Gamom3 Posted March 29, 2013 Share Posted March 29, 2013 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. Quote Link to comment Share on other sites More sharing options...

Arcadia Posted March 29, 2013 Share Posted March 29, 2013 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. Quote Link to comment Share on other sites More sharing options...

Gamom3 Posted March 29, 2013 Author Share Posted March 29, 2013 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. Quote Link to comment Share on other sites More sharing options...

Arcadia Posted March 29, 2013 Share Posted March 29, 2013 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 Quote Link to comment Share on other sites More sharing options...

sgo95 Posted March 29, 2013 Share Posted March 29, 2013 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. Quote Link to comment Share on other sites More sharing options...

Gamom3 Posted March 30, 2013 Author Share Posted March 30, 2013 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 Quote Link to comment Share on other sites More sharing options...

Arcadia Posted March 30, 2013 Share Posted March 30, 2013 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 Quote Link to comment Share on other sites More sharing options...

sgo95 Posted March 30, 2013 Share Posted March 30, 2013 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. Quote Link to comment Share on other sites More sharing options...

Gamom3 Posted March 30, 2013 Author Share Posted March 30, 2013 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. Quote Link to comment Share on other sites More sharing options...

Cosmos Posted March 30, 2013 Share Posted March 30, 2013 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. Quote Link to comment Share on other sites More sharing options...

Arcadia Posted April 2, 2013 Share Posted April 2, 2013 This MEP unit on scale drawing has good worked examples similar to your question. Maybe that might help your nieces. Quote Link to comment Share on other sites More sharing options...

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