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Winter packet assistance (Math) - pg 6











































I would greatly appreciate your help with the attached math problems. Thank you.

Comments for Winter packet assistance (Math) - pg 6

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Dec 31, 2011
Winter packet assistance (Math) - pg 6
by: Staff

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Part II

The large square on the graph paper represents the combined area of all three bedrooms.

You can now draw ANY three rectangles within the large square to answer the question 4. There is only one restriction: together, the three rectangles must take up all the space inside the large square drawn on the graph paper.

As an example, I have (arbitrarily) drawn three rectangles which answer the question. To view, open the link shown below.

(1) If your browser is Firefox, click the following link to VIEW; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/Math-Grade_4_2011-pg6-graph-02-2011-12-30-03.png

The first rectangle (shown in yellow) is 30 squares high and 4 squares wide:

Area = Length x Width

Length = 30 x 4 = 120 feet
Width = 4 x 4 = 16 feet

Area (yellow rectangle) = 120 feet x 16 feet = 1920 sq feet


The second rectangle (shown in grey) is 30 squares high and 18 squares wide:

Area = Length x Width

Length = 30 x 4 = 120 feet
Width = 18 x 4 = 72 feet

Area (grey rectangle) = 120 feet x 72 feet = 8640 sq feet


The third rectangle (shown in blue) is 30 squares high and 8 squares wide:

Area = Length x Width

Length = 30 x 4 = 120 feet
Width = 8 x 4 = 32 feet

Area (blue rectangle) = 120 feet x 32 feet = 3840 sq feet


The sum of the areas of all three rectangles is:

Area (yellow rectangle) + Area (grey rectangle) + Area (blue rectangle)

= 1920 sq feet + 8640 sq feet + 3840 sq feet

= 14400 sq feet






5. Juanita used popsicle sticks as the edges of solid geometric figures built in the snow. She has 24 popsicle sticks. Can she build a cube and a square pyramid? Explain why or why not?


Since there are 12 edges in a cube, Juanita can build a cube using 2 popsicle sticks per edge.

A square pyramid has 8 edges. Juanita can build a square pyramid using 3 popsicle sticks per edge.


Thanks for writing.


Staff
www.solving-math-problems.com


Dec 31, 2011
Winter packet assistance (Math) - pg 6
by: Staff


Part I

Question:


I would greatly appreciate your help with the attached math problems. Thank you.


Answer:

4. Your teacher wants to buy a new house. She wants a three-bedroom home with a square footage between 1,300 and 1,500 feet combined in the bedrooms.

Use graph paper to design three rectangular bedrooms whose total area is between 1,300 and 1,500 square feet. Include a diagram with dimensions.


The area of a rectangle can be calculated as follows:

Area = Length x Width


A typical bedroom would have dimensions in the approximate range of 11 ft by 11 ft.

Area of a typical bedroom = 11 ft x 11 ft = 121 sq feet

The total area of three typical bedrooms = 3*121 = 363 sq feet


The question states that the total area of the three bedrooms (not the house) in the problem is between 1300 and 1500 square feet – almost five times the typical size. These are truly giant bedrooms.

Although I’m sure the original intent of the question was a home of 1300 to 1500 square feet, I have answered the question exactly as it is stated: three rectangular bedrooms whose total area is between 1,300 and 1,500 square feet.



If the side each small square on the graph paper represents 4 feet, then the area of each small square represents 16 sq feet (4 x 4 = 16).

If you draw a square on the graph paper which is 30 squares wide and 30 squares tall, then the area of that large square represents 14,400 sq feet (30 x 30 = 900 small squares, 900 small squares x 16 sq feet for each small square = 14,400 sq feet).

This area is within the range stated in the problem (total area is between 1,300 and 1,500 square feet).

Open the following link to view this large square drawn on the graph paper provided with the winter packet.

(1) If your browser is Firefox, click the following link to VIEW; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/Math-Grade_4_2011-pg6-graph-01-2011-12-30-03.png

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