Area of Parallelograms
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to carefully analyze and compare four figures with shaded regions. The figures are similar to the ones for which students found the area earlier in the unit. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear how students talk about attributes of figures and two-dimensional regions.
While students may or may not think to compare the four areas, they are likely to notice regions that can be decomposed, rearranged, and subtracted. They may also notice that figures that look different can have the same area. These observations will support students in reasoning about the areas of parallelograms and other polygons later.
Launch
Arrange students in groups of 2–4. Display the four figures for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three figures that go together and can explain why. Next, tell each student to share their response with their group and then together find as many sets of three as they can.
Student Task
Which three go together? Why do they go together?
Sample Response
Sample responses:
A ,B, and C go together because:
- They all show two squares of different sizes.
- There is a small square inside a larger square. The smaller square is not shaded.
- There is at least one square that is tilted (or that has no horizontal or vertical sides).
A, B, and D go together because:
- They have shapes with vertical and horizontal sides.
- We can tell the side lengths of the outer shape.
A, C, and D go together because:
- The shapes are on a grid.
- The sides are not labeled with their length.
B, C, and D go together because:
- The area of the shaded region is 16 square units.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure that the reasons given are correct.
During the discussion, ask students to clarify their reasoning as needed. For example, a student may claim that each of the Figures A, B, and C has a smaller square removed from a larger square. Ask how they know that the smaller unshaded rectangles in Figures A and C are squares.
If no students mentioned the areas of the shaded regions, ask them if and how the areas could be compared. As needed, reiterate strategies for reasoning about area and the idea that different shapes can have the same area.
Standards
- 3.OA.A·Represent and solve problems involving multiplication and division.
- 3.OA.A·Represent and solve problems involving multiplication and division.
25 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Area of Parallelograms
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to carefully analyze and compare four figures with shaded regions. The figures are similar to the ones for which students found the area earlier in the unit. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear how students talk about attributes of figures and two-dimensional regions.
While students may or may not think to compare the four areas, they are likely to notice regions that can be decomposed, rearranged, and subtracted. They may also notice that figures that look different can have the same area. These observations will support students in reasoning about the areas of parallelograms and other polygons later.
Launch
Arrange students in groups of 2–4. Display the four figures for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three figures that go together and can explain why. Next, tell each student to share their response with their group and then together find as many sets of three as they can.
Student Task
Which three go together? Why do they go together?
Sample Response
Sample responses:
A ,B, and C go together because:
- They all show two squares of different sizes.
- There is a small square inside a larger square. The smaller square is not shaded.
- There is at least one square that is tilted (or that has no horizontal or vertical sides).
A, B, and D go together because:
- They have shapes with vertical and horizontal sides.
- We can tell the side lengths of the outer shape.
A, C, and D go together because:
- The shapes are on a grid.
- The sides are not labeled with their length.
B, C, and D go together because:
- The area of the shaded region is 16 square units.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure that the reasons given are correct.
During the discussion, ask students to clarify their reasoning as needed. For example, a student may claim that each of the Figures A, B, and C has a smaller square removed from a larger square. Ask how they know that the smaller unshaded rectangles in Figures A and C are squares.
If no students mentioned the areas of the shaded regions, ask them if and how the areas could be compared. As needed, reiterate strategies for reasoning about area and the idea that different shapes can have the same area.
Standards
- 3.OA.A·Represent and solve problems involving multiplication and division.
- 3.OA.A·Represent and solve problems involving multiplication and division.