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Problem Solving Strategies Questions - All Grades

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Grade 2 Problem Solving Strategies
How would the inverse operation of addition be used to solve this equation?
P + 62 = 100
  1. 100 - 62 = P
  2. 62 - 100 = P
  3. 100 + 62 = P
  4. P - 100 = 162
Grade 3 Problem Solving Strategies
Read the word problem:
Christmas - Santa - Small
A toy store has 4 shelves of Santa toys. Each of the Santa toys is 5 inches tall. There are a total of 28 Santa toys. How many Santa toys are on each shelf?

What is the extra information?
  1. A toy store has 4 shelves of Santa toys.
  2. Each of the Santa toys is 5 inches tall.
  3. There are a total of 28 Santa toys.
  4. How many Santa toys are on each shelf?
Grade 5 Problem Solving Strategies
David went shopping for school clothes. He bought 2 pairs of slacks, 3 shirts, and 1 sweater. What do you NOT need to know to find out how much money David had left after shopping?
  1. how many hours David shopped
  2. how much money David started with
  3. how much money each pair of slacks cost
  4. how much money the sweater cost
Grade 3 Problem Solving Strategies
Read the word problem:
Christmas - Stocking - Small
Taylor's family has 6 stockings hanging by the chimney. Cedric's family has 4 stockings hanging by the chimney. All of the stockings are red and green. How many total stockings are hanging by the chimneys?

What is the extra information?
  1. Taylor's family has 6 stockings hanging by the chimney.
  2. Cedric's family has 4 stockings hanging by the chimney.
  3. All of the stockings are red and green.
  4. How many total stockings are hanging by the chimneys?
Grade 6 Problem Solving Strategies
How do you represent "is," "equals," or "result?"
  1. =
  2. +
  3. %
  4. x
Grade 3 Problem Solving Strategies
Read the word problem:
Christmas - Tree - Small
Julia hangs 12 candy canes on the tree. Clare hangs 8 snowmen on the tree. Alex hangs 9 candy canes on the tree. How many candy canes were hung on the tree?

What is the extra information?
  1. Julia hangs 12 candy canes on the tree.
  2. Clare hangs 8 snowmen on the tree.
  3. Alex hangs 9 candy canes on the tree.
  4. How many candy canes were hung on the tree?
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
A moving company chargers $65 per hour, plus a fee that depends on the distance between where the objects are being moved ($35 for every mile). What variable(s) would be good to define if one were to create an expression that would determine the total cost of moving?
  1. One variable: C, the cost of moving.
  2. One variable: t, for the amount of time.
  3. Two variables: C, for the total cost, and t, for the amount of time.
  4. Two variables: t, for the amount of time, and d, for the distance traveled.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
Carl is planting a vegetable garden, but will need to build a fence around it so the deer cannot eat the plants. He has 30 m of fencing, and wants to enclose an area of 50 square meters to accommodate all the plants he wants to grow. If Carl were to create a mathematical model to help him know how to build the fencing appropriately, what variable(s) would be useful to create?
  1. One variable, the length of the side of the garden.
  2. One variables, the total perimeter of the garden.
  3. Two variables, the length and width of the garden.
  4. Two variables, the amount of fence he has, and the area of the garden.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
There is a leak in the ceiling of Kara's room. She puts a bucket underneath the drip. After an hour, there's about a half liter of water. She checks back in another 3 hours, and there is about 2 liters of water. If she wants to determine how much water there will be in 12 hours, what quantity or quantities would she need to determine?
  1. The rate of the water's increase, in liters per hour.
  2. The amount of water in the bucket, in liters.
  3. The amount of water in the bucket in liters and the amount of time that has passed in hours.
  4. The size of the bucket in liters and the rate of the drip in liters per hour.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Near the end of class, Jillian's physics teacher writes a formula up on the board. Jillian quickly writes it down before leaving. Later that night while doing homework, she is unsure if she correctly copied the formula. What she wrote is:
d=d0+v0t+12at2
where d,d0 are distances measured in meters; v0 is velocity, measured in meters per second; t is time, measured in seconds; and a is acceleration, measured in meters per second squared.

She decides she will use dimensional analysis to determine if it is correct or not. She reasons that each term has to have the same units, and since the term on the left side of the equation and the first term on the right side of the equation are in meters, the other two terms need to be as well. The second term on the right side of the equation is

ms⋅s1=m

and the last term is

ms2⋅s21=m.

Since all terms are in meters, she decides that the equation she wrote down is right. Is she correct, and if not, what mistake did she make?
  1. Yes, she is correct.
  2. No. She assumed that all terms need to have the same units, when all terms need to be without units.
  3. No. Although the variable t is squared, the units are not. Therefore, the units of the last term are m/s, which are different than the rest of the terms.
  4. No. Jillian did the dimensional analysis incorrectly. The units of the second term on the right side come out to m/s2 and the units of the last term are m/s4.
Grade 5 Problem Solving Strategies
In 2000, Texas contained 79.6 people per square mile. What information do you need to find how many people lived in the state of Texas?
  1. The number of square miles per each person.
  2. The number of square miles in Texas.
  3. The number of square miles in the United States.
  4. There is enough information to solve the problem.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Rob is writing a physics test. For one of the problems, he needs the gravitational force formula for the force of gravity between two objects. He's not sure he remembers it correctly. He believes it is
Fg=G m1 m2r,
where Fg is the force, measured in Newtons; G is the gravitational constant, measured in N⋅m2/kg2; m1,m2 are the masses of the two objects measured in kilograms; and r is the distance between the objects, measured in meters. Using dimensional analysis, is his formula correct? Why or why not?
  1. Yes, since N⋅mkg2×kg1×kg1×1m=N.
  2. No, since N⋅m2kg2×kg1×kg1×1m=N⋅m.
  3. No, since N⋅m2kg2×1kg×1kg×m1=N⋅m3kg4.
  4. No, since N⋅m2kg2×kg1×kg1×m1=N⋅m3.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
Colin has been asked to create a mathematical model of the penguin population on a remote island. He wants to be able to predict the growth of the penguin colony. He decides that important variables and quantities to consider in the model include: availability of food, presence of predators, the current number of penguins, and the historic growth rate of penguin population. Is Colin's list correct? Why or why not?
  1. Yes, this is the correct model, and there are no more important factors to consider.
  2. No, this model leaves out many important variables, such as climate, water currents, diseases, and many more.
  3. No, only the current number of penguins and the historic rate of population growth are important. All the other factors are simply over-complicating the problem.
  4. Neither correct nor incorrect. Any real world problem can be modeled in multiple ways and with varying degrees of complexity.
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