One of Mr. Terry’s students, Yvonne, found the answer to the problem 3/8×2/9 as represented in the following work. When Mr. Terry asked Yvonne to explain her work, she said, “It’s easier to just switch the numerators to make simpler fractions.” Which of the following statements is true of Yvonne’s strategy?

C. Yvonne’s strategy can be used to rewrite any product of two fractions, but it will not always result in fractions that can be simplified.

A. Yvonne’s strategy can only be used to rewrite products of fractions where the difference between the numerators is 1 and the difference between the denominators is 1.

B. Yvonne’s strategy can only be used to rewrite products of fractions where both fractions are less than 1.

D. Yvonne’s strategy can be used to rewrite any product of two fractions, and it will always result in fractions that can be simplified.

Ms. Hammonds asked one of her students, John, to write the number five hundred. John wrote “500” in his workbook. Next, Ms. Hammonds asked John to write the number that is ten more than five hundred. John immediately said, “Five hundred ten,” and wrote “50010” in his workbook. Which of the following mathematical skills is most evident in John’s response?

C. Mentally adding ten to a three-digit number

A. Reading any three-digit number

B. Writing any three-digit number

D. Understanding the value of the digits in a three-digit number

Ms. Lee is teaching her first graders addition and subtraction within 20 by counting. She has her students work individually on finding the answer to 7+5. During the whole-class discussion of the answer to the problem, James says, “I think 7 plus 5 equals 11, because I counted 7, 8, 9, 10, 11.” James puts up a finger each time he says a number in the sequence. Which of the following statements most likely explains the reason behind James’s error?

B. James did not start his count on the correct number.

A. James does not know the count sequence.

C. James does not understand that the last count word indicates the amount of the set.

D. James does not know how to decompose numbers greater than 10 into tens and ones.

Which TWO of the following word problems can be answered by dividing 4 by 1/5?

C. Each person at a dinner was served 1/5 of a fish fillet. A total of 4 fish fillets were served. How many people were served at the dinner?

D. A roll of copper wire that was 4 meters long was cut into sections that were each 1/5 meter long. How many sections were made from the roll of copper wire?

A. A quilt requires 1/5 square meter of purple cloth. How many square meters of purple cloth are needed for 4 of these quilts?

B. A machine working at a constant rate takes an hour to sort 4 bins of mail. How many bins of mail does the machine sort in 1/5 hour?

E. Each of 4 people in a study group read 1/5 of the total chapters in a book. No student read the same chapter as any other student. What fraction of the total chapters in the book did the study group read?

Mr. Bennett’s class was discussing strategies for adding whole numbers. One student, Katie, said, “When I add two numbers, I get the same answer as when the numbers switch places.” Mr. Bennett asked his students to explain why Katie’s claim is true when adding any two whole numbers. After giving the class time to work, he asked another student, Joel, to present his explanation. Joel said, “If the answer is a little number like 4, then 2 plus 2 is the same either way. And if the answer is a big number like 400, then 200 plus 200 is the same either way.” Which of the following statements best characterizes Joel’s explanation?

C. It neither gives useful examples for showing that Katie’s claim is true, nor does it establish in general why her claim is true.

A. It clearly explains why Katie’s claim is true when adding any two whole numbers.

B. It assumes that Katie’s claim is true, but it does not establish in general why her claim is true.

D. It gives only two examples that show that Katie’s claim is true, but more examples are needed to establish in general why her claim is true.

Ms. Chambers writes the following equation on the board. 5×19−40=40−5×19 Ms. Chambers asks her students to determine if the equation is true. One student says, “The equation is true because on both sides of the equation, you subtract after you multiply 5 times 19.” Which of the following statements most likely gives the reason underlying the student’s error?

D. The student has overgeneralized by applying the commutative property to subtraction.

A. The student disregarded the order of operations.

B. The student incorrectly applied the associative property.

C. The student does not understand the meaning of the equal sign.

A student is asked to compare three pairs of decimal numbers. The student correctly states that 0.59 is less than 0.721. The student correctly states that 0.96 is greater than 0.008. The student incorrectly states that 0.7 is less than 0.021. Which of the following misconceptions most likely explains the student’s answers?

