## Recommended Posts

For some reason I can not seem to get this in my mind. I am hoping someone here would be able to help.

This is from my nieces homework and it is driving me crazy that I can't figure it out.

Make the Scale Drawing

Your scale is one inch = four feet

On the next page you will find a piece of graph paper. Each square is ¼ (or 0.25) of an inch wide. Four squares are one inch long. You may use this or any program you may have to make your drawing.

â€¢ First, figure out the scale dimensions of the room and draw it on the paper.

â€¢ Then figure out the scale dimensions of each item you are placing in the room.

A. Room 20 feet by 25 feet Scale Dimensions =

1/4 = w/20

4w = 20

w = 20/4

w= 5

1/4 = L/25

4L = 25

L = 25/4

L = 6.25

Draw the outline of the room on the graph paper or in the computer program you are using.

B. Fill in the table.

Furniture or Item

Actual Dimensions

Scale Dimensions

Hutch

54â€w x 15â€d x 78â€h

54/12 = 4.5

15/12 = 1.3

(w = 4.5, d = 1.3)

1/4 = w/4.5

4w = 4.5

w = 1.125

1/4 = d/1.3

4d = 1.3

d = 1.3/4

d = 0.325

Table

53â€w x 31â€d x 30â€h

53/12 = 4.4

31/12 = 2.6

(w = 4.4, d = 2.6)

1/4 = w/4.4

4w = 4.4

w = 4.4/4

w = 1.1

1/4 = d/2.6

4d = 2.6

d= 0.65

Chairs (6)

19.25â€w x 18.25â€d

19.25/12 = 1.6

18.25/12= 1.5

(w = 1.6, d = 1.5)

1/4 = w/1.6

4w = 1.6

w= 1.6/4

w = 0.4

1/4 = d/1.5

4d = 1.5/4

d = 0.375

Buffet

63â€w x 16â€d x 33â€h

63/12 = 5.3

33/12 = 1.3

(w = 5.3, d = 1.3)

1/4 = w/5.3

4w= 5.3

w = 5.3/4

w = 1.325

1/4 = d/1.3

4d = 1.3

d = 1.3/4

d = 0.325

It looks to me that she has the math correct, but for some reason I can not wrap my brain around how to do the graph( I think I have been looking at numbers to much today).

Make the scale drawing. Use the graph paper on the next page or any computer program which you know how to use.

##### Share on other sites

Looks like your nieces are suppose to draw a floorplan of a room on the provided graph paper. So 20 squares by 25 squares on the graph paper would be the outline of the room. Than draw in the furniture like the table, hutch, chairs and buffet ignoring the height dimension and label the actual 3d (length, width, height) dimensions on the graph paper. The hutch is kind of overhang on the table by an inch but would fit on top of the buffet easily.

##### Share on other sites

Looks like your nieces are suppose to draw a floorplan of a room on the provided graph paper. So 20 squares by 25 squares on the graph paper would be the outline of the room. Than draw in the furniture like the table, hutch, chairs and buffet ignoring the height dimension and label the actual 3d (length, width, height) dimensions on the graph paper. The hutch is kind of overhang on the table by an inch but would fit on top of the buffet easily.

I get that part I just am not sure how she is to calculate how many squares(I know it might sound silly) but for some reason it isn't making sense--I reallly think I am overthinking this.

##### Share on other sites

Hope below explanation is clearer

Your scale is one inch = four feet -> 0.25 inch = one feet

Each square is ¼ (or 0.25) of an inch wide -> one square = one feet

Room 20 feet by 25 feet so 20 squares by 25 squares on the graph paper

Hutch

54â€w x 15â€d x 78â€h

width = 4.5 square on graph

depth = 1.25 square on graph

hutch is a rectangle of 4.5 square by 1.25 square on the graph paper

Table

53â€w x 31â€d x 30â€h

width = 4.4 square

depth = 2.6 square

Table is a rectangle of 4.4 square by 2.6 square on the graph paper

Chairs (6)

19.25â€w x 18.25â€d

width = 1.6 square

depth = 1.5 square

Chair is a rectangle of 1.6 square by 1.5 square on the graph paper

Buffet

63â€w x 16â€d x 33â€h

width = 5.3 square

depth = 1.3 square

Buffet is a rectangle of 5.3 square by 1.3 square on the graph paper

##### Share on other sites

Your scale is one inch = four feet

...a piece of graph paper....Four squares are one inch long...

A. Room 20 feet by 25 feet Scale Dimensions =

...

w= 5

...

L = 6.25

...

(I've taken excerpts of your post.) Since the scale is 1 in = 4 ft and the graph paper is sized 4 squares = 1 inch, each square on the graph paper is supposed to be 1 ft long. The calculations for the room in A. ends up with w=5, and L=6.25, which are in inches (remember that we're converting feet into inches at the rate of 4 ft : 1 in). So you need to draw a rectangle 5 inches wide and 6.25 inches long for the room (or 20 squares by 25 squares). The rest of the converted dimensions are also in inches.

##### Share on other sites

I must be totally blind(I am actually good at math)..I am still not seeing how to draw this out--pulling hair out!

Let me ask--do the numbers look correctly calculated?

