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Finding Length by Using Scale Factor and a proportion.

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Finding Length by Using Scale Factor and a proportion.

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This website provides students with a core lesson and different resources that they could use to deepen their study with scale factors and proportions.

Forster, S. (2019, September 18). Find a length by using a scale factor and a proportion. Retrieved October 9, 2019, from https://learnzillion.com/lesson_plans/8714-find-a-length-by-using-a-scale-factor-and-a-proportion/.

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Find a length by using a scale factor and a proportion.

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In this lesson you will learn how to calculate actual lengths from a scale drawing by using ratios and proportions.

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This video shows students how they can apply proportions and fractions to their work with scale factors.  This allows them to relate previous learning to what they're doing now.

Lopez, A. (2015, November 18). Solving Proportions with Scalar Factors. Retrieved October 9, 2019, from https://www.youtube.com/watch?v=8fN3h0FlF4Y.

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This interactive activity takes students on a scavenger hunt where they find the scale factor of different objects and apply them to different activities that they are to do.

Brooks, S. (2014, June 11). Apply Scale Factor. Retrieved October 9, 2019, from https://www.internet4classrooms.com/grade_level_help/solve_scale_factor_problems_math_seventh_7th_grade.htm.

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to solve problems involving area and volume

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Apply Scale Factor | Geometry & Measurement Seventh 7th Grade Math I4C

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Apply Scale Factor, Learn Math, Geometry & Measurement, Seventh 7th Grade Math Standards, Grade Level Help, Internet 4 Classrooms resources, teachers, students, parents

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This video is an interactive in which students are solving problems to get the town back to normal as someone evil is changing the length, width, and area of objects.

Scale Ella Animation. (n.d.). Retrieved October 9, 2019, from https://mathsnacks.com/scale-ella.html.

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The evil Scaleo has escaped from prison and is transforming the length, width, and height of objects until they become useless... or dangerous. Who can put things right? Our super heroine uses the power of scale factor to foil the villain.

Scale Ella addresses Common Core numbers and operations standards and the process standard.

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The evil Scaleo has escaped from prison and is transforming the length, width, and height of objects until they become useless... or dangerous. Who can put things right? Our super heroine uses the power of scale factor to foil the villain. Scale Ella addresses Common Core numbers and operations standards and the process standard.

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This virtual practice quiz gives students practice problems on finding scale factors and drawing scale factors.

Scale drawings and scale factors. (2005). Retrieved October 9, 2019, from http://www.softschools.com/ccss/7th_grade/7th_grade_math_skills/scale_drawings_and_scale_factors/.

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Scale drawings and scale factors - Skill Practice

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This is a practice activity that guides students through scale factors.  It starts by giving them a lesson followed by practice so that they can reiterate and build upon what they already know.

Scale Drawings . (2019). Retrieved October 9, 2019, from https://www.learningfarm.com/web/practicePassThrough.cfm?TopicID=1401.

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Common Core Standards

Grade:

7th Grade

Standard:

Description:

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Start Practicing!

7th Grade Math - Scale Drawings Lesson

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Common Core Standards Grade: 7th Grade Standard: Description: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Start Practicing! 7th Grade Math - Scale Drawings Lesson

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This website contains different activities that students can complete to find scale factor and missing sides.

Rachel. (2017, January 16). 8 Scale Drawing Activities. Retrieved October 9, 2019, from https://ideagalaxyteacher.com/8-scale-drawing-activities/.

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Looking for ideas on teaching scale drawings? You're in the right place! Scale drawings can be so much fun for students, and they're definitely a fun way to look at math. In this post you'll find 8 engaging scale drawing activities to practice in your classroom. For even more scale drawing ideas & tips, check out this post about using I Can Statements to break down teaching scale drawings. Or, for a guide to introducing scale drawings through discovery & interactive notes, check out this post. The eight scale drawing activities below include independent practice opportunities, technology-based tools, review games, and enrichment activities. Let's dig in!

