CertifyT Math Questions Competency – Flashcards
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Competency - - 016 Mathematical Connections
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A chemistry experiment requires four fluid ounces of vinegar be mixed with one teaspoon of soda. How many milliliters of vinegar should be poured into a beaker? Hint: 1 tbsp = 15 ml = 0.5 fl oz
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120 ml ~ 15*8=120 ~
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Determine the choice that best describes the characteristics of the slope-intercept form of a line. y = mx + b
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The m and b are fixed. The m represents the slope, and the b represents the y-intercept. As x changes, the y changes.
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Determine which property describes: (a*b)*c=a*(b*c)
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Associative ~The associative property of multiplication is (a*b)*c = a*(b*c). Terms stay in the same order on each side of the equals sign, but are associated differently
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Troy and Rosa want to purchase a house. The bank will approve a loan for a house including property tax and insurance on the house for 24% of their adjusted monthly income. Their combined gross monthly income is $5150. They have a car payment of $320 and pickup payment of $465. Also, they have a furniture payment of $250. What is the maximum payment the bank will approve?
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$988.00 ~$5150 - $320 - $465 - $250 = $4115 ~Now, multiple by 24%. $4115 x 0.24 = $988
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A teacher decides to assign students a project where they will develop an amortization schedule of a purchase so they can apply a lesson using the future value formula and observe the details line by line as payments are made. What would be the best approach in assigning a purchase?
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Have the class research products online such as stereos, game stations, and etc, and choose an item they would like to purchase.
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The principal is $127,000 and the monthly payments are $583.56. The students want to know how much interest over the period of the note (30 years) will accrue. They decide the first step is to calculate the total amount to be invested in the house. Payment amount x Number of payments = Total amount invested What should the next step of the algorithm be?
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Total amount invested - Principal
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The symbol Æ is often used in mathematics. This symbol does not represent (the) ___________________.
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zero ~ Zero is a number. Zero can be a solution. Zero has a value and is only represented by 0.
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Competency - - 017 Skills, Procedures and Concepts
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In teaching a lesson for the first time on decay function models using the formula [ y = y0ekt ] where y0 is the amount present at any time t, students are having a hard time understanding how to find the y0 in the problem given below. They understand that it seems like it would be 700, but are confused at how to derive 700 from the formula. Which choice below would not be a good approach for the teacher to handle this learning situation if the teacher is trying to stress critical thinking?
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Work through an example of this problem with the class changing the numerical values in this problem to other numbers.
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What previous lessons taught for exponents should be reviewed before teaching a lesson on properties of logarithmic functions involving a problem like the following? Write the expression as a single logarithm with coefficient 1. - 2 log 5(3m2) + 1 log 6(9m2) 3 2
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The product rule, power rule, and negative exponent rule for exponents.
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Not knowing where to begin, the students began to urge her to give them some help. Wanting them to feel successful and stay engaged, Ms. Jones pointed out to the students that the problem involved subtracting from the time Pat and her sister got home the minutes and hours they were out. She told her students that they needed to convert hour to minutes when subtracting minutes, and that there are 60 minutes in an hour.
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Her discourse cut off opportunities for sense-making by hurrying students through the solution of the task.
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Three sudents are playing a game using the spinner above. Each student draws three boxes on a piece of paper. The spinner is spun, and each student writes the number in any one of the three boxes. The spinner is spun two more times, and each time the students write the number in a remaining empty box. The students then compare numbers, and whoever has the largest three-digit number wins the game. This game would be particularly useful in helping students' understanding of:
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Place value
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Mr. Grant wants his fourth-grade math students to learn to work collaboratively, to discuss alternative approaches to solving tasks, and to justify their solutions. Students are grouped in pairs and Mr. Grant gives his students the following task: Express the ratios below in the lowest forms: 15/25, 18/6, 9/36, 18/15 Which of the following best describes the level of student engagement expected with the given task?
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It will not engage students in high level forms of thinking
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Ms. Senath teaches math to a diverse group of students in her fourth-grade class, some of them with learning disabilities. It is important for her to remember when presenting math instruction to her students that —
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she should teach math concepts from the concrete to the representational to the abstract.
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Mr. Jansen's second-grade students have been working on addition and are now ready to begin learning two-digit subtraction. To introduce this new unit of study he first has students work on addition problems they are familiar with and then follows up by demonstrating to them how those problems are related to subtraction. This approach best demonstrates Mr. Jansen's understanding that — A. students with learning disabilities learn much slower than other students. B. instruction in math should build on existing knowledge of math. C. he must first review students to make sure they understand addition. D. he must build student confidence before beginning new instruction.
