Deforestation at Scale
15 min
Narrative
The goal of this activity is to refresh students’ understanding of scale drawings. Depending on how recently the students worked with scale drawings, it may be beneficial to discuss different approaches to this problem before they begin.
Monitor for students who use these different strategies:
- Decompose the region into shapes to find the area
- Enclose the region with a rectangle and then subtract the missing parts
- Find each actual length and then use those to determine the area of the actual room
- Find the area of the scale drawing and then multiply by the (scale factor)2 to find the area of the actual room
Launch
Student Task
Here is a scale drawing of a room. The drawing has the following scale:
1 unit in the drawing represents 4 feet in the actual room.
Calculate the area of the actual room. Be prepared to explain your reasoning.
Sample Response
Activity Synthesis (Teacher Notes)
The goal of this discussion is to highlight different approaches for determining the area of the actual room, including different ways to decompose the region and how to use the scale.
After all strategies have been presented, display 2–3 approaches from previously selected students for all to see. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:
-
“What do the approaches have in common? How are they different?”
-
“How does the scale factor show up in each method?”
-
“Why do the different approaches lead to the same outcome?”
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.6·Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
- 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.
- 7.G.B.6·Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
10 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Deforestation at Scale
15 min
Narrative
The goal of this activity is to refresh students’ understanding of scale drawings. Depending on how recently the students worked with scale drawings, it may be beneficial to discuss different approaches to this problem before they begin.
Monitor for students who use these different strategies:
- Decompose the region into shapes to find the area
- Enclose the region with a rectangle and then subtract the missing parts
- Find each actual length and then use those to determine the area of the actual room
- Find the area of the scale drawing and then multiply by the (scale factor)2 to find the area of the actual room
Launch
Student Task
Here is a scale drawing of a room. The drawing has the following scale:
1 unit in the drawing represents 4 feet in the actual room.
Calculate the area of the actual room. Be prepared to explain your reasoning.
Sample Response
Activity Synthesis (Teacher Notes)
The goal of this discussion is to highlight different approaches for determining the area of the actual room, including different ways to decompose the region and how to use the scale.
After all strategies have been presented, display 2–3 approaches from previously selected students for all to see. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:
-
“What do the approaches have in common? How are they different?”
-
“How does the scale factor show up in each method?”
-
“Why do the different approaches lead to the same outcome?”
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.6·Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
- 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.
- 7.G.B.6·Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.