Dog House and Run

DOG HOUSE AND RUN

Enduring Understanding: Develop a better understanding of how to find the surface area of a figure and use that area appropriately within the context of a situation. Develop a better understanding of how to convert units of measure within the US system. Develop a better understanding of how the change in a linear dimension will affect the volume of a figure.

Essential Questions:

 How does the change in one linear dimension affect the volume?  How are units of measure converted within the US system?  What properties of special triangles such as equilateral, isosceles and right triangles assist in determining solutions to problems?  How can a conclusion be supported using mathematical information and calculations?

Lesson Overview:

 Before allowing the students the opportunity to start the activity: access their prior knowledge regarding how to find the volume of a rectangular prism. Allow for collaborative time for the students, possibly activities around the room, discuss with the students.  With the first essential question, while students may think they are finding the surface area of the dog house, they need to include the door in the cost because you are required to buy a full sheet of plywood. Therefore, a person would then cut out the door and have extra wood left over. Good real-life dilemma for classroom discussion.  A good warm-up for this activity is Geometry Gift.  What are the relationships that exist among the units of measure for linear dimensions, area and volume?  What would happen if one linear dimension of a rectangular prism is changed?  How is a problem situation decoded so that a person understands what is being asked?  What mathematical information should be used to support a particular conclusion?  How will the students make their thinking visible?  Use resources from your building.

EALRs/GLEs:

1.2.1 1.2.3 1.2.5 2.2.2 4.2.2

Item Specifications: ME01; ME02; ME03; SR02; CU02

Assessment:

 Use WASL format items that link to what is being covered by the classroom activity  Include Multiple Choice items Dog House and Run

You will need to determine the amount of materials needed to construct a dog house and a dog run according to the measurements given. You will also determine the total cost based on the prices listed.

Part I: The Dog House

1. Figure the total surface area of this dog house in square inches:

Roof ______= ______

Sides ______= ______

Floor ______= ______

Ends ______= ______

______= ______

Total of all surfaces = ______

2. Convert total square inches to square feet: ______Show the work that supports your answer. 3. Compute number of sheets of plywood needed. Each sheet measures 4 feet x 8 feet which

converts to ______

Number of plywood sheets needed = ______Show the work that supports your answer.

Part II: The Run

Use the dimensions given in this drawing to complete the following information:

1. Number of feet of 4 feet high cyclone fencing required to surround the run. Show the work that supports your answer ______

2. Number of posts needed if they are spaced 6 feet apart (include one extra to support a gate).

Draw in the posts = Post ______posts 3. Volume of concrete necessary to form a 3 inch slab under the run. ______Show the work that supports your answer.

4. What would happen to the volume of concrete needed if the longest side of the slab is reduced by 25%? Support your answer using words, numbers and/or diagrams.

______

Part III: The Cost

Builders’ Supply Price List

Plywood ………………………………………………………$ 14.89 per 4’ x 8’ sheet

Cyclone fencing: 36 inch high ……………………………………………$ 26.99 per 50 foot roll 48 inch high ……………………………………………$ 34.99 per 50 foot roll

Fence posts……………………………………………………..$ 3.49 each

Gates: 36 inch high ……………………………………………$ 21.99 each 48 inch high ……………………………………………$ 24.99 each

Concrete ……………………………………………………….$ 2.15 per cubic foot Compute:

______sheets of plywood @ ______= ______

______roll(s) of fencing @ ______= ______

______posts @ ______= ______

______gate @ ______= ______

______cu. ft. concrete @ ______= ______

Total Cost $ ______

Less 15% discount - ______

Cost - Discount ______

Plus 7.5% sales tax + ______

Amount payable $ ______2. You work for a paving company that recently did some paving work at a school. You now need to give the school a bill for paving the playground and putting a concrete border around its perimeter. A scale drawing of the playground is shown below.

The cost (labor and materials) for the pavement is $54 per square yard.

The cost (labor and materials) for the concrete border is $18 per linear foot.

What was the cost for paving the playground and putting a concrete border around its perimeter?

______Support your answer using words, numbers and/or diagrams. 3. A right triangle is removed from a rectangle as shown in the figure.

Which is the area of the remaining part of the rectangle?

O A. 40 in² O B. 44 in² O C. 48 in² O D. 52 in²

4. Marie has been hired to paint the walls and ceilings of three rooms. Room 1 is 12 feet by 12 feet, room 2 is 10 feet by 15 feet and room 3 is 10 feet by 12 feet. All three rooms are 10 feet high. A gallon of paint covers between 250 and 300 square feet.

Which is the best estimate of the number of gallons of paint that Marie needs to buy?

O A. 2 O B. 6 O C. 8 O D. 10

5. The length and width of the smaller box are doubled. The result of the changes is the larger box.

Which is the effect on the volume of the bigger box in relation to the smaller box?

O A. Half as great. O B. Two times as great. O C. Four times as great. O D. Eight times as great.