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# Mathematical Process Questions - All Grades

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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
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.
Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.2
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.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.1

8 snowmen have red mittens. 5 snowmen have green mittens. 7 snowmen have blue mittens. How many more snowmen have red mittens than green mittens?

What is the extra information?
1. 8 snowmen have red mittens.
2. 5 snowmen have green mittens.
3. 7 snowmen have blue mittens.
4. How many more snowmen have red mittens than green mittens?
Palace, Sabrina, and Leon want to buy a pizza that costs $9.95. Palace has$4.25, Sabrina has $2.00, and Leon has$3.75. Do they have enough money to buy the pizza?
Which best describes what the question is asking?
1. Who has the most money?
2. Does their money total more or less than $9.95? 3. How much does their money plus the cost of the pizza equal? 4. What is the average contribution each person is making? Grade 10 Logical Thinking Which of the following is the biconditional statement for the conditional statement below? If today is Saturday or Sunday, then it is the weekend. 1. It is the weekend if and only if it is Saturday or Sunday. 2. If is not the weekend, then it not Saturday or Sunday. 3. If it is not Saturday or Sunday, then it is not the weekend. 4. It is not Saturday or Sunday if and only if it is the weekend. 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 4 Problem Solving Strategies Jodi bought cans of tennis balls that cost$2.50 per can. What else do you need to find out how much money Jodi spent in all?
1. If she is playing singles or doubles.
2. How many cans of tennis balls bought.
3. Whether she won or lost the match.
4. How many cans of tennis balls the store had.