Praxis 2 5017 Form 2 Mathematics

A fourth-grade teacher is planning two lessons for introducing the concept of equivalent fractions. In these lessons, the teacher plans to have students develop a procedure for generating fractions equivalent to a given fraction and work on practice problems in groups. The students will also utilize fraction strips to model equivalence of various pairs of fractions whose denominators are factors of 12. Which of the following is the best way in which to sequence the activities within the two lessons? A. Lesson I: model equivalence with fraction strips; Lesson II: develop procedure, then work on practice problems B. Lesson I: develop procedure, then work on practice problems;Lesson II: model equivalence with fraction strips C. Lesson I: develop procedure, then confirm its correctness using fraction strips; Lesson II: model equivalence with fraction strips, then work on practice problems D. Lesson I: develop procedure, then model equivalence with fraction strips.Lesson II: work on practice problems

A

A math teacher plans a lesson in which students will use the nets shown to create figures with one open face. The figures, a prism and a pyramid, will have square bases of equal area, and each figure will have the same height. The teacher then has the students fill the pyramid with sand and pour it into the prism. Which of the following is most likely the purpose of the lesson? A. Discovering the volume formula of a pyramid as it relates to a prism B. Discovering the volume formula of a pyramid as it relates to a cone C. Discovering the surface area formula of a pyramid as it relates to a prism D. Discovering the surface area formula of a pyramid as it relates to a cone

A

A second-grade student has made the following error in subtracting multidigit numbers. 1 1 372 652 - 347 - 418 _________ __________ 35 244 Which of the following is most likely the cause of the student's error? A. The student did not correctly record the tens after decomposing a ten into ones. B. The student decomposed the tens when it was not required. C. The student transposed the numbers during the process of regrouping. D. The student regrouped the ones when it was not required.

A

A teacher gave students an assignment in which they will determine the class's favorite cafeteria food. Which of the following is best for the students to use to summarize the distribution of data collected from surveying 25 fourth-grade students about their favorite cafeteria food? A. A pictograph with the food categories listed and a drawing to represent the number of students that chose each food B. An alphabetical list of the students surveyed with their food choices indicated next to their name C. A computer slide presentation with a picture of each student with his or her favorite food D. A bar graph with the names of the students listed at the bottom of the graph and the foods chosen listed vertically

A

For a lesson on central tendency of data, a teacher plans to have students line up at the front of the classroom in increasing order according to each student's height. The students will then be instructed how to compute the mean, median, and mode of the resulting data set. At what point in the lesson should the teacher use the activity to most effectively promote student learning? A. The activity should be used at the very beginning of the lesson to introduce and contextualize the notions of mean, median, and mode. B. The activity should be used early in the lesson, after the teacher has defined the notions of mean, median, and mode. C. The activity should be used late in the lesson, after students have had a chance to compute means, medians, and modes of some simple data sets. D. The activity should not be used as a part of the lesson, as it is not an effective use of time.

A

The Number on the White Cube, x The Number on the Black Cube, y A teacher asks students to roll one white number cube and one black number cube, each numbered 1 through 6. The numbers that appear face up are recorded in the table and then plotted on the grid shown. Which of the following is most likely the objective of the lesson? A. Ordering coordinates correctly to plot points B. Understanding simple probability C. Learning counting techniques D. Graphing linear equations

A

Through observation and classroom discussion, a sixth-grade math teacher discovers that several students are having difficulty adding integers. Which of the following will most likely help students understand this concept? A. Using two-sided colored counters to model selected problems B. Allowing students to use calculators C. Providing students with a reference sheet describing the rules for adding integers D. Assigning additional practice problems

A

"In a bag of red and blue marbles, there is 1 red marble for every 2 blue marbles. The bag contains 16 blue marbles. How many red marbles does the bag contain?" A group of students who have not previously studied proportions are working on the problem shown. Which TWO of the following strategies will enable the students to solve this problem and build an understanding of proportional reasoning? A. Drawing a picture of 16 blue marbles arranged in groups of 2, drawing 1 red marble for each group of blue marbles, and then counting the red marbles B. Generating a table with pairs of possible numbers of red and blue marbles and verifying that the ratio between the number of red and the number of blue marbles in each pair is equivalent to 1/2 C. Setting a proportion 1/2 = R/16, where R is the number of red marbles, and then teaching how to solve for R D. Showing students that for every 3 marbles, 2 are blue and 1 is red, therefore 2/3 of the marbles in the bag must be blue and 1/3 must be red

A and B

Which THREE of the following teacher actions are most effective for gauging students' understanding of the notions of acute, right, and obtuse angles in order to determine whether further instruction is needed? A. Distributing a work sheet on identifying angles as acute, right, or obtuse to student groups; circulating around the room to check answers as groups are working B. Including problems about identifying angles as acute, right, or obtuse on a unit test; noting the average performance by students on these problems C. Distributing small whiteboards to students; asking them to sketch examples of acute, right, or obtuse angles and hold up their whiteboards D. Sketching three angles on the board at the end of class; telling students to write down whether each angle is acute, right, or obtuse, and turn in their answers before leaving the room

