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

2. How would you find the AREA of this 4-sided shape?
PARALLELOGRAM
Launch
Quadrilateral … 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

3. Can I use Area = base x height???
TRAPEZOID
Launch
Quadrilateral … 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
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

4. 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

5. 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 = x = 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

6. 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 = 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

7. 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

8. Practice #1 A = (b1 + b2) x h 2 A = (9 + 5) x 4 2 A = (14) x 4 2
A = 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

9. 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 = x = 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

10. 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

11. 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 =( ) 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 = x = in2
Agenda
b1 = 18 in

12. 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