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## 7th grade (Eureka Math/EngageNY)

### Course: 7th grade (Eureka Math/EngageNY) > Unit 1

Lesson 4: Topic D: Ratios of scale drawings- Exploring scale copies
- Explore scale copies
- Corresponding points and sides of scaled shapes
- Corresponding sides and points
- Identifying scale copies
- Identify scale copies
- Identifying scale factors
- Identify scale factor in scale drawings
- Identifying values in scale copies
- Scale drawing: centimeters to kilometers
- Making a scale drawing
- Construct scale drawings
- Interpreting a scale drawing
- Solving a scale drawing word problem
- Scale drawing word problems

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# Identifying scale copies

CCSS.Math:

Sal looks at side measures on figures to determine if they are scale copies.

## Want to join the conversation?

- how can we actually calculate the scale copy of one figure to the other figure?

Any answers or comments will be helpful.

Thanks to people who help to answer this question.

#patient for answer#(12 votes)- Eunice, first you have to look at one of the sides of the scaled copy. If they are divisible by the numbers in the original shape, then try and see if the others sides of the scaled copy are scaled by the same factor. If they are, then they are a scaled copy. Hope this helped!(15 votes)

- on your practice can you make the lines for the squares more visable, it is kind of hard to see.(3 votes)
- At the Olympic games, many events have several rounds of competition. One of these is the men's 100 meter backstroke. The upper dot plot shows the times in seconds of the top 8 finishers in the semifinal round at the 2012 Olympics. The lower dot plot shows the times of the same 8 swimmers, but in the final round. Which pieces of information can be gathered from these dot plots? In the semifinal round, we see that these are the 8 times of the 8 swimmers. We see 3 swimmers finished in exactly 53.5 seconds. One swimmer finished in 53.7 seconds right here. And one swimmer right over here finished in 52.7 seconds. And we can think about similar things for each of these dots. Now, in the final round, one swimmer here went much, much, much faster. So this is in 52.2 seconds. While this swimmer right over here went slower. We don't know which dot he was up here. But regardless of which dot he was up here, this dot took more time than all of these dots. So his time definitely got worse. And this is at 53.8 seconds. So let's look at the statements and see which of these apply. The swimmers had faster times, on average, in the finals. Is this true? Faster times on average in the finals? So if we look at the finals right over here, we could take each of these times, add them up, and then divide by 8, the number of times we have. But let's see if we can get an intuition for where this is, because we're really just comparing these two plots, or these two distributions, we could say. And so let's see, if all the data was these three points and these three points, we could intuit that the mean would be right around there. It would be around 53.2 or 53.3 seconds, right around there. And then we have this point and this point, if you just found the mean of that point and that point, so halfway between that point and that point, would get you right around there. So the mean of those two points would bring down the mean a little bit. And once again, I'm not figuring out the exact number. But maybe it would be around 53.2, 53.1, or 53.2 seconds. So that's my intuition for the mean of the final round. And now let's think about the mean of the semifinal round. Let's just look at these bottom five dots. If you find their mean, you could intuit it would be maybe someplace around here, pretty close to around 53.3 seconds. And then you have all these other ones that are at 53.5 and 53.3, which will bring the mean even higher. So I think it's fair to say that the mean in the final around and the time is less than the mean up here. And you could calculate it yourself, but I'm just trying to look at the distributions and get an intuition here. And at least in this case, it looks pretty clear that the swimmers had faster times, on average, in the finals. It took them less time. One of the swimmers was disqualified from the finals. Well, that's not true. We have 8 swimmers in the semifinal round. And we have 8 swimmers in the final round. So that one's not true. The times in the finals vary noticeably more than the times in the semifinals. That does look to be true. We see in the semifinals, a lot of the times were clumped up right around here at 53.3 seconds and 53.5 seconds. The high time isn't as high as this time. The low time isn't as low there. So the final round is definitely-- they vary noticeably more. Individually, the swimmers all swam faster in the finals than they did in the semifinals. Well, that's not true. Whoever this was, clearly they were one of these data points up here. This data point took more time than all of these data points. So this represents someone who took more time in the finals than they did in the semifinals. And we got it right.(6 votes)

- what is a scale copy? Help me plz.(0 votes)
- A scale copy of a figure is a figure that is geometrically similar to the original figure.

