Document Sample

```					                                THE LADDER PROBLEM

Enduring Understanding: Develop a better understanding of how the properties of special right
triangles can be used to solve a problem.

Essential Questions:

Original Lesson Design                          Suggestions for English Language Learners
 How are special properties of right           Enhance vocabulary:
triangles used to solve a problem?
 How can the Pythagorean Theorem be            Right triangle
used to solve a problem?                     Pythagorean Theorem
 Does the Pythagorean Theorem always
have to be used when solving for the sides
of a right triangle?

Lesson Overview:

Original Lesson Design                          Suggestions for English Language Learners
 Before allowing the students the                  Additionally have some students display
opportunity to start the activity: access          and explain their solution to warm up
their prior knowledge with regards to              activities.
properties of right triangles. Warm-up           Use a web-site to provide background
exercises, discussion in collaborative             information and a visual proof of the
groups, problems on the wall around the            Pythagorean Theorem such as:
room can be used.                                  http://www.arcytech.org/java/pythagoras/
 What is meant by special right triangles?
 Discuss the Pythagorean Theorem.
 What is the relationship between the
hypotenuse and the legs of a right
triangle?
 Develop the relationship through                    Have students work in pairs. Have them
a segment from one vertex to the middle
of the opposite side to form two triangles.
Have students measure the sides and
angles of one of the smaller triangles to
discover the relationships between the
sides and angles of a 30-60-90 right
triangle.
   What is being asked by the questions in
the problem? How do you decode what
the problem is asking you to do?
   How can the students make their thinking
visible?
   What do you think the minimum and
maximum means in this problem?
    How is a table read in order to extract the
necessary information?
    How can you support a conclusion that
you make?
    Use resources from your building.                   Have students work in small groups to
provide and support a conclusion that
they will share with the whole class.

EALRs/GLEs:

1.3.2
2.2.2
3.3.1
3.3.2

Item Specifications: GS01; SR05

Assessment:

Original Lesson Design                             Suggestions for English Language Learners
 Use WASL format items that link to what              Have students create a rubric to score the
is being covered by the classroom activity            activity.
 Include multiple choice questions

You are a TV cable installer who needs to buy a ladder to reach access points at two different heights
on a big apartment building. Lower access points are 15 feet high and upper access points are 25 feet
high. You must use a ladder that reaches those heights. Joe, the cable TV installer, was told that the
angle between the ladder and the ground must be 60°.
upper
access
25 feet

lower
access

15 ft

ground

bottom       this angle must be 60°
of wall

1. What is the length a ladder would need to be to reach just the lower access? Support your answer
with a clearly labeled sketch, calculations, and an explanation.

2. What is the length the ladder would need to be to reach just the upper access point? Support your
answer with a clearly labeled sketch, calculations, and an explanation.

longer or shorter, depending on the need.

Ladders Available at the Local Hardware Store
Ladder Name             Length when fully       Length when fully closed    Price    Warranty
open (max. length)          (minimum length)                    life
Sturdyfoot             25 ft.                  15 ft.                      \$80      12 years
HighReach              27 ft.                  16 ft.                      \$100     15 years
Steadytop              29 ft.                  17 ft.                      \$150     20 years
3.Which ladder would you buy if you only needed to reach the lower access point and you wanted

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4.Which ladder would you buy if you only needed to reach the upper access point and you wanted to

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5.Which of the ladders, if any, can reach both access points safely (if you adjusted the lengths)?
Draw a sketch and show all necessary calculations to prove that this ladder can be used safely for
both heights.

6. Research and then discuss whether or not ladders should be safely used at 60 .
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7. Triangle ABC is a right triangle.

A.     2.0 units
B.     16.0 units
C.     64.0 units
D.     90.5 units

8.
A design is formed by joining isosceles right triangles and 60° - 30° right triangles as shown in the
diagram. The hypotenuse of the 60° - 30° triangle is 12 centimeters.

Which is closest to the length of one leg of the isosceles right triangle?

A.     6.0 cm
B.     8.4 cm
C.     20.7 cm
D.     24.0 cm

9. Using the measures shown in the sketch.

What is the length of the section of the ladder from the point where it rests on the ground to the point
where it touches the house?

A       4.8 ft.
B       17.0 ft.
C       23.0 ft.
D       26.2 ft.

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