The 8 scale drawing activities are:

Practice activities

There are many ways to practice any concept. Finding a good combination for modeling, practicing, and reinforcing learning is the art of being a teacher. Below, I've included some activities that I use while teaching this concept. They work for different parts of the lesson like anticipatory set, modeling, practice, and closure. You can mix and match them to work for your students. This variety of approaches can be used as math centers, partner work, independent work, or with the whole class depending on the activity.

Coloring page for independent practice

This Scale Drawings Coloring Activity (2 Pages) engages students by having the fun of coloring a picture while they complete their work. It makes it easy for the teacher to monitor progress. In my experience, students don't want to get the answers wrong so they'll check with the teacher to make sure they're correct before coloring the image. This is a great opportunity to give feedback and take note of who gets it, and who still is missing a piece. This particular coloring activity has 12 problems, all short story problems. They'd be good to use with an annotating strategy like the one we use with this foldable. I would use this activity after notes are taken as a first round of independent practice.

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Fast finishers

Every class has some students who finish before everyone else and it can be had to always have something for them to do. During scale drawings practice, this activity from Glencoe is something that students can do on their own with a computer. The program basically walks them through a couple of hands-on activities of scale drawings in real life. It's something that students who are fast finishers should be able to complete on their own. This activity will challenge students a little, but not too much.

More independent practice for scale drawing

I like to use computer games for some independent practice. Many of them can be found on the internet for free. You'll want to preview any game before you assign it to students because students will ask you questions about it and you want to make sure it's high quality.

The following links are computer-based games that students can play to reinforce this topic. They're free and I find that students really get motivated when they can practice on the computer, especially when there's a game involved. These would be great for anticipatory sets, fast finishers, or independent practice. Students really seem to get excited when they can play games together, so you might want to let them complete the game with a friend.

The scale factory x- game from Math Playground is a fun game that has students working with proportions. It also lets students play in a video game format where they collect keys and solve missions. I use this as an anticipatory set and then let students go back to it if they finish their assignment early. My kids love games like this.

This game from Math Playground is much less game-like than the first one. It's a collection of story problems and students can enter their answer and see if they're right or wrong. Partners can play this. If they get a question right they could roll a dice or spin a spinner to see how many points they get. You could also use this with the whole class and have students keep track of their stars as they answer the questions. The questions are simple and they're already prepared for you.

One great way to review for a test or to see how the class is doing is through playing whole class games. My favorite class review game is called Knockout. This game can be played with or without an interactive whiteboard. All you need to have is a projector.

This scale drawings knockout game has a fun Taco Tuesday theme which middle school students love. The questions consist of a variety of short story problems, a couple of shape problems, and a couple of questions with fractions and decimals.

To play, I project the game screen onto the front board and all students have a whiteboard. A student chooses an icon revealing a scale drawings problem. A student chooses one of the items on this screen:

Then, their choice leads to a question or problem. All students solve the problem on their white board.

All students answer the question on either a printed scorecard or a whiteboard. Then, we reveal the answer and students keep track of their points for the problems they get right. I don't emphasize the points very much, but many students love the points side of the game. When needed, I coach students through the problems if they seem to be struggling. You then will go back to the first board and choose another item that leads to a question. To add some fun there are some bonuses.

When they get to the bonus page they have three choices. Whichever one they choose will lead to a good or a bad bonus.

The kids love the bonuses, especially the negative ones. They think it is very funny and therefore they are more engaged in the game. Just today we played this game and near the end of the game one student got the bonus and he got the surprise of losing all of his points. Everyone chuckled including the student and it was silly because there really is nothing attached to the points. The stakes are low, but my students still get into it.

We play this type of game the day before or the day of a test. These games work as a final boost before the test. You can get this scale drawing knockout game in our TPT store.

Remediation

The students that I work with usually need more practice than the average bear. During this particular unit I used something that I bought on TPT to give students more practice. It was a set of worksheets from Math on the Move. I really liked this resource because it was easy to understand and simple. When I had to go back and reteach part of this concept, these assignments were easy for me to get ready. All I had to do was print and go.

