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Four directions that go around in order, the corners between them, and how to count from one to another.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will name the four directions in order, give the opposite of any of them, and find something on a map from the direction it lies in.
You can already say left and right, up and down the page. Those are words about you and about the paper. The four directions in this lesson are words about the ground, and the map's arrow is what ties the two together.
| Term | What it means |
|---|---|
| Cardinal directions | The four main directions: north, east, south and west. |
| Opposite | The direction that faces the other way, two steps around. |
| Clockwise | Going around the way the hands of a clock go. |
| Intermediate direction | A direction halfway between two, such as northeast. |
| Directly north | Straight north, with no sideways movement at all. |
| Compass rose | A drawing on a map that shows the directions. |
North, east, south, west. They go around in that order, the way the hands of a clock go, and then around again. That is the whole idea, and everything else is counting.
Two steps around from any of them is its opposite: north and south are opposite, east and west are opposite. Turn all the way around and you are facing your opposite.
Halfway between two of them gets a name made of both, with north or south said first: northeast, southeast, southwest, northwest. That gives eight directions, which is enough for anything in this course.
On the park plan in this lesson the arrow points north and it points up the page, so east is to the right, south is down and west is to the left. That is true of this map.
Another way: story
Stand up and face the way you call north. East is now on your right hand, west on your left, and south is behind you. Turn a quarter turn to the right four times and you have gone north, east, south, west and back to north.
Another way: diagram
Draw a cross. Put north at the top, then go around clockwise writing east, south and west. The two words on each straight line of the cross are always opposites.
Counting clockwise from north, the eight directions come in this order.
| Step | Direction | Its opposite |
|---|---|---|
| 0 | north | south |
| 1 | northeast | southwest |
| 2 | east | west |
| 3 | southeast | northwest |
| 4 | south | north |
| 5 | southwest | northeast |
| 6 | west | east |
| 7 | northwest | southeast |
The opposite of any direction is four steps along this list, halfway around.
Many American classrooms use a saying to remember the order clockwise from the top: Never Eat Soggy Waffles. The first letters are N, E, S, W: north, east, south, west.
Say it while pointing around a clock face: never at twelve, eat at three, soggy at six, waffles at nine. If you ever mix up east and west, the saying puts them back in place. Some classes make up their own saying instead, and any saying works as long as its letters go N, E, S, W.
Many maps draw a compass rose: a star or cross with the directions marked at its points. Sometimes only the N is labeled, and you count around from it.
A compass rose does the same job as a north arrow. It ties the directions on the ground to the directions on the page. On the maps in this lesson, north is up the page, so the rose's N points to the top.
Directly north means straight north: on a map with north up, straight up the page, not one step sideways. If you move up and to the right, you are going northeast, not north.
Everyday speech is looser. People say "Canada is north of the United States" even for places that are also a long way east or west. On a map question, read the word directly carefully; it rules out any sideways movement.
Directions can be counted like numbers. Walking north and then south partly cancel out: walk seven squares north and three south, and you end four squares north of where you began, because seven minus three is four.
East and west work the same way. And to get home, walk the opposite directions: if you ended north and east of home, walk south and west.
Directions are about the ground, not about the paper. In the morning the sun rises in the east, and in the evening it sets in the west, wherever you stand.
In many American towns the streets run north-south and east-west in a grid, so people give directions like "go two blocks north, then one block east." A map of such a town, with north up the page, turns those words straight into moves up and across. In a town whose streets curve, the same words still work, but you have to check the arrow more often.
Checking an answer. Point around a clock face saying the order. East should land at three, on the right when north is up.
Reading the arrow first is allowed, and needed, because only the arrow says where north is on this page. Counting around is allowed because the directions always keep the same order, on every map and on the ground.
Subtracting south steps from north steps is allowed because they point exactly opposite ways along one line, so one step south undoes one step north.
The most common slip is swapping east and west. Another is naming an in-between direction backward, eastnorth instead of northeast, or on the wrong side, northwest instead of northeast.
A third is calling something directly north when it is also across. A fourth, which the next lesson is all about, is assuming north is always up the page.
Many American cities were laid out as a grid, with streets running north-south and east-west. In Salt Lake City, Utah, the grid starts at Temple Square, and every address says how far and which way from there: an address on "400 South" is four blocks south of the center, and "700 East" is seven blocks east.
Visitors find their way by counting. To get from 400 South and 700 East to 100 South and 200 East, walk north from 400 to 100, which is three blocks, and west from 700 to 200, which is five blocks. Eight blocks in all, by the grid.
Chicago, Phoenix and many other cities work in a similar way, with numbered streets counting out from a starting line. On a map of such a city with north up the page, north is straight up and west is straight left, so the directions a person speaks turn into moves on the paper with no guessing at all.
