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KS2 Maths: Coordinates

TEACHERS NOTESAbout this activity

This activity helps pupils practice plotting and using coordinates, using a real life scenario set at Manchester Airport. Taking off can be the noisiest part of a flight and so aircraft follow Preferred Noise Routes (PNRs) that guide them away from built-up areas wherever possible. Pupils use coordinate data to plot PNRs and then check whether aircraft are flying the correct route. They then use translations to guide aircraft back on the right course if necessary.

Single and four quadrant versions of the coordinate grid support a differentiated approach.

Learning outcomes

Pupils can: describe position on a coordinate grid (single or four quadrant). Use translations.

Curriculum links

Maths: position and direction (years 5 and 6).

Resources and preparation

• Choose whether you will use the single or four quadrant version of the coordinate grid (or both, to support differentiation). Print enough pupil sheets and maps for the class.

• Review the presentation slides. You will need a whiteboard and data projector for the activity.• Pupils will need pencils, rulers and pens.

Timings

The activities can be delivered in a single lesson of approximately one hour but you may wish to extend over two lessons.

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LESSON PLANStarter activity ideas

Before you begin you may wish to:

• Review how to plot coordinates on a single or four quadrant grid. Use a blank grid, or the Pupil Maps, and ask pupils to plot the positions of some aircraft using random coordinates.

• Review how to use a translation to move within a grid. Ask pupils to move an aircraft from one position to another by giving the correct translation. These can include combinations of positive and negative values, eg (2, 2), (3, -1), (-2, -4).

Main activities

Introduce the activity and explain that pupils are going to use coordinate data to plot some important routes aircraft follow after taking off from Manchester Airport. These routes have been chosen so whenever possible aircraft don’t cause too much noise for people living nearby and avoid flying low over places like the nearby Peak District National Park.

Show slide 1 and talk about what pupils think Manchester Airport might be like.

Show slide 2. Briefly discuss why take off may be the noisiest part of a flight. (It is because the aircraft is at its heaviest as it is carrying all its fuel for the journey, and is working against gravity to gain height.) Ensure pupils understand that a Preferred Noise Route (PNR) is a pathway through the sky.

Task 1: which way should aircraft take off?

Show slide 3 and ask pupils to look at their copies of the Pupil Map. Explain that the first task is to work out which way aircraft should take off. Explain that aircraft must always take off and land into the wind, and on about 4 days out of 5, this comes from the southwest. The Airport is said to be in ‘westerly operation’ on these days.

All: ask the class to point to show the direction aircraft should take off and land from the Airport (from the top right corner towards the bottom left corner.

Less able: Highlight the runways on slide 3. Invite pupils to point to show where aircraft might fly when taking off, and from where they might arrive when landing.

More able: Highlight the runways on slide 3. Ask pupils which quadrant aircraft might fly into when taking off (quadrant 3), and from where they might arrive when landing (quadrant 2).

If time permits, explain that the rest of the time, the wind tends to come from the northeast and the Airport is in ‘easterly operation’ on these days. Repeat the above questions for this scenario.

KS2 Maths: Coordinates

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LESSON PLANTask 2: plot PNRs

Explain that in this activity, aircraft will take off towards the southwest. Establish that for simplicity and because the grid covers quite large squares, every PNR begins at the centre of the two runways, at (10, 7) on single quadrant grids, and (0, 0) on four quadrant grids.

Review the Westerly Operation table on the Pupil Sheet One, using either the single or four quadrant version. Each line shows the codename for a PNR (these appear on the maps that pilots and Air Traffic Controllers use).

All: ask pupils to plot each PNR and label it with its codename.

Less able: Assign one or more PNRs according to ability or allow pupils to work with a partner.

More able (only for pupils using the four quadrant version of the pupil sheets and map): Pupils complete all five PNRs for Westerly Operation. Explain that pupils now need to complete three PNRs for Easterly Operation by performing translations, starting from (0, 0), to find each point that makes up these three PNRs.

Review answers on slide 4 (single quadrant) and / or slide 5 (four quadrant).

Task 3: are these aircraft following their PNR?

Explain that the Air Traffic Controllers at Manchester Airport carefully monitor every aircraft’s flight to make sure it stays on its PNR.

Show slide 6. Explain that in real life each PNR curves gently to reflect how aircraft turn in the air (they can’t turn a sharp corner), so the PNRs pupils plotted are just rough approximations. There are also more PNRs – eight for Westerly Operations and six for Easterly Operations. PNRs are also very wide, 3km, or 3000m. This gives aircraft plenty of space because, for safety, it’s vital that aircraft stay well apart from one another.

Establish that for this task the PNR extends to one grid square’s distance either side of the routes pupils have plotted. Briefly discuss this using slide 4 or 5 to help you. Show how to approximate this distance a tangent (90o) to the line of the PNR.

Review the four aircraft A - D.

All: Ask pupils to plot their position and report back on which ones are outside of their PNR (Aircraft A and D).

More able: Ask pupils to tell you a translation that will get each aircraft back to a point on the correct PNR:

- For aircraft A to move to point (4, 14) (single quadrant) or (-6, 7) (four quadrant) - For aircraft D to move to point (6, 0) (single quadrant) or (-4, -10) (four quadrant)

Answers: A should move (-4, -1) and D should move (1, -3).

KS2 Maths: Coordinates

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LESSON PLANPlenary

Remind pupils that PNRs are the routes aircraft follow after taking off from Manchester Airport, so whenever possible they don’t cause too much noise for people living nearby and avoid places like the nearby Peak District National Park.

Task 4: can we define an area using coordinates?

Show slide 4 or slide 5 (or ask pupils to look at their Pupil Maps). Ask if pupils can identify the areas that form the edge of the Peak District (the shaded areas at the right of the map). Can pupils name some coordinates that would form a simple boundary for the area aircraft should not flow low over?

