What Is Scale?

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SWBAT identify how things can be represented by scale models

Big Idea

Big is big, little is little. What happens when we use little to show big?

Teacher Notes

The standard K-2ETS1 - 2 says that students should be able to draw a sketch or make a model to show how the shape of an object influences the problem it is designed to solve. Before students can draw the sketch, or make the model, they need to understand what a model is. This lesson is a first step in building a model. Students need to grasp the idea that a model is not the actual object, but a representation and that usually the representation is a different size than the actual object.

This lesson has 3 basic parts: introducing a model,  measuring an area to model and building the model.

I suggest introducing the idea of a model and possibly measuring larger objects during math the first day, measuring the area to model the second day, and building the model on the third day. 

It may be helpful to draw the area first and to have that map ready for when students measure the area so they can record the measurements on the map. I asked the students to draw maps on their own. This also lends itself to a discussion on mapping and the difference between a photographic view and a bird's eye view.

When you choose a scale to build the model at, keep it as simple as possible such as 1 inch equals 1 foot so students can look at the measurements and then quickly convert them to the scale size. 

Introduction Day 1

10 minutes

In the center of the rug I place a globe, and a model car. I ask students, "what are these?" (a globe, a car). I say, "what do they show us?" (the world, about the car) "Are they full size?" (no) "Why not?" (because the full size one would be too big, it wouldn't fit in the room.) 

Here I am trying to get students to see that models represent a real thing but are much smaller so that we can work with them. I want students to begin to understand that models can be used in science. The use of models crosses through many scientific disciplines.

"Do you know what they call it when something smaller represents something bigger?" (a model). If students do not come up with the term on their own I refer them back to the I Can statement for a hint. Then I ask, "have any of you ever built a model of anything?" I see if any students have made model cars, etc. I let them share what they built. 

Next I pick up the model car and ask students how it is the same or different from the real car. (It is smaller and has less detail, there is no real engine, the doors don't open..etc.) I pick up the globe and ask, "do you think this globe shows everything in the world?" (no) "why not?" (It wouldn't all fit.) "Can you see where something might be missing?" (Maine isn't on there - their state, etc.) "What is different about a model and the real thing?" (there are no words on the earth but there are on the globe model..)

"You have made some great observations. Not everything fits on a model. Can you think of why someone might want to build a model?" ( I want students to begin to identify that models can be used by a variety of people when the real thing is not manageable.) 

"Many scientists use models to help them figure things out. The bio-chemist we visited uses simple cells to figure out how other cells might work. That is a model too. Some scientists might build a model of a volcano to better understand how the top of the volcano is formed. Can you think of anyone else who might use a model?" (I listen to and reinforce student suggestions.)

"Today we are going to think about how a model is made and then get ready to build our own model."

I Can Statement and Drawings Day 1

20 minutes

Now that I have introduced the idea of a model, I present the I can statement. This statement helps students to understand what is expected of them in this lesson and allows them to assess their own learning at the end of the lesson.

I post the I Can statement on the board and ask students to read it with me. It says, "I can make a scale model of the playground."

 I say, "today we will start with a map. We just looked at the globe and it is a kind of map. Does it have every detail on it?" (no) "Are there things that are on the map that are not real?" (Words) "Yes, we talked about words on maps are not really on the ground. Today I would like you to sketch a map of the playground. What kinds of things might be on your map?" (swings, slide, climber, pathway, fence, etc.) "Right, and what might not be there?" (kids playing, leaves from the trees, soccer balls, jump ropes, etc.). "Ok so imagine the playground in your mind and then I will hand you a piece of paper and I want you to go to your seat and draw a map of the playground. You can write labels on your map, just like we saw on the globe."

I am interested in having children think about relative position and size in their maps. Because we will be building a scale model, I want to first see how they visualize the playground. I will have them use their maps as a place to record sizes when we go outside to measure the actual playground. 

I circulate around to talk to students about their drawings.

Measuring the Area to Model Day 2

30 minutes

If your students do not know how to measure a larger object, you may want to conduct a math lesson first where you show them how to use a ruler or tape measure and to add those feet together to get the total size.

I have children use a ruler the first time because then they can see that it is one ruler, the next child puts down a second ruler and says 2, the first child moves his ruler to the end of the second and says 3,etc. I have students measure to the nearest foot. We practice this together so students are comfortable with this form of measurement before going outside. (Check out the Better Lesson Common Core Math section for lessons on measurement.)

Once students are comfortable measuring end to end with rulers and recording the number of feet (or rulers) they have measured I introduce the yardstick. I ask students how many feet in a yardstick. I have a child lay the ruler on the yardstick end over end so we see that the yardstick has 3 feet in it. Next I give each group of 2 students 1 yardstick and ask them to measure the distance across the room. I watch to make sure that students understand how to use the yardstick end to end, and count by 3s to get the number of feet. This will be needed when we go outside.