This means that the scale copy and the original figure have the same shape but possibly different sizes.

More precisely, the angles of the scale copy are equal to the corresponding angles of the original figure, and the ratio of the side lengths of the scale copy is the same as the ratio of the corresponding side lengths of the original figure.

In real life, a scale copy is often smaller than the original figure. For example, the drawing of a floor plan for a room is a scale copy of the actual floor of the room. The floor plan drawing has the same shape as but is smaller than the actual floor. For example, if the actual floor is a rectangle measuring 12 feet by 16 feet, a scale copy could be a drawing of a 6-inch by 8-inch rectangle (because 12ft:16ft is the same ratio as 6in:8in).(11 votes)

- This was a very informational video about math, I admire and appreciate this video because it helps learn by giving examples which makes me smarter. Then will then proceed to make me happy. Thank you, have a good day.(3 votes)
- why dont you count the top thats the key to finding the answer.(2 votes)
- I have no questions for this video(2 votes)
- why do we mesure sides of the scale copies(2 votes)
- how do we find out the volume of x(2 votes)
- what is a scale copy? Help me plz.(2 votes)
- Watch the video "Exploring scale copies".(0 votes)

- what is a scale copy help me plz(1 vote)
- It is a copy of another shape just made smaller or larger. But it must be able to be divisible or multiplied by the same number for all of the sides.(1 vote)

## Video transcript

- [Instructor] What we're
going to do in this video is look at pairs of figures, and see if they are scaled
copies of each other. For example, in this diagram, is Figure B a scaled version of Figure A? Pause the video and see if
you can figure that out. There's multiple ways that
you could approach this. One way is to say, "Well, let's see what the
scaling factor would be." We could look at the side lengths. This side right over here
has length three on Figure A. This side length right over here has length one, two, three, four, five. This side length has length five as well. This has length five. This length, we could figure it out with the Pythagorean Theorem, but I won't even look
at that one just yet. But let's look at corresponding sides. To go from this side. If we scale up, the
corresponding side to that would be this side right over here. What is its length? Well, its length, when you
scale it up, looks like five. So to go from three to five you would have to multiply by 5/3. 5/3. But let's look at this side now. It's five in Figure A. What length is it in Figure B? Well, it is one, two, three, four, five. It's still five, so to
go from five to five, you have to multiply it by one, and so you have a different scaling factor for corresponding, or what could have been
corresponding sides. This side right over here,
you're scaling up by 5/3, while this bottom side,
this base right here, you're not scaling at all. So these actually are not
scaled versions of each other. Let's do another example. In this example, is Figure B
a scaled version of Figure A? Pause the video and see
if you can figure it out. All right, well we're
gonna do the same exercise, and here they've given us the measures of the different sides. This side has length two. This side has length the corresponding side, or what could be the
corresponding side has length six. To go from two to six, you
have to multiply by three. If we look at these two
potentially corresponding sides, that side and that side, once again, to go from four to twelve,
you would multiply by three, so that is looking good as well. Now to go from this side down
here, this has length six. The potentially corresponding
side right over here has the length 14. Well here we're not multiplying by three. If these were scaled If Figure B was a scaled-up
version of Figure A, we would multiply by three, but six times three is not 14, it's 18, so these actually are not Figure B is not a scaled
version of Figure A. Let's do one more example. Once again, pause this video and see if Figure B is a
scaled version of Figure A. We're gonna do the same exercise. Let's look at potentially
corresponding sides. That side to that side, to go from four to 12, we would multiply by three, and then we could look at
this side and this side, to go from four to 12, once
again you multiply by three, so that's looking good so far. We could look at this side and this side, potentially corresponding sides. Once again, we're going from four to 12, multiplying by three. Looks good so far. And then we could look at
this side and this side. 2.2 to 6.6, once again
multiplying by three. Looking really good. And then we only have
one last one to check. 2.2 to 6.6, once again
multiplying by three, so all of the side lengths
have been scaled up by three, so we can feel pretty good that Figure B is indeed a scaled-up
representation of Figure A.