Task 5: which PNR should these aircraft follow?

Review the final activity on the Pupil Sheet. Ask pupils to imagine that the wind is coming from the southwest, as normal. What PNR might be the best choice for the aircraft flying to New York? (Banana) What about to Rome? (Pear or Plum).

If time permits ask pupils to imagine the Airport is in Easterly Operation and the direction of take off and landing has been reversed. What PNRs are now most appropriate? (Grape and Apricot respectively.)

KS2 Maths: Coordinates

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EXTENSION IDEAS

Sometimes an aircraft may need to urgently return and land after take off.

Ask pupils to imagine that an aircraft has taken off towards the southwest and has got as far as (8, 5) (single quadrant) or (-2, -2) (four quadrant). Can pupils give coordinates for two rectangles that would allow the aircraft to fly round and land again, approaching the runway from the northeast? One rectangle should be for an aircraft flying partway along Banana and the other for if the aircraft were flying partway along Pear.

• Search online to find some images of real aircraft charts. What things might need an accurate location on charts for pilots, (these include airports or small airfields, tall buildings, aerials, pylons, hills etc.)

• Explore more accurate ways to plot position, such as the OS grid reference system (see https://www.youtube.com/watch?v=KK19-rJHNP8 for a helpful video from Ordnance Survey), and the latitude and longitude used by sea vessels and aircraft (see https://www.youtube.com/watch?v=swKBi6hHHMA for a video).

• Aircraft measure distance in nautical miles (one nm = 1852m). Convert some local distances between m, km, miles and nautical miles.

KS2 Maths: Coordinates

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PUPIL SHEET ONE – SINGLE QUADRANT

Manchester Airport is a busy place. Each year, there are nearly 170,000 flights in and out of the Airport. Taking off can be the noisiest part of a flight. Preferred Noise Routes (PNRs) guide aircraft away from built-up areas wherever possible. PNRs have titles that are combinations of numbers and letters but to make things simpler we have called them by different fruit names.

Use these coordinates to plot each PNR on a map

Every PNR starts at (10,7).

Westerly Operation

Apple (8, 5), (5, 6), (0, 4)

Orange (8, 5), (6, 6), (5, 4), (6, 0)

Banana (8, 5), (7, 6), (4, 15)

Pear (8, 5), (9, 3), (11, 0)

Plum (9, 6), (10, 3), (12, 0)

Make sure these aircraft are following the correct PNR

PNRs are 3km (3000m) wide – much wider than the lines you have plotted.

Which of these aircraft is within one grid square of the correct PNR?

Aircraft A is at (8, 13) and should be following PNR BANANA

Aircraft B is at (4, 12) and should be following PNR BANANA

Aircraft C is at (1, 5) and should be following PNR APPLE

Aircraft D is at (7, 3) and should be following PNR ORANGE

Which PNRs should these aircraft follow?

After take-off, aircraft flying to the USA should head north, while aircraft flying to Europe should head south.

Aircraft E is heading to New York and aircraft F is heading to Rome. Which PNR should Air Traffic Control tell each aircraft to follow?

KS2 Maths: Coordinates

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PUPIL MAP ONE – SINGLE QUADRANT

Manchester AirportSingle Quadrant Map

Key: Runway 1 Runway 2

12345678910111213141516171819202122

1

23

4

5

6

7

8

9

10

11

12

13

14

15

0

N

E

S

W

KS2 Maths: Coordinates

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PUPIL SHEET ONE – FOUR QUADRANT

Manchester Airport is a busy place. Each year, there are nearly 170,000 flights in and out of the Airport. Taking off can be the noisiest part of a flight. Preferred Noise Routes (PNRs) guide aircraft away from built-up areas wherever possible. PNRs have titles that are combinations of numbers and letters but to make things simpler we have called them by different fruit names.

Use these coordinates to plot each PNR on a map

Every PNR starts at (0,0).

Westerly Operation

Easterly Operation

Every PNR starts at (0,0).

Each pair of numbers below is a translation, not a coordinate. Complete each translation one by one to draw each PNR.

Apple (-2, -2), (-5, -1), (-10, -3)

Orange (-2, -2), (-4, -1), (-5, -3), (-4, -7)

Banana (-2, -2), (-3, -1), (-7, 8)

Pear (-2, -2), (-1, -4), (1, -7)

Plum (-1, -1), (0, -4), (2, -7)

Grape (1,1), (0,1), (-8, 6)

Peach (1,1), (7, 7)

Apricot (1,1), (2, -1), (-1,-7)

Make sure these aircraft are following the correct PNR

PNRs are 3km (3000m) wide – much wider than the lines you have plotted.

KS2 Maths: Coordinates

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PUPIL SHEET ONE – FOUR QUADRANT

Which of these aircraft is within one grid square of the correct PNR?

Aircraft A is at (-2, 6) and should be following PNR APPLE

Aircraft B is at (-6, 5) and should be following PNR BANANA

Aircraft C is at (-9, -2) and should be following PNR APPLE

Aircraft D is at (-3, -4) and should be following PNR ORANGE

Which PNRs should these aircraft follow?

After take-off, aircraft flying to the USA should head north, while aircraft flying to Europe should head south.

Aircraft E is heading to New York and aircraft F is heading to Paris. Which PNR should Air Traffic Control tell each aircraft to follow?

KS2 Maths: Coordinates

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PUPIL MAP ONE – FOUR QUADRANT

Manchester AirportFour Quadrant Map

-10-9-8-7-6-5-4-3-2-10123456789101112

-10

1

2

3

4

5

6

7

Runway2

8

-2

-3

-4

-5-6

-7

Key: Runway 1 Runway 2

N

E

S

W

KS2 Maths: Coordinates