In the next science block I have students find their science buddy and tell them what they will be measuring on the playground. I ask them to bring their map to record the distance on, a pencil and the yardstick. I ask, "how many feet in a yard?" (3). "You will need to record how many feet long your object or distance are." I check for understanding before heading outside. 

I take students outside with their yardsticks, clipboards with the maps, and a pencil and help them find what they will be measuring. As students work, I try to help groups that may be having trouble measuring the larger distances. Measuring the Playground When everyone is done I call the group together to return inside.

Converting to a Model Size Day 3

30 minutes

When everyone is settled at their seats, I take the maps and project my original on the Smart Board. I write the sizes people found on the map. I say to students, "now that we know how big the playground is, what might we do to build a model? We have these sizes so should we build our swing set model 16 feet by 6 feet?" (no) "Why not?" (It would be too big) "Right, our model needs to fit on the table so 16 feet long would be way too big. What can we do?" (make it smaller) "So can I just make it any old size I want?" 

Here I am trying to get students to recognize that a model is in the same proportion as the original. They may not know the term, but they can understand the concept that if we want a model of something, it needs to be come out looking basically the same just smaller. This introduces the concept of proportion.

"What if I make the model of the swing set so I make it this big, (I show a size with my hands), but the group making the fence makes it this big?" (I show a size that is smaller.) "Would that be a good model if my swing set didn't fit inside the fence?" (no) "So what can we do?" (I take some suggestions and try to build on the ideas that suggest proportion.) "We all have to agree on how to make our things the same size. We can't build it the real size, but what if instead of feet like you just measured outside, we pretended that each foot was only an inch? I would say my swing set has to be 16 inches long instead of 16 feet and my fence has to be 28 inches long instead of 28 feet. Now would my swing set fit inside the fence?" (yes) "Would it look the same only smaller?" (yes)

"Lets think what would happen if we wanted to make a model of ourselves. (Invite two students to come up - choosing a taller and a smaller student to help clarify the idea of proportion, and I measure them to the nearest foot.)" ____ is 3 feet tall and _____ is 4 feet tall. If I want to make a picture of both of them and my paper is only this big," (I hold up a 8 X 11 piece of paper), "I need to make them fit so what if I say ___ is 3 inches and ___ is 4 inches. Now I can make them in a scale to the real thing." (I sketch the 2 children quickly measuring out the 3 and 4 inches and fitting my people in the space.) "Can you see how I shrunk them down but _____ is still taller than _____. That is what we want to do with our playground. We want to shrink it but we want to make sure that the swing set is longer than the slide just like it is outside." 

I use a model of the students because it is a very real example. Students can clearly see that 1 child is taller than the other, so if I draw the tall child smaller and the small child taller, students can see from my example that in order to show how things really are, we need to use the same "relative shrinking" process. 

"Scientists do that when they make a model. They decide that everything they will build will be now measured in inches or centimeters instead of feet or meters."

"We will try it with our model of the playground. You are going to use pipe cleaners and tape to build the parts of the playground that you measured. But now you must take the number you found and pretend it is inches." I point to several of the lines on the map and ask how many inches they would be now. I have each person show on their ruler how many inches that would be. We talk briefly about how they might measure something that is more than 12 inches, by either adding and counting on a second ruler, or getting a new tool such as a tape measure or yardstick."

"You and your partner will build what you measured and then we will put our model together."

I hand out pipe cleaners to each group and remind them to think about how big their piece should be when it is finished. I give students the time they need to build their part." Building to Scale

Assembling the Model Day 3

10 minutes

I have covered a small table with paper and have drawn a basic outline of the playground. I ask students to come with their object and to stand around the table.

I start with the fence pieces and ask those students to come and tape their fence to the map. Next I say, "ok now we need to put in the structures. I see from the map on the Smart Board that the swing set is 8 feet from the back fence. Can anyone measure 8 what?" (inches) "right, 8 inches from the fence?" I let a volunteer show us where the swing set should be and the swing group tapes their swing set to the map.  We repeat this with the other 3 playground structures.

"Wow, did we build a model of the playground? Does it look like our playground only smaller?" The Finished Scale Model (yes) "Does it have all the details of our playground?" (no) "What is missing?" (wood chips on the ground, the colors of the structures, the climber doesn't have all the stairs, the rollers on the slide, etc.)

"Right, we built a model that we could use if we wanted to redesign the playground, or see where would be a good place to build a garden, or to add another structure, but we don't have every detail."


Closing Day 3

5 minutes

After everyone has written in their journal I ask students to refer back to our I Can statement. It said, "I can make a scale model of the playground." I ask students for a thumbs up , sideways or down to measure if they felt they helped to make a model of the playground. 

I ask students to fill in a journal entry: A model is________ . A scientist uses a model _______. I collect these to assess understanding. A student who understands that a model is bigger or smaller than the actual item and that a scientist uses a model to better understand things is what I am looking for. Student Journal Entry

I end with any student questions or comments about models. I want to give students time to reflect upon what they have done and their new understanding of what a model is.