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What a place looks like from directly overhead, and why height disappears.
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 look at a room and a park from straight above, and work out the shape each thing in them makes on a plan.
You already know what a circle, a square and a rectangle are, and you can tell which of two shapes is longer. You can count squares in a row and multiply to find how many squares cover a rectangle. That is everything this lesson needs. The new part is where you are standing when you look.
| Term | What it means |
|---|---|
| Plan | A drawing of a place seen from straight above. |
| Footprint | The patch of floor or ground a thing covers. |
| From above | From directly overhead, not from a window or a hill. |
| Side view | What a thing looks like when you stand beside it. |
| Key | The part of a map that says what each shape or color stands for. |
A map is a drawing of a place made by somebody looking straight down on it from above. Not from a hill, not from a window, but from directly overhead, so that every part of the place is the same way up.
When you look at something that way, you see the patch of ground it covers and you see nothing else. A round table becomes a circle. A bed becomes a long rectangle. A tree becomes a small round blob, because the top of a tree is the spread of its branches.
That patch is called the thing's footprint, and drawing the footprint is the whole job.
Another way: story
Hold a mug over your head and look up at the bottom of it. You see a ring, and you cannot see the handle, the pattern or how tall it is. That ring is what the mug would be on a plan of the table.
Another way: diagram
Trace around your own shoe on a sheet of paper. What you have drawn is the shoe's footprint, and it is exactly what a mapmaker would put there: the shoe's color, its laces and its height are all gone.
Here is a bedroom drawn the way a mapmaker draws it: from straight above.
| Thing in the room | What it looks like from above |
|---|---|
| bed | a long, wide rectangle |
| round table | a big circle |
| square mat | a square |
| bookcase | a long, narrow rectangle |
| wastebasket | a small circle |
Not one of those shapes tells you how tall anything is. The bookcase may reach the ceiling and the mat is flat on the floor, but on the plan they are just two shapes of floor.
Why do mapmakers go to all this trouble? Because from the side, near things hide far things. Stand at a classroom door and the front desks hide the back ones. Look down from the ceiling and every desk shows at once, none in front of another.
Looking straight down also keeps sizes fair. A far-away desk looks small from the door, but from above every desk is drawn the size it really is. That is why every map in this course, and nearly every map you will ever use, is drawn from directly overhead.
A footprint keeps two things you can trust. It keeps how big the floor patch is: a bed takes more floor than a chair, so its shape is bigger. It keeps which way round a thing is: a bed along the left wall is a rectangle pointing up and down the page.
What a footprint loses is everything about height and everything about sides: legs, handles, doors, pictures and colors. Those have to be told some other way, usually by a key.
Many plans are drawn on a grid of squares, like graph paper. Then you can count a footprint. A bed that is three squares across and six squares long covers three rows of six squares: three times six is eighteen squares of floor.
Counting lets you compare footprints fairly. A desk two squares across and five long covers ten squares, so the bed covers eight squares more than the desk. Notice that the count is about floor. A tall desk and a short desk with the same footprint count the same.
Outdoors nothing changes. A park seen from above is a patchwork of footprints: a pond is the shape of its water, a playground is the shape of its sand or wood chips, a parking lot is a gray rectangle, and a path is a long thin strip.
Trees are the tricky ones. From above you see the spread of the branches, not the trunk, so a tree becomes a round blob, and a group of trees becomes a cluster of blobs touching each other.
Today many maps begin as photographs taken from airplanes or satellites looking straight down. In such a photo you can see roofs, not walls; treetops, not trunks; the tops of cars, not their wheels.
A mapmaker traces those shapes and turns them into clean footprints: a roof becomes a rectangle for a house, and a treetop becomes a green circle. The map is simpler than the photo, but it is still a view from straight above.
Checking an answer. If your shape shows how tall something is, or has legs or a headboard, you have drawn it from the side. Try again from above.
Imagining yourself above is allowed because that is exactly how the map was made, so reading it the same way gets the same answer the mapmaker meant.
Dropping the height is allowed, and needed, because a flat sheet of paper has no room for up and down. Counting squares is allowed because each square of the grid stands for the same amount of floor, so more squares always means more floor.
The most common slip is drawing a side view and laying it flat: a bed with a headboard, a tree with a trunk, a house with a pointed roof and a door. Another is judging size by height, so a tall bookcase gets a big shape even though it covers little floor.
A third is trusting color. On a plan, a green circle is a tree only because the key says so. Mapmakers choose the colors; the ground does not.
Fire departments across the United States ask every family to draw a home fire escape plan, and many schools send the job home with third graders. The plan is a map of the home drawn from straight above.
Each room becomes a rectangle, with its doors and windows marked on the walls. Beds become long rectangles, so everyone can see where each person sleeps. Then the family draws two ways out of every room, usually a door and a window, and marks a meeting place outside, such as a mailbox or a tree in the front yard.
A side view would be no use here. From the side, one wall hides everything behind it, and you could not see the doors of other rooms at all. From above, every room, door and hallway shows at once, so a child can trace a finger from the bed to the door to the hall to the way out. That is why the plan must be a view from straight above, and why families practice with it twice a year.