Ok neice says that her teacher told her that she would use 20 squares to graph the width of the room. So I am assuming that she multiplied 5 x 4

If that is so then she will need to use 25 for the lenght 6.25 x 4

On the furniture--in blue for the graph

Hutch

54â€w x 15â€d x 78â€h

width = 4.5 square

depth = 1.25 square

4.5 x 4 = 18 (this makes no sense since the room is 20 x 25 squares on the graph and originally the table was only 54inches)

1.25 x 4 = 5

##### Share on other sites

On the furniture--in blue for the graph

Hutch

54â€w x 15â€d x 78â€h

width = 4.5 square

depth = 1.25 square

4.5 x 4 = 18 (this makes no sense since the room is 20 x 25 squares on the graph and originally the table was only 54inches)

1.25 x 4 = 5

Hutch

54â€w x 15â€d x 78â€h

width = 4.5 square on graph

depth = 1.25 square on graph

so the hutch is a rectangle of 4.5 square by 1.25 square on the graph paper.

My 2nd post at 4:49pm has all the measurements for drawing

##### Share on other sites

I'll tag team this with Arcadia :tongue_smilie:. Let's look at the Hutch. (BTW, who made these calculations? You or your niece? It's very confusing to use w and d twice like this.) My notes are in blue.

Hutch

54â€w x 15â€d x 78â€h

54/12 = 4.5 (ft) These two steps convert the measurements of the Hutch from inches to feet.

15/12 = 1.3 (ft) Actually, the answer is 1.25 ft.

(w = 4.5, d = 1.25) So the hutch is 4.5 ft x 1.25 ft. in actual dimensions.

We can actually stop at this point and realize that since each square of the graph paper = 1 ft, the hutch will take up 4.5 squares x 1.25 squares (Arcadia's post provides all the necessary dimensions to graph all the items).

But since the assignment appears to require you to convert actual dimensions (ft) to scale dimensions (in) in order to fill out a chart, the following steps are useful.

1/4 = w/4.5

4w = 4.5

w = 1.125 (in)

1/4 = d/1.25

4d = 1.25

d = 1.25/4

d = 0.3125 (in) So the hutch's scale dimensions are 1.125 in x 0.3125 in.

But in order to graph the Hutch, it's easier to go back to its actual dimensions in feet, as mentioned earlier.

Hutch

54â€w x 15â€d x 78â€h

width = 4.5 square

depth = 1.25 square

4.5 x 4 = 18 (this makes no sense since the room is 20 x 25 squares on the graph and originally the table was only 54inches) You don't want to multiply by 4 here; the hutch is not 4.5 in in scale dimensions--it's 4.5 ft (in actual dimensions).

1.25 x 4 = 5

Hope I'm helping here and not making things more confused.

##### Share on other sites

I'll tag team this with Arcadia :tongue_smilie:. Let's look at the Hutch. (BTW, who made these calculations? You or your niece? It's very confusing to use w and d twice like this.) My notes are in blue.

Hope I'm helping here and not making things more confused.

No my neice did the calculations--she said she had to do ratios and was following her lesson from that day.

Thanks that is what I was thinking as well, but I forgot to mention that the teacher told her that the hutch which is 4.5 would take 6 full squares(4 full squares for the whole number and then 4 x 0.5 = 2 more squares)--this does not make sense to me. To me it should only take 4 full squares and half of another. If you do it the way the her teacher says, then when you get to the 1.25 you would take 1 square for the whole number and then another full square(0.25 x 4=1)--which would make the decimal larger than the whole number. This is where I was lost.

##### Share on other sites

Thanks that is what I was thinking as well, but I forgot to mention that the teacher told her that the hutch which is 4.5 would take 6 full squares(4 full squares for the whole number and then 4 x 0.5 = 2 more squares)--this does not make sense to me. To me it should only take 4 full squares and half of another. If you do it the way the her teacher says, then when you get to the 1.25 you would take 1 square for the whole number and then another full square(0.25 x 4=1)--which would make the decimal larger than the whole number. This is where I was lost.

I wonder if the teacher was talking about area rather than linear dimensions. The hutch will be drawn on graph paper as a rectangle that is 4.5 units long by 1.25 units wide. (I don't like to say "squares" here, because that implies an area measurement, but here we are talking about a linear measurement.) If you draw that on graph paper, you will see that it takes up an area of four full squares plus some extra. The "extra" is where the width exceeds 1.00 units and where the length exceeds 4.0 units. Of course we can calculate this area simply by multiplying 4.5 units x 1.25 units to get 5.625 square units. This is not the same as "6 squares", of course, but perhaps the teacher was showing the students how to quickly estimate an area from the graph, like this --

First you see the "full squares" = 1 unit x 4 units = 4 square units

You would get one long skinny bit along the length = 0.25 units x 4 units = 1 square unit

Also one fatter bit along the width = 0.5 units x 1 unit = 0.5 square units

Then there's one more tiny bit in the corner = 0.5 units x 0.25 units = 0.125 units

If you want an estimate of the area to the nearest square unit, it would be 6 square units.

BTW, in problems like this, I would strongly encourage your niece to use units in all of her work. That will help clarify her thinking as well as help prevent some simple mistakes.

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account. ×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.