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Grid reference, direction and distance — three ways to answer *where*, and how to tell when one of them has worked.
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 describe where a place is by grid square, by direction and by distance, and judge whether a description picks out one place or several.
You can give a grid reference, name a direction from a north arrow and follow a route. This lesson does not add a fourth tool. It asks which of the three to reach for, and how to tell when a description has actually done its job.
| Term | What it means |
|---|---|
| Description | Anything said to tell somebody where a place is. |
| Exact | Fitting one place and no other. |
| Vague | Fitting several places, so it has not said where. |
| Starting point | The place a direction or distance is measured from. |
| Landmark | Something easy to see and name, used as a starting point. |
There are three ways of saying where something is, and you have met all three.
A grid reference names a square: 3 across, 1 up. It works without any other place being mentioned, but only for somebody holding the same map.
A direction says which way from somewhere else: east of the school. It needs a starting point you both agree on.
A distance says how far from somewhere else: one kilometer from the school. It needs a starting point too, and a direction, or you are somewhere on a circle.
The test for any of them is the same: how many places does this fit? If the answer is more than one, it has not said where anything is.
Another way: story
Think of arranging to meet somebody at a big train station. By the clock works if there is one clock. Near the entrance does not, because there are six entrances, and you will both be standing at one, annoyed.
Another way: example
Two squares from the school fits a whole ring of squares all around it. Add a direction, two squares east of the school, and the ring collapses to one square.
Begin with a question about a place that you can check. For example: where can a class wait under cover beside a library? A map places the entrance on the north side and the courtyard on the south side. An invented observation sheet records two covered seats at the north entrance and none in the courtyard on Tuesday morning. Combining them supports waiting by the north entrance at that time. The map supplies where; the observation supplies what was seen. Neither alone gives the full answer. Record the date, time, what was counted and where you stood. Compare equal things: count usable seats rather than mixing seats with whole shelters. State what remains unknown, such as whether the entrance is open after school. A new question needs new evidence rather than a more confident guess.
Each way of saying where has a job it does well and a way it fails.
| Tool | Example | Needs | Fails when |
|---|---|---|---|
| grid reference | 3 across, 1 up | the same map | the listener has no map |
| direction | east of the school | a starting point | there is no how-far |
| distance | 500 m from the school | a starting point | there is no which-way |
A direction and a distance together, from a starting point both people know, work without any map at all.
Put a direction and a distance together and they name one place: three squares east of the school. On a grid map with north up the page, that description turns straight into a grid reference.
If the school is at 1 across, 2 up, then three squares east is 1 plus 3, which is 4 across, and still 2 up. Add some squares north and the up number grows the same way. The two kinds of description agree, which is a good check.
The best description depends on who is listening. A friend holding the same map can use a grid reference. A friend standing at the school with no map needs a direction and a distance from there.
A visitor who knows neither the map nor the school needs a landmark they can see from where they are: the big red barn by the highway, and then a direction and a distance from it. A good speaker watches the listener's face while talking: a puzzled look means the description still fits too many places, or starts from somewhere the listener does not know. Then it is time to add a clue, or to choose a new starting point that both people can see from where they stand.
A good landmark is small enough to be one spot and easy enough to find: a flagpole, a water tower, a particular statue. A poor landmark covers a lot of ground: near the river, by the woods, next to the highway.
Before using a landmark, ask how much ground it covers. If it stretches a long way, add a direction or distance to pin down which part you mean.
Sometimes no single clue is exact, but several together are. Northwest of the parking lot fits several things. On the far side of the path fits several things too. Only one thing fits both.
This is how detectives and search teams work: each clue crosses off some places, and whatever survives every clue is the answer.
A count of squares is not yet a distance. It becomes one when you know what one square is worth on the ground. If each square is 500 meters, then three squares is three times 500, which is 1500 meters.
That idea, a piece of the map standing for a piece of the ground, is called scale, and the next lessons are all about it.
Checking an answer. Say your description to yourself as if you had never seen the map. If you could end up in two places, it is not finished.
Adding east steps to the across number is allowed because, with north up the page, east moves right along a row, and the across number counts columns to the right. Adding north steps to the up number works the same way for rows.
Crossing off places clue by clue is allowed because the right answer must fit every true clue; anything that fails one clue cannot be it, however well it fits the others.
The most common slip is giving half a description: a direction without a distance, or a distance without a direction. Another is using a landmark that covers too much ground.
A third is giving a grid reference to somebody without the map. A fourth is reading a count of squares as if it were already a distance.
When somebody calls 911 in the United States, the first question the dispatcher asks is usually "What is the address of your emergency?" Every second counts, so the description has to fit one place and no other.
A street address works like a grid reference: a number and a street name pick out one building for anyone with a map. But callers are not always at an address. On a highway, a dispatcher asks for the direction of travel and the nearest mile marker, the small green signs that count miles along the road: "northbound, near mile marker 42." That is a direction and a distance from a starting point.
In a park or on a trail, dispatchers ask for landmarks: a trail name, a bridge, a lake, which way the caller walked and for how long. Rescuers cross off places clue by clue until only one fits. Teachers practice this with children, because a clear description can bring help minutes sooner.
Geocaching is a treasure hunt played all over the United States and the world. Players hide small waterproof boxes, called caches, in parks and forests, and post a description of where each one is so that other players can find it.