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instruction in math should build on existing knowledge of math.
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Which choice best describes an explanation a teacher could give a student to help him/her judge the reasonableness of the solution in the following scenario. Evaluate: -7 - 12 The student gives an answer of 5.
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Think of your checking account being overdrawn by $7 and you write another check for $12. How much would be in your checking account?
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After a lesson in finding the area and the domain of the length of a side of a rectangle given the perimeter of the rectangle, the teacher finds that almost all the students have answered the following question this way. What would be the best approach for the teacher to respond to the answers?
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Congratulate the students on their efforts of critical thinking through a tough question and their ability to calculate the area correctly. Follow up with a mini lesson on multiplication property of zero. Let students work in pairs to analyze if they want to change their answer for the domain.
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The teacher plans to look at the quizzes to determine the level of comprehension of the topics taught that day, mark corrections, hand back the quizzes to the students the next day, and adjust the contents taught the next day based on the results. What type of assessment techniques is the teacher utilizing?
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Formative ~ Formative assessment is embedded in the sequence of instruction and is designed to enhance learning with non-threatening results and adapt to student needs. ~ Summative assessment is designed to allocate grades based on how a student proves their understanding of the subject.
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A teacher begins a new lesson on Trigonometry on Monday. She would like to identify which concepts of the new lesson are most difficult for students to comprehend, so that she can adjust her lesson plans for Tuesday as the lesson progresses. Which of the following assessment methods would be least appropriate for achieving this goal?
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summative ~ Summative assessments should be used once the concepts are believed to be understood by the students not in the initial learning process, because these assessments contain formal grades.
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A teacher that uses constructivism will not practice which of the following in the classroom?
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Lecture based classroom ~ Constructivism is a theory of learning through experiencing things, reflecting on experiences, and assessing what is being learned through the activity.
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The lesson today is to determine whether equations such as the following have a circle as their graph. And, if they are a circle, then graph them. x2 + y2 + 6x − 2y = −6 As a lead into this lesson, the teacher should review which method of solving a quadratic equation?
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Completing the Square ~Circle Radius (x-h)^2 +(y-k)^2=r^2 ~ Zero Factor Ax2+Bx+C=0
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The use of mathematics manipulatives and technological tools help which of the following learners?
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Kinesthietc, Logical, Spatial ~ Spatial learners benefit from seeing interesting visual ways to solve problems, and graphics help them make connections in the solving process. ~ Kinesthetic learners perform best when given a tactile model that they can manipulate to find the answer. ~ Logical learners usually use step-by-step procedures to solve mathematical problems.
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The teacher leads the classroom outside to measure the sidewalks from the parking lot to the doorway of the school. She divides the students into groups of 4 and divides the sidewalk into 4 pieces. Each group is given the task to measure how many feet are in their section of the sidewalk. Part 2 of the exercise includes each student in each group taking a normal step. The group measures the inches of each student's step. Part 3 of the exercise is for each group to calculate the average inches in a step of their group. Part 4 of the exercise is the groups are to work together and determine the weighted average of a normal step. Part 5 is for the class to determine the average number of steps a student makes on the sidewalk walking one time from the parking lot to the door. Which of the following is this exercise lacking?
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Individual Accountability ~ The teacher did not give guidelines for individual responsibility and accountability, and for that matter neither were instructions given for small group or large group responsibility and accountability. There are openings where only a few students could do most of the work involved in solving this problem.
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Competency 18 - Instructional Implementation
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Which of the following concepts or procedures best describes how to find the following retail solution? A $100 pair of shoes is on sale for 25% off. The department store offers a one day special on Saturday: take an additional 20% off. What is the price of the shoes if purchased on Saturday?
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Composition of functions ~ The composite function of ( represents how to solve for the retail price on Saturday. This can be represented by ( where solves for the price any day with the 25% off and ( solves for the price on Saturday taking an additional 20% off of the remaining 75%. ~ The sum of the functions (f + g)(x) will result in taking 45% off the merchandise when the actual amount to be taken off is 25% + 20% of the remaining 75%.
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Mr. Taylor wants to introduce his students to the concept of place value. Which of the following sets of manipulatives best describe those that can effectively be used to teach the given concept?
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base-ten materials, decimal squares, 10-frames, Cuisenaire rods, math balance, cubes, 2-color counters Non options= spinner, geoboards, dominoes
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Ms. Brown wants to introduce her students to the concept of ratios. Which of the following sets of manipulatives best describe those that can effectively be used to teach the given concept?
