Chapter 8 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

M2.5.8 Chapter 8

Grids and directions

How do I tell a friend which box to look in?

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

  • Give a position on a grid by column and row
  • Use north, south, east and west to describe a route

A grid is a set of boxes in rows and columns. It names a place exactly.

Draw it first

Find the box B3

  1. A grid with columns A, B, C, D and E across the top and rows 1, 2, 3 and 4 down the side. Step 2 outlines column B and is labelled column B. Step 3 outlines row 3 and is labelled row 3. Step 4 marks the box where they meet with a dot and is labelled B3.ABCDE1234

    1 Letters name the boxes across. Numbers name the boxes down.

  2. A grid with columns A, B, C, D and E across the top and rows 1, 2, 3 and 4 down the side. Step 2 outlines column B and is labelled column B. Step 3 outlines row 3 and is labelled row 3. Step 4 marks the box where they meet with a dot and is labelled B3.ABCDE1234column B

    2 A column goes up and down. This is column B.

  3. A grid with columns A, B, C, D and E across the top and rows 1, 2, 3 and 4 down the side. Step 2 outlines column B and is labelled column B. Step 3 outlines row 3 and is labelled row 3. Step 4 marks the box where they meet with a dot and is labelled B3.ABCDE1234row 3

    3 A row goes across. This is row 3.

  4. A grid with columns A, B, C, D and E across the top and rows 1, 2, 3 and 4 down the side. Step 2 outlines column B and is labelled column B. Step 3 outlines row 3 and is labelled row 3. Step 4 marks the box where they meet with a dot and is labelled B3.ABCDE1234B3

    4 Column B and row 3 meet in one box. Its name is B3.

Say the column first, then the row. B3 means column B, row 3.

Maps show direction too. North is at the top of a map. South is at the bottom.

East is on the right. West is on the left. These four are the compass points.

Four arrows leave a middle point. The arrow up points to the label north. The arrow right points to east. The arrow down points to south. The arrow left points to west.northeastsouthwest
Go round the way a clock hand turns: north, east, south, west.

Face north. East is on your right. West is on your left. South is behind you.

To find north where you live, use a map or a compass. Ask a neighbour if you are not sure.

A route is the path you follow from one box to another. Say it in boxes and compass points.

A grid with columns A, B, C and D and rows 1, 2 and 3. A route starts at A1, goes east along row 1 to D1, then south down column D to D3. The labels are start A1 and end D3.ABCD123start A1end D3
East 3 boxes, then south 2 boxes.

Worked example

Start at A1. Go east 3 boxes. Then go south 2 boxes. Which box are you in?

  1. East is to the right, along the letters. From A, go 3 boxes: B, C, D.
  2. You are in column D. You are still in row 1.
  3. South is down, along the numbers. From row 1, go 2 boxes: 2, 3.
  4. Column D and row 3 make the box D3.

Answer: D3

See it three ways

With things

Draw a grid on paper. Put a bean in one box. Tell a friend its name, column first.

As a picture

A map grid with columns A, B, C, D and E and rows 1, 2, 3 and 4. A tree is in D1, a hut in B2, a well in C3 and a pond in E4. The labels are tree, hut, well and pond.ABCDE1234treehutwellpond

In symbols

The well is in column C and row 3. Its name is C3.

Try it

Walk a route on a floor grid

You need: floor tiles, or chalk or a stick for drawing boxes, a stone to mark north.

  1. Make a grid 4 boxes wide and 4 boxes long.
  2. Put the stone by one edge. That edge is north, like the top of a map.
  3. Face the stone. Write A to D along that edge, from left to right.
  4. Write 1 to 4 along a side. Start next to the stone. East is on your right.
  5. Stand in B2. Walk east 2 boxes. Say your box. You are in D2.
  6. Walk south 1 box, then west 3 boxes. Say your box each time. You end in A3.

What you will see: Each step changes one thing. East and west change the column letter. North and south change the row number.

If you cannot try it, this is what happens.
A grid with columns A, B, C and D and rows 1, 2, 3 and 4. A route starts at B2, goes east to D2, then south to D3, then west to A3. The labels are start B2 and end A3.ABCD1234start B2end A3

A wrong idea many people have

The order of a grid position does not matter.

Why it feels right: Adding can swap places. 2 + 3 and 3 + 2 are equal.

The test that breaks it: Draw a grid. Count 2 boxes across and 3 down. Mark the box. Now count 3 across and 2 down. Mark that box too. They are different boxes.

What is true: A position has a fixed order. Say the column first, then the row. 2 across and 3 down is B3. 3 across and 2 down is C2.

Key words

column
boxes in a line going up and down.
row
boxes in a line going across.
compass points
north, east, south and west.
route
the path you follow from one place to another.

Back to your guess

The answer is C: Say the column and the row, like B3.

