Praxis 2 5017 Form 1 Mathematics

"A retailer wants to determine the size most often purchases of a certain type of children's shoe to ensure that enough of that item is available to meet consumer demand. Sizes sold last month: 2, 2, 2, 3, 5, 5, 7, 8" A fifth-grade teacher poses the question above to the class during a lesson. The lesson most likely addresses which of the following concepts? A. Mode B. Median C. Mean D. Range

A

30 ÷ 6 53 ÷ 7 84 ÷ 8 75 ÷ 9 Third graders studying division were asked to solve and check the four division problems above and then write a story for each problem. Which of the following is the most likely reason for asking the students to write the stories? A. To have students demonstrate that division can mean partitioning a set of objects B. To have students practice division skills through drill-and-check exercises C. To help students write quotients that might contain a decimal D. To have students practice the strategy of solving a simpler problem than those presented

A

A teacher provides students with a list of all the numbers from 2 through 46, as shown. Which of the following activities will best help students develop an understanding of the concept of prime numbers? A. Circle 2 and cross out all multiples of 2. Then circle the next largest remaining number and cross out all multiples of that number. Repeat this procedure. B. Cross out 2 and circle 3. Cross out 4 and circle 5. Continue crossing out the next largest number and circling the number adjacent to it. C. Make a list of all the numbers that divide 2. Then add to the list any numbers that divide 3 that are not in the list. Continue expanding the list by considering the divisors of each successively larger number. D. Separate the even numbers and the odd numbers into two lists. Make a list of every number that will divide both an even and an odd number.

A

Fred, a student in a math class, showed the following solutions for two problems. Problem: Dan cooked 60 of the 200 burgers at a company picnic. What percent of the burgers did he cook? Work: 200 × 0.60 = 120 Answer: 120% Problem: Tara watered 50 of the 180 plants in her mother's garden. What percent of the plants did she water? Work: 180 × 0.50 = 90 Answer: 90% Which of the following strategies could best help the student check answers to word problems and look for errors? A. Estimate the answer first, use an algorithm, and compare results. B. Practice multiplication with decimals outside the context of a word problem. C. Multiply the first digits and add the appropriate number of zeros. D. Complete the multiplication, then use division to check the answer.

A

Which of the following is the most appropriate strategy to use when first teaching primary-grade students the mathematical concept of regrouping? A. Using manipulatives and concrete materials B. Presenting mathematics problems devised from newspaper articles and advertisements C. Lecturing and allowing time for questions and answers D. Having students write a story about regrouping

A

While teaching a unit on plotting points in the xy-coordinate plane, Ms. Santos noticed that some students were confusing the x-coordinate with the y-coordinate. Which of the following strategies will help these students correctly plot points? A. Beginning at the origin and moving right or left the number of units of the first coordinate of the point, then moving up or down the number of units of the second coordinate of the point B. Beginning at the origin and moving up or down the number of units of the first coordinate of the point, then moving right or left the number of units of the second coordinate of the point C. Beginning at the first coordinate of the point on the y-axis and moving up and down the number of units of the second coordinate of the point D. Beginning at the first coordinate of the point on the x-axis and moving right and left the number of units of the second coordinate of the point

A

2/3x + 4(-3 - x) = 1/2(-x + 1) - 3 Which TWO of the following are the most helpful to teach students to use as a first step in solving the equation shown? A. Using the distributive property of multiplication over addition to distribute 4(-3 - x) and 1/2(-x + 1) B. Multiplying both sides of the equation by 6 to eliminate all fractions C. Adding 2/3x and -x on the left side of the equation to combine the variable terms D. Subtracting 4(-3 - x) from each side of the equation to move all the x terms to one side of the equation

A and B

"Two whole pizzas of the same size are shared equally among three people. What is each person's share of pizza?" A teacher gives the word problem shown to a fifth-grade class. Which THREE of the following concepts are most likely addressed by the use of the word problem? A. 2/3 is the same as 2×1/3 B. 2÷3 is the same as 2/3 C. Division is thought of as repeated subtraction. D. Division is thought of as a partitioning.

A, B, and D

To facilitate student ability in displaying and analyzing categorical data, a teacher gives each student in a third-grade class a collection of interlocking cubes in four different colors. The teacher uses a piece of grid paper to demonstrate how to construct a bar graph by stacking the cubes according to color and placing them along the horizontal axis of the grid paper. Which of the following questions are appropriate for the teacher to ask the students in reference to the data display? Select all that apply. A. What is the total number of cubes in the collection? B. Which color occurs most frequently in the collection? C. Of the cubes, which of the four colors is the class favorite? D. How many more cubes of the color that is most represented are there than the color that is least represented in the collection?