Challenge activity

I'm a math specialist and I'm also a math coach on my campus. We've been struggling this year to make sure that we are pushing all students. Sometimes we seem to be teaching to the middle and not pushing everyone as far as they can go. I've looked into a lot of resources to help find challenging problems for students. The best source I found was Illustrative Mathematics. They have multiple performance tasks on almost every topic. They have 6 performance tasks for scale drawings. These activities are easy to bring into the classroom and offer a great challenge for students.

Extended project

There are a lot of extended real world projects that would work with this topic. One of the them is to take a candy bar wrapper and to make a scale drawing that's 10 times larger than the original. Another very popular project related to scale drawings is to recreate a room or house in a scaled down drawing. These types of activities are something that I don't have time to do until after our state testing in April, but this is one that we will do for sure in my 7th grade class. Check out this candy bar wrapper activity from Fast Times of a Middle School Math Teacher:

Putting it all together

There's never enough time to do all of the activities that I want to do with my students. For this topic in particular we only had 4 days to teach it and test it. I'm going to save some of these ideas for later in the year when I have more time to go deeper into this topic. I can't wait.

Check out our activity pack for five great scale drawing activities & resources at a great discoung. It includes two games I talked about above, the discovery lab and foldable notes I talked about here, and the task cards I showed you here. Thanks for reading! Until next time!

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Looking for ideas on teaching scale drawings? You're in the right place! Scale drawings can be so much fun for students, and they're definitely a fun way to look at math. In this post you'll find 8 engaging scale drawing activities to practice in your classroom.

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This activity goes through the use proportional relationships to identify scale factor relationships.

8.9 Proportions to Find Scale Facto. (2019). Retrieved October 9, 2019, from https://www.ck12.org/book/CK-12-Middle-School-Math-Concepts-Grade-6/section/8.9/.

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This video goes through examples of helping students find the scale factor of items through real world application.  It uses word problems and items that they are familiar with to find the answer.

Hays, D. (2013, August 13). Scale Drawings and Scale Factors 7th Grade Math. Retrieved October 9, 2019, from https://www.youtube.com/watch?v=5HU_LCR5C7s&app=desktop.

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Scale Drawings and Scale Factors 7th Grade Math

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This BrainPOP video shoes multiple examples of scale drawings in relation to geometry.  Following the video, there's a:
- quiz
- vocabulary game
- games to play

Scale Drawing. (n.d.). Retrieved October 9, 2019, from https://www.brainpop.com/math/ratioproportionandpercent/scaledrawing/.

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Learn to use math to scale a drawing so you can create maps, grids, and even buildings that are perfectly proportional.

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Identifying Scale Factor in Scale Drawings

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Identifying Scale Factor in Scale Drawings

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This Khan Aademy goes through allowing students to find the scale factor between shapes.  They are to solve for missing sides, find the actual scale factor, and determine whether or not there is a scale factor at all.

Khan Academy. (n.d.). Identify scale factor in scale drawings. Retrieved October 9, 2019, from https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/scale-copies/e/scale-factor-in-scale-drawings.

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This online game allows students to practice working through solving factors and matching them to the answer choices.

MathGames. (2019). Scale Drawings and Scale Factors. Retrieved October 9, 2019, from https://www.mathgames.com/skill/7.159-scale-drawings-and-scale-factors.

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Scale Drawings and Scale Factors - Grade 7 - Practice with Math Games

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This link is to an actual lesson scale factors.  It has an introduction piece that takes students through what scale factors are and leads them into identifying scale factors.  It then shows them solving scale factors and filling in the missing side.

Morgan. (2018, August 28). Math 7 1 7 Homework Help Morgan. Retrieved October 9, 2019, from https://www.youtube.com/watch?list=PLfuJ6kc7tzESHSeC8B-wSkDgIMdIsKtz7&index=7&v=a7DA3XpQ0iA&app=desktop.

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This online virtual scale factor activity allows students to build upon what they've learned and apply that to the activity.  This allows them to use their application skills to solve for the scale factor.

NCTM. (2015). Scale Factor. Retrieved October 9, 2019, from https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/WSP-Scale-Factor/.

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Use this applet to investigate how changes in the scale factor influence the ratio of perimeters and the ratio of areas between two figures.

