Exploring Areas of Parallelograms: Activity Synthesis

2. Activator (pg. 41) You have  2 minutes of quiet think time to determine how many dots are in the image WITHOUT counting them. If you find an answer, try to find it in a different way.

3. Activity synthesis • “Who can restate the way ___ saw the dots in different words?” • “Did anyone see the dots the same way but would explain it differently?” • “Does anyone want to add an observation to the way ____ saw the dots?” • “Do you agree or disagree? Why?”

4. Possible solutions…

5. Sometimes dreams. are wiserthan waking. Black Elk – Oglala Sioux Medicine Man

6. Objective Lesson 6 • Today I will be able to explain (orally and in writing) how to apply the formula for area of a parallelogram to find the area by identifying the length of the base and height. • So that I can (verbally) reason which measurements to use in order to be able to calculate the area of a parallelogram when more than one base or height measurement is given. • I will know I got it when can find the area of a parallelogram and explain what measurement I did not use (and why) to answer my ticket to go with at least 80% accuracy. • 6.G.A.1 (6.EE.A.2.c)

7. Vocabulary • Parallelogram • Area • Base • Height • Corresponding • Horizontal • vertical

8. 6.2: area of parallelograms (pg. 41) • You will have 5 minutes of quiet think time to find the area of the parallelograms in question 1. You can use your geometry toolkits Then, you will each be assigned a parallelogram (A, B, C or D). Please explain to the group, one at a time, how you found the area of the assigned parallelogram. After each student shares, check for agreement or disagreement from the rest of the group. Discuss any disagreement and come to a consensus on the correct answer before moving to the next parallelogram.

9. Let’s work with a partner… You will have 5-7 minutes to complete remaining questions on page 42. When the time is up we will discuss.

10. Responses

11. How do you feel? topic.

12. Are you ready for more?

13. Sample Responses 3.2 square inches. The area of one shaded parallelogram is 12 square inches, because one base is 5 inches and its corresponding height is 2.4 inches (5⋅(2.4)=12). This means the corresponding height for the side that is 3 inches is 4 inches (3⋅4=12). The height of the small parallelogram is the difference between 4 inches and 2.4 inches, which is 1.6 inches. The horizontal side of the the unshaded parallelogram, which can be a base, is 2 inches (5−3=2). The area of the unshaded parallelogram is therefore 2⋅(1.6) or 3.2 square inches. • The base of the overall parallelogram is 8 inches (5+3=8). Its height is 6.4 inches (4+2.4=6.4). Its area is therefore 8⋅(6.4) or 51.2 square inches. The area of the four shaded parallelograms is 4⋅12 or 48 square inches. The area of the unshaded region is therefore 51.2−48or 3.2 square inches. 

14. Activity Synthesis • “When multiple measurements are shown, how did you know which of the measurements would help you find area?” • “Which pieces of information in parallelograms B and C were not needed? Why not?” • We need base and height information to help us calculate the area of a parallelogram, so we generally look for the length of one side and the length of a perpendicular segment that connects the base to the opposite side. Other measurements may not be as useful.

15. A parallelogram generally has two pairs of base and height. Both pairs produce the same area (it's the same parallelogram), so the product of pair of numbers should equal the product of the other pair. Who can share how they went about finding the missing height in the second question? Who can share their pair of parallelograms with equal area and an explanation of how they know the areas are equal. • Two parallelograms with different pairs of base and height can have the same area, as long as their products are equal. So a 3-by-6 rectangle and a parallelogram with base 1 and height 18 will have the same area because 3⋅6=1⋅18.

16. How do you feel? topic.

17. Lesson Summary • We used the formula for area to practice finding the area of various parallelograms. • “When a parallelogram is on a grid, how do we know which side to choose for a base? Can we use any side?” • It is helpful to use a horizontal or a vertical side as a base; it would be easier to tell the length of that side and of its corresponding height. • “Off a grid, how do we know which measurements can help us find the area of a parallelogram?” • We need the length of one side of the parallelogram and of a perpendicular segment that connects that side to the opposite side.  • “Do parallelograms that have the same area always look the same?” • No. • “Can you show an example?” • “Do parallelograms that have the same base and height always look the same?” • No. • “Can you show an example?” • “How can we draw two different parallelograms with the same area?” • We can find any two pairs of base-height lengths that have the same product.  We can also use the same pair of numbers by draw the parallelograms differently.

18. Ticket to go (Cool Down)

19. Homework • Pages 44-46

20. Accommodations • Read or reread presentation or activity directions, as needed or after prompting • Use examples to model and act as a guide for emerging learners