A, B, and D

"Leo has five fewer magnets than Su-Ling." A teacher in a fifth-grade math class asks the students to write an equation in two variables that represents the word problem shown. Many students write an incorrect equation. Which of the following strategies will best help the students learn how to write a correct equation? A. Translating each word into a symbol or operation as the sentence is read left to right B. Writing pairs of numbers that make the problem statement true and identifying a pattern in the numbers before using variables C. Representing the number of magnets one person has by using a variable and then representing the number of magnets the other person has using the same variable D. Using counters to represent the number of magnets Leo has and taking away five to get the number of magnets Su-Ling has

B

25÷10=N A third-grade teacher asks students to write a word problem for the number sentence above, where N is the exact answer to the problem. Which of the following student responses best satisfies the conditions set by the teacher? A. A team of 10 students wins 25 movie tickets. How many tickets will each student get? B. Ten students tied for the winning prize of $25 in a contest. How many dollars will each student receive? C. Twenty-five children at a birthday party will eat 10 pizzas. How many slices will each child have? D. A tub of paint holds 25 gallons. How many 10-pint cans can be completely filled with paint before the tub is empty?

B

A fourth-grade class is discussing the problem shown. "Sid is traveling by train from Little City to Big City. The train departs Little city at 8:30 AM and arrives in Big City at 9:15 PM. How long does it take the train to travel from Little City to Big City?" During the discussion, one student says, "All you have to do is subtract 830 from 915, and you have the answer! It's 85 minutes." For which of the following reasons is the student incorrect? A. The student did not consider how fast the train was traveling. B. The student used an inappropriate number-base system to calculate elapsed time. C. The student did not consider the distance between the cities. D. The student made a subtraction error in calculating elapsed time.

B

A fourth-grade teacher uses a group activity to introduce a unit. During the activity, the students in each group find all the factors of several numbers. Students then sort the numbers by writing any number with only two factors on one sheet of paper and any number with more than two factors on another sheet of paper. What is most likely the purpose of the activity? A. To determine the number of factors for numbers B. To distinguish between prime and composite numbers C. To develop the concept of greatest common factor for numbers D. To find and use factor trees for numbers

B

Fifth-grade students create Table A to represent the number of sandwiches they each ate during the last month. The teacher then shows the students that redistributing the pictures of sandwiches equally among the students creates Table B. The activity will best help students understand which of the following mathematical concepts? A. Probability B. Mean C. Range D. Proportions

B

Students place unit cubes in a rectangular solid until the base is covered. Students continue adding layers of cubes until the solid is filled to the top. Which of the following concepts does the activity address? A. Area B. Volume C. Perimeter D. Circumference

B

To introduce students to geometry, a first-grade teacher selects a variety of classroom objects having different shapes and passes them to the students. Which of the following concepts is most appropriate for the students to explore? A. Measurement of angles B. Plane and solid figures C. Area and perimeter D. Reflection and rotation

B

Which of the following activities will best help kindergarten students understand the concept of negative numbers? A. Watching a needle on a dial that shows how fast a wheel is turning B. Using a thermometer to illustrate extreme temperatures recorded at the South Pole C. Moving the hands of a clock back an hour at the beginning of daylight saving time D. Placing money from a change purse into a piggy bank

B

A fifth-grade teacher has students cut some two-dimensional shapes from paper and then fold them into three-dimensional figures. Which of the following concepts are the students most likely exploring? A. Rotations B. Reflections C. Nets D. Tessellations

C

A teacher arranges 12 tiles on two rows, as shown above, and then asks a student if one of the rows has more tiles than the other. Pointing to the bottom row, the student says, "There's more here." The response suggests that the student does not yet understand the concept of A. ordering B. sequencing C. equivalent sets D. counting by doubles

C

Alex and Juanita have a total of 10 apples. If the number of apples that Alex has is 2 less than the number of apples that Juanita has, what is the number of apples that Alex has? A sixth-grade teacher wants students to write equations from a given context such as the word problem shown. Which of the following strategies will best help students to translate the word problem into an equation? A. Asking students to make a graph of the situation B. Asking students to guess and test different number pairs C. Asking students to model the situation with hypothetical numerical expressions D. Asking students to find an answer to the word problem before writing the equation

