Mathematics CKT Sample Test Questions

4. Josh is a third-grade student in Ms. Carter's classroom. Josh's answer 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?

8812 Content knowledge Type: Task of Teaching Mathematics: Topic:

6 , 2 = 3 3 ' 2 = 6 21 , 7 = 3 3 ' 7 = 21 Mr. Khan's Are discussing the problem shown. Mr. Khan Asks his students what relations they notice in the problems. One Student Response with the following conjecture. Provided that division by zero is excluded, for which of the following sets of number is the student conjecture true? Select all that apply. A.Whole numbers B. Integers C. Fractions and decimals

A B C Content knowledge Type: Task of Teaching Mathematics: Topic:

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 values. In one lesson, she asked her students to find numbers whose whole 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 students' answers are most likely related to Miss Dale's goal that the 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 E Content knowledge Type: Task of Teaching Mathematics: Topic:

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 definitions of quadrilaterals

A C

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 a 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 size 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 a present?

A and B Content knowledge Type: Word of the student curriculum Task of Teaching Mathematics: not applicable Topic: III. Fractions, Operations with Fractions, and Ratios

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

A, B, D Content knowledge Type: Word of the student curriculum Task of Teaching Mathematics: not applicable Topic: II. place value and decimals

Miss Hayes asked her students to calculate the difference between 0.7 - 0.07 by converting the decimals into base 10 fractions. 1 students, Darrell, answered the problem is represented in the work shown: 0.7 -0.07 = 7/10 - 7/100 = 70/100 - 7/100 = 63/100 = 0.63 When Miss hangs a sterile to explain his tragedy, he says, that answer is 63 hundredths. . I wrote the decimal 7 tenths and 7 hundredths as a fraction and subtracted them. Since I wanted the denominators to be the same, I added a zero to the first 7 and zero to 10. 70 hundredths minus 7 hundredths is 63 hundredths. Which of the following changes to Darrell's explanation is the best for clarifying the mathematics that underlines his strategy? A.He should indicate why 0.7 =7/10 and 0.07 =7/100 B. he should point out that 7 ' 10/10 ' 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 Content knowledge Type: Task of Teaching Mathematics: Topic:

Mr. Keller's 6th grade class is learning about algebraic equations. In his teacher edition of the textbook, mr. Keller finds a page that has suggestions he ask students to critique the following two solutions to determine whether they are valid. Which of the following is most likely highlighted by asking the students to critique the Invalid strategies? A. Understanding the meaning of 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

B Content knowledge Type: Task of Teaching Mathematics: Topic:

Miss howl students are learning how to use models to help them answer word problems. The models use bars to represent relationships between the given quantities and the unknown quality. And each model, the unknown quality is represented with question marks. The quantities even in the word problem will occupy the other boxes. Miss howl presents the following word problem to her students. Max has 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 with a given word problem?

C

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 the sums greater than 10

C Content knowledge Type: Task of Teaching Mathematics: Topic:

Rosa had a total of 9 shirts. She gave two to Emily. How many shirts does Rosa have now? Which of the following problems has the same mathematical structure as the problem above? A. Rose U7 paint colors for her project. Emily used two different paint colors for her project. How many paint colors did Rose and Emily use together? B. Rose had some books. She brought one more book. Now she has eight books. How many books did Rose start with? C. Rose had a total of three stickers Emily has 6 more stickers than Rose. How many stickers does Emily have? D. Rose of 5 cookies for lunch. How many cookies did she have after she ate four of these cookies?

D Content knowledge Type: Task of Teaching Mathematics: Topic:

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 + ¾ = 9/11 + 10/11 = 19/22 D.1/2 + 7/9 = 9/18 + 14/18 = 23/36

D Content knowledge Type: Task of Teaching Mathematics: Topic: