Lesson Plan Lesson: Inequalities and Triangles Length: 45 minutes Age or Grade Level Intended: High school Geometry Academic Standard(s): G.4.8 Prove, understand, and apply the inequality theorems:

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Lesson Plan


Lesson:
Inequalities and Triangles

Length: 45 minutes

Age or Grade Level Intended:
High school Geometry


Academic Standard(s):


G.4.8 Prove, understand, and apply the inequality theorems:
triangle inequality, inequality in one triangle, and h
inge theorem.


G.8.7 Construct logical arguments, judge validity, and give
counterexamples to disprove statements.


Performance Objective(s):


The class will be able to
orally answer questions that involve
find
ing

an
angle and side of
a triangle

with
80%

accuracy when given
the definition of inequalities and Inequality Theorems.





The class will be able to provide logical arguments that explain
why certain angles and sides are bigger or smaller than each other two
out of three times.


Assessment:

Ora
lly ask

random
student
s
to find an angle or side of a triangle and
make sure
12 out of the 15 students get the side or angle correct.


Orally ask for logical arguments to support why certain angles and
sides are bigger and smaller than others two out of t
hree times.


Advance Preparation by Teacher:

Prepare examples to write on the board.

Attached on note cards


Procedure:


Introduction/Motivation:

We are going to explore Inequalities and Triangles. This lesson will lead up
being able to solve problems that

involve triangles that can come from real
life situations such as
architecture and geography.



Step
-
by
-
Step Plan:

1.

Present the
Definition of Inequalities: for any real numbers a and b, a
> b if and only if there is a positive number c such that a = b +

c
.

2.

Explain with numbers because with letters some students can get
confused
.


Example: 6 > 4 because 6 = 4+2

3.

Have students turn to
the properties of inequalities on page 247 of text
book.

4.

These inequality properties are ones they have seen in previous
algeb
ra classes.

5.

Stress the transitive property because that is probably the one they
will use when giving reasoning for the inequality between angles and
side.

6.

Question:
Can someone choose three numbers that would exemplify
the transitive property of inequali
ties?
(Bloom: Application)


Example 6 > 4 4 > 2 therefore 6 > 2

7.

Question:
A
re
there
any questions about these properties or the
definition of an inequality
?

8.

Present

the Exterior Angle Inequality Theorem: if a triangle has an
exterior angle, then it is a
lways greater than either of its corresponding
remote interior angles.

9.

Question:
Is there

anyone can remember back in Chapter 4 another
theorem that dealt with exterior angles
?
(Bloom: Knowledge)


10.

Answer is the Exterior Angle Theorem on page 186 that states

the
exterior angle is equal to the sum of the two remote interior angles.

11.

So
if an exterior angle is the sum of two other angles the exterior angle
is bound to be larger than one of the angles on its own.

12.

Example using attached note card labeled #1
.

13.

Hav
e students turn to a neighbor and come up with

as many inequality
statements about the triangles angles. Have a group share a few
statements.
(Gardner: Interpersonal)

Some answers are provided and they could use the transitive
property to give more. Just g
et maybe two or three statements
and
make sure they can provide reason using the Exterior Angle
Inequality Theorem.



14.

Introduce new theorem
Thm: The angle opposite the l
arg
est side will
be the largest angle.

The word largest can be replaced by medium and
s
mallest.

15.

Draw a triangle with sides and angles that is difficult to tell which side
and angle is the longest. (this triangle can be seen on note card #3)
If
we look at this triangle with no numbers
it is going to be hard to tell
what angle is the biggest
or which side is the longest. However,
knowing this theorem and given the lengths of this triangle we can
compare each side and angle.

16.

Question:
What side is the largest, middle, and smallest?
(Bloom:
Knowledge)
label each side L,M,S (largest, middle, sma
llest).

17.

Question:
Now using this new theorem who can tell me the largest,
middle, and smallest angle and explain why?
(Bloom: Application)

Answers on card #4.

18.

We can also use this sam
e theorem backwards and states Thm:
The
side opposite the largest angle w
ill be the largest side.”

Again

we can
say this theorem by replacing largest by middle and smallest.


19.

If we look at a triangle without sides but with angles

(Seen on card
#5)
.

20.

Question:
Now using this new theorem who can tell me the largest,
middle, and s
mallest side and explain why?
(Bloom: Application)

21.


Another example:

Applying the last theorem explained.

(Found on
card #6)



Question:
Determine the inequality relationship between
:

(
Bloom: Application)



DH and GH, DE and DG, EG and FG
, DE and EG






Answers with explanation on card.

22.


Another example: Applying
Exterior Angle Inequality Theorem.

Question:
What angles are less than angle 1?
(Bloom:
Application)

Answer is on card. (card #7)

23.


Assign homework assignment located on card #8
.



Closure:

Tomorrow we will go over your homework and move into section 5.3. You
will need to master applying these theorems in order to understand the next
section so make sure if you have any questions while working on your
homework you ask me.


Adap
tations/Enrichment:


Girl with ADHD
-
Hyperactive:
Make sure she does not sit by other
students that could be distracting and encourage her to not pay attention. Be
sure to continuously ask her questions to keep her attention.

Boy with Autism:
Prepare him w
ith typed notes so that he knows the
routine that is going to take place. Also when given homework to work on
at the end of class allow him to
go with his aide to have one
-
on
-
one
assistance.

Boy with High Ability:
Keep him involved in the examples so he d
oesn’t
start to day dream
.

Give him challenge problems as an extension to the
homework assignment.



Self
-
Reflection:

I will be able to evaluate the lesson and my teaching by:

1.

How well the students
respond to the examples and questions

2.

How well students d
o on the homework assignment

3.

How many questions were asked during the lesson

4.

How smooth the presentation went











Self
-
Reflection: