Scale Drawings
5 min
Teacher Prep
Setup
Required Preparation
Prepare to display the examples and non-examples of scale drawings for all to see. Consider adding to the collection a local map showing the actual route of a train or bus line (example of scale drawing) and a diagrammatic transit map (non-example).
In the “Doing Math” teacher section of the Math Community Chart, add 2–5 commitments you have for what your teaching practice “looks like” and “sounds like” this year.
Narrative
This activity encourages students to notice characteristics of scale drawings by observing examples and counterexamples and to articulate what a scale drawing is. Though students are not expected to come up with precise definitions, they are likely able to intuit that scale drawings are accurate two-dimensional depictions of what they represent, in the sense that all shapes, arrangements of parts, and relative sizes match those of the actual objects.
Expect student observations about scale drawings to be informal and not mathematical. For example, they might say that a scale drawing looks just like the object it is portraying, with the parts shown having the right size and being in the right places in the drawing. Or that in a scale drawing, a smaller part in the actual object does not end up being larger in the drawing.
Like any mathematical model of a real situation, a scale drawing captures some important aspects of the real object and ignores other aspects. It may not be apparent to students that scale drawings prioritize features of one plane of the object (and sometimes features of other planes parallel to it) and ignore other surfaces and dimensions. Monitor for students who show insights around this idea.
Launch
Arrange students in groups of 2. Before students look at the materials, poll the class to find out who has seen scale drawings. Ask a few students who are familiar with them to give a couple of examples of scale drawings they have seen. Then, give students 2 minutes to observe the examples and counterexamples of scale drawings and discuss in groups what they think a scale drawing is.
Student Task
Here are some drawings of a school bus, a quarter, and the subway lines around Boston, Massachusetts.
The first three drawings are scale drawings of these objects.
The next three drawings are not scale drawings of these objects.
Discuss with your partner what a scale drawing is.
Sample Response
Sample responses:
- A scale drawing is a drawing that shows the object accurately and all parts in the drawing match the parts in the actual object.
- No parts in a scale drawing are distorted.
- A scale drawing is like a scaled copy of a real object, but it is a drawing that shows one flat surface of the object.
Activity Synthesis (Teacher Notes)
Ask a few students to share what they noticed about characteristics of scale drawings and to compare and contrast scaled copies and scale drawings. Discuss questions such as the following. Record common themes and helpful descriptions.
- “What do the examples have or show that the counterexamples do not?”
- “How are scale drawings like scaled copies you saw in earlier lessons? How are they different from scaled copies?”
- “What aspects of the bus, coin, and the city of Boston do the scale drawings show? What aspects of the actual objects do scale drawings not show?”
Notice misconceptions, but it is not necessary to address them right away, as students’ understanding will be shaped in this and upcoming lessons. Tell students that they will continue to analyze scale drawings and revise their definitions in upcoming activities.
Math Community
After the Warm-up, display the Math Community Chart with the “Doing Math” actions added to the teacher section for all to see. Give students 1 minute to review. Then share 2–3 key points from the teacher section and your reasoning for adding them. For example,
- If “questioning vs. telling,” a shared reason could focus on your belief that students are capable mathematical thinkers and your desire to understand how students are making meaning of the mathematics.
- If “listening,” a shared reason could be that sometimes you want to sit quietly with a group just to listen and hear student thinking and not because you think the group needs help or is off-track.
After sharing, tell students that they will have the opportunity to suggest additions to the teacher section during the Cool-down.
Anticipated Misconceptions
If students struggle to characterize scale drawings, offer prompts to encourage them to look closer. For example, ask: “How do the shapes and sizes of the objects in the drawings compare to those of the actual objects?” Students may say that sizes of the objects in the scale drawings are smaller than those of the actual objects. Ask them if any parts of the scale drawings are distorted, compared to the actual object—ask them to focus on the two images of the quarter, one of which is circular in shape while the other is not.
Standards
- 7.G.1·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.
