on a ruler. It stops at the 9 mark. How long is it, in cm?

    A ruler marked from 0 to 9 with the word cm. A line runs from a cross above the 3 mark to a cross above the 9 mark.0123456789cm
    Tap your answer.

    1. Not this one. You read the end mark only. The line starts at 3. The first 3 cm of the ruler are not in it. Try another.

    2. Not this one. You counted the marks 3, 4, 5, 6, 7, 8, 9. Count the gaps between marks instead. Each gap is 1 cm. Try another.

    3. Yes, that is right. From 3 to 9 is 9 − 3 = 6 gaps of 1 cm. The line is 6 cm long.

    See the answer

    6 cm

    From 3 to 9 is 9 − 3 = 6 gaps of 1 cm. The line is 6 cm long.

    • If you chose A: You read the end mark only. The line starts at 3. The first 3 cm of the ruler are not in it.
    • If you chose B: You counted the marks 3, 4, 5, 6, 7, 8, 9. Count the gaps between marks instead. Each gap is 1 cm.

  7. Look at the picture. Are line A and line B parallel?

    Two straight lines, line A above line B. Two dashed lines join them, one at each end. The dashed line at the left end is labelled 4 cm. The dashed line at the right end is labelled 2 cm. The lines are labelled line A and line B.line Aline B4 cm2 cm
    Tap your answer.

    1. Not this one. Almost is not enough. The gap is 4 cm at one end. It is 2 cm at the other. Try another.

    2. Yes, that is right. The gap is 4 cm at the left. It is 2 cm at the right. The lines get closer, so they will meet.

    3. Not this one. Parallel lines can have different lengths. What counts is the gap. Here the gap changes. Try another.

    See the answer

    No. The gap is not the same at both ends.

    The gap is 4 cm at the left. It is 2 cm at the right. The lines get closer, so they will meet.

    • If you chose A: Almost is not enough. The gap is 4 cm at one end. It is 2 cm at the other.
    • If you chose C: Parallel lines can have different lengths. What counts is the gap. Here the gap changes.

  8. Amina draws two lines that do not touch. She makes both longer and they cross. What does that show?

    Tap your answer.

    1. Yes, that is right. Parallel lines stay the same distance apart and never meet. Lines that cross were never parallel.

    2. Not this one. On a small page, lines can seem never to meet. Parallel lines never cross, however long you draw them. Try another.

    3. Not this one. Parallel lines never cross, however long they run. Two lines that cross were not parallel. Try another.

    See the answer

    The lines were not parallel.

    Parallel lines stay the same distance apart and never meet. Lines that cross were never parallel.

    • If you chose B: On a small page, lines can seem never to meet. Parallel lines never cross, however long you draw them.
    • If you chose C: Parallel lines never cross, however long they run. Two lines that cross were not parallel.

Keep it

Copy this into your exercise book.

Put the 0 mark on the start of the line. Parallel lines stay the same distance apart and never meet.

Draw: A line 6 cm long. Draw a parallel line 2 cm below it. Mark the gap.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (773 KB). It opens on any phone.