Problem Solving In Mathematics

Make a Drawing or Model

Sometimes making a drawing or model of the problem allows you to visualize how to find the solution.

Here's an example: A 12" by 16" rectangular sheet is to have 2" squares cut out of each corner. Find the volume.

Other problems involving drawings or models are given below.

Here are the other problem solving strategies:

Day 12 - Billy, Ray , Gary, Clayton, and Pete just completed a 3000 meter race. Use these clues to help you determine the order in which they finished. - Floyd finished 10 seconds behind Gary. - Ray beat Pete by 20 seconds. - Billy finished 4 seconds behind Gary and 30 seconds ahead of Ray. - Clayton's finish was halfway between Floyd and Pete.

Day 13 - A 9 metre by 12 metre rectangular garden has a walk one metre side all around it. What is the area of the walk?

Day 14 - One painter can paint a wall in ten minutes. Another painter can paint it in 6 minutes. About how long will it take both painters to do the job?

Day 15 - Julie can eat a medium size pepperoni pizza in 8 minutes. Her friend Samantha can eat the same pizza in 6 minutes. If both of them ate at their same rates, how long would it take them to eat one medium sized pepperoni pizza together?

Day 36 - How many triangles can be drawn having any of these points as vertices?

Day 37 - The number of diagonals of a regular polygon is subtracted from the number of sides of the polygon and the result is zero. What is the number of sides of this polygon?

Day 38 - What is the maximum number of points of intersection when two distinct circles and three distinct lines intersect each other?

Day 39 - A straight concrete sidewalk is to be 3 feet wide, 60 feet long, and 3 inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of yards?

Day 40 - If 120 seats are arranged in a row, what is the least number of seats that must be occupied so the next person seated must sit next to someone?

Day 61 - Two opposite sides of a square are increased by 25 % while the other two are decreased by 40 %. Find the percent of decrease in the area of the square.

Day 62 - Alice is 100 meters from Bill and Bill is 300 meters from Chelsea. They all move to the right at constant speeds. In 6 minutes, Alice overtakes Bill, and in another 6 minutes, Alice overtakes Chelsea. How many minutes did it take for Bill to overtake Chelsea?

Day 63 - A man is digging a hole and standing in it. He is 5 feet 10 inches tall. He says that he is one-fourth done and that when he is finished, the top of his head will be three times as far below the ground as it is now above the ground. How deep will the hole be when finished?

Day 64 - An officer on horseback starts at the back of a column of marching soldiers and rides to the front of the column, then turns around and rides back to the rear of the column. If the rider travels three times as fast as the column moves and the column is 100 meters long, how far does the column move by the time the officer completes the tour of inspection?

Day 65 - If the radius of a circle is increased by 20 percent, by what percent is the area increased?

Day 86 - True or false: An equation of the bisector of the angle formed by the x-axis and the line y= x is y = 1/2 x

Day 87 - 18 people numbered 1 - 18 are seated equally spaced around a circular table. What is the number of the person directly across from the person numbered 6?

Day 88 - Bessy is tied on a 50 foot rope attached to the barn at point A. How much grazing area does Bessy have?

Day 89 - A golfer hits a ball 250 yards but 2 degrees left of the intended line. How many yards from the intended spot did the ball land?

Day 90 - At a concert are 4 seats in a row. Phillip must sit next to Sally but not next to Gerald. If Gerald will not sit next to John, who is sitting next to John?

Day 111 - 100 students were asked if they liked Country-Western or classical music. 5 students said they liked neither, 85 liked Country-Western, and 23 liked classical. How many students liked both?

Day 112 - A square is the only distinct monomino.

Two squares is the only distinct domino.

Triominoes, however, can be formed two ways:

Draw all the distinct tetrominoes.

Day 113 - Can this figure be retraced without lifting your pencil or retracing any lines?

Day 114 - A man calculated that if he skis 10 km/hr, he will arrive at his cabin at 1:00 PM . If he skis at a rate of 15 km/hr, he will arrive at his cabin at 11:00 AM. How fast must he ski to arrive at his cabin at noon?

Day 115 - When the midpoints of the side of a square are joined, a new square is formed. If this process continues indefinitely, what is the sum of all the perimeters of the squares if the original square was 4 cm.?

Day 136 - What is the perimeter of a square with a diagonal of 36?

Day 137 - Determine the largest number of boxes of dimensions 2x2x3 that can be placed inside a box 3x4x5.

Day 138 - A hexagon is inscribed in a circle, which is inscribed in a square of side 10 cm. What is the length of each side of the hexagon?

Day 139 - A golf ball falls randomly into a circular green 10 meters in radius, with the cup at the center. What is the probability that the ball falls within 1 meter of the cup?

Day 140 - Three vertices of a parallelogram are ( 1, 1), ( 3, 5 ), and ( -1, 4 ). Find all possible ordered pairs that could be the coordinates of the fourth vertex.