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This video from Khan Academy goes over ways to identify scale factors.  It talks about different things to look for and how to create a scale factor to solve for the shapes.

Khan Academy. (n.d.). Identifying Scale Factors. Retrieved October 9, 2019, from https://www.khanacademy.org/math/7th-engage-ny/engage-7th-module-1/7th-module-1-topic-d/v/identifying-scale-factors.

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- [Instructor] So right over here, Figure B is a scaled copy of Figure A and what we wanna do is figure out what is the scale factor to go from Figure A to Figure B? Pause the video and see if you can figure that out. Well, all we have to do is look at corresponding sides and think about how much they have been scaled by. So for example, this side right over here would correspond to this side right over here on Figure B and over here, it had length two and over here, it has length one, two, three, four, five, six. So it looks like that side has been scaled up by a factor of three and so if Figure B truly is a scaled copy then every side should be scaled up by a factor of three and we could verify that. We don't have to do it with every side. We're being told that these are scaled copies but we can see that this is the case. For example, this side right over here corresponds to this base right over here. This has length three. So if we're scaling up by a factor of three, we should multiply that by three and this should be of length nine. Let's see if that's the case. One, two, three, four, five, six, seven, eight and nine. And so you can see we can feel pretty good that Figure B is a scaled copy of Figure A and that scaling factor is three. Let's do another example. So here, we are told Ismael made a scaled copy of the following quadrilateral. He used a scale factor less than one, alright, and then they say what could be the length of the side that corresponds to AD? So AD is right over here. AD has length 16 units in our original quadrilateral. What could be the length of the side that corresponds with AD on the scaled copy of the quadrilateral? So it's a scale factor less than one. So we're gonna get something that is less than 16 for that side and the rest of it will all be scaled by the same factor. So the resulting quadrilateral might look something, might look something like this. This is just my hand-drawn version. So the key realization is is if our scale factor is less than one, this thing right over here is going to be less than 16 units. So let's look at the choices and it says choose three answers. So pause the video and which of these would match if we're scaling by a factor of less than one? Well, we just have to see which of these are less than 16 units. This is less than 16. This is less than 16. This is less than 16 and those are the only three that are less than 16. 32 units, this would be a scale factor of two. 64 units, this would be a scale factor of four. Clearly a scale factor that is not less than one.

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Identifying scale factors (video) | Khan Academy

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Instructor] So right over here, Figure B is a scaled copy of Figure A and what we wanna do is figure out what is the scale factor to go from Figure A to Figure B? Pause the video and see if you can figure that out.

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This is a picture of an anchor chart that will show students:
- what a scale factor is
- what happens to scale factors when the size changes
- different rules to remember about scale factor
- an example of a scale factor.

Scale Factor Anchor Chart. (n.d.). Retrieved October 9, 2019, from https://www.pinterest.com/pin/412853490838043171/.

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Scale factor anchor chart #mathhacks | ideas for school | Math classroom, Sixth grade math, Math anchor charts

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This video, created by a math teacher, goes through finding the missing side of similar figures when dealing with scale factors.

Mathtrain. (2015, October 25). Finding Missing Length on Similar Figures using Scale Factor. Retrieved October 9, 2019, from https://www.youtube.com/watch?v=qa5pgULMLq4&app=desktop.

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Finding Missing Length on Similar Figures using Scale Factor

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This Quizizz was made by a secondary education math teacher who needed a way to help her students review scale factors.  This Quizizz gives students practice problems to identify scale factors, solve for area of scale factors, and finding missing side.

Perardi, K. (2016). Scale Factors Quiz - Quiz. Retrieved October 9, 2019, from https://quizizz.com/admin/quiz/571f7371757813b534cc2b84/scale-factors-quiz.

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Free gamified quizzes on every subject that students play in class and at home. Pick an existing quiz or create your own for review, formative assessment, and more.

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This video from Khan Academy goes over specific problems that work through finding scale factors.  It also gives students an example of how to find the area in relation to scale factors.

Khan Academy. (2019). Scale Factors and Area. Retrieved October 9, 2019, from https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-scale-drawings/v/scale-factors-and-area.

