Back to the on-screen lesson ·
Instructions that only work in one order, each with a direction and a distance — and what happens on the way back.
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 follow a route on a map one instruction at a time, and work out the instructions for the same walk in reverse.
You can name the four directions, give the opposite of any of them, and read a north arrow to see which way around a map is printed. A route is those three things used one after another, with some adding and subtracting of squares.
| Term | What it means |
|---|---|
| Route | A list of instructions for getting from one place to another. |
| Instruction | One step of a route: a direction and how far. |
| Leg | One straight part of a walk between two turns. |
| Follow | To do a route's instructions in order. |
| Reverse | To do a route backward, with every direction turned to its opposite. |
A route is a set of instructions for getting from one place to another. It is a list, and the order matters. On an open grid go north two squares, then east three happens to land on the same square as go east three, then north two, because each instruction only counts squares. Real routes are not like that: cross the bridge, then turn left and turn left, then cross the bridge do not land you anywhere near each other, because the second instruction starts from wherever the first one left you.
Every good instruction has two parts: which way and how far. 'Go west' leaves you walking west forever. 'Two squares' leaves you not knowing which way. Put them together and you have named one place.
And a route run backward is not the same list read upside down. The list turns around and every direction turns into its opposite.
Another way: story
Think of telling somebody how to get to your front door. You would not say 'it's near the mailbox'. You would say 'past the mailbox, then second on the left': a which-way and a how-far, in order.
Another way: steps
To check a route, put your finger at the start and do the instructions one at a time, in order, without reading ahead. If your finger ends up in the right place, the route works; if it ends up in the wrong place, the instruction you were on when it went wrong is the broken one.
Here is a walk out, and the walk home that undoes it.
| Walk out | Walk home |
|---|---|
| 1. north two squares | 1. west two squares |
| 2. east three squares | 2. north one square |
| 3. south one square | 3. west three squares |
| 4. east two squares | 4. south two squares |
Read the home list from the bottom of the out list upward, and flip each direction. The distances never change.
An instruction with only a direction, like go east, gives you a line that goes on and on. An instruction with only a distance, like go three blocks, could send you any way at all.
Put the two together, go east three blocks, and there is exactly one place you can end up. That is the test of a good instruction: could two people follow it and end up in different places? If they could, it needs its missing half.
Many real directions use landmarks: things along the way that are easy to spot, such as a bridge, a gas station or a big oak tree. Turn left at the red barn tells you where to turn without counting.
A landmark still needs a which-way. At the red barn says where; turn left says which way. Good directions use both, and a map lets you check that the landmark is really on the route. A landmark that has been torn down or painted a new color can send a traveler the wrong way, so a map and a count of blocks are a good backup.
On a grid, a walk can be added up. Legs that go the same way add together: two squares east and then three more squares east is five squares east.
Legs that go opposite ways subtract: six squares north and then one square south leaves you five squares north. To find the whole distance walked, add every leg, whatever its direction, because your feet walked all of it.
On an empty grid, some instructions can swap places and still end in the same square. On real ground they usually cannot. A road may only go one way; a river may only have one bridge; a door may only open from one side.
So a route should always be followed in the order it is written. The second instruction starts from wherever the first one left you, and only from there.
A route's directions belong to the ground, so they do not change when a map is printed sideways. Turn north still means turn north.
What changes is which way your finger moves on the page. On a map whose arrow points to the right, walking north means moving your finger toward the right-hand edge. Read the arrow first, then follow the route.
Checking an answer. Walk the route home from where you ended. If it brings you back to the start, both routes are right.
Doing instructions in order is required because each one starts from where the last one ended. Reversing the order on the way home is required because the last step taken is the nearest to where you are.
Flipping each direction is required because walking a leg backward means facing the other way. Adding same-way legs and subtracting opposite legs is allowed because a step one way cancels a step the opposite way.
The most common slip is reversing the order of a route but forgetting to flip the directions, which sends you farther away. Another is flipping the directions but keeping the order.
A third is giving half an instruction: a direction with no distance, or a distance with no direction. A fourth is reading ahead instead of doing one instruction at a time.
When a family drives somewhere new, a phone or car screen often reads out a route one instruction at a time: "In half a mile, turn right onto Main Street. Then, in two miles, turn left onto Route 9." Each instruction has both halves: a how-far (half a mile, two miles) and a which-way (right, left).
The instructions only work in order. If the driver turned left onto Route 9 first, they would be on a different road entirely, and the next instruction would make no sense. That is why the screen waits until one step is done before giving the next.
Getting home is its own route. The app does not just read the same list backward, because some streets only run one way. It works out a new route that turns each right into a left and starts from the end. On a simple trip with two-way roads, the way home is the way out with the order reversed and every turn flipped, just as in this lesson.
