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May Problem of the Day 2014. Problem Solving. May 1, 2014.
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May Problem of the Day2014 Problem Solving
May 1, 2014 • A magnifying glass is a lens that makes objects appear larger than they really are. Suppose a 35°angle is observed through a magnifying glass that enlarges objects to twice their actual size. How big is the angle when viewed through this magnifying glass? Explain your answer.
May 2, 2014 • In construction, floor space must be given for staircases. If the second floor is 12’ above the first floor and a contractor is using a step pattern of 10 inches of tread (run) for 6 ½ inches of rise then how many steps (round to whole number) are needed to get from the first to the second floor and how much linear distance will need to be used for the staircase? How long is the railing that is parallel to the steps? Explain how you determined the length of the railing (round to 1/8 inch). • Pythagorean Theorem states a² + b² = c², where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse.
May 5, 2014 • When the ancient Egyptians were building the great pyramids at Giza, they checked each course or level of stones to make sure they were being laid square by measuring the diagonals. If each course of stones has the length of the square reduced by 6 ½’ what is the reduction in the length of each diagonal? Explain why your answer makes sense. • Pythagorean Theorem states a² + b² = c², where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse.
May 6, 2014 • The most practical and efficient kitchen is designed as a “work triangle.” The ideal distances of the sides of the triangle are: 4 to 6 ft, 4 to 7 ft, & 4 to 9 ft. What is the largest perimeter of the ideal work triangle? What is the smallest perimeter of the ideal work triangle? Explain why a homeowner would need this information when remodeling a kitchen.
May 7, 2014 • A checkerboard contains 8 squares along the sides of the board and 8 squares along the top and bottom. Each of these squares is 1 by 1. The total number of 1 by 1 squares is 64. Find the total number of squares on a checkerboard (include 2 by 2 squares, 3 by 3 squares, and so on). Explain your method of solving this problem
May 8, 2014 • Each side of a checkerboard measures 16 inches. The board contains 8 rows of 8 squares per row. Find the area of each small square on the board. Increase the size of the square by 10 times and then estimate how many squares you could paint on a wall that was 12’ long and 8’ high. What are some of the issues with painting this design on a wall? • Square area is A = s².
May 9, 2014 • The size of the dollar bill of today is smaller than the dollar bills printed before 1929. The dimensions of those bills were 7.2 by 3.13 inches. The bills in circulation today are 6.14 by 2.61 inches. Find the area of each and determine about what percentage has our dollar bill reduced its’ area? Why do you think the area of a dollar bills has been reduced? • Rectangular area is A = lw
May 12, 2014 • Raising your own chickens for egg production is a current trend. In 1897 the recommended size for a chicken house was given as “ten feet is wide enough and every ten feet in length will afford space for 15 hens.” According to this advice, find the area of a coop that could accommodate 60 hens. Currently the advice is a minimum of 4 square feet per chicken. How does that compare with the advice from 1897? • Rectangular area is A = lw.
May 13, 2014 • Roofing shingles are packaged in groups called “squares”. One square covers 100 square feet of a roof. The roof of a house is made of two rectangles, each 13 feet by 36 feet. The two rectangles meet to form the peak of the home. How many squares of shingles are needed? If you want to have 10% more shingles as an overage, will that effect the number of squares you purchase? • Rectangular area is A = lw.
May 14, 2014 • A 1-inch by 12-inch rectangle has an area of 12 square inches. A standard sheet of letter size paper is 8½ inches by 11 inches and has an area of 93.5 square inches. Pete claims he can cut a 1-inch by 12-inch rectangle from this paper. Explain how he can do this and what is the area of the remaining paper? • Rectangular area is A = lw.
May 15, 2014 • In the past lighthouse beams could not be seen until the ship was 15 miles from the light source. A series of reflectors has increased the distance. A beam of light from a lighthouse may be seen for 30 miles in all directions. What is the area in square miles in which the light may be seen? What factors might interfere with the light being seen in this area and why is the increase in distance important in ship safety? • Formula for the area of a circle is A = πr².
