Position and movement
🎯 In this topic you will
- Use the eight compass directions to describe direction.
- Use coordinates to describe position.
🧠 Key Words
- compass
- coordinates
- quadrant
Show Definitions
- compass: A tool used to show direction, usually indicating north, south, east, and west.
- coordinates: A pair of numbers that show the exact position of a point on a grid.
- quadrant: One of the four sections into which a coordinate grid is divided.
📍 Describing Position and Movement
T his section is about using coordinates to describe a position and using compass directions to describe movement.
🧭 Using a Compass
A compass is useful for finding your way at sea or in unfamiliar places.
❓ EXERCISES
$1.$ What do the letters NE stand for on a compass?
👀 Show answer
$2.$ What compass direction is missing from this compass?
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$3.$ Use the map to see where Arnold is standing.
a. If Arnold travels north-west, what town will he reach?
b. What direction does Arnold walk to get to each of these places?
i. Woolham
ii. Jurby
iii. Melford
👀 Show answer
a. Arnold will reach Burd.
b.
i. Woolham: South-East
ii. Jurby: North-East
iii. Melford: South
$4.$ This map shows the roads between Ibri and Sheki. One way to get from Ibri to Sheki is to travel: $1$ square north-west, $1$ square north-east, $1$ square north-west, $1$ square north-east. List all the different ways you can describe travelling back from Sheki to Ibri using compass directions.
👀 Show answer
- North-West → South-East
- North-East → South-West
❓ EXERCISES
$5.$ Write the coordinates of the four points that are marked on this grid.
👀 Show answer
A: $(1, 2)$
B: $(2, 1)$
C: $(3, 3)$
D: $(5, 6)$
$6.$ Safiya says that the point marked on this grid has coordinates $(4, 1)$. Explain why she is wrong.
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$7.$ Copy this grid. Mark these coordinates on your grid with a cross.
$(5, 3)$ $(1, 1)$ $(4, 6)$ $(3, 0)$
👀 Show answer
$(5, 3)$, $(1, 1)$, $(4, 6)$ and $(3, 0)$.
🧠 Think like a Mathematician
Task:
- Draw a coordinate grid from $0$ to $6$ on the horizontal ($x$) axis and from $0$ to $6$ on the vertical ($y$) axis.
- Choose one of the numbers on the $y$-axis. Draw a horizontal line through that number across the grid.
- Write down all the coordinates you can name that lie on this horizontal line.
- Think about what is similar and what is different about the coordinates on this line. Write a general statement about what they all have in common.
- Choose one of the numbers on the $x$-axis. Draw a vertical line through that number across the grid.
- Write down all the coordinates you can name that lie on this vertical line.
- Think about what is similar and what is different about the coordinates on this line. Write a general statement about what they all have in common.
- Write down the coordinates where the two lines cross.
- Use your results to explain how someone else could work out the coordinates of any point that lies on your two lines.
👀 Show answers
- On a horizontal line, the $y$-value stays the same and the $x$-value changes.
- On a vertical line, the $x$-value stays the same and the $y$-value changes.
- All points on a horizontal line have the same second coordinate.
- All points on a vertical line have the same first coordinate.
- The point where the two lines cross has coordinates $(x, y)$, where $x$ comes from the vertical line and $y$ comes from the horizontal line.