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21 st Century Lessons

21 st Century Lessons. Trapezoids Lesson. Mrs. Thompson Level 1. OBJECTIVE 1: SWBAT prove whether the area formula for a parallelogram (A = b x h) can also be used to find the area of a trapezoid OBJECTIVE 2: Students will practice finding the area of trapezoids using the correct formula.

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21 st Century Lessons

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  1. 21st Century Lessons Trapezoids Lesson Mrs. Thompson Level 1

  2. OBJECTIVE 1:SWBAT prove whether the area formula for a parallelogram (A = b x h) can also be used to find the area of a trapezoid OBJECTIVE 2:Students will practice finding the area of trapezoids using the correct formula. Warm Up 1) Greg and his sister, Laura, have a snack everyday after school. Yesterday, Greg put these cookies on the table and Laura began crying “that’s not fair! Mamaaaaa!” To even out the piles, how many cookies should each kid have? How would you do this? 2) José got back 3 quizzes today at school with the following grades: 80, 65, 95. What is the average grade for all 3 quizzes? Laura Greg (6 cookies) (10 cookies) Agenda video Warm up 2 Warm up 1

  3. Warm Up #1 . To even out the piles, how many cookies should each kid have? How would you do this? Laura Greg 8 cookies 8 cookies Finally, Laura stopped crying! Agenda Scaffolding Questions

  4. Warm Up #2 José got back 3 quizzes today at school with the following grades: 80, 65, 95. What is the average grade for all 3 quizzes? Average = Mean 80% = B- 80 65 +95 240 65% = D 95% = A ÷ 3 = 80 Agenda Scaffolding Questions

  5. Agenda: OBJECTIVE:SWBAT prove whether the area formula for a parallelogram (A = b x h) can also be used to find the area of a trapezoid • Warm Up – Cookies! 2) Launch– Can we just do base x height ??? 3) Explore – Partners 4) Summary – Yes or No? 5) Mini-Lesson 6) Practice– with Interleaving 7) Assessment Agenda

  6. Quadrilateral … 4-sided shape Launch RECTANGLE What kind of quadrilateral is shown here? h = 4 b = 10 How would you find the AREA of this 4-sided shape? Area = base x height Agenda

  7. Quadrilateral … 4-sided shape Launch SQUARE What kind of quadrilateral is shown here? h = 5 b = 5 How would you find the AREA of this 4-sided shape? Area = base x height Agenda

  8. Quadrilateral … 4-sided shape Launch PARALLELOGRAM How would you find the AREA of this 4-sided shape? Area = base x height What kind of quadrilateral is shown here? h = 8 b = 12 Agenda

  9. Quadrilateral … 4-sided shape Launch TRAPEZOID What kind of quadrilateral is shown here? How would you find the AREA of this 4-sided shape? Can I use Area = base x height??? Agenda

  10. Launch Remember the objective: OBJECTIVE:SWBAT prove whether the area formula for a parallelogram (A = b x h) can also be used to find the area of a trapezoid Agenda

  11. Launch Before you test the formula, what are strategies for finding area that always work? • Count the unit squares • Decompose (cut into pieces) • & compose (put back together) • into a different shape With your partner, you will use these strategies FIRST, and THEN test the formula A = b x h ! Agenda

  12. Explore KEY QUESTION: Can the formula A = base x height be used to find the area of a trapezoid??? You will provewhether the formula works by… • Counting the unit squares of your trapezoid • Decomposing (cutting into pieces) & composing (putting back together) your trapezoid into a different shape • Using A = base x height …and comparing your results! Agenda

  13. Summary When you counted the unit squares… 12 11 1 2 3 4 5 6 7 8 9 10 Area = 12 square units Agenda

  14. Did anyone decompose and (re)compose like this? height = 2 base = 6 Area = 12 square units Agenda

  15. Did anyone decompose and (re)compose like this? height = 2 base = 6 Area = 12 square units Agenda

  16. Did anyone decompose and (re)compose like this? height = 2 Area = ½ b h Area = ½ x 8 x 2 Area = 8 base = 4 Area = 4 + 8 Area = ½ b h Area = 12 square units Area = ½ x 4 x 2 Area = 4 height = 2 base = 8 Agenda

