MTTC Elementary Education – MATHEMATICS Questions and Answers 2023

MTTC Elementary Education – MATHEMATICS Questions and Answers 2023 Which of the following problem-solving strategies would be most effective and appropriate to use in solving the problem below: A company puts a free toy in each box of cereal and states that there is a one in four chance of getting the astronaut toy with each purchase. On average, how many boxes will need to be purchased to get an astronaut? A. expressing numbers in base four B. working backwards to find an equation C. simulating the situation using a random process D. graphing points on a coordinate system to find a pattern C A fifth-grade teacher is writing an article on mathematics activities in the classroom. The article describes how students use manipulatives to solve measurement problems. The teacher included trademark symbols with he name of the manipulative. The teacher also included photographs of students working with the manipulatives. None of the students in the photographs were identified by name. To ensure compliance with ethical guidelines, the teacher should take which of the following actions prior to posting the article on the internet? A. providing links to the manufacturers of the manipulative that have trademarked names B. providing a disclaimer stating that the school district does not endorse the pedagogical methods used C. explicitly identifying the manipulative used in a caption below each photograph D. obtaining permission from parents/guardians before posting pictures of the students D A fourth-grade teacher is planning a unit in which students will use a computer application to create their own tessellations. The teacher would like to develop a series of related activities and assessments to help develop students' mathematical reasoning skills related to the use of the application. Which of the following topics would be most appropriate for the additional materials to address? A. reflections, rotations, and translations B. area of composite figures C. similarity and proportional reasoning D. graphs of simple equations A Using the distributive property can best be described as: A. an axiom B. a proof C. a postulate D. a definition B Integers are a subset of which of the following sets of numbers? A. negative numbers B. natural numbers C. rational numbers D. irrational numbers C Which of the following activities is most effective for creating a foundation for understanding the concept of multiplication? A. practicing basic addition facts with numbers 1 through 10 B. using base-ten blocks to model two-digit numbers C. modeling equality of numbers with a balance scale D. skip counting by different intervals on a number line D If the least common denominator is used to perform the operation a/6 + b/15, what will be the value of the numerator for the equivalent representation of a/6? A. 2a B. 5a C. 6a D. 15a B In which of the following pairs are the numbers equivalent? A. 106.0 x 10 ^ 4 and 1060.0 B. 8.63 x 10 ^ -5 and 0.00863 C. 5.72 x 10 ^ 5 and 572,000.0 D. 0.3374 x 10 ^ -4 and 0. C A person buys an item that costs $3.60 and pays for it with a $5.00 bill. The amount of change, in dollars, represents a number from which of the following sets? A. natural numbers B. rational numbers C. whole numbers D. nonnegative integers B According to the order of operations, what could be the first step in simplifying the expression below? 4/3 [(6^2 - 3^2) + 9 - 6] A. (8^2 - 4^2) + 12 - 8 B. 4/3 [(3^2) + 9 - 6] C. 4/3 [(6^2 - 3^2) - 3] D. 4/3 [(36 - 9) + 9 - 6] D An individual wants to purchase an air conditioner and can choose between two different options. Both options have an original price of $200. The first option offers 30% off the original price and charges $20 for shipping. The second option offers 15% off the original price and shipping is free. What is the difference in savings between the two options? A. $5 B. $10 C. $15 D. $20 B A teacher shows students how they can improve their computational fluency by providing them with frequent opportunities to use mental math to solve problems such as the ones below. 2 + 8 + 7 + 3 = ? 9 + 4 + 3 + 3 = ? 3 + 7 + 2 + 3 = ? Which of the following best describes the teacher's approach? A. finding sums by working left to right B. using a combination of addition and subtraction together C. finding number pairs that sum to easily recognizable numbers D. converting addition problems into multiplication problems C In solving the division problem 47 / 2.4, a student transforms the problem to 470 / 24. This operation is equivalent to which of the following? A. 47 / 2.4 x 10/10 B. (47 / 10 ) / 2.4 C. 2.4 / 47 x 10/10 D. (47 / 2.4) / 10 A Twenty-seven cubic centimeters is equivalent to how many liters? A. 0.03 liters B. 0.027 liters C. 0.003 liters D. 0.0027 liters B A table has a rectangular center portion and two semicircular ends that can be folded out to increase its size. When the ends are folded down, the rectangular portion has a length of 5 feet and an area of 30 square feet. Which of the following expressions represents the area of the table when the semicircular ends are folded out? A. 30 + 6pi square feet B. 30 + 9pi square feet C. 36pi square feet D. 39pi square feet B Students in a fifth-grade class draw a 1 unit by 1 unit square on a piece of paper, cut the square out, and use a scale to find its mass. The students then draw various irregular shapes on the same type of paper, cut them out, and find their masses, and compare them with the mass of the square. This activity is an example of using: A. indirect measurement to determine area B. direct measurement to determine area C. indirect measurement to determine perimeter D. direct measurement to determine perimeter A a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve ellipse The use of a balance and two different shapes would be most appropriate in promoting students' skills in which of the following areas? A. equations in two variables B. volumes of irregular solids C. decimals and percentages D. negative and positive integers A If the pattern continues, what will be the sixth term in the sequence? 1/3 , 5/3 , 13/3, 29/3, ___ , ___? A. 58/3 B. 61/3 C. 122/3 D. 125/3 D Given the two equations below, what is the value of b in terms of c? 2a = 2b + 6 a = 3c A. b = 2c - 6 B. b = 3c - 3 C. b = 6c + 6 D. b = 3c + 6 B A small company wants to produce toy robots. The company determines that they will have an initial investment of $10,000 for equipment and tools and that each robot will cost an additional $15 to make. If n equals the number of toy robots made, which of the following functions gives the total cost, C(n), of producing n robots? A. C(n) = 10,000n + 15n B. C(n) = 10,000n + 15 C. C(n) = 10,000 + 15n D. C(n) = 10,000 + 15 + n C A box of cookies contains 8 chocolate chip cookies, 12 peanut butter cookies, and 4 oatmeal cookies. A child randomly selects 2 cookies, one at a time. Which of the following expressions represents the probability that both cookies will be peanut butter? A. 12/24 + 12/23 B. 1/12 + 1/11 C. 12/24 x 11/23 D. 1/12 x 1/11 C A teacher would like to have an activity in which students can compare a theoretical probability with an experimental probability. Answering which of the following questions would be most appropriate for this activity? A. What is the probability that a student in the school selected at random will be wearing a red shirt? B. What is the probability that a six-sided number cube will come up 5 when rolled? C. What is the probability of correctly guessing a number between 1 and 1000? D. What is the probability that the third-grade class will have 100% attendance on Mondays? B