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Lines ruled over a map so places can be named, and the two numbers that name one square — across first, up second.
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 find the square a grid reference names, and give the reference for a square you are shown.
You can count, multiply small numbers, and find something on a map from the direction it lies in. A grid reference is a different way of saying where: instead of a direction from something else, it gives a square that stands still whoever is asking.
| Term | What it means |
|---|---|
| Grid | The set of straight lines ruled over a map to cut it into squares. |
| Column | A line of squares running up and down the map. |
| Row | A line of squares running across the map. |
| Grid reference | The pair of numbers that names one square: across, then up. |
| Index | A list of places with the grid square where each is found. |
A grid is a set of straight lines ruled across a map, cutting it into squares. The lines are not on the ground. Nobody has painted them across Barrow; the mapmaker drew them on top so that places could be named.
Each square is named by two numbers. The first says how far across from the left. The second says how far up from the bottom. So 3 across, 2 up means: count three columns in from the left edge, then two rows up from the bottom edge, and take the square where they meet.
That order is fixed, and it matters more than it looks. 1 across, 3 up and 3 across, 1 up are two different squares in opposite corners of Barrow. Getting the order wrong is not a small error.
Another way: story
It is like finding a seat at a movie theater with numbered seats and rows: along the row to your seat number, and the right row. Mix up the two numbers and you sit in somebody else's seat across the theater.
Another way: diagram
Put your finger on the bottom-left corner of the grid. Walk it right along the bottom, counting columns, until you reach the first number. Now walk it straight up, counting rows, until you reach the second. Stop. That square is the answer.
Barrow's map has four columns and three rows. Here is where six places sit.
| Place | Across | Up |
|---|---|---|
| the park | 1 | 3 |
| the school | 2 | 2 |
| the bridge | 3 | 1 |
| the church | 4 | 2 |
| the store | 1 | 1 |
| the station | 4 | 3 |
Look at the park and the bridge: the same two numbers, 1 and 3, in opposite orders, and the two places are in opposite corners of the map.
Without a grid, telling somebody where a place is on a big map means pointing, or long descriptions like "a bit above the river, left of the big road." With a grid, two numbers are enough, and anyone with the same map finds the same square.
That is why road atlases and city maps have an index: a list of streets and places, each with its grid square. You look up the name, read the square, and search only that one small part of the map.
A map grid works the same way as a graph in math class. You go along the bottom first, then up. The bottom-left corner is where you start counting.
Mathematicians call the pair of numbers coordinates and write them in parentheses: (3, 2) means 3 along and 2 up. Map grids use the same order, so learning one helps with the other.
Because every row has the same number of columns, you can count a grid's squares by multiplying. Barrow's grid is four columns across and three rows up, so it has four times three, which is twelve squares.
Subtraction helps too. If the church is in column 2 of a grid five columns wide, then five minus two, which is three squares, lie east of it in its row when north is up the page.
Many American road maps use a letter for one direction and a number for the other: C4 means column C and row 4. The letter stops you mixing the two up, because a letter cannot be a row by mistake.
Some of these maps count their rows from the top instead of the bottom. The map always shows its letters and numbers along the edges, so read the edges before you trust a habit.
A grid line is drawn on the paper, not on the land. Walk across Barrow and you will never step over one. A road that crosses a grid line is the same road on both sides, and a field that a grid line cuts in half is still one field.
So a place can be split between two squares. A long river may pass through five or six. An index then gives the square where its name is printed, or the square that holds most of it.
Checking an answer. Say the reference out loud as "across, up" and trace it again with your finger. Then try the swapped pair and see that it lands somewhere else.
Reading the edges is needed because the mapmaker, not a law, decides where the counting starts. Counting across first is required because that is the order the reference is written in; the first number always belongs to the columns.
Multiplying to count squares is allowed because every row has the same number of columns, and equal groups are what multiplication counts.
The most common slip is swapping the two numbers. Another is counting the rows from the top when the map counts from the bottom, or the other way around.
A third is counting the columns from the right. A fourth is thinking a grid line is a real boundary, like a fence or a street.
Before phones had maps, American families on road trips carried a thick road atlas with one map for every state. Many still keep one in the car, because it works where there is no signal. Each state's map is ruled into a grid, with letters along the top and numbers down the side.
Next to the map is an index of every town. Suppose a family driving across Kansas wants to find the small town of Lucas. The index says "Lucas ... E-6." They run a finger down column E and across row 6, and the town is in that one small square, instead of hidden somewhere on a map the size of a table.
The index only works if everyone reads the square the same way. Read as 6-E, or with the rows counted from the wrong edge, the reference points to empty prairie miles away. So the atlas prints the letters and numbers on every edge, and families learn to check them before they search.
A ticket to a baseball game in an American stadium names a seat with numbers: a section, a row and a seat. Inside a section, the rows run one way and the seats run the other, just like the rows and columns of a map grid.
Picture a section with 20 rows of 12 seats. It holds 20 times 12, which is 240 seats, counted by multiplying, as with the squares of a grid. A ticket for row 5, seat 3 sends a fan up to the fifth row and along to the third seat. A fan who swaps the numbers and sits in row 3, seat 5 is in somebody else's seat, and an usher will be along shortly.
