Coordinates and Position: a week of ready-to-teach maths

Five days of lessons for Year 5 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus game boards for hidden treasure, journey and move cards to match, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Print the game boards once per child and the cards once per pair, and find masking tape or chalk for Day 1.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: two numbered axes meeting at the origin turn a space into a grid of points, and a pair of numbers, across first and then up, names each point exactly. A move from one point to another is the change in each number, and on a map the same move can be said in compass words.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 builds the grid; Days 2 and 3 read and plot points on it; Day 4 moves between points; and Day 5 says the moves in compass words. It builds on Year 4’s grid references, which name squares (AC9M4SP02), and it leads to Year 6, where the axes run past the origin into four quadrants (AC9M6SP02).

Materials for the week (one trip)

• From the classroom: masking tape or chalk for a floor grid, rulers, a coloured pencil each, 1 cm grid paper, this pack printed.
• Print once per child: the game boards (Day 5). Print once per pair: the journey and move cards (Day 4).

Words for the word wall

coordinates, axis, axes, origin, horizontal, vertical, plot, point, move, north, south, east, west

Dear families

This week in maths, Year 5 learns to name places with coordinates: a pair of numbers that says how far across and how far up a point is from a starting corner called the origin. The point (4, 1) is 4 across and 1 up, a different place from (1, 4).

Try this at home

• Draw a grid on paper and hide a coin at a point. Your child guesses its coordinates; tell them which way to go: north, south, east or west.
• Look at a street map or a seating plan together. How does it name a place?
• Give directions round the house in moves: 3 steps forward, turn right, 2 steps.

Places I named this week

Fill one row a day. Draw a small grid, mark a place, and write its coordinates.

Printed from the free seegongsik Coordinates and Position teaching pack · seegongsik.com/au/y5/space/AC9M5SP02/pack

A grid of points

A coordinate grid is built from two number lines, the axes, at right angles: the horizontal axis runs across and the vertical axis runs up. They meet at the origin, (0, 0). The numbers go on the lines, not in the spaces, so a pair of numbers names a point where two lines cross. That is the change from Year 4, where a letter and a number named a square.

We are learning to

• build a coordinate grid: two axes at right angles, numbered from the origin,
• tell a grid of points from a grid of squares,
• name a point by how far across and how far up it is.

Success criteria

• I can draw and number the axes of a coordinate grid.
• I can name a point where two lines cross by its coordinates.

You need

Masking tape or chalk for a floor grid with lines about half a metre apart. Rulers. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the floor grid; start Session B with Part A.

Watch for these ideas

• Numbering the spaces instead of the lines, as on a Year 4 grid of squares.
• Starting at 1 at the origin, so every point comes out one too many.
• Counting up before across. The first number is always across.

Answers

• Part A: 0 to 7 along each axis, 0 at the origin; the points are (4, 6) and (7, 2).
• Part B: square B3; the point (4, 2); the left grid names squares (a letter and a number in the spaces), the right grid names points (numbers on the lines). Part C: with the axes along the bottom and left edges, (1, 1), (7, 2), (3, 5).

A grid of points

A. Number the axes

B. Squares or points?

1. On the left grid, the tree is in square ________.

2. On the right grid, the tree is at the point ( ____ , ____ ).

3. Which grid names a square, and which names a point? How can you tell?

C. Build your own grid

Across, then up

The first number of a pair says how far across from the origin, along the horizontal axis; the second says how far up. Across, then up, every time: (6, 2) and (2, 6) use the same numbers but are different points. A point on an axis has a zero: (0, 5) is on the vertical axis, 5 up, and (5, 0) is on the horizontal axis, 5 across.

We are learning to

• read the coordinates of a point, across first and then up,
• read points that sit on an axis,
• explain why the order of the two numbers matters.

Success criteria

• I can write the coordinates of any point on the grid.
• I can explain why swapping the numbers moves the point.

You need

The floor grid from Day 1. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with Parts B and C.

Watch for these ideas

• Reading up before across, so the two numbers come out swapped.
• Counting the origin line as 1, so each number comes out one too many.
• Leaving out the zero for a point on an axis.

Answers

• Part A: A (2, 5), B (6, 1), C (1, 6), D (0, 4), E (7, 3), F (4, 0), G (5, 7), H (8, 6).
• Part B: 1. B and C; not the same point (B is 6 across and 1 up, C is 1 across and 6 up). 2. D and F; each has a 0. Part C: they read up first. E is (7, 3); (3, 7) is 3 across and 7 up, a different point.

Across, then up

A. Write the coordinates of each point

B. Look again

1. Two points have the same two numbers in a different order. Which two? Are they the same point?

2. Which points sit on an axis? What do their coordinates have in common?

C. A mistake

Someone wrote the coordinates of point E as (3, 7). What went wrong? Mark (3, 7) on the grid with a cross.

Plot a picture

To plot a point, start at the origin, count across along the horizontal axis to the first number, then up to the second, and mark where the two lines cross. Points plotted in order and joined make a picture, so a picture can be kept as a list of coordinates and drawn again by anyone who has the list.

We are learning to

• plot a point from its coordinates,
• join plotted points in order to make a picture,
• use coordinates to find a missing corner.

Success criteria

• I can plot any point from its coordinates.
• I can write a picture as a list of coordinates for someone else to draw.

You need

Rulers and a coloured pencil. 1 cm grid paper for Part C. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the rectangle in Part B.

Watch for these ideas

• Plotting up before across, so the picture comes out flipped onto its side.
• Marking a point in the middle of a square instead of where two lines cross.
• Joining the last point of one line to the first point of the next. Lift the pencil between lines.

