Praxis 5008 Math and Science

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?

• A.

  Finding equivalent fractions

• B.

  Finding a common denominator

• C.

  Finding the simplest forms of fractions

• D.

  Finding the least common multiple of the denominators

• E.

  Finding the greatest common factor of the denominators

• 1, 9, 17, 25, 33, 41, 49, 57

Which of the following statements best describes the numbers in the preceding list?

• 
  A.

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

• B.

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

• C.

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

• D.

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

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?

• 
  A.

  Asking students to read the numbers 20 through 29

• B.

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

• C.

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

• D.

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

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?

• 
  A.

  1/3+1/4+1/3

• B.

  1/3+1/4+2/3

• C.

  2/3+2/3+2/32

• D.

  3/5+2/5+2/3

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.

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

• B.

  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?

• C.

  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?

• D.

  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?

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?

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?

• A.

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

• B.

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

• C.

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

• D.

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

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?

• 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.

• 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.

• 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?

• A.

  Reading any three-digit number

• B.

  Writing any three-digit number

• C.

  Mentally adding ten to a 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?

• A.

  James does not know the count sequence.

• B.

  James did not start his count on the correct number.

• 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.