Rangers in national parks often give directions with compass words: "Follow the trail north to the lake, then take the path east to the waterfall." A hiker with a map and the order north, east, south, west in their head can follow those words even in a forest where every tree looks the same.
Hikers also carry directions home. If the trail went north and then east, the way back is west and then south: the opposite directions, in the opposite order. Getting the order right matters, because walking south first might lead the wrong way around a lake.
The sun helps check. Early in the day it rises in the east, so a hiker facing the morning sun knows north is on the left hand. Late in the day the sun sets in the west. Search-and-rescue teams teach children to know these facts, so a lost child can say which way they walked.
The first slip is saying northeast when you mean northwest, because halfway between was taken to mean past. Northeast sits between north and east. Count around: north, northeast, east.
The second is saying eastnorth. Both parts are right and the order is not; north or south always comes first.
The third is the big one, and the next lesson is about it. North is a direction on the ground, not a place on the paper. Most maps are printed with north up the page because that is the habit, and the arrow is there for the ones that are not. Read the arrow before you say which way anything is. On the plan here it happens to be up the page, because the arrow says so, not because the top of a page is north.
The arrow says north is up the page. Find south and east.
$\text{south down, east right}$
Read the arrow first.
Combine the two directions.
$\text{southeast: down and right}$
Not one or the other.
Find that corner of the plan.
$\text{bottom-right}$
Both directions at once.
Name what is there.
$\text{the parking lot}$
The bordered rectangle.
Find what is directly north of the parking lot. Say what directly means.
$\text{no sideways movement}$
Straight along one line.
Read the arrow.
$\text{north is up the page}$
On this plan.
Look straight up from the parking lot.
$\text{the same column}$
Up only.
Name what is there.
$\text{the yellow square}$
The play equipment.
Rule out the trees.
$\text{up and across: northwest}$
Directly means directly.
On a grid map, walk $7$ squares north, then $3$ south. Find how far north you are.
$7 - 3 = 4$
South undoes north.
Then walk $6$ squares east and $2$ west. Find how far east you are.
$6 - 2 = 4$
West undoes east.
Say where you are.
$4 \text{ north}, 4 \text{ east}$
Northeast of the start.
Name the ways home.
$\text{south and west}$
The opposites.
Count the squares back.
$4 + 4 = 8$
Along the grid.
Check by walking it.
$4 \text{ south}, 4 \text{ west}: \text{home}$
Back to the start.
Say the order around from east.
$\text{east, south, west}$
Clockwise.
Count two steps.
$\text{west}$
Halfway around.
Check with the pairs.
If you turned all the way around and walked back the way you came, which way would you be going?
| north | west | south | |
|---|---|---|---|
| south | |||
| east | |||
| north |
Complete the worked solution: on a grid map with north up the page, you start at the school. You walk $8$ squares north, then $2$ squares south, then $7$ squares east, then $4$ squares west. How far north and how far east of the school are you, and how many squares is it back along the grid?
Find how far north you ended.
$\text{north} - \text{south} =$ n
South steps undo north steps.
Find how far east you ended.
$\text{east} - \text{west} =$ e
West steps undo east steps.
Count the squares back.
$\text{north left} + \text{east left} =$ t
South, then west, along the grid.
Name the ways home.
$\text{south and west}$
The opposites of north and east.
Put the four directions in the order you meet them going around the way the hands of a clock go, starting at north.
Number the steps in order (write the number in the box):
A path leaves the gate and goes exactly halfway between north and east. Which direction is it going?
A village map whose arrow points north, up the page. The flag is the school. Around it are a well (a black dot), a barn (a small house shape), an oak (a tree) and a pond (a blue patch). Put each direction on the place that lies that way from the school.
This task has no paper form; do it on a device.
The arrow beside this plan points north, and on this map it points up the page. So east is to the right, south is down the page and west is to the left. Click the thing in the **southeast** corner of the park.
This task has no paper form; do it on a device.
North is up the page on this plan. The parking lot is in the southeast corner. Click the thing that is **directly north** of the parking lot: the same distance across the page, but farther up it.
This task has no paper form; do it on a device.
A town map now, ruled into squares. Its arrow points north, up the page. The school is the yellow rectangle in the square 2 columns from the left and 2 rows up from the bottom. Click the square **directly north** of the school.
This task has no paper form; do it on a device.
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A village map whose arrow points north, up the page. The flag is the school. Around it are a well (a black dot), a barn (a small house shape), an oak (a tree) and a pond (a blue patch). Put each direction on the place that lies that way from the school.
This task has no paper form; do it on a device.
You can use the four directions on a map. Tell somebody how you work out the opposite of east without having to remember it.
20. Your turn: you walk east, then turn all the way around and walk back. Which way are you going now?, step 3
$\text{east and west are opposites}$
One straight line.