  17. When you used the formula Area = base x height did you get the same answer of 12? NO!! A = base x height A = 8 x 2 A = 16 TOO BIG! A = base x height A = 4 x 2 A = 8 TOO SMALL! Agenda

  18. Summary When you counted the unit squares… 1 2 3 4 5 6 ? Area = 24 square units Agenda

  19. Did anyone decompose and (re)compose like this? height = 3 base = 8 Area = 24 square units Agenda

  20. Did anyone decompose and (re)compose like this? height= 3 height= 3 base= 6 base= 4 Area = ½ b x h ½ x 4 x 3 ½ x 12 6 Area = b x h 6 x 3 18 Area = 24 square units Agenda

  21. When you used the formula Area = base x height did you get the same answer of 24? NO!! A = base x height A = 10 x 3 A = 30 TOO BIG! A = base x height A = 6 x 3 A = 18 TOO SMALL! Agenda

  22. Mini-Lesson The formula for the Area of a Trapezoid is… A = (b1+b2) x h 2 b2 height or h b1 Agenda

  23. A = (b1+b2) x h 2 Let’s Test it out using the Trapezoids from the Explore… A = (8+4) x 2 2 A = (12) x 2 2 It works! A = 6 x 2 = 12 sq. units b2 = 4 Trapezoid A h = 2 b1 = 8 Agenda

  24. A = (b1+b2) x h 2 Let’s try the formula again… A = (10+6) x 3 2 A = (16) x 3 2 Trapezoid B A = 8 x 3 A = 24 sq. units b2 = 6 h = 3 It works! b1 = 10 Agenda

  25. HOLD UP! I feel like I’ve seen this trapezoid somewhere before… it reminds me of something… wait for it… b2 = 6 h = 3 h = 3 b1 = 10 Agenda

  26. YES! Greg and Laura’s cookies! See what I mean? The piles of cookies had to even out just like the trapezoid’s bases!!! b = 8 h = 3 Agenda

  27. So, this part of the formula means…. we take the AVERAGE of the base lengths, then multiply by the height to get the Area of a Trapezoid! Agenda

  28. Now that we know the formula for the area of a trapezoid, let’s try to use it together!

  29. Practice #1 A = (b1+b2) x h 2 A = (9+5) x 4 2 b2 = 5 A = (14) x 4 2 h = 4 A = 7 x 4 = 28 sq. units b1 = 9 Agenda

  30. Practice #2 Now you try one… A = (b1+b2) x h 2 b2 = 3 A = (9+3) x 10 2 A = (12) x 10 2 h = 10 A = 6 x 10 = 60 sq. units b1 = 9 Agenda

  31. Practice #3 Let’s try another one together, but make it a little more interesting! A = (b1+b2) x h 2 Edward wants make a curtain for his living room window so he can sit in the dark and think of ways to get rid of Jacob! Calculate the area so that she knows how much fabric to buy. b2 = 4 ft A = (2+4) x 7 2 A = (6) x 7 2 h = 7 ft A = 3 x 7 = 21 ft2 b1 = 2 ft Agenda

  32. Practice #4 Now you try another one… A = (b1+b2) x h 2 Brian is getting a custom sticker to completely cover the back of his guitar. How much space will it take up? A =(18+12) x 40 2 A = (30) x 40 2 b2 = 12 in A = 15 x 40 = 600 in2 h = 40 in Agenda b1 = 18 in

  33. Independent Practice Continue practicing on your own… Agenda

  34. Independent Practice Answers 5. a) 6 ft2 b) 11 cm2 c) 27.6 sq. units d) 20 yd2 6. Juan’s Area: 90 m2 Cheyanne’s Area: 50 m2 Agenda

  35. Assessment Agenda

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