The main description is a pair of numbers from a satellite positioning system, which works like a very fine grid reference covering the whole planet. A phone reads the numbers and points the way. But the numbers are only good to within a few yards, and a few yards of forest can hold a lot of hiding places.
So cache owners add a hint in words, often a direction and a distance from a landmark: "ten steps north of the big split oak, at the foot of the stone wall." Players use the numbers to get close and the words to finish the search, which is exactly this lesson: several descriptions that each narrow the answer until only one place fits.
The commonest fault is a description with one half missing. Go east has a which-way and no how-far. Two squares away has a how-far and no which-way. Neither picks out a place, and both feel like they have said something.
The second is a landmark that is not one. Near the river sounds exact and fits the whole bottom row of Barrow. Before using a landmark, ask how much ground it covers.
The third is thinking a grid reference is always best. It is the most exact of the three and it is no use at all to somebody without the map in their hand. The best description is the one that works for the person you are talking to.
Three people describe one place. Start with the grid reference.
$4 \text{ across}, 2 \text{ up}$
It stands alone.
Check it against east of the school, at 2 across, 2 up.
$\text{same row, farther right}$
It fits.
Check it against two squares away.
$4 - 2 = 2$
It fits.
Draw the conclusion.
$\text{all three agree}$
So none of them is wrong.
On the park plan there are no squares. Say what a reference is worth.
$\text{nothing here}$
Use what the map does give.
Apply northwest of the parking lot.
$\text{things up and to the left}$
More than one thing still.
Apply on the far side of the path.
$\text{things across the path}$
Crosses off more.
Find what survives both.
$\text{the pond}$
Only one thing fits.
Name the lesson.
$\text{two loose clues, one answer}$
Together they are exact.
The school is at $1$ across, $2$ up, with north up the page. Record it.
$(1, 2)$
The starting point.
The café is $4$ squares east. Find its across number.
$1 + 4 = 5$
East moves right.
It is also $3$ squares north. Find its up number.
$2 + 3 = 5$
North moves up.
Write the café's grid reference.
$5 \text{ across}, 5 \text{ up}$
Across first.
Count the squares between along the grid.
$4 + 3 = 7$
East steps and north steps.
Check by walking it.
$(1, 2) \to (5, 2) \to (5, 5)$
East, then north.
Say what the distance alone fits.
$\text{a ring around the station}$
Every point 300 m away.
Say what is missing.
$\text{a direction}$
Which part of the ring.
Write the finished description.
Three ways of saying where the church is. What kind of description is each one?
| a grid reference | a direction | a distance | |
|---|---|---|---|
| 4 across and 2 up | |||
| east of the school | |||
| one kilometer from the school |
Complete the worked solution: on a grid map with north up the page, the school is at $2$ across, $2$ up. A friend says the café is $5$ squares east and $1$ squares north of the school. Give the café's grid reference, and the squares between the two along the grid.
Find the café's across number.
$\text{school across} + \text{east steps} =$ x
East moves right.
Find the café's up number.
$\text{school up} + \text{north steps} =$ y
North moves up.
Count the squares between.
$\text{east steps} + \text{north steps} =$ t
Along the grid.
Check the two descriptions agree.
$\text{one square either way}$
Both name the same place.
You are telling a friend where to meet you in Barrow. Which description actually says where one place is?
A friend describes two places on a village map whose north is up the page. The church is marked by a small square with a cross on top, and the bus stop by a black square. The café is in the square directly east of the church. The library is in the square directly north of the bus stop. Put the café and the library on the map.
This task has no paper form; do it on a device.
Three people describe the same place on Barrow's map. The first says it is 4 columns across and 2 rows up. The second says it is east of the school, which is 2 across and 2 up. The third says it is two squares from the school. Click the square all three of them mean.
This task has no paper form; do it on a device.
Each grid square on Barrow's map stands for 500 m of ground. Two places are $3$ squares apart, straight along one row. How far apart are they on the ground? Give your answer in meters.
Answer: unit: m / km
The school is at 2 across and 2 up on Barrow's map. The park is in the top-left square, the bridge is in the bottom row three columns along, and the church is in the middle row in the last column. Give each one's square, and the direction it lies in from the school. North is up the page.
| Across | Up | Direction from the school | |
|---|---|---|---|
| the park | |||
| the bridge | |||
| the church |
This plan has no grid on it at all, so a grid reference is no use here. Somebody describes a place as 'northwest of the parking lot, on the far side of the path from it'. North is up the page. Click the place they mean.
This task has no paper form; do it on a device.
A class asks: which side of an invented school has more shaded waiting space at noon? A dated map places the gate east of the building and the yard west of it. Today's observations at noon count 3 shaded benches by the east gate and 1 shaded bench in the west yard; benches are the same size. Read the field-note analysis below. Select both source observations needed to answer the class, AND the conclusion with an appropriate time limit. Leave unsupported claims unmarked.
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 friend describes two places on a village map whose north is up the page. The church is marked by a small square with a cross on top, and the bus stop by a black square. The café is in the square directly south of the church. The library is in the square directly south of the bus stop. Put the café and the library on the map.
This task has no paper form; do it on a device.
You can say where a place is in three different ways. Tell somebody why 'two squares from the school' does not say where anything is.
21. Your turn: 'the store is 300 m from the station'. What has to be added before that names one place?, step 3
$\text{300 m north of the station}$
Now it fits one place.