WEBVTT

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Narrator:  In this video, the teacher uses explicit, systematic
instruction during a mathematics lesson. During the first step of

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explicit, systematic instruction, the teacher prepares the students
for the lesson.

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Teacher: Today during math class, we are going to use the tangent
function to help us find the height of objects. And if you recall,

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this week we’ve been learning all about right triangles. Mateo, do you
remember what angle makes right triangles so special.

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Mateo: Ninety degrees.

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Teacher: That’s right. They always contain a 90-degree angle. And when
we have a right triangle, we know we can figure out the other angles

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or the lengths of the sides of the triangle using special functions.
And we learned the phrase Soh Cah Toa to help us remember what

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these ratios are. Raise your hand if you remember what the “S” stands
for. Yes, Jermaine.

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Jermaine: Sign.

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Teacher: That’s right. The “S” stands for “sign.” The “C” stands for
the “cosign.” And, Susan, do you remember what the “T” stands for?

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Susan: Tangent.

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Teacher: That’s right. The “tangent.” This is what we’re going to be
focused on today.

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Teacher: So using this knowledge and thinking about Soh Cah Toa to
help us remember what those ratios are, we are going to solve a

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problem and figure out the height of a flagpole. Now, you wouldn’t
normally be able to climb a flagpole or have a tape measure in your

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pocket at all times to help you find the height of the flagpole, so
you can use one of these functions to help you figure out what the

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height is without having to go climb it.

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Narrator: During the next step, the teacher models several problems,
asking questions throughout to check for understanding and to ensure

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student engagement.

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So, to start, I’m going to draw a picture to help me figure out what the
problem’s telling me. I have a flagpole, and I know 11 feet from the

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base of the flagpole is Juan.

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I’m going to look back at my problem, and I notice that it says “the
angle of elevation from Juan’s feet to the top of the flagpole—so here

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to here—is 70 degrees. So I’m going to label that on my diagram. And
looking back at the problem, I’ve created a diagram showing me

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everything the problem is telling me. But I notice something else. I
notice that this flagpole and the ground make a 90-degree angle, which

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means this is a right triangle, and we can use one of our ratios to
help us figure out the height of the flagpole. And for this I know I

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want to figure out the side opposite to the 70-degree angle. So
looking back up there, I notice that tangent is the ratio between the

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side opposite and the side adjacent to my target angle, so that’s what
I’m going to use. Sophie, remind me what the ratio for tangent is.

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Sophie: Opposite over adjacent.

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Teacher: That’s right! The tangent is the ratio of the opposite side
over the adjacent side. Great thinking, Sophie. Given this equation,

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I’m going to then fill in all the information I have from the problem.
So what is my angle in this problem? Yes.

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Student: Seventy degrees.

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Teacher: Great! It is 70 degrees. So the tangent of 70 degrees equals
the opposite. I don’t know what the opposite side is, so I’m just

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going to leave in the word “opposite” over the adjacent side. I notice
my side adjacent to the 70-degree angle is 11 feet, so I can write

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“11” right there. Now that my equation is written, all I have to do is
solve…equals 30.25.  So I know the length of the side opposite to my

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target angle is, which is also the height of the flagpole, is 30.25
feet.

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Narrator: After the teacher leads the students through several more
problems, she implements guided practice.

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Teacher: Next, I’m going to have you work with a partner on the next
two problems. Again, you’re going to be solving for the tangent

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function, and I’m going to be walking around, answering questions or
providing help as needed.

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Narrator: After the teacher has monitored guided practice and provided
corrective feedback to each pair of students, she asks the students to

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complete problems independently. To ensure maintenance, the teacher
plans opportunities for ongoing practice and provides additional

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instruction for students who have not mastered the concept or
procedure.