Find the Area of a Figure with Unknown Side Lengths
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that we can find the area of a figure even though not all side lengths are given, which will be useful when students find unknown side lengths and areas in a later activity. While students may notice and wonder many things about this figure, the unknown side lengths are the important discussion points.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Solution Steps (4)
- 1Notice the figure is a 6-sided shape that can be decomposed into 2 rectangles→L-shaped figure with straight sides meeting at right angles
- 2Notice some side lengths are given and some are unknown→Known: bottom 4cm, vertical 2cm, top 10cm, right 9cm. Unknown: two sides marked ?
- 3Reason about finding the unknown horizontal side→Top is 10cm total, bottom is 4cm, so missing horizontal = 10-4=6cm
- 4Reason about finding the unknown vertical side→Right is 9cm total, one vertical is 2cm, so missing vertical = 9-2=7cm
Sample Response
Students may notice:
- We can break this figure into 2 rectangles.
- Some of the side lengths are unknown.
- Some of the side lengths are given in centimeters.
Students may wonder:
- Can we still find the area of this figure?
- Is there a way to find the unknown side lengths?
- Is there only 1 possible number for the unknown side lengths?
Activity Synthesis (Teacher Notes)
- “Do you think we still could find the area of this figure even though some of the side lengths are unknown? Why or why not?” (Yes, we could use the side lengths we know to find the unknown side lengths.)
- “How would you find the unknown side lengths?” (I know the top side is 10 cm, and that is the horizontal length of the entire figure. If one part of that length is 4 cm, then the unknown length is 6 cm. I know the vertical length of the figure is 9 cm. If one part of it is 2 cm, then the unknown length is 7 cm.)
Standards
- 3.MD.7.d·Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
- 3.MD.C.7.d·Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
10 min
25 min
Knowledge Components
All skills for this lesson
Find the Area of a Figure with Unknown Side Lengths
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that we can find the area of a figure even though not all side lengths are given, which will be useful when students find unknown side lengths and areas in a later activity. While students may notice and wonder many things about this figure, the unknown side lengths are the important discussion points.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Solution Steps (4)
- 1Notice the figure is a 6-sided shape that can be decomposed into 2 rectangles→L-shaped figure with straight sides meeting at right angles
- 2Notice some side lengths are given and some are unknown→Known: bottom 4cm, vertical 2cm, top 10cm, right 9cm. Unknown: two sides marked ?
- 3Reason about finding the unknown horizontal side→Top is 10cm total, bottom is 4cm, so missing horizontal = 10-4=6cm
- 4Reason about finding the unknown vertical side→Right is 9cm total, one vertical is 2cm, so missing vertical = 9-2=7cm
Sample Response
Students may notice:
- We can break this figure into 2 rectangles.
- Some of the side lengths are unknown.
- Some of the side lengths are given in centimeters.
Students may wonder:
- Can we still find the area of this figure?
- Is there a way to find the unknown side lengths?
- Is there only 1 possible number for the unknown side lengths?
Activity Synthesis (Teacher Notes)
- “Do you think we still could find the area of this figure even though some of the side lengths are unknown? Why or why not?” (Yes, we could use the side lengths we know to find the unknown side lengths.)
- “How would you find the unknown side lengths?” (I know the top side is 10 cm, and that is the horizontal length of the entire figure. If one part of that length is 4 cm, then the unknown length is 6 cm. I know the vertical length of the figure is 9 cm. If one part of it is 2 cm, then the unknown length is 7 cm.)
Standards
- 3.MD.7.d·Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
- 3.MD.C.7.d·Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.