A. The student is comparing decimals as if they are whole numbers.

B. The student is assuming the longer decimal will always be the greater decimal.

C. The student thinks that the decimal with more zeros will always be the greater decimal.

D. The student thinks that the decimal with the larger digit in the rightmost place will always be the greater decimal.

Mr. Varela asked his students to define a square in terms of other two-dimensional geometric figures. Which TWO of the following student definitions precisely define a square?

A. A square is a rectangle that has 4 sides of equal length.

D. A square is a rhombus that is also a rectangle.

B. A square is a parallelogram that has 4 angles of equal measure.

C. A square is a parallelogram that has 4 sides of equal length.

E. A square is a rectangle that is not a rhombus.

Ms. Lussier asked one of her students, Matthew, to explain how he found the answer to the subtraction problem 54−37. Matthew explained his answer as follows. “I didn’t want to have to trade, so I added 3 to 54 so I would have 7 like in 37. Then I added 3 to 37 to keep the problem the same, but now I have 57 minus 40 so I just do 7 minus 0 and 5 minus 4.” Which of the following statements best characterizes Matthew’s strategy for finding the answer to two-digit subtraction problems?

C. Matthew’s strategy is valid, but it will not always provide an equivalent subtraction problem where the ones digit of the number to be subtracted is less than the ones digit of the number from which to subtract.

A. Matthew’s strategy is not valid because he solved a different subtraction problem than the one given.

B. Matthew’s strategy is not valid because it can only be used when the ones digit of the number to be subtracted is greater than the ones digit of the number from which to subtract.

D. Matthew’s strategy is valid, and it will always provide an equivalent subtraction problem where the ones digit of the number to be subtracted is less than the ones digit of the number from which to subtract.

While Mr. Lynch’s students were working on finding the answer to the problem 5/6÷1/3, one student, Maggie, said the following. “I think that fraction division works just like fraction multiplication. You can divide the numerators and the denominators to find the answer. Like in this problem, 5 divided by 1 is 5, and 6 divided by 3 is 2, so the answer is 5 over 2.” Which of the following is true of Maggie’s conjecture about fraction division?

C. Maggie’s conjecture is true for all fraction division problems, but in some problems, the resulting quotients from the numerators and denominators will not be whole numbers.

A. Maggie’s conjecture is not true, because her method did not produce the correct answer to the problem.

B. Maggie’s conjecture is not true, because division of fractions requires multiplying by the reciprocal of the second fraction.

D. Maggie’s conjecture is partially true. Her method gave the correct answer in this problem because the denominators and numerators divided evenly, but the method will not give the correct answer in other problems.

In a classroom activity using images of the night sky, a teacher helps the students observe that the positions of stars seen in the summer at 11 P.M. are different than those seen in the winter at the same time. Which of the following statements best helps explain the observation?

A. Earth revolves around the Sun.

B. The Moon revolves around Earth.

C. Constellations are moving away from Earth.

D. Constellations revolve around Earth.

An elementary school class has been learning about how animals can change the environment to meet their needs. After viewing a video of a beaver building a dam, the students are asked to explain how changing its environment helps the beaver to support its needs. Their explanation needs to be supported by evidence. Which explanation responds to the teacher’s direction and is most likely to be supported by evidence from a video about beavers?

D. “Because the beaver lives in a lodge in the lake formed by the dam, it is protected from predators.”

A. “When the dam is built, the flow of water in the river changes, and a lake is formed.”

B. “Dams are good for beavers, and beavers that build dams are better off than beavers without dams."

C. “Beavers are very good swimmers and can stay underwater for long periods of time.”

A student investigated whether matter is conserved during a change of state. The student weighed an empty glass beaker and then filled it with water before weighing it again to determine the weight of the water. The student then poured the water from the beaker into an ice-cube tray and placed it in a freezer. The student later removed the ice cubes from the tray and weighed them. After repeating the procedure five times, the student found that the weight of the ice cubes was slightly less than the initial weight of the water. The student concluded that freezing the water reduced its mass. Which of the following modifications to the procedure would best remove the error that affected the student’s data?