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- [Instructor] We're told that Polygon Q is a scaled copy of Polygon P using a scale factor of one half. Polygon Q's area is what fraction of Polygon P's area? Pause this video and see if you can figure that out. Alright, my brain wants to make this a little bit tangible and once we get some practice, you might be able to do it without drawing pictures but they're saying some arbitrary Polygon Q and P so let's just make a simple one. Since we're talking about area, I like to deal with rectangles since it's easy to think about areas of rectangles. And so, let's see, Polygon Q is a scaled copy of Polygon P. So let's start with Polygon P. And I will do this in red. So Polygon P, let's just say, I'm just gonna create an arbitrary polygon. So let's say that this is, and I'm gonna scale it by one half so I'm gonna make its sides have nice even numbers. So let's say this side right over here is four and this side right over here is equal to eight, this is Polygon P right over here, it's a quadrilateral, it's in fact a rectangle and its area is just going to be four times eight which is 32. Now let's create Polygon Q, and remember, Polygon Q is a scaled copy of P using a scale factor of one half. So we're gonna scale it by one half. So instead of this side being four, it's going to be two and instead of this side over here being eight, the corresponding side in the scaled version is going to be four. So there you go, we've scaled it by one half, and now what is our area going to be? Well our area, and this Polygon Q, and so our area is going to be two times four which is equal to eight. So notice that Polygon Q's area is one fourth of Polygon P's area and that makes sense because when you scale the dimensions of the Polygon by one half, the area is going to change by the square of that. One half squared is one fourth and so the area has been changed by a factor of one fourth or another way to answer this question, Polygon Q's area is what fraction of Polygon P's area? Well it's going to be one fourth of Polygon P's area. And the big takeaway here is if you scale something, if you scale the sides of a figure by one half each, then the area is going to be the square of that and so one half squared is one over four. If it was scaled by one third, then the area would be scaled, or the area would be one ninth. If it was scaled by a factor of two, then our area would have grown by a factor of four. Let's do another example. Here we're told, Rectangle N has an area of five square units. Let me do this in a different color. So Rectangle N has an area of five square units. James drew a scaled version of Rectangle N and labeled it Rectangle P. So they have that right over here. This is a scaled version of Rectangle N. What scale factor did James use to go from Rectangle N to Rectangle P? So let's think about it. They gave us Rectangle P right over here, and let's think about its dimensions. This height is one, two, three, four, five, it's five high, and it is, one, two, three, four, five, six, seven, eight, nine wide, and so its area is equal to 45. Now, Rectangle N had an area of five square units. So our area, let me write this down, so N area to P area, N area to P area, we are multiplying by a factor of nine. If we're going from an area of five square units to 45 square units, you notice N area is five, N's area is five square units, P's area, we just figured out is 45 square units, and so we have it growing by a factor of nine. Now what would be the scale factor if our area grew by a factor of nine? Well we just talked about the idea that area will grow, the factor with which area grows is the square of the scale factor. So one way to think about it is scale factor, scale factor squared is going to be equal to nine, or another way to think about it, our scale factor is going to be equal to three to go from N to P. Now let's verify that we answered their question but I just want us to feel good about it. Let's draw a rectangle that is scaled down from P by a factor of three. So a rectangle if we were to scale it up by a factor of three, we get rectangle P. So its bottom would have length three instead of nine. So it'd be like this. So that would be three, and its height instead of being five, it would be five thirds. Five thirds is one and two thirds, so it'd go about that high, it would look something like that. It would be five thirds. And so our Rectangle N would look like this, and what is its area? Well five thirds times three is indeed five square units. So notice, when we have the area growing by a factor of nine, the scale factor of the size to go from five thirds to five, you multiply by three. To go from three to nine, you multiply by three.

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Instructor] We're told that Polygon Q is a scaled copy of Polygon P using a scale factor of one half. Polygon Q's area is what fraction of Polygon P's area? Pause this video and see if you can figure that out.

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This anchor chart leads students to work on solving for scale factors.  It gives them a visual that they could use to remember the steps to solving scale factors. (http://msmarciteachesmath.blogspot.com/2018/11/anchor-charts.html?m=1 )