Answers

• Part A: a sailboat, a hull and two sails.

  Part B: (2, 5), straight above (2, 2) and level with (7, 5). Part C: pictures vary; a partner’s matching drawing is the check.

Plot a picture

A. Plot each line of points in order and join them. Lift your pencil between lines.

B. Three corners of a rectangle

C. Your own picture

On 1 cm grid paper, draw and number two axes, then a picture with 4 to 8 corners, each where two lines cross. Write its points in order here, then swap with a partner.

Moves on the grid

A move from one point to another is the change in each coordinate. From (1, 2) to (5, 3) the first number grows by 4 and the second by 1, so the move is 4 right and 1 up. A smaller first number means a move left, and a smaller second number a move down. A path is a list of moves, each starting where the last one landed.

We are learning to

• describe a move by the change in each coordinate,
• say right or left, and up or down, for each change,
• follow a path of moves and give the point where it ends.

Success criteria

• I can describe the move from one point to another.
• I can follow a list of moves and give the coordinates where it ends.

You need

The journey and move cards (cut-out sheet 2), one set per pair, cut out. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the cards; start Session B with Part A.

Watch for these ideas

• Giving the second point’s coordinates as the move, as in ‘4 right and 3 up’ on the board.
• Saying right or up when a number gets smaller.
• On a path, starting each move from the start instead of from where the last move landed.

Answers

• Cards: 1 C, 2 F, 3 H, 4 B, 5 E, 6 D, 7 A, 8 G.
• Part A: 4 right and 3 up; 4 left and 3 down; 5 right; 2 left and 5 up. Part B: (3, 3), (5, 0), (1, 5), (6, 6), (4, 2); it ends at (4, 2). Part C: 3 left and 3 up; back: 3 right and 3 down.

Moves on the grid

A. Describe each move

B. Follow the path

Start at (0, 1). Write the point each move lands on.

C. There and back

A move took a counter from (6, 2) to (3, 5). What was the move? What move brings it back?

North, south, east and west

On a map, north is up and east is to the right, so a move on a coordinate grid can be said in compass words: from (2, 2) to (6, 3) is 4 east and 1 north. The words give the way to go and the numbers say how far. Between the four main directions lie north-east, north-west, south-east and south-west.

We are learning to

• say where one place is from another in compass words,
• follow directions given in compass words,
• use directions to find a hidden point.

Success criteria

• I can say where a place is from another using north, south, east and west.
• I can give a clue that leads a partner to a point.

You need

The game boards (cut-out sheet 1), one per child. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with hidden treasure.

Watch for these ideas

• Mixing up east and west. East is the way the numbers grow along the horizontal axis.
• Giving the way back: ‘where is the library from the hall’ starts at the hall.
• In the game, saying north-east to a guess level with the treasure. A level guess gets east or west only.

Answers

• Part A: 4 east and 2 north; 2 east and 3 north; 4 east and 5 south; 3 west and 1 north.
• Part B: 1. (7, 6), the bench; 2. (6, 1), the slide. Part C: guesses vary; check that each clue is the way from the guess to the treasure.

North, south, east and west

A. The park map: where is it?

B. Follow the directions

1. Start at the gate. Go 3 north, then 6 east, then 2 north.
Where do you end?   ( ____ , ____ )    What is there?   ______________

2. Start at the tap. Go 2 east, then 6 south.
Where do you end?   ( ____ , ____ )    What is there?   ______________

C. Hidden treasure

Play on the game boards. Write each guess and the clue your partner gives.

Hidden treasure: game boards

One sheet per child (Day 5). North is up each board, and east is to the right.

1. Mark a secret treasure at a point on “My treasure”. Keep it hidden.
2. Take turns. Say a guess by its coordinates, such as (3, 5), and mark it on “My guesses”.
3. Your partner says which way the treasure is from your guess: north, south, east or west, or north-east, north-west, south-east or south-west. Record the guess and the clue in Part C of the Day 5 worksheet.
4. Guess until you land on the treasure. The fewest guesses wins. Then hide a new one.

Teacher note: a clue of north-east means the treasure is further north and further east than the guess.

Journey cards and move cards

One set per pair (Day 4). Cut out all sixteen cards and match each journey to its move.

Teacher note: each journey has exactly one move card. The matches are on the Day 4 plan.

What we know: Coordinates and Position

1. What are the coordinates of P?   ( ____ , ____ )
2. What are the coordinates of R?   ( ____ , ____ )
3. Mark the point (5, 2) on the grid with a cross, and label it S.
4. Describe the move from P to Q.   ______________________________
5. Start at (2, 1). Move 4 right and 3 up. Where do you land?   ( ____ , ____ )
6. Someone says (2, 7) and (7, 2) are the same point because they use the same numbers. Are they right? Explain.
7. On a map with north at the top, the school is at (1, 2) and the shop is at (4, 6). Where is the shop from the school, in compass words?   ______________________________
8. Three corners of a square are (1, 1), (4, 1), (4, 4). What are the coordinates of the fourth corner?   ( ____ , ____ )

Answers and marking guide

Answers

1. (6, 3)
2. (0, 2), on the vertical axis
3. S at 5 across and 2 up, where two lines cross
4. 3 left and 3 up
5. (6, 4)
6. No: (2, 7) is 2 across and 7 up, and (7, 2) is 7 across and 2 up.
7. 3 east and 4 north
8. (1, 4)

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by counting across first and then up from the origin, and by reading a move as the change in each number.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: building a grid, reading points, plotting points, describing moves, and compass directions.