B. Weighing the water after it is placed in the tray and the ice cubes before they are removed from the tray

A. Removing the water from the beaker and the ice cubes from the tray using a spatula

C. Repeating the experiment three times instead of five times

D. Drying the beaker and ice-cube tray with a paper towel before water is added

Which of the following activities would best introduce students to a method of erosion control?

D. Students are presented with two trays of soil set at a slight angle, one containing growing grass. The students pour water on both samples and compare the amounts of soil lost.

A. Students form mounds of soil that vary in height. After pouring water on the mounds, they compare the amount of erosion in each sample.

B. Students blow through a straw on a tray of sand. They blow with varying force and compare the amount of sand that is blown away after each test.

C. Students pour a different amount of water onto each of three identical trays of soil set at various slope angles, graphing the relationship between the amount of runoff and the slope angle.

Students are studying various aspects of magnetism. Which of the following questions should upper-elementary students be able to answer experimentally with classroom resources?

A. What would cause a compass to not point to the north?

B. Why do all magnets have a north and south pole?

C. Is navigation using a compass more accurate than using the Sun and stars?

D. Why are magnets made of particular materials?

During a class demonstration, a teacher floats a small toy boat in the center of a long, narrow rectangular tank filled with water. Initially, the water is still and the boat is not moving. The teacher asks students to predict what will happen if they use their hand to create a wave crest that travels toward the other end of the tank. A student predicts that the boat will be carried by the wave to the other end of the tank. Which of the following statements indicates a misconception that the student most likely has about water waves?

C. Water particles at the surface move along the surface with the wave.

A. Water waves get smaller as they get further away.

B. Water waves transfer energy from one location to another.

D. Water waves slow down when they encounter an obstacle.

Mr. Wilson’s upper elementary class is researching the positive and negative effects of pesticide and herbicide use in local agriculture. The class has already spent many hours searching on the Internet but has collected very little information. He would like to provide two additional opportunities for the students to collect information that would be the most useful. Which TWO activities would provide the best opportunities to collect useful information?

C. Mr. Wilson can meet with the school librarian, outlining his objectives and requirements. He can then bring his class to the library for several research periods after the librarian has had a chance to collect and lay out relevant journals, newspapers, and books.

D. Mr. Wilson can schedule a panel discussion with representatives from the Environmental Protection Agency, United States Department of Agriculture, and the local extension service. They can provide materials that may not be available on the Internet, provide suggestions for additional resources, and answer student questions.

A. Mr. Wilson can schedule a trip to a local soybean farm. The students will tour the farm and interview the farmer for information on his farming practices.

B. Mr. Wilson can schedule a trip to a pesticide production plant. The students will have a chance to interview the scientists employed by the company and receive materials that may not be present on the Internet.

Praxis 5008 Math and Science

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MULTIPLE SELECT QUESTION

45 sec • 1 pt

Ms. O’Neil asked her students to find the sum five sixths plus seven tenths, plus two fifteenths56+710+21556+710+215. One student found the sum as represented in the following work.
The figure shows a student's work. The work is as follows. Five sixths plus seven tenths, plus two fifteenths, equals the fraction with numerator 25 plus 21, plus 4, and denominator 30, which equals the fraction 50 over 30.
End figure description.
Which THREE of the following mathematical strategies were used in the student’s process?

Finding equivalent fractions

Finding a common denominator

Finding the simplest forms of fractions

Finding the least common multiple of the denominators

Finding the greatest common factor of the denominators

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

1, 9, 17, 25, 33, 41, 49, 57
Which of the following statements best describes the numbers in the preceding list?

All whole numbers that are not divisible by 4 and are less than 60

All whole numbers that are not divisible by 8 and are less than 60

All whole numbers that are less than 60 and have a remainder of 1 when divided by 4

All whole numbers that are less than 60 and have a remainder of 1 when divided by 8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Ms. Simeone is working with her first-grade students on writing two-digit numerals. She wants to use an activity to assess whether her students are attending to the left-to-right directionality of the number system.
Which of the following activities is best aligned with Ms. Simeone’s purpose?

