Maths and Geography Inquiry Worksheet for 12-Year-Olds | Portal 2-Themed Learning

Instructions

1. Imagine you are a test subject helping an Aperture Science team map a new Portal testing area.
2. Complete each section in order. Show your working for calculations.
3. Use a ruler for map distances and remember that a coordinate is written as (across, up).
4. Some questions have more than one possible answer. Explain your thinking clearly.
5. Complete the optional challenge if you want to stretch yourself.

Get Curious

What is this? Why do people use it?

A map is a smaller, organised representation of a real place. Maps help people describe locations, plan journeys, measure distances, and understand how places are connected.

A coordinate grid gives every location a pair of numbers:

• The first number shows how far across to move.
• The second number shows how far up or down to move.
• For example, (3, 2) means move 3 squares across and 2 squares up.

Portal 2 connection: In a test chamber, coordinates could help a robot locate a portal, button, cube, or exit.

1. Circle the best answer.

   A map is usually used to:

   • a) make places harder to find
   • b) show where places are and how they connect
   • c) replace all journeys
   • d) measure temperature only

2. What does the coordinate (5, 4) tell you to do?

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3. Why might a delivery driver, explorer, or emergency worker use a map?

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Look Around

Where do I see this? How does it connect to my world?

Coordinates and maps appear in many real-life situations:

• Finding a seat in a cinema or a place on a sports field
• Locating a shop on a town map
• Using a grid reference in a video game
• Reading a weather map
• Planning a route with a phone or satnav

Use the grid below. The Aperture Entrance is at (1, 1), and the Exit is at (8, 6).

1. Plot or imagine these locations on a coordinate grid supplied by your teacher. Then answer the questions.

2. Which location is farthest east, meaning farthest to the right?

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3. If the Portal Station is at (4, 2), how many squares across and how many squares up is it from the entrance?

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4. The Companion Cube is at (6, 5). Is it closer to the entrance or the exit if you measure using horizontal and vertical moves?

   Show your working:

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5. Draw a route from (1, 1) to (8, 6) using only horizontal and vertical moves. How many moves does your shortest route use?

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Find the Pattern

What is the big idea? What rules make it work?

When moving between two coordinates:

• Horizontal distance = difference between the first numbers.
• Vertical distance = difference between the second numbers.
• A shortest route using only horizontal and vertical moves has length:
  • horizontal distance + vertical distance

Example: From (2, 3) to (6, 5):

• Horizontal distance: 6 - 2 = 4
• Vertical distance: 5 - 3 = 2
• Shortest route: 4 + 2 = 6 moves

Complete the table. The example row shows what to do.

Use these pairs for the blank rows:

• (1, 1) to (4, 7)
• (3, 6) to (8, 2)
• (5, 2) to (5, 9)
• (7, 8) to (2, 4)
• (4, 4) to (9, 9)

1. What pattern do you notice when the two coordinates have the same first number?

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2. What pattern do you notice when the two coordinates have the same second number?

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3. A portal makes a route 3 squares shorter. If the original route was 12 moves, how many moves is the new route?

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Have a Go

How can I use this idea? What can I make, test or solve?

The Aperture Science team has provided a map scale:

1 grid square = 5 metres

1. The shortest route from the entrance to a test chamber is 9 squares. What is the real distance?

   Calculation: _____

   Answer: __

2. A maintenance robot travels 35 metres. How many grid squares is this?

   Calculation: _____

   Answer: __

3. A route has 4 horizontal moves and 6 vertical moves. Each move is 5 metres. What is the total distance?

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4. The team has 100 metres of cable. A route uses 13 grid squares. Will there be enough cable? Explain.

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5. Design your own mini test chamber. Include:

   • An entrance and an exit
   • At least two obstacles
   • One portal or shortcut
   • At least five labelled coordinates
   • A scale of your choice

   Label your design on squared paper or in the space below.

   Coordinates and labels to include:

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6. Write instructions for a partner to travel from your entrance to your exit. Use words such as east, west, north, and south, or use coordinate pairs.

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Think Deeper

What did I learn? How can I improve or use this somewhere else?

1. Explain, in your own words, how coordinates help people find locations.

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2. Which was more useful for planning a route: coordinates, a scale, or compass directions? Give a reason.

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3. Imagine your map is used by a real rescue team. What information would you add to make it safer and easier to use?

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4. Check your work. Tick each statement when it is true.

   • I wrote coordinates in the correct order: across, then up. [ ]
   • I calculated horizontal and vertical distances separately. [ ]
   • I used the map scale correctly. [ ]
   • I explained at least one answer using mathematical reasoning. [ ]

Optional Challenge

A Portal can connect two distant points. On a normal route, a robot travels from (2, 2) to (9, 7) using only horizontal and vertical moves.

1. What is the shortest normal route?

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2. A portal connects (4, 5) directly to (8, 3). The robot can walk to the first portal, teleport, and then walk to the destination. How many walking moves does this route use?

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3. How many moves does the portal save compared with the normal route?

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Answer Key

Get Curious

1. b) show where places are and how they connect
2. Move 5 squares across and 4 squares up.
3. Sample answer: They can use a map to locate people or places, plan the quickest route, and avoid hazards.

Look Around

1. Answers depend on the learner's plotted map.
2. The Exit, at (8, 6), is farthest east.
3. It is 3 squares across and 1 square up from the entrance.
4. From the entrance to (6, 5): 5 + 4 = 9 moves. From (6, 5) to the exit (8, 6): 2 + 1 = 3 moves. The Companion Cube is closer to the exit.
5. Horizontal distance: 8 - 1 = 7. Vertical distance: 6 - 1 = 5. The shortest route uses 12 moves.

Find the Pattern

1. If the first numbers are the same, there is no horizontal distance; the route is vertical only.
2. If the second numbers are the same, there is no vertical distance; the route is horizontal only.
3. 12 - 3 = 9 moves.

Have a Go

1. 9 x 5 = 45 metres.
2. 35 / 5 = 7 grid squares.
3. 4 + 6 = 10 moves; 10 x 5 = 50 metres.
4. 13 x 5 = 65 metres. Yes, there is enough cable, with 35 metres left.
5. Answers will vary. The design should include all five required features.
6. Answers will vary. The instructions should clearly lead from the entrance to the exit.

Think Deeper

1. Sample answer: Coordinates give each location a precise address on a grid, so people can find it accurately.
2. Answers will vary if they include a sensible reason. For example, a scale is useful for working out real distances.
3. Sample answers: Add a legend, hazards, landmarks, north arrow, emergency exits, or distances.

Optional Challenge

1. Horizontal distance: 9 - 2 = 7. Vertical distance: 7 - 2 = 5. Normal route = 12 moves.
2. Walk from (2, 2) to (4, 5): 2 + 3 = 5 moves. After teleporting to (8, 3), walk to (9, 7): 1 + 4 = 5 moves. Total walking = 10 moves.
3. 12 - 10 = 2 moves saved.