- 7.G.A.1·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.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Scale Drawings
5 min
Teacher Prep
Setup
Required Preparation
Prepare to display the examples and non-examples of scale drawings for all to see. Consider adding to the collection a local map showing the actual route of a train or bus line (example of scale drawing) and a diagrammatic transit map (non-example).
In the “Doing Math” teacher section of the Math Community Chart, add 2–5 commitments you have for what your teaching practice “looks like” and “sounds like” this year.
Narrative
This activity encourages students to notice characteristics of scale drawings by observing examples and counterexamples and to articulate what a scale drawing is. Though students are not expected to come up with precise definitions, they are likely able to intuit that scale drawings are accurate two-dimensional depictions of what they represent, in the sense that all shapes, arrangements of parts, and relative sizes match those of the actual objects.
Expect student observations about scale drawings to be informal and not mathematical. For example, they might say that a scale drawing looks just like the object it is portraying, with the parts shown having the right size and being in the right places in the drawing. Or that in a scale drawing, a smaller part in the actual object does not end up being larger in the drawing.
Like any mathematical model of a real situation, a scale drawing captures some important aspects of the real object and ignores other aspects. It may not be apparent to students that scale drawings prioritize features of one plane of the object (and sometimes features of other planes parallel to it) and ignore other surfaces and dimensions. Monitor for students who show insights around this idea.
Launch
Arrange students in groups of 2. Before students look at the materials, poll the class to find out who has seen scale drawings. Ask a few students who are familiar with them to give a couple of examples of scale drawings they have seen. Then, give students 2 minutes to observe the examples and counterexamples of scale drawings and discuss in groups what they think a scale drawing is.
Student Task
Here are some drawings of a school bus, a quarter, and the subway lines around Boston, Massachusetts.
The first three drawings are scale drawings of these objects.
The next three drawings are not scale drawings of these objects.
Discuss with your partner what a scale drawing is.
Sample Response
Sample responses:
- A scale drawing is a drawing that shows the object accurately and all parts in the drawing match the parts in the actual object.
- No parts in a scale drawing are distorted.
- A scale drawing is like a scaled copy of a real object, but it is a drawing that shows one flat surface of the object.
Activity Synthesis (Teacher Notes)
Ask a few students to share what they noticed about characteristics of scale drawings and to compare and contrast scaled copies and scale drawings. Discuss questions such as the following. Record common themes and helpful descriptions.
- “What do the examples have or show that the counterexamples do not?”
- “How are scale drawings like scaled copies you saw in earlier lessons? How are they different from scaled copies?”
- “What aspects of the bus, coin, and the city of Boston do the scale drawings show? What aspects of the actual objects do scale drawings not show?”
Notice misconceptions, but it is not necessary to address them right away, as students’ understanding will be shaped in this and upcoming lessons. Tell students that they will continue to analyze scale drawings and revise their definitions in upcoming activities.
Math Community
After the Warm-up, display the Math Community Chart with the “Doing Math” actions added to the teacher section for all to see. Give students 1 minute to review. Then share 2–3 key points from the teacher section and your reasoning for adding them. For example,
- If “questioning vs. telling,” a shared reason could focus on your belief that students are capable mathematical thinkers and your desire to understand how students are making meaning of the mathematics.
- If “listening,” a shared reason could be that sometimes you want to sit quietly with a group just to listen and hear student thinking and not because you think the group needs help or is off-track.
After sharing, tell students that they will have the opportunity to suggest additions to the teacher section during the Cool-down.
Anticipated Misconceptions
If students struggle to characterize scale drawings, offer prompts to encourage them to look closer. For example, ask: “How do the shapes and sizes of the objects in the drawings compare to those of the actual objects?” Students may say that sizes of the objects in the scale drawings are smaller than those of the actual objects. Ask them if any parts of the scale drawings are distorted, compared to the actual object—ask them to focus on the two images of the quarter, one of which is circular in shape while the other is not.
Standards
- 7.G.1·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.
- 7.G.A.1·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.