Many state parks mark their trails with colored blazes, painted stripes on trees, and give hikers a map with each trail's legs and distances: "Blue Trail north 1.2 miles to the lake, then Red Trail east 0.8 miles to the overlook."
A careful hiker adds up the legs before starting. Going out is 1.2 miles plus 0.8 miles, which is 2 miles, so the whole hike there and back is 4 miles. That tells the family how long it will take and how much water to carry.
On the way back, the hiker reverses the route: Red Trail west to the lake first, then Blue Trail south to the parking lot. Rangers say one of the most common ways hikers get lost is taking the right trails in the wrong order, or the right order in the wrong direction, at a junction on the way home.
The commonest mistake with a walk home is reversing the list and leaving the directions alone, so a walker who went north and east comes home going east then north and finishes even farther away. Both things have to turn: the order, and each direction.
The second is an instruction with only half of itself. 'Go toward the church' has a which-way and no how-far; 'go three squares' has a how-far and no which-way. Neither names a place.
The third is reading ahead. A route is checked by doing one instruction at a time from the start, which is also how you find the one that is wrong.
Put the park instructions in order. Start outside.
$\text{go in at the gate}$
Nothing else can come first.
Follow the only way in.
$\text{the path north}$
Up the middle.
Follow the path's turn.
$\text{the path east}$
Where it bends.
Stop at the end.
$\text{the play equipment}$
Four steps, one order.
Going out was north two, then east three. Find which leg to undo first.
$\text{east three}$
The last thing done is undone first.
Flip its direction.
$\text{west three}$
The distance stays the same.
Undo the first leg.
$\text{north two becomes south two}$
Flip it too.
Write the walk home.
$\text{west three, then south two}$
Back to front, every direction flipped.
Check it by walking.
$\text{back at the start}$
Both routes agree.
A walker goes $6$ north, $2$ east, $1$ south, $3$ east. Combine the north and south legs.
$6 - 1 = 5 \text{ north}$
South undoes north.
Combine the east legs.
$2 + 3 = 5 \text{ east}$
Same direction, so add.
Say where the walk ends.
$5 \text{ north}, 5 \text{ east}$
Northeast of the start.
Add every leg.
$6 + 2 + 1 + 3 = 12$
Squares actually walked.
Find the shortest way home by the grid.
$5 + 5 = 10$
South five, west five.
Compare the two.
$12 - 10 = 2$
The south leg cost two extra squares.
Flip the direction.
$\text{south becomes north}$
Walking back faces the other way.
Keep the distance.
$\text{four squares}$
The same leg, walked back.
Write the instruction.
These four instructions take somebody from the gate of Oakfield Park to the play equipment, but they have been jumbled. Put them back in order.
Number the steps in order (write the number in the box):
Complete the worked solution: on a grid map with north up the page, a walker goes $6$ squares north, then $2$ east, then $1$ south, then $3$ east. How far north and how far east of the start do they end, and how many squares did they walk in all?
Find how far north they end.
$\text{north} - \text{south} =$ n
South undoes north.
Find how far east they end.
$\text{first east} + \text{second east} =$ e
Both legs go east.
Add every leg of the walk.
$\text{all four legs} =$ t
Squares walked, whatever the direction.
Name the ways home.
$\text{south, then west}$
The opposites of north and east.
Here are three instructions from a walk. For each one, which way would you go to walk that bit backward?
| west | south | north | |
|---|---|---|---|
| go east three squares | |||
| go north two squares | |||
| go south one square |
Going out, a walker went north two squares, then east three squares, then south one square, then east two squares. Put the instructions for the walk **home** in order.
Number the steps in order (write the number in the box):
Two people give you directions to the store. One says 'it's near the bridge'. The other says 'from the bridge, go west two squares'. Why is the second one better?
A park map ruled into squares, with north up the page. The gate is the flag. Follow this route from the gate: go 2 square(s) east, then 1 square(s) north. Put the place where the route ends on the map.
This task has no paper form; do it on a device.
Follow this route on the park plan. Go in at the gate, follow the path north up the middle, then follow it east until it stops. North is up the page here. Click the thing that is just **north** of where the path stops.
This task has no paper form; do it on a device.
A new place, and a map whose north arrow points at the right-hand edge, so north is to the right and east is down the page. A walker lands at the bay on the island's east side and goes to the lighthouse at its north end. Put their four instructions in order.
Number the steps in order (write the number in the box):
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A park map ruled into squares, with north up the page. The gate is the flag. Follow this route from the gate: go 2 square(s) east, then 2 square(s) north. Put the place where the route ends on the map.
This task has no paper form; do it on a device.
You can follow a route and reverse one. Tell somebody the two things that both have to change when a walk is done backward.
20. Your turn: you went south four squares. What is the one instruction that takes you home?, step 3
$\text{go north four squares}$
A direction and a distance.