Asking students to read the numbers 20 through 29

Asking students to represent the numbers 35 and 53 using base-10 blocks

Asking students how many tens and how many ones are in the number 33

Showing students 23 cubes and 32 cubes and asking them which quantity is greater

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Ms. Marley is working with her students on fraction addition. She wants to highlight how the commutative property of addition can be used to make landmark numbers when adding fractions.
Which of the following expressions best highlights the use of the commutative property of addition for this purpose?

1/3+1/4+1/3

1/3+1/4+2/3

2/3+2/3+2/32

3/5+2/5+2/3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In word problems that have a multiplicative comparison problem structure, two different sets are compared, and one of the sets consists of multiple copies of the other set.
Which of the following best illustrates a word problem that has a multiplicative comparison problem structure?

There are 4 shelves in Joaquin’s bookcase, and there are 28 books on each shelf. How many books are in Joaquin’s bookcase?

Marcus drives 3 times as many miles to get to work as Hannah does. Hannah drives 16 miles to get to work. How many miles does Marcus drive to get to work?

A football field is 360 feet long and 160 feet wide. A soccer field is 300 feet long and 150 feet wide. The area of the football field is how many square feet greater than the area of the soccer field?

An ice cream parlor sells 29 different flavors of ice cream and 4 different types of cones. How many different combinations consisting of an ice cream flavor and a type of cone are available at the ice cream parlor?

OPEN ENDED QUESTION

3 mins • 1 pt

A student uses cubes to build a rectangular solid. Each of the cubes has a side length of 1 1/2 inch. The rectangular solid has a length of 4 inches, a width of 3 inches, and a height of 2 and 1 1/2 inches.
How many cubes does the student use to build the rectangular solid?

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Ms. Karp gives each of her students 24 counters. She asks the students to count the number of counters each of them has and to write the number on their worksheets. All the students write “24” on their worksheets. Next, she asks the students to explain the meaning of the 2 and the 4 in “24.”
Which of the following student explanations provides the most evidence of place-value understanding?

The 2 is in the tens place and the 4 is in the ones place.

The 2 is twenty counters and the 4 is four single counters.

The 2 is two groups of ten counters and the 4 is four counters.

The 2 is two counters and the 4 is four counters, and so it’s twenty-four.

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Praxis 5008 Math and Science

1, 9, 17, 25, 33, 41, 49, 57Which of the following statements best describes the numbers in the preceding list?

Ms. Simeone is working with her first-grade students on writing two-digit numerals. She wants to use an activity to assess whether her students are attending to the left-to-right directionality of the number system.Which of the following activities is best aligned with Ms. Simeone’s purpose?

In word problems that have a multiplicative comparison problem structure, two different sets are compared, and one of the sets consists of multiple copies of the other set.Which of the following best illustrates a word problem that has a multiplicative comparison problem structure?

A student uses cubes to build a rectangular solid. Each of the cubes has a side length of 1 1/2 inch. The rectangular solid has a length of 4 inches, a width of 3 inches, and a height of 2 and 1 1/2 inches.How many cubes does the student use to build the rectangular solid?

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Education

1, 9, 17, 25, 33, 41, 49, 57
Which of the following statements best describes the numbers in the preceding list?

Ms. Simeone is working with her first-grade students on writing two-digit numerals. She wants to use an activity to assess whether her students are attending to the left-to-right directionality of the number system.
Which of the following activities is best aligned with Ms. Simeone’s purpose?

In word problems that have a multiplicative comparison problem structure, two different sets are compared, and one of the sets consists of multiple copies of the other set.
Which of the following best illustrates a word problem that has a multiplicative comparison problem structure?

A student uses cubes to build a rectangular solid. Each of the cubes has a side length of 1 1/2 inch. The rectangular solid has a length of 4 inches, a width of 3 inches, and a height of 2 and 1 1/2 inches.
How many cubes does the student use to build the rectangular solid?