The U.S. Department of Agriculture flies airplanes over the whole country, taking photographs straight down, so that farmers and planners can see every field. Mapping websites use pictures like these too, from airplanes and satellites.
Open such a picture of your own neighborhood and you are looking at footprints. Houses are rectangles of roof. Swimming pools are blue shapes. Trees are round, fuzzy green blobs, because you see the tops of their branches. Cars in a parking lot are tiny rectangles in neat rows.
What you cannot see is height. A two-story house and a one-story house with the same footprint look almost alike. A tall pine and a short bush can both be small green circles. Mapmakers trace these photographs to draw their maps, turning each roof into a neat rectangle and each tree into a circle, and then they add a key so readers know what every shape stands for.
Almost everybody's first plan has a bed with a headboard on it, drawn the way a bed looks from the side and then laid flat on the paper. That is a picture, not a plan.
On a plan, height is gone. A tall bookcase and a low bench that cover the same floor make the same shape, and the plan cannot tell them apart; the key does that. If your drawing shows how tall something is, you have drawn it from the side.
The other trap is color. A green circle on a plan is a tree because the key says so, not because trees are green in real life. Mapmakers choose colors; the ground does not.
A round table stands in a room. Imagine yourself above it.
$\text{looking straight down}$
The way a plan is drawn.
Find what you see first.
$\text{the round top}$
It hides the legs.
Name the shape.
$\text{a circle}$
A round top makes a ring.
Say what is not drawn.
$\text{the legs and the height}$
Only the floor patch goes on the plan.
A bookcase is about three feet wide and only as deep as a book. Look down on it.
$\text{its top}$
From directly overhead.
Say how it is shaped.
$\text{long one way, thin the other}$
Wide but shallow.
Name the shape.
$\text{a long, narrow rectangle}$
The shelves do not show.
Compare a bench with the same footprint.
$\text{the same rectangle}$
Height is gone.
Say how a reader tells them apart.
$\text{the key}$
The shape says where; the key says what.
On a grid plan, a bed is $3$ squares across and $6$ long. Picture its footprint.
$3 \text{ rows of } 6$
A rectangle of squares.
Count the bed's squares.
$3 \times 6 = 18$
Rows times squares in a row.
A desk is $2$ squares across and $5$ long. Count its squares.
$2 \times 5 = 10$
The same way.
Find how many more the bed covers.
$18 - 10 = 8$
Take the smaller from the bigger.
Check it against the plan.
$\text{the bed's shape is bigger}$
More floor, bigger footprint.
Say what the counts leave out.
$\text{how tall each one is}$
A footprint is floor only.
Picture the wastebasket from above.
$\text{its round rim}$
Looking straight down.
Name the shape.
$\text{a circle}$
A round top makes a ring.
Decide its size.
Look straight down on each of these. What shape does it make on the plan?
| a circle | a square | a long rectangle | |
|---|---|---|---|
| a wastebasket | |||
| a square mat | |||
| a bookcase |
Complete the worked solution: a bedroom plan is drawn on a grid of squares. The bed's footprint is $3$ squares across and $6$ squares long. The desk's footprint is $2$ squares across and $5$ squares long. How many squares of floor does each cover, and how many more does the bed cover?
Count the bed's squares.
$\text{across} \times \text{long} =$ b
Its footprint.
Count the desk's squares.
$\text{across} \times \text{long} =$ d
Its footprint.
Find how many more the bed covers.
$\text{bed} - \text{desk} =$ m
Compare the floor each takes.
Say what the count leaves out.
$\text{how tall each one is}$
A plan shows floor, not height.
A tall bookcase and a low bench stand side by side. Both cover the same patch of floor. On a plan drawn from straight above, what is true?
This bedroom is drawn from straight above. Two of the shapes are long rectangles: the bed and the bookcase. A bed is wide enough to lie on; a bookcase is narrow, because it is only as deep as a book. Click the bed.
This task has no paper form; do it on a device.
Finish the plan-maker's notes. For each thing in the room, say what shape it makes when you look at it from straight above.
| Shape from above | |
|---|---|
| a round table | |
| a bed | |
| a square mat |
Two things in this room are round, so both make circles on the plan: the table people sit at, and the wastebasket. A table is about three feet across; a wastebasket is about the width of your two hands. Click the table.
This task has no paper form; do it on a device.
Outdoors now, and the same idea. This park is drawn from straight above. Three trees grow close together in one corner of it, and from above a tree is a round blob, because what you see is the top of it. Click the trees.
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.
An invented room plan is drawn from straight above on equal floor squares. A low storage chest covers 3 squares across and 7 squares along. Its tall lid is open, but the part standing on the floor stays the same. How many floor squares does its footprint cover?
Answer:
You can read a drawing made from straight above. Tell somebody what happens to a bookcase's height when it is put on a plan, and how you would still tell it from a bench.
20. Your turn: what shape does a wastebasket make on a plan?, step 3
$\text{a small circle}$
A wastebasket covers little floor.