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color tiles, cubes, Cuisenaire rods, tangrams, pattern blocks, 2-color counters Non options=dominoes, geoboard, money
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Base-ten blocks, attribute blocks, Cuisenaire rods and cubes are some of the manipulatives a math teacher has available to teach several mathematical concepts to his class. Cuisenaire rods is a type of manipulative most effectively used to teach which of the following concepts?
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Sorting, ordering, counting, number concepts, comparisons, fractions, ratio, proportion, place value, patterns, even and odd numbers. ~ Different size fraction pieces identified with different colors.
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Cuisenaire rods
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Which of the following is a reflection the teacher of mathematics should engage to ensure that every student is learning sound and significant mathematics and is developing a positive disposition toward mathematics?
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Observing, listening to and gathering other information about the students to assess what they are learning ~ engage in ongoing analysis (reflection) of teaching and learning by observing, listening to, and gathering other information about students to assess what they are learning; examining effects of the task, discourse (thinking, talking, and agreeing and disagreeing that teachers and students use to engage in tasks), and learning environment on students' mathematical knowledge, skills, and dispositions.
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Which of the following would be the least effective approach in teaching a lesson of algebra?
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After a lecture-based instructional teaching model, have students complete a worksheet on the topic before leaving class. ~ Many students today do not do well with a passive learning mode. A more active approach will most often give better results.
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The greatest benefit of providing elementary students with mathematical tools such as geoboards is that these tools:
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Provide students with visual representations that promote their conceptual understanding. ~ geoboards help students identify simple geometric shapes, describe their properties, and develop spatial sense.
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Calculators, base-ten blocks, attribute blocks and cubes are some of the manipulatives a math teacher has available to teach several mathematical concepts to his class. Attribute blocks is a type of manipulative most effectively used to teach which of the following sets of concepts?
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Sorting, classification, investigation of size, shape, color, logical reasoning, sequencing, patterns, symmetry, similarity, congruence, thinking skills, geometry, organization of data. ~Different color shapes triangles, square, rectangles, octagons
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|3x + 2| = 9 |3x -4| ≤10 |7x +9| > 16 Next, he gives the students an absolute value problem as a quiz for the day. Which problem below would not be consistent with what has been taught? A. |-2x + 4 | = 7 B. |4x -5| -2 D. | x + 9 | ≥ 9
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|2x + 9 | > -2
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Which of the following is NOT a prerequisite for children to recognize patterns? A. exploration of many objects B. determine similarities and differences C. compare sets D. classify objects
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Compare sets ~ In the sequence of prenumeration steps, comparing sets is after recognizing patterns. Children have to be able to recognize patterns and be further able to tag items one to one in order to compare sets.
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After studying a basic section on factoring quadratics that does not include complex numbers, the students are given a quiz the next day. Determine the following that is not an appropriate question for the quiz. A. x2 + x − 6 = 0 B. x2 + 6x + 9 = 0 C. x2 − 2x − 8 = 0 D. x2 + 6x + 14 = 0
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x2 + 6x + 14 = 0
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Determine the best problem to put on a quiz to check for a common misconception with exponents. A. −3^2 B. (−5)^2 C. −2^3 D. −3^5
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-3^2 ~This is the most common mistakes with basic exponents. The tendency is to square (-3) instead of only squaring 3 and multiplying that by a negative one. Essentially this is (−1)(32) = −9. So, this is the best problem above to check for complete student understanding of exponents.
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The teacher asks students to evaluate the following problem.-------3x − (2 − 9x) After a few seconds, the teacher puts these answers on the Smart Board. A. 12x − 2 B. −6x − 2 60% of students chose Answer A and 40% chose Answer B with their classroom Clickers. What property does the teacher need to re-teach?
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Distributive
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Determine the best choice to assess each student's comprehension of a concept. A. Quiz B. Clickers C. Group Work D. Both A and B
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Quiz and Clickers
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The teacher wants the grade for this project to reflect different levels of performance of arithmetic skills, well-defined processes in solving the problem and checking the answer, use of quantitative language in writing that supports their answers, and their applications of the mathematics to a real-world problem. What method of assessment would be best for this project?
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Form a rubric using the different items to be evaluated for the columns of the rubric and rows progressing with levels (1 to 4) of understanding and predetermined points associated with each level of understanding. With the rubric, students can get full credit for calculating the sum of the first n terms as long as the sum is correct with the n-value they use.
