21st Century Lessons Trapezoids Lesson Mrs. Thompson Level 1

How would you find the AREA of this 4-sided shape? PARALLELOGRAM Launch Quadrilateral … 4-sided shape How would you find the AREA of this 4-sided shape? Area = base x height What kind of quadrilateral is shown here? b = 12 h = 8 (1 min) 11 – 12 In-Class Notes Click to show the parallelogram More specifically, what kind of quadrilateral is this? (Click for the Answer -> Parallelogram) How would you find the area of this 4-sided shape? A = base x height Remind students that you can do this because the parallelogram can be decomposed and recomposed into a rectangle Agenda

Can I use Area = base x height??? TRAPEZOID Launch Quadrilateral … 4-sided shape 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??? (1 min) 12 – 13 In-Class Notes Today we’re going to find the area of another quadrilateral called a trapezoid ***QUICK EXPLANATION http://www.mathsisfun.com/definitions/trapezoid.html How would you find the area of this 4-sided shape? Can you use A = base x height?? That is what you will be exploring with your partner! Agenda

A = (b1 + b2) x h 2 Mini-Lesson The formula for the Area of a Trapezoid is… A = (b1 + b2) x h 2 b2 height or h Whole Mini-Lesson (5 min) 30 – 35 In-Class Notes Show the (intuitive, not formal) formula for finding the area of a trapezoid: A= (b1 + b2) x h 2 Let’s break this formula down so we can understand it Let’s start with the easier question: What is the h? (CLICK for the height to appear) So what is b1? What is b2? (CLICK for the bases to appear) Does it matter which measurement is b1 or b2? (No) Why are both bases included in the formula? (Both are important and affect the area of the shape!) Why can’t you use just one or the other? (One will give you an area too small, one too large) What happens to those numbers in the formula? (They get added together, then divided by 2) What are we really doing here? What is it called when we add numbers and then divide by the number of numbers? (Finding the mean!) b1 Agenda

Let’s Test it out using the Trapezoids from the Explore… 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 Whole Mini-Lesson (5 min) 30 – 35 In-Class Notes Show line by line how to substitute (“plug in”) each value Did it give us the same answer from when you counted squares and decomposed/recomposed shapes? YES! Reiterate that both bases are included, they are both important But look, what are we really doing with these bases? We’re adding them together, then dividing by two… what are you really doing?? Finding the MEAN!! h = 2 b1 = 8 Agenda

It works! A = (b1 + b2) x h 2 A = (10 + 6) x 3 2 A = (16) x 3 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 Whole Mini-Lesson (5 min) 30 – 35 In-Class Notes Show line by line how to substitute (“plug in”) each value Reiterate that both bases are included, they are both important But look, what are we really doing with these bases? We’re adding them together, then cutting the answer in half! ***Again show the formula 2nd to last line with the ½ and 2 flipped in order When you take 2 numbers, add them, then cut the answer in half or divide by 2 – what are you really doing?? Finding the MEAN!! What is the mean of 6 and 10? h = 3 It works! b1 = 10 Agenda

then multiply by the height to get the Area of a Trapezoid! So, this part of the formula means….   we take the AVERAGE of the base lengths,   Whole Mini-Lesson (5 min) 30 – 35 In-Class Notes Wait a second… Click to trigger the animation, which shows the trapezoid being rotated so it more closely resembles the two piles of cookies (6 and 10 each) Make sure students see the connection between the two piles of cookies and the two bases What did we do to “even out” or “average out” the number of cookies each person had? When the piles were evened out, how many cookies did the brother and the sister have each? (8) When the trapezoid is decomposed and recomposed into a rectangle, what are the new dimensions? 2 by 8! Pass out second CW then multiply by the height to get the Area of a Trapezoid! Agenda

Practice #1 A = (b1 + b2) x h 2 A = (9 + 5) x 4 2 A = (14) x 4 2 A = 7 x 4 = 28 sq. units (1 min) 35 – 36 In-Class Notes Demonstrate the first problem, showing how to plug in for h, b1 and b2 Explain again why both bases are included If you just use one, your area will be too big or too small You need to “even” them out, which is why the formula has you find the mean of the two bases and then multiply that by the height Preparation Notes The strategy of “interleaving” is included here in the lesson because research shows that students learn new material best when they are able to see an example (either on paper or led by a teacher), and then try a similar problem on their own, see another example, then try another one on their own, etc. b1 = 9 Agenda

Practice #2 A = (b1 + b2) x h 2 A = (9 + 3) x 10 2 A = (12) x 10 2 Now you try one… A = (b1 + b2) x h 2 b2 = 3 A = (9 + 3) x 10 2 h = 10 A = (12) x 10 2 A = 6 x 10 = 60 sq. units (2 min) 36 – 38 In-Class Notes INTERLEAVE the first 4 problems Give students a minute to write down the formula, substitute the dimensions, solve Explain again why both bases are included If you just use one, your area will be too big or too small You need to “even” them out, which is why the formula has you find the mean of the two bases and then multiply that by the height Preparation Notes The strategy of “interleaving” is included here in the lesson because research shows that students learn new material best when they are able to see an example (either on paper or led by a teacher), and then try a similar problem on their own, see another example, then try another one on their own, etc. b1 = 9 Agenda

Practice #3 A = (b1 + b2) x h 2 A = (2 + 4) x 7 2 A = (6) x 7 2 Let’s try another one together, but make it a little more interesting! 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 b1 = 2 ft h = 7 ft A = (b1 + b2) x h 2 A = (2 + 4) x 7 2 (1 min) 38 – 39 In-Class Notes INTERLEAVE the first 4 problems Point out with this real-world trapezoid that it is “upside-down” Briefly remind students that it doesn’t really matter what is b1 or b2 (because they get added) so the formula can still be used! Demonstrate how to plug in for h, b1 and b2 Explain again why both bases are included If you just use one, your area will be too big or too small You need to “even” them out, which is why the formula has you find the mean of the two bases and then multiply that by the height Preparation Notes The strategy of “interleaving” is included here in the lesson because research shows that students learn new material best when they are able to see an example (either on paper or led by a teacher), and then try a similar problem on their own, see another example, then try another one on their own, etc. A = (6) x 7 2 A = 3 x 7 = 21 ft2 Agenda

Practice #4 A = (b1 + b2) x h 2 A =(18 + 12) x 40 2 A = (30) x 40 2 Now you try another one… Brian is getting a custom sticker to completely cover the back of his guitar. How much space will it take up? A = (b1 + b2) x h 2 b2 = 12 in A =(18 + 12) x 40 2 A = (30) x 40 2 h = 40 in (2 min) 39 – 41 In-Class Notes INTERLEAVE the first 4 problems Give students a minute to write down the formula, substitute the dimensions, solve Explain again why both bases are included If you just use one, your area will be too big or too small You need to “even” them out, which is why the formula has you find the mean of the two bases and then multiply that by the height Have students work on the rest independently Preparation Notes The strategy of “interleaving” is included here in the lesson because research shows that students learn new material best when they are able to see an example (either on paper or led by a teacher), and then try a similar problem on their own, see another example, then try another one on their own, etc. A = 15 x 40 = 600 in2 Agenda b1 = 18 in

Assessment Agenda (5 min) 50 – 55 In-Class Notes Give students a few minutes to work in their math notebooks on this final question. Then use hand signals to assess where students are at and gauge what review needs to happen tomorrow (or who it needs to target) Agenda