Like a map, a stadium labels its rows and seats where everyone can see them, at the ends of each row. And like a map grid, those labels are not part of the field or the game; they are a naming system laid on top so that thousands of people can each find one exact place.
A grid reference goes across the bottom first and up the side second. Every square has two numbers and so does the square next door but one, so getting them the wrong way round does not give you a slightly wrong answer — it gives you a completely different square.
The second slip is counting the rows from the top, because that is how lines on a page are usually numbered. On most map grids they are counted from the bottom, the way a graph is. If a map says otherwise it says so, and one of the items here is a map that does.
The third is thinking the grid lines are things. They are not. Nothing changes at a grid line: a street crossing one is the same street on both sides, and a field cut in half by one is one field.
Find the square 3 across, 1 up. Start at the corner.
$\text{the bottom-left}$
Always start there.
Count three columns to the right.
$1, 2, 3$
The first number.
Count one row up from the bottom.
$1$
The second number.
Name the square.
$\text{the bridge}$
Across, then up.
Take 1 across, 3 up. Find its column.
$\text{column } 1$
The left edge.
Find its row.
$\text{row } 3: \text{ the top}$
So top-left: the park.
Now swap the numbers: 3 across, 1 up. Find its column.
$\text{column } 3$
Right of the middle.
Find its row.
$\text{row } 1: \text{ the bottom}$
So the bridge.
Compare the two squares.
$\text{opposite corners}$
The order is the whole answer.
A grid is $5$ columns across and $4$ rows up. Count its squares.
$5 \times 4 = 20$
Equal rows.
The church is at $2$ across, $1$ up. Find its row.
$\text{the bottom row}$
Row 1.
Count the squares east of it in that row.
$5 - 2 = 3$
Columns after its own.
Count the squares north of it in its column.
$4 - 1 = 3$
Rows after its own.
Check by counting on the grid.
$3, 4, 5 \text{ across}; 2, 3, 4 \text{ up}$
Three each way.
Say what the counts rely on.
$\text{north up the page}$
So east is right and north is up.
Say where across starts.
$\text{the left-hand edge}$
Columns count from the left.
Say where up starts.
$\text{the bottom edge}$
Rows count upward.
Say what to check first.
Barrow's grid is four columns across and three rows up. The park is in the top-left square. The school is one column to the right of the park and one row lower. The bridge is in the bottom row, three columns from the left. Give each one its grid reference.
| 1 across, 3 up | 2 across, 2 up | 3 across, 1 up | |
|---|---|---|---|
| the park | |||
| the school | |||
| the bridge |
Complete the worked solution: a town map's grid is $5$ columns across and $3$ rows up, with north up the page. The church is in the square $1$ across, $1$ up. How many squares does the grid have, how many squares lie east of the church in its row, and how many lie north of it in its column?
Count every square.
$\text{columns} \times \text{rows} =$ t
Equal rows of columns.
Count the squares east of the church.
$\text{columns} - \text{its column} =$ e
The columns after its own.
Count the squares north of it.
$\text{rows} - \text{its row} =$ u
The rows after its own.
Say what the counts rely on.
$\text{across first, up second}$
Swapped numbers name another square.
Barrow's map is ruled into four columns and three rows. You will find the store in the square 1 columns from the left and 1 rows up from the bottom. Click that square.
This task has no paper form; do it on a device.
North is up the page on Barrow's map, so east is to the right. Click the square that is directly **east** of the square 2 columns along and 2 rows up.
This task has no paper form; do it on a device.
Finish the index to Barrow's map. The store is in the bottom-left square. The church is in the middle row, in the last column on the right. The station is in the top row, in the last column on the right.
| Columns from the left | Rows up from the bottom | |
|---|---|---|
| the store | ||
| the church | ||
| the station |
No landmark this time, just the two numbers. Click the square 4 columns from the left and 1 rows up from the bottom.
This task has no paper form; do it on a device.
A new village map. A small square with a cross on top is the church, and a blue patch is the pond. The grid has 4 columns, numbered across from the left, and 3 rows, numbered up from the bottom. Put the church and the pond in their squares.
This task has no paper form; do it on a device.
Barrow's map is being reprinted by a company that numbers its rows **from the top** instead of from the bottom. Everything else stays the same: across first, then down. On the new map, click the square 2 columns from the left and 1 row down from the top.
This task has no paper form; do it on a device.
On this invented trail map north is up. A flag marks a meeting point. The drinking fountain is one grid square east of the flag, in the same row. Place the fountain label. Columns count from the left; rows count from the bottom.
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 new village map. A small square with a cross on top is the church, and a blue patch is the pond. The grid has 4 columns, numbered across from the left, and 3 rows, numbered up from the bottom. Put the church and the pond in their squares.
This task has no paper form; do it on a device.
You can read and give a grid reference. Tell somebody what happens to the answer if the two numbers are said the wrong way around.
20. Your turn: where do you start counting the rows from?, step 3
$\text{the numbers on the edges}$
Some maps count from the top.