A, C, and D

A teacher noticed that many students were struggling with finding common denominators during a formative assessment on adding fractions. Which of the following will best address this issue? A. Giving the students another assessment on finding common denominators during the next class B. Reviewing the lesson on finding common denominators during the next class C. Recording the grades and moving on to the next section D. Repeating every lesson on adding fractions

B

A teacher plans to define the term "integer" as part of a lesson. Which of the following is most appropriate for the teacher to do next to build students' understanding of the integer concept? A. Defining the opposite of an integer and showing several examples B. Identifying and placing several integers on a number line C. Modeling addition and subtraction of several pairs of integers with chips or counters D. Showing several examples of how to determine the absolute value of an integer

B

During a unit on writing expressions and equations, a fifth-grade teacher asks students to create several verbal statements that can be written as equations. Which of the following verbal statements was most likely created for writing an equation containing the operation of division? A. Twice a certain number is 48. B. The quotient of a number and 3 is 48. C. The sum of a number and twice the number is 48. D. Two more than a number is 48 more than the opposite of the number.

B

The sum of three consecutive even integers is 102. What are the three integers? A teacher asks the students in an algebra class to write an equation to represent the problem situation shown. Which of the following approaches is best for helping the students write an algebraic equation that represents the problem situation? A. Asking the students to highlight keywords "3," "consecutive," "even," and "sum" in the problem and use the keywords to write the expression B. Asking the students to complete a graphic organizer where n is the middle number of three consecutive even integers and find algebraic expressions for the other two integers and the sum C. Asking the students to compute the sums of three consecutive integers, starting with 0 + 2 + 4, then 2 + 4 + 6, etc. D. Asking the students to solve (n − 2) + n + (n + 2) = 102 for n

B

Which of the following activities is most likely to help students build an understanding of how three-dimensional shapes can have the same number of faces while having different numbers of edges or vertices? A. Analyzing and comparing the nets of a cube and a pyramid with a four-sided base B. Analyzing and comparing the nets of a cube and a pyramid with a five-sided base C. Analyzing and comparing the nets of a prism with a four-sided base and a pyramid with a four-sided base D. Analyzing and comparing the nets of a cube and a prism with a four-sided base

B

Which of the following expressions will best demonstrate to students how to use the distributive property to simplify expressions? A. (x^2 + 1) + (x^2 + x + 1) B. (x^2 − 1) − (x^2 + 2x + 1) C. (x^2 − 1) + 1 D. x^2 + x + 1

B

Which THREE of the following strategies are most appropriate to help students understand how to calculate the amount of time, in hours and minutes, that it takes a child to clean a room starting at 3:20 P.M. and finishing at 5:07 P.M.? A. Using a clock face manipulative to count the total number of minutes from 3:07 P.M. to 5:20 P.M., then dividing the total by 60 B. Using a clock face manipulative to count the total number of minutes from 3:20 P.M. to 3:30 P.M., the number of hours and minutes from 3:30 P.M. to 5:00 P.M., and the number of minutes from 5:00 P.M. to 5:07 P.M., then adding the totals together C. Using a clock face manipulative to count the total number of hours and minutes from 3:07 P.M. to 5:07 P.M., then subtracting 13 minutes from the total D. Using a number line to count the number of hours from 3:20 P.M. to 4:20 P.M., the number of minutes from 4:20 P.M. to 4:50 P.M., and the number of minutes from 4:50 P.M. to 5:07 P.M., then adding the totals together

B, C, and D

A teacher asked a student to simplify the expression 5x−3x, and the student gave the answer 2. The teacher asked the student to explain this answer, and the student said, "5 take away 3 is 2, and the x's cancel one another out." Which of the following activities is most likely to help the student understand why this reasoning is incorrect? A. Factoring terms that involve more than one variable B. Subtracting whole number multiples of 3 from whole number multiples of 5 C. Evaluating the expression 5x−3x for several values of x D. Reviewing the statement of the distributive property

C

A teacher plans a class activity for students in which they determine the median family size for all students in the class. Which of the following strategies is most likely to be helpful to the students? A. Adding up all the data entries with a calculator B. Using a graphic organizer to identify the highest and lowest entries C. Entering the data in a spreadsheet so that values can be sorted in ascending or descending order D. Grouping together all entries that are the same

C

A teacher plans a lesson on operations with decimals for a small class. The teacher wants to evaluate student learning at the end of the lesson. Which of the following is an appropriate design for a summative assessment? A. Asking students questions orally to stimulate a student discussion about operations with decimals B. Assigning homework problems and reviewing the answers at the next class meeting C. Giving students a ten-point quiz focusing on operations with decimals D. Having each student create a model for operations with decimals and present it to the class

C

A teacher wants to assess student learning after completing a unit on converting measurements. Which of the following is the most effective assessment for the teacher to use? A. Determining which metric unit is most appropriate to measure the length of a pencil, the length of a classroom door, and the length of a baseball field B. Determining how much more of each ingredient for a recipe is needed if three times the number of people the recipe serves intend to eat the dish C. Determining whether a suitcase meets weight restrictions on an airline flight given the weight of the suitcase in grams and the airline weight limits in kilograms D. Determining the weekly salary of a worker given the worker's hourly rate of pay

