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Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Using dimensional analysis, the following calculation can be performed to convert between 3 pounds and its equivalent in grams (using the rate of 1 oz equals 28.3 g).

$(3 \ "lb")/1 xx (16 \ "oz") / (1 \ "lb") xx (28.3 \ "g")/(1 \ "oz") = 1,358.4 \ "g"$

Mathematically, why can 3 be multiplied by the factors $(16 \ "oz") / (1 \ "lb")$ and $(28.3 \ "g")/(1 \ "oz") ?$
1. Because this is dimensional analysis, regular rules of math do not apply.
2. Since the necessary units cancel out, there is no problem.
3. Because each of these factors is equal to one (the numerator and denominator are equal, but in different units).
4. By the Multiplicative Property of Equality.
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
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.2
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.
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:
$d = d_0 + v_0t + 1/2 at^2$
where $d, d_0$ are distances measured in meters; $v_0$ 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

$"m"/"s" *"s"/1 = "m"$

and the last term is

$"m"/"s"^2 * "s"^2/1 = "m"$.

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 $"m"//"s"^2$ and the units of the last term are $"m"//"s"^4$.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
Angela sells baked goods at a summer market each year. The two main baked goods are apple turnovers and chocolate caramel cupcakes. Unfortunately, she does not keep very good records, and cannot remember exactly what price she sold each for last year. She remembers that one day she sold 50 cupcakes and 30 turnovers, and made about $135. Another day, she sold 40 cupcakes and 40 turnovers, and made$140. If she were to create a model to solve for how much she sold each baked good for, what would be a good variable(s) to create?
1. Just one variable, the average cost of a baked good.
2. Two variables, one for the cost to make the baked goods, and another for the total revenue of the baked goods.
3. Two variables, one for the total number of turnovers sold, and another for the total number of cupcakes sold.
4. Two variables, one for the cost of a turnover, and one for the cost of a cupcake.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
Hannah wants to buy an indoor plant for her apartment. Which of the following factors would be important to investigate in order to determine which plant would be appropriate to buy? Choose all that apply.
1. Amount of sunlight the plant will get.
2. The size of the apartment.
3. Whether she will put the plant on the floor or on a table.
4. Average temperature of her apartment.
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