C

Students in a fourth-grade class are asked to find the length of the line segment shown. A common incorrect answer given by fourth graders is 4 inches. A teacher who is developing a lesson plan on measurement wants to help students avoid the misconception that results in the incorrect answer. Which of the following tasks is best for the teacher to include in the lesson plan? A. Completing a table with the lengths of several different objects and comparing the objects based on their measurable attributes B. Using a piece of string that is the length of the line segment to measure the length of different objects around the room C. Creating and using homemade rulers that use unit models of length so students realize that the spaces on the rulers are more important than the marks on the rulers D. Using a ruler to measure pictures of objects

C

The Evergreen Shoe Factory received an order for 100 pairs of shoes. The factory ships shoes in cartons that each holds up to 12 pairs. How many cartons will the factory need to ship this order? Most of the fourth graders who worked on the problem above gave answers such as 8 R4, 8.333, and 8 1/3. These responses suggest that the students need practice in A. rounding down B. expressing remainders C. applying number sense D. using fractions rather than decimals

C

The expression 2w+3 represents the difference, in dollars, between Jane's savings and Eve's savings after w weeks of saving for a trip. Which of the following must be used to determine the value of the difference between Jane's savings and Eve's savings after three weeks? A. The associative property B. The distributive property C. Substitution D. Multiplicative inverse

C

The following three lesson summaries share a common objective: The students will understand and solve multiplication problems with accuracy and efficiency. Lesson 1: Students create and test their own strategy, often mentally, to find an answer to a given multiplication word problem. Lesson 2: Students practice using the traditional algorithm to find an answer to a given multiplication word problem. Lesson 3: Students use a variety of concrete models to find an answer to a given multiplication word problem. Which sequence of the lessons will best support the stated objective? A. 1, 3, 2 B. 2, 3, 1 C. 3, 1, 2 D. 2, 1, 3

C

Which of the following is most important for a student to consider before creating a net of a geometric solid? A. The number of cubes with sides of unit length that can fit inside the geometric solid B. The number of vertices of the geometric solid C. The shape of each face of the geometric solid and where the faces can be connected D. The total surface area of the geometric solid

C

"While traveling through Belgium, Sam purchases gasoline at a price of 1.60 euros per liter. If there are 3.79 liters per gallon and at that time, 0.74 euros per dollar, what is the price of gasoline in dollars per gallon?" Ms. Samuels presented the question shown to her class. Which of the following strategies will best help the students understand how to solve the problem? A. Making two graphs that show the conversions from euros to dollars and liters to gallons B. Making two tables that show the conversions from euros to dollars and liters to gallons C. Showing the multiplication and division of each unit rate; i.e., euros/liters × liters/gallons ÷ dollars/euros = dollars/gallons D. Finding the new ratio in parts; i.e., first euros/liters × liters/gallons = euros/gallons, then euros/gallons × dollars/euros = dollars/gallons

D

29×57 Before students in a fifth-grade class solve the problem above, the teacher has them use mental mathematics to compute 9×7, 20×7, 9×50, and 20×50. For which of the following reasons is it appropriate to have the students use mental mathematics that way? A. To reinforce the connection between multiplication and addition B. To practice rounding to the nearest 10 C. To introduce the associative property of multiplication D. To recall the partial products used in the algorithm

D

4 2 284 x 27 __________ 1888 + 5680 __________ 7,568 A teacher shows students the problem above and asks them to identify the first error that occurs in the solution. Which of the following student answers is correct? A. The sum in the ones column is incorrect. B. There is an addition mistake in the tens column. C. The number of tens that were composed from ones is incorrect. D. The number of hundreds that were composed from tens in incorrect.

D

A kindergarten teacher shows students how to count objects in a set and then represent the number of objects with a numeral. The activity best fosters students' understanding of which of the following mathematical concepts? A. Identifying patterns and relationships B. Recognizing and naming numbers C. Comparing two- and three-dimensional shapes D. Applying the cardinality principle

D

A math teacher shows students the three chains of pattern blocks in the figure and then asks the students to find a pattern that will produce the perimeter of a chain made with any number of pattern blocks. Which of the following is best for the teacher to use for showing the students how to write a linear equation for the perimeter? Number of Hexagons / Perimeter A. 1 / 6 2 /10 3 /14 B. 1 / 6 2 / 6 + 4 3 / 6 + 8 C. 1 / 6 2 / 10 = 6 + 4 3 / 14 = 6 + 4 + 4 D. 1 / 6 2 / 10 = 6 + (2 - 1) x 4 3 / 14 = 6 + (3 - 1) x 4

D

Which of the following is best to do as part of a formative assessment that is given to evaluate students' levels of understanding? A. Have students revisit assignments after they have been graded to find and correct mistakes B. Praise students for discovering the correct solution to a problem C. Give cumulative assessments at the end of each teaching unit D. Hold student and teacher discussions on how to improve learning

D