Year 4: Routes, robots and treasure maps
Part of the Year 4 coordinates and translation chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Routes, robots and treasure maps
Robots follow programs. A program is a list of instructions. Here are three instructions for a robot on a grid:
- F3 means go forward 3 squares in the way the robot is facing.
- R means turn right a quarter turn (a right angle).
- L means turn left a quarter turn (a right angle).
A half turn is two quarter turns, so we write R R. Remember, left and right are from the robot’s point of view, not yours.
On a treasure map we use coordinates and compass points together. Going east makes the x-coordinate bigger. Going west makes it smaller. Going north (up) makes the y-coordinate bigger. Going south (down) makes it smaller. A treasure clue can also use a move: “the treasure is 4 right and 3 up from the old tree”.
The shortest route along the grid lines from one point to another goes across and then up or down. Add the number of squares across and the number of squares up or down.
Key ideas
- F n = forward n squares. R = turn right a quarter turn. L = turn left a quarter turn. A half turn is R R.
- A quarter turn is a right angle. Left and right are from the robot’s point of view.
- East: x gets bigger. West: x gets smaller. North: y gets bigger. South: y gets smaller.
- Shortest route along grid lines = squares across + squares up or down.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the instructions one at a time. F means forward, R means turn right (a quarter turn) and L means turn left (a quarter turn). Write the position after each instruction.
- Write the start point and the way the robot faces. We follow the program from here. The robot’s left and right depend on the way it is facing.Start at (1, 1), facing north.
- Instruction 1: F3. Forward 3 squares north.(1, 1) → (1, 4)
- Instruction 2: R. Turn right a quarter turn: now facing east.north → east
- Instruction 3: F2. Forward 2 squares east.(1, 4) → (3, 4)
- Write where the robot finishes. Look at the last position and the last way it faces.The robot ends at (3, 4), facing east.
Check. Draw the path on the grid from (1, 1): it ends at (3, 4). ✓
Watch out. Turn left or right from the way the robot is facing, not from the way you are looking at the page.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the instructions one at a time. F means forward, R means turn right (a quarter turn) and L means turn left (a quarter turn). Write the position after each instruction.
- Write the start point and the way the robot faces. We follow the program from here. The robot’s left and right depend on the way it is facing.Start at (5, 1), facing north.
- Instruction 1: F2. Forward 2 squares north.(5, 1) → (5, 3)
- Instruction 2: L. Turn left a quarter turn: now facing west.north → west
- Instruction 3: F3. Forward 3 squares west.(5, 3) → (2, 3)
- Instruction 4: R. Turn right a quarter turn: now facing north.west → north
- Instruction 5: F1. Forward 1 square north.(2, 3) → (2, 4)
- Write where the robot finishes. Look at the last position and the last way it faces.The robot ends at (2, 4), facing north.
Check. Draw the path on the grid from (5, 1): it ends at (2, 4). ✓
Watch out. Turn left or right from the way the robot is facing, not from the way you are looking at the page.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Look at each straight part of the path. If the robot is not facing the right way, turn first. Then write F and the number of squares.
- Look at the start and the way the robot faces. We start with the robot at the first point.Start at (1, 1), facing north.
- Do the path one straight part at a time. For each part: turn to face the right way if needed, then go forward the number of squares.(1, 1) to (1, 4): forward 3.
(1, 4) to (4, 4): turn right (now facing east), then forward 3.
(4, 4) to (4, 2): turn right (now facing south), then forward 2. - Write the program. Join all the instructions in order.Program: F3 R F3 R F2
Check. Run the program from (1, 1): F3 R F3 R F2 ends at (4, 2). ✓
Watch out. Check which way the robot is facing before you choose R or L.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Look at each straight part of the path. If the robot is not facing the right way, turn first. Then write F and the number of squares.
- Look at the start and the way the robot faces. We start with the robot at the first point.Start at (2, 2), facing north.
- Do the path one straight part at a time. For each part: turn to face the right way if needed, then go forward the number of squares.(2, 2) to (2, 5): forward 3.
(2, 5) to (2, 3): turn right twice, a half turn (now facing south), then forward 2. - Write the program. Join all the instructions in order.Program: F3 R R F2
Check. Run the program from (2, 2): F3 R R F2 ends at (2, 3). ✓
Watch out. Check which way the robot is facing before you choose R or L.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the directions one at a time. East and west change the x-coordinate. North and south change the y-coordinate.
- Write the start point. The map starts here.Start at (2, 2).
- Follow each direction. East makes x bigger. West makes x smaller. North makes y bigger. South makes y smaller.3 east: (2, 2) → (5, 2) (x gets bigger)
4 north: (5, 2) → (5, 6) (y gets bigger)
2 west: (5, 6) → (3, 6) (x gets smaller) - Write where the treasure is. The last point is the place the map shows.The treasure is at (3, 6).