May 16, 2014 • A CD that is 120 mm in diameter can hold up to 74 minutes of music. The unrecorded portion of this particular disc has a diameter of 50 mm. Find the area of the recorded portion of this disc. How could you determine how many more minutes you could record on this disc? • Formula for the area of a circle is A = πr².
May 19, 2014 • The diameter of an archery target is 48 inches. The diameter of the innermost circle is 9.6 inches. What percentage of the area of the target is the area of the smallest circle? Explain why the size of the circle could affect the archer’s chance of hitting a bull’s-eye? • Formula for the area of a circle is A = πr².
May 20, 2014 • Two pizzas have a 12-inch diameter. One pie is cut into eight equal slices, and the other is cut into 6 equal slices.If the 8 slice pie sells for $1 a slice, what would be the cost per slice of the 6 slice pie so that you would make at least the same amount of money per pie? Explain what you think about the trend to reduce serving size with regards to restaurant profits? What do you think about reducing the amount of product in the same size boxes, cans or bags with regards to the consumer price?
May 21, 2014 • A shoe box measures 6.5 inches by 3.5 inches by 12 inches. How many boxes of this size can be place on a 12-inch by 25-inch shelf if the shelf is one foot from the ceiling? What is the volume of wasted space? By how much could you adjust the distance of the shelf from the ceiling to reduce the amount of unused space? • Volume of a rectangular prism is V=lwh.
May 22, 2014 • The surface area of a 3-Dimensional figure is the sum of the areas of all the faces and bases of the figure. Dice are cubes with 6 faces. Each side of a die is a face. Twelve ¾ by ¾ by ¾ inch dice are boxed in two layers of two rows of three dice per row (six dice are in each layer). Find the surface area of the box. Explain your solution process.
May 23, 2014 • The Smith family likes to take trips in the car. Traveling south on the highway, the Smiths will pass cutoffs for three cities: Allenville, Browning, and Cooperton. The distance from Allenville to Browning is 16 miles. The distance from Browning to Cooperton is 8 miles, and the distance from Allenville to Cooperton is 24 miles. What town is between the other two? Explain why your answer makes sense.
May 24, 2014 • Slopes are used in planning and constructing roofs of buildings. The slope of a roof is called the pitch. You can find the pitch of a roof with the following formula. Pitch = rise of the roof ÷ ½ the span of the roof. If the rise of the roof is 0 feet and the span is 24 feet, find the pitch. Compare the pitch of a roof to the slope of a line, using the formula slope = rise/run.
May 27, 2014 • Rachael the roofer is carrying shingles over her shoulder and a bucket of nails as she is climbing up the ladder to the roof. The total weight she is carrying is 75 lbs. the shingles weigh 4 times as much as the nails. How much do the nails and the shingles weigh? If she weighs 135 lbs herself, what percentage of her weight is she carrying up the ladder?
May 28, 2014 • Paul the painter had to paint three walls each of different heights. The tallest wall, which will be painted white, is 12’ taller than the wall that is to be painted blue. The difference between the white wall and the red wall is 8’ more than the difference between the red wall and the blue wall. If the blue wall is 8’ feet in height, how tall are the other two walls? Explain how you solved this problem.
May 29, 2014 • Sharon was told by her boss to hoist up a load of cinderblock to the second story of the building under construction. She asked her boss how much the load of cinderblock weighed. The boss replied that it weighed 400 pound plus ⅓ of the total weight. Scratching her head, Sharon tried to figure out what the boss just said. Can you figure out the weight of the cinderblocks? Explain how you figured it out.
May 30, 2014 • At a construction site two masons were building brick wall. Each wall of bricks requires 10 pounds of mortar. While building the wall a little of the mortar is left over. After four walls are built there is enough mortar to build another wall. If the masons start the day with 160 pounds of mortar, how many walls can be built? Explain why your answer makes sense.