C

Which of the following activities will best help students learn about the cross sections formed when a plane intersects a sphere? A. Having students draw several concentric circles and the common center point B. Drawing several circles and ellipses on a whiteboard C. Slicing an orange at different angles D. Having students trace various circular objects, such as coins

C

Which of the following is the most effective way to help students understand why 49×80 equals 3,920? A. Using manipulatives to show that when 49 is added to itself 80 times, the result is 3,920 B. Using manipulatives to show that when 80 is added to itself 49 times, the result is 3,920 C.Using an area model comprised of two adjacent rectangles with sides 80 and 49 and sides 80 and 1, respectively D.Using the algorithm of multiplication to show all partial products, and pointing out that 8×9=72, 8×4=32, 72+320=392, and 392×10=3,920.

C

Which of the following lists of shapes is best for a teacher to use in a lesson in which students identify shapes as two-dimensional or three-dimensional based on their properties? A. Cube, rectangular prism, pyramid, octahedron B. Rhombus, kite, parallelogram, square, rectangle C. Cube, circle, square, sphere, triangle, tetrahedron D. Sphere, cylinder, cone, slanted cone

C

Which of the following word problems is best to use to introduce multiplication of whole numbers to students? A. Five friends are sharing 40 candies so that each person has the same amount. How many candies will each person have? B. Mr. Brennan has only 23 of a box of pencils left. Pencils come in boxes of 30. Does Mr. Brennan have enough pencils that each of his 24 students can have one? C. Alonzo is drawing a picture with stars in which he has 3 rows of stars with 4 stars in each row. How many stars will he need to draw altogether? D. Sophia has 7 pairs of mittens, but she donates 4 pairs and then buys 1 new pair. How many pairs does she have now?

C

1. Start with a table of all counting numbers from 2 through 100. 2. Circle the number 2 and cross out all of the multiples of 2. 3. Circle the next available number that is not crossed out — in this case 3. Then cross out all of the multiples of 3. 4. Continue circling the next available number that is not crossed out, followed by crossing out all of the multiples of that number, until every number through 100 is either circled or crossed out. A fifth-grade math teacher uses the directions above as a class starter to reinforce a lesson previously introduced. Which of the following best describes the content being addressed by the lesson? A. Composite numbers B. Ordinal numbers C. Cardinal numbers D. Prime numbers

D

56 -> 7 and 8 -> 4 and 2 -> 2 and 2 80 -> 8 and 10 -> 4 and 2, 2 and 5 -> 2 and 2 Venn Diagram A teacher organized an activity in which the work shown was presented to students. Which of the following best describes the objective of the activity? A. Identifying odd and even numbers B. Identifying prime and composite numbers C. Practicing multiplying single-digit numbers D. Finding greatest common factors and least common multiples

D

5x = 20, x = 100; x - 2 = 5, x = 3; p + 3 = 6, p = 9; t / 3 = 9, t = 3 A student's work for solving four equations is shown. Which of the following is best for a teacher to have the student review? A. Multiplying whole numbers B. Adding whole numbers C. Using inverse operations with whole numbers D. Applying properties of equality

D

8 / (4 - 1) = 2 - 1 = 1 16(9 + 1) = 144 + 1 = 145 3 + (6 / 3) = 9 / 3 = 3 The work shown is from a student's homework assignment. The student is most likely struggling with which of the following rules for the order of operations? A. Division must be performed before subtraction. B. Multiplication must be performed before addition. C. Operations with exponents must be performed first. D. Operations within parentheses must be performed first.

D

A fair, six-sided number cube has each face labeled with a different number from 1 through 6. The face with the number 3 is relabeled with a 2. How is the likelihood of rolling the cube and getting a number less than 3 affected by the relabeling? (A) Increases the likelihood (B) Decreases the likelihood (C) Does not change the likelihood A teacher uses the question above for a class discussion. Which of the following is best for the teacher to address with this question? A. Reasoning about conditional probability B. Computing probabilities of independent events C. Computing probabilities of mutually exclusive events D. Linking likelihood that an event will occur with probability

D

The amount of money that Daniela has in her pocket is at least 7 dollars more than 3 times the amount of money that Emily has in her pocket. A teacher plans to use the statement shown during a lesson on translating sentences into linear inequalities. Which of the following is best for the teacher to do to help the students write an inequality that correctly models the relationship between the amount of money that Daniela has in her pocket, D, to the amount of money that Emily has in her pocket, E? A. Having students make a table of values for possible amounts of money Daniela and Emily each have in their pockets B. Having students work several practice exercises solving inequalities like 3E + 7 ≤ D for E C. Having students parse the sentence into "Daniela has at least 7 dollars" and "more than 3 times the amount that Emily has" to write D ≥ 7 > 3E D. Having students parse the sentence into "Daniela has," "at least," and "7 dollars more than 3 times the amount that Emily has" to write D ≥ 7 + 3E

D

Which of the following will most likely help students understand the concept of the factors of a whole number? A. Using a stem-and-leaf plot B. Using a factor tree C. Memorizing a multiplication table D. Using rectangular arrays

D