Check. Count the squares on the grid from (2, 2): you arrive at (3, 6). ✓
Watch out. North is up the grid, so going north makes the y-coordinate bigger.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. “4 right and 3 up” is a translation. Do it to the old tree’s coordinates.
- Write the old tree’s coordinates. Along first, then up.Old tree = (3, 2)
- Move 4 right. Right adds to x.x: 3 + 4 = 7
- Move 3 up. Up adds to y.y: 2 + 3 = 5
- Write the treasure. The treasure is at (7, 5).
Check. From (3, 2) count 4 right and 3 up: (7, 5). ✓
Watch out. Right and left change x. Up and down change y.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Along the grid lines you must go across and then up or down. Add the two distances.
- Find how far across. Compare the x-coordinates.x: 1 to 6 is 5 squares.
- Find how far up or down. Compare the y-coordinates.y: 2 to 5 is 3 squares.
- Add them. Moving along the grid lines, you go across and then up or down.5 + 3 = 8 squares
Check. Another route (up first, then across) also has 3 + 5 = 8 squares. ✓
Watch out. Do not count the lines you start on twice. Count the squares between the points.
Watch out
Left and right belong to the robot. If the robot is facing south, turning left makes it face east, not west. Also, do not count the start square as a step: F3 moves the robot 3 squares from where it is. And remember each turn is only a quarter turn.Exercise 10G Robots, routes and treasure maps
Non-calculatorKey words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the instructions one at a time. F means forward, R means turn right (a quarter turn) and L means turn left (a quarter turn). Write the position after each instruction.
- Write the start point and the way the robot faces. We follow the program from here. The robot’s left and right depend on the way it is facing.Start at (1, 1), facing north.
- Instruction 1: F3. Forward 3 squares north.(1, 1) → (1, 4)
- Instruction 2: R. Turn right a quarter turn: now facing east.north → east
- Instruction 3: F4. Forward 4 squares east.(1, 4) → (5, 4)
- Write where the robot finishes. Look at the last position and the last way it faces.The robot ends at (5, 4), facing east.
Check. Draw the path on the grid from (1, 1): it ends at (5, 4). ✓
Watch out. Turn left or right from the way the robot is facing, not from the way you are looking at the page.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the instructions one at a time. F means forward, R means turn right (a quarter turn) and L means turn left (a quarter turn). Write the position after each instruction.
- Write the start point and the way the robot faces. We follow the program from here. The robot’s left and right depend on the way it is facing.Start at (2, 5), facing east.
- Instruction 1: F3. Forward 3 squares east.(2, 5) → (5, 5)
- Instruction 2: R. Turn right a quarter turn: now facing south.east → south
- Instruction 3: F4. Forward 4 squares south.(5, 5) → (5, 1)
- Instruction 4: L. Turn left a quarter turn: now facing east.south → east
- Instruction 5: F1. Forward 1 square east.(5, 1) → (6, 1)
- Write where the robot finishes. Look at the last position and the last way it faces.The robot ends at (6, 1), facing east.
Check. Draw the path on the grid from (2, 5): it ends at (6, 1). ✓
Watch out. Turn left or right from the way the robot is facing, not from the way you are looking at the page.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the instructions one at a time. F means forward, R means turn right (a quarter turn) and L means turn left (a quarter turn). Write the position after each instruction.
- Write the start point and the way the robot faces. We follow the program from here. The robot’s left and right depend on the way it is facing.Start at (6, 6), facing south.
- Instruction 1: F2. Forward 2 squares south.(6, 6) → (6, 4)
- Instruction 2: R. Turn right a quarter turn: now facing west.south → west
- Instruction 3: F3. Forward 3 squares west.(6, 4) → (3, 4)
- Instruction 4: R. Turn right a quarter turn: now facing north.west → north
- Instruction 5: F1. Forward 1 square north.(3, 4) → (3, 5)
- Write where the robot finishes. Look at the last position and the last way it faces.The robot ends at (3, 5), facing north.
Check. Draw the path on the grid from (6, 6): it ends at (3, 5). ✓
Watch out. Turn left or right from the way the robot is facing, not from the way you are looking at the page.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Each R is a quarter turn clockwise. Each L is a quarter turn anticlockwise. Do the turns one at a time.
- Remember the order of the compass points. Turning right goes clockwise: N, E, S, W. Turning left goes anticlockwise.North → East → South → West → North
- Do each turn in order. One turn at a time, each is a quarter turn.Start: facing north
R: north → east
R: east → south
L: south → east - Write the answer. The robot faces east.
Check. The total turn is 3 quarter turns, each one a right angle. ✓
Watch out. R and L are quarter turns, not half turns.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Each R is a quarter turn clockwise. Each L is a quarter turn anticlockwise. Do the turns one at a time.