A column alone names a whole stripe of boxes. A column and a row meet in one box. Everyone must say them in the same order. This book gives the column first.

Check yourself

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

  1. Which box has the well?

    A map grid with columns A, B, C, D and E and rows 1, 2, 3 and 4. A tree is in D1, a hut in B2, a well in C3 and a pond in E4. The labels are tree, hut, well and pond.ABCDE1234treehutwellpond
    Tap your answer.

    1. Yes, that is right. The well is in column C and row 3. Column first, then row, so C3.

    2. Not this one. This book says the column letter comes first, then the row number. Write C3. Try another.

    3. Not this one. Look at the letter above the well. It is C, not B. Box B3 is under the hut. Try another.

    See the answer

    C3

    The well is in column C and row 3. Column first, then row, so C3.

    • If you chose B: This book says the column letter comes first, then the row number. Write C3.
    • If you chose C: Look at the letter above the well. It is C, not B. Box B3 is under the hut.

  2. Start at B1. Go east 2 boxes. Then go south 3 boxes. Which box are you in?

    See the answer

    D4

    East 2 from B is C, D. South 3 from row 1 is 2, 3, 4. So you are in D4.

  3. Mei is in box E3. She walks west 2 boxes. Which box is she in?

    See the answer

    C3

    West is left, along the letters. From E, go back 2 boxes: D, C. The row stays 3.

  4. You face north. Where is east?

    Tap your answer.

    1. Yes, that is right. Face north. East is on your right. West is on your left. South is behind you.

    2. Not this one. West is on your left when you face north. East is the other side. Try another.

    3. Not this one. South is behind you when you face north. East is to the side. Try another.

    See the answer

    On your right

    Face north. East is on your right. West is on your left. South is behind you.

    • If you chose B: West is on your left when you face north. East is the other side.
    • If you chose C: South is behind you when you face north. East is to the side.

  5. From an earlier chapter

    Ravi faces north. He turns a quarter turn clockwise, so he faces east. How many degrees did he turn?

    See the answer

    90°

    A quarter turn is one right angle. A full turn is 360°, and 360 ÷ 4 = 90.

  6. Tariq is in box B2. He walks east 2 boxes. Which box is he in?

    Tap your answer.

    1. Not this one. You counted the box you stand in as 1. Step 2 boxes away from B: C, then D. Try another.

    2. Not this one. That changes the row number. East and west change the letter. North and south change the number. Try another.

    3. Yes, that is right. East is to the right, along the letters. From B, go 2 boxes: C, D. The row stays 2.

    See the answer

    D2

    East is to the right, along the letters. From B, go 2 boxes: C, D. The row stays 2.

    • If you chose A: You counted the box you stand in as 1. Step 2 boxes away from B: C, then D.
    • If you chose B: That changes the row number. East and west change the letter. North and south change the number.

  7. Ana walked from A1 to D3. She went east 3 boxes, then south 2 boxes. How does she walk back?

    A grid with columns A, B, C and D and rows 1, 2 and 3. A route starts at A1, goes east along row 1 to D1, then south down column D to D3. The labels are start A1 and end D3.ABCD123start A1end D3
    Tap your answer.

    1. Yes, that is right. Going back, the last walk comes first. South 2 becomes north 2. Then east 3 becomes west 3.

    2. Not this one. Those are the same directions as the way there. To go back, turn each direction round. Try another.

    3. Not this one. The directions are right, but the numbers are swapped. She went south 2 boxes and east 3. Try another.

    See the answer

    North 2 boxes, then west 3 boxes

    Going back, the last walk comes first. South 2 becomes north 2. Then east 3 becomes west 3.

    • If you chose B: Those are the same directions as the way there. To go back, turn each direction round.
    • If you chose C: The directions are right, but the numbers are swapped. She went south 2 boxes and east 3.

  8. Which name tells where the dot is?

    A grid with columns A, B, C, D and E and rows 1, 2, 3 and 4. A dot sits in one box, in column D and row 2.ABCDE1234
    Tap your answer.

    1. Not this one. You read the row first. This book says the column letter comes first, then the row number. Try another.

    2. Yes, that is right. The dot is in column D. It is in row 2, counting down from the top. Column first, so D2.

    3. Not this one. You counted the rows from the bottom. Rows are numbered from the top, so this is row 2. Try another.

    See the answer

    D2

    The dot is in column D. It is in row 2, counting down from the top. Column first, so D2.

    • If you chose A: You read the row first. This book says the column letter comes first, then the row number.
    • If you chose C: You counted the rows from the bottom. Rows are numbered from the top, so this is row 2.

Keep it

Copy this into your exercise book.

Name a box by column, then row: B3. North is up, east is right, south is down, west is left. East and west change the letter. North and south change the number.

Draw: A grid of 4 columns and 3 rows. Label it A to D and 1 to 3. Mark B2 with a dot.

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.