Practice Math - CKT Test Questions

Josh is a third-grade student in Ms. Carter's classroom. Josh's answers to three addition problems are shown. He incorrectly answered the first two problems but correctly answered the third problem. If Josh uses the same strategy to answer the following problem, what will his answer be? 328 + 564 =

8812

Which of the following word problems can be answered by finding the quotient of 3 1/4 and 1/3? Select all that apply. (A) Casey poured 3 1/4 quarts of fruit punch into cups. She filled each cup with 1/3 quart of fruit punch. How many cups did Casey fill? (B) A pump working at a constant rate filled 3 1/4 equal-sized tanks of water in 1/3 hour. At the same rate, how many tanks will the pump fill in 1 hour? (C) Laura uses 1/3 of a piece of ribbon that is 3 1/4 feet long to wrap a present. What is the length of the ribbon she used to wrap the present?

A and B

Mr. Bass is working on defining quadrilaterals with his students. He notices that many students are focused on the number of sides, saying things like "a quadrilateral is a shape with four sides." Which two of the following figures are most likely to support students in refining their definition of quadrilaterals?

A and C

6/2 = 3 | 3 x 2 = 6 21/7 = 3 | 3 x 7 = 21 Mr. Khan's students are discussing the problems shown. Mr. Khan asks his students what relationships they notice in the problems. One student responds with the following conjecture. "I noticed that when you divide by a number and then multiply the result by the same number, you always get back the first number." Provided that division by zero is excluded, for which of the following sets of numbers is the student's conjecture true? Select all that apply. (A) Whole numbers (B) Integers (C) Fractions and decimals

A, B, and C

Which three of the following expressions are equivalent to 3,956 x 4 ? (A) 3,000 x 4 + 900 x 4 + 50 x 4 + 6 x 4 (B) (4,000 x 4 - 100 x 4) + (60 x 4 - 4 x 4) (C) 4 x 3 + 4 x 9 + 4 x 5 + 4 x 6 (D) 4,000 x 4 - 40 x 4 - 4 x 4 (E) 3 ́1,000 x 4 + 95 x 100 x 4 + 6 x 1 x 4

A, B, and D

Ms. Hayes asked her students to calculate the difference 0.7 − 0.07 by converting the decimals into base-ten fractions. One student, Daryl, answered the problem as represented in the work shown. 0.7 - 0.07 = 7/10 - 7/100 = 70/100 - 7/100 = 63/100 = 0.63 Ms. Hayes asked her students to calculate the difference 0.7 − 0.07 by converting the decimals into base-ten fractions. One student, Daryl, answered the problem as represented in the work shown. When Ms. Hayes asked Daryl to explain his strategy, he said, "The answer is 63 hundredths. I wrote the decimals 7 tenths and 7 hundredths as fractions and subtracted them. Since I wanted the denominators to be the same, I added a zero to the first 7 and a zero to 10. 70 hundredths minus 7 hundredths is 63 hundredths." Which of the following changes to Daryl's explanation is best for clarifying the mathematics that underlie his strategy? (A) He should indicate why 0.7 = 7/10 and 0.07 = 7/100. (B) He should point out that (7 x 10) / (10 x 10) = 70 / 100. (C) He should point out that 70/100 - 7/100 = (70 - 7) / 100. (D) He should indicate why 0.63 = 63 / 100.

B

Ms. Dale wants her students to develop mental strategies that can be used to find the answer to addition and subtraction problems, including composing and decomposing numbers based on place value. In one lesson, she asks her students to find numbers whose sum or difference is 28. She then has seven students share their answers as she writes them on the board. Which three of the following student answers are most closely related to Ms. Dale's goal that students will be able to compose and decompose numbers based on place value? (A) 7 + 7 + 7 + 7 (B) 8 + 10 + 10 (C) 14 + 14 (D) 20 + 8 (E) 20 + 10 − 2 (F) 25 + 3 (G) 39−11

B, D, and E

Mr. Keller's sixth-grade class is learning about algebraic equations. In his teachers' edition of the textbook, Mr. Keller finds a page that suggests he ask students to critique the following two solutions to determine whether they are valid. Which of the following is most clearly highlighted by asking students to critique the invalid strategies? (A) Understanding the meaning of the equal sign (B) Understanding the importance of combining like terms (C) Understanding the use of properties of operations to simplify expressions (D) Understanding the use of inverse operations to solve equations

BB

Dora made a pile of 5 counters. Then Mr. Levy asked her to add counters to her pile of 5 so that the pile would have 7 counters. Dora counted out 7 more counters and added them to the pile of 5 counters. Which of the following most likely explains the reason behind Dora's error? (A) Dora does not fully understand one-to- one correspondence between numbers and objects. (B) Dora does not yet have a concept of the quantity 7. (C) Dora does not yet understand that one quantity can be composed of two smaller quantities. (D) Dora does not yet know her number facts for sums greater than 10.

C

Ms. Howe's students are learning how to use models to help them answer word problems. The models use bars to represent the relationships between the given quantities and the unknown quantity. In each model, the unknown quantity is represented with a question mark. The quantities given in the word problem will occupy the other boxes. Ms. Howe presents the following word problem to her students. "Max had $24. He gave 1/3 of his money to Sarah and the rest to Olivia. How much money did he give to Olivia?" Which of the following models best corresponds to the given word problem?

C

"Rosana had a total of 9 shirts. She gave 2 to Emily. How many shirts does Rosana have now?" Which of the following problems has the same mathematical structure as the problem above? (A) Rosana used 7 paint colors for her project. Emily used 2 different paint colors for her project. How many paint colors did Rosana and Emily use together? (B) Rosana has some books. She bought 1 more book. Now she has 8 books. How many books did Rosana start with? (C) Rosana has a total of 3 stickers. Emily has 6 more stickers than Rosana. How many stickers does Emily have? (D) Rosana brought 5 cookies for lunch. How many cookies did she have after she ate 4 of the cookies?

D

A student found an incorrect answer to the problem 3/4 + 5/6. The student's answer is represented in the work shown. 3/4 + 5/6 = 9/12 + 10/12 = 19/24" Which of the following student work samples shows work that is most similar to the preceding work? (A) 3/8 + 2/3 = 3/24 + 2/24 = 5/24 (B) 4/5 + 1/2 = 16/20 + 10/20 = 26/20 (C) 5/7 + 3/4 = 9/11 + 10/11 = 19/22 (D) 1/2 + 7/9 = 9/18 + 14/18 = 23/36

D

Ms. Kress asked her students to compare 1/3 and 7/8. Four of her students correctly answered that 7/8 is greater than 1/3, but they gave different explanations when asked to describe their strategies to the class. Indicate whether each of the following student explanations provides evidence of a mathematically valid strategy for comparing 1/3 and 7/8.

The first and fourth explanations do not provide evidence of a mathematically valid strategy for comparing 1/3 and 7/8, but the second and third explanations do.