- Remember the order of the compass points. Turning right goes clockwise: N, E, S, W. Turning left goes anticlockwise.North → East → South → West → North
- Do each turn in order. One turn at a time, each is a quarter turn.Start: facing east
L: east → north
L: north → west
L: west → south - Write the answer. The robot faces south.
Check. The total turn is 3 quarter turns, each one a right angle. ✓
Watch out. R and L are quarter turns, not half turns.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Each R is a quarter turn clockwise. Each L is a quarter turn anticlockwise. Do the turns one at a time.
- Remember the order of the compass points. Turning right goes clockwise: N, E, S, W. Turning left goes anticlockwise.North → East → South → West → North
- Do each turn in order. One turn at a time, each is a quarter turn.Start: facing south
R: south → west
L: west → south
R: south → west
R: west → north - Write the answer. The robot faces north.
Check. The total turn is 4 quarter turns, each one a right angle. ✓
Watch out. R and L are quarter turns, not half turns.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Look at each straight part of the path. If the robot is not facing the right way, turn first. Then write F and the number of squares.
- Look at the start and the way the robot faces. We start with the robot at the first point.Start at (1, 1), facing north.
- Do the path one straight part at a time. For each part: turn to face the right way if needed, then go forward the number of squares.(1, 1) to (1, 3): forward 2.
(1, 3) to (5, 3): turn right (now facing east), then forward 4.
(5, 3) to (5, 5): turn left (now facing north), then forward 2. - Write the program. Join all the instructions in order.Program: F2 R F4 L F2
Check. Run the program from (1, 1): F2 R F4 L F2 ends at (5, 5). ✓
Watch out. Check which way the robot is facing before you choose R or L.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Each R and each L is one quarter turn, which is one right angle. Count the turns in the program.
- Write the program. From part (a).F2 R F4 L F2
- Count the turns. Count each R and each L.The turns are R, L: 2 turns.
- Write the answer. Each turn is one right angle.The robot turns through 2 right angles.
Check. 2 quarter turns is 2 right angles. ✓
Watch out. Count every R and L. Do not count the F instructions.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Look at each straight part of the path. If the robot is not facing the right way, turn first. Then write F and the number of squares.
- Look at the start and the way the robot faces. We start with the robot at the first point.Start at (5, 1), facing north.
- Do the path one straight part at a time. For each part: turn to face the right way if needed, then go forward the number of squares.(5, 1) to (5, 4): forward 3.
(5, 4) to (2, 4): turn left (now facing west), then forward 3.
(2, 4) to (2, 2): turn left (now facing south), then forward 2. - Write the program. Join all the instructions in order.Program: F3 L F3 L F2
Check. Run the program from (5, 1): F3 L F3 L F2 ends at (2, 2). ✓
Watch out. Check which way the robot is facing before you choose R or L.
A: F3 R F2 B: F2 R F3 C: R F2 L F3
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow each program from the start (1, 1) facing north. Find the one that finishes at the star (4, 3).
- Follow program A. F3 R F2Ends at (3, 4).
- Follow program B. F2 R F3Ends at (4, 3). This is the star.
- Follow program C. R F2 L F3Ends at (3, 4).
- Write the answer. The program that reaches the star is B.
Check. B: F2 takes the robot to (1, 3). It turns right to face east. F3 takes it to (4, 3). ✓
Watch out. Follow every program fully. Do not stop when one looks right.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the directions one at a time. East and west change the x-coordinate. North and south change the y-coordinate.
- Write the start point. The map starts here.Start at (1, 1).
- Follow each direction. East makes x bigger. West makes x smaller. North makes y bigger. South makes y smaller.4 east: (1, 1) → (5, 1) (x gets bigger)
3 north: (5, 1) → (5, 4) (y gets bigger) - Write where the treasure is. The last point is the place the map shows.The treasure is at (5, 4).
Check. Count the squares on the grid from (1, 1): you arrive at (5, 4). ✓
Watch out. North is up the grid, so going north makes the y-coordinate bigger.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the directions one at a time. East and west change the x-coordinate. North and south change the y-coordinate.
- Write the start point. The map starts here.Start at (7, 6).
- Follow each direction. East makes x bigger. West makes x smaller. North makes y bigger. South makes y smaller.5 west: (7, 6) → (2, 6) (x gets smaller)
4 south: (2, 6) → (2, 2) (y gets smaller)
2 east: (2, 2) → (4, 2) (x gets bigger) - Write where the treasure is. The last point is the place the map shows.The treasure is at (4, 2).
Check. Count the squares on the grid from (7, 6): you arrive at (4, 2). ✓
Watch out. North is up the grid, so going north makes the y-coordinate bigger.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. “3 right and 2 up” is a translation. Add 3 to the x-coordinate and 2 to the y-coordinate.
- Write the start. The rock is at (3, 4).x = 3, y = 4
- Move 3 right and 2 up. Right adds to x. Up adds to y.x: 3 + 3 = 6
y: 4 + 2 = 6 - Write the treasure. The treasure is at (6, 6).
Check. Count on the grid from (3, 4): 3 right and 2 up gets to (6, 6). ✓
Watch out. Right and left change x. Up and down change y.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Along the grid lines you must go across and then up or down. Add the two distances.
- Find how far across. Compare the x-coordinates.x: 1 to 5 is 4 squares.
- Find how far up or down. Compare the y-coordinates.y: 2 to 4 is 2 squares.
- Add them. Moving along the grid lines, you go across and then up or down.4 + 2 = 6 squares
Check. Another route (up first, then across) also has 2 + 4 = 6 squares. ✓
Watch out. Do not count the lines you start on twice. Count the squares between the points.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Along the grid lines you must go across and then up or down. Add the two distances.
- Find how far across. Compare the x-coordinates.x: 0 to 6 is 6 squares.
- Find how far up or down. Compare the y-coordinates.y: 0 to 3 is 3 squares.
- Add them. Moving along the grid lines, you go across and then up or down.6 + 3 = 9 squares
Check. Another route (up first, then across) also has 3 + 6 = 9 squares. ✓
Watch out. Do not count the lines you start on twice. Count the squares between the points.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Along the grid lines you must go across and then up or down. Add the two distances.
- Find how far across. Compare the x-coordinates.x: 7 to 2 is 5 squares.
- Find how far up or down. Compare the y-coordinates.y: 5 to 1 is 4 squares.
- Add them. Moving along the grid lines, you go across and then up or down.5 + 4 = 9 squares
Check. Another route (up first, then across) also has 4 + 5 = 9 squares. ✓
Watch out. Do not count the lines you start on twice. Count the squares between the points.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the program carefully. Then compare it with what Leo said.
- Follow F2. The robot starts at (1, 1) facing north. Forward 2 means 2 up.(1, 1) → (1, 3)
- Follow R. Turn right from north to face east.Now facing east.
- Follow F3. Forward 3 means 3 along.(1, 3) → (4, 3)
- Compare. Leo said (3, 4). That has the numbers the wrong way round.The robot finishes at (4, 3).
Check. (4, 3) is 4 along and 3 up. ✓
Watch out. Along first, then up.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Test the sentence with some examples.
- Try it. Start facing north. Turn right four times.N → E → S → W → N
- Think about why. Four quarter turns make one whole turn.4 right angles = a whole turn.
- Decide. This is always true.
Check. Four quarter turns is 360 degrees, a whole turn. ✓
Watch out. Try different starting directions.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Test the sentence with some examples.
- Try it. Start facing north. Turn right.N → E
- Compare. The robot faces east, not west.West is a turn left.
- Decide. This is never true.
Check. North to east is a quarter turn clockwise, which is right. ✓
Watch out. Try different starting directions.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Test the sentence with some examples.
- Try facing north. F4 goes 4 up.(2, 2) → (2, 6): y changed.
- Try facing east. F4 goes 4 along.(2, 2) → (6, 2): y stayed the same.
- Decide. It depends on the way the robot faces.This is sometimes true.
Check. North and south change y. East and west do not. ✓
Watch out. Try different starting directions.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Follow the program. Then look at the shape the robot’s path makes.
- Follow the program one instruction at a time. Each F3 goes 3 squares. Each R is a quarter turn right.F3: (2, 2) → (2, 5)
R: north → east
F3: (2, 5) → (5, 5)
R: east → south
F3: (5, 5) → (5, 2)
R: south → west
F3: (5, 2) → (2, 2) - Look at where the robot finishes. Compare the end with the start.The robot ends at (2, 2), where it started, but now it is facing west.
- Name the shape. The path has 4 sides of 3 squares and 4 right angles.The path is a square.
Check. The robot turned right 3 times and then went forward. The 4 sides are all 3 long. ✓
Watch out. Check the end of the path. The robot is back at the start.
Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.
Method. Work out how far across and how far up the robot must go. Then use the fewest instructions.
- Find the distances. The robot goes from (2, 2) to (6, 5).Across: 6 − 2 = 4. Up: 5 − 2 = 3.
- Use the way the robot faces. It faces north, so first it goes up 3. Then it turns right to face east and goes 4 across.F3, then R, then F4
- Write the program. This has only 3 instructions.Program: F3 R F4
Check. F3 R F4 ends at (6, 5). The other way, R F4 L F3, needs 4 instructions. ✓
Watch out. The robot starts facing north, so going up first saves a turn.