Competency 9

Question 1

22. A survey has found that about 12 of every 500 airline flights are canceled due to bad weather. This ratio is equivalent to which of the following?
A. 1/24 of the flights 
B. 1/240 of the flights 
C. 0.24% of the flights 
D. 2.4% of the flights

Answer 1

D. 2.4% of the flights

Option D is correct because 12 of 500 is equivalent to 2.4%.

Question 2

23. Use the diagrams below to answer the question that follows.
    Bricks are stacked in the pattern shown above. If the pattern continues, how many bricks will there be in a stack that has seven layers?
    A. 27
    B. 28
    C. 35
    D. 36

Answer 2

Option B is correct because according to the figure, there are
7 bricks in the bottom layer and 1 less brick in each of the next layers. If
the pattern continues using these numbers, the result would be 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28. Based on logic, if there were 7 rows, there would be 7 bricks in the bottom row. A visual solution can be created by drawing a stack that has 7 layers and adding up the number of bricks in each layer.

Question 3

24. Students in a third-grade class are playing a board game. On each player’s turn, the player spins a spinner that is divided into four quadrants, as shown below.
    The teacher overhears a student remark, “Since I haven’t spun a four yet, I’ll probably get a four on this turn.” The student has demonstrated a misconception regarding which of the following mathematical concepts?
    A. Rational numbers
    B. Mean and median
    C. Independent events
    D. Even and odd numbers

Answer 3

Option C is correct because independent events are not affected by previous events. So if the student did not get a 4 in the previous rounds of spinning the wheel, there is no guarantee that the student will get a 4 in the next round of spinning.

Question 4

25. A special education teacher provides math instruction in the resource room for individuals and small groups of students who have learning disabilities. When teaching the students, the teacher should follow which of the following instructional guidelines?
    A. Emphasize the use of mathematics in science and technology.
    B. Focus primarily on mathematical concepts that are likely to be useful in everyday life.
    C. Emphasize the role of deductive reasoning in mathematics.
    D. Connect mathematical concepts to concrete examples with which the students are already familiar.

Answer 4

D. Connect mathematical concepts to concrete examples with which the students are already familiar.

Option D is correct because concrete examples using manipulatives help students with disabilities understand the abstract symbolic language of mathematics.

Question 5

26. A third grader with special needs has been having trouble memorizing basic arithmetic facts. The student’s classroom teacher asks the special education teacher’s advice on how to help the student. In general, which of the following suggestions is most important for the special education teacher to give the teacher?
    A. Suspend for the present all mathematical activities other than those aimed directly at memorizing arithmetic facts.
    B. Modify math instruction to focus primarily on the use of manipulatives to build conceptual understanding.
    C. Address the problem now so that lack of automaticity will not impede more advanced math learning later on.
    D. Discontinue memorization of facts in favor of teaching the student to use a calculator efficiently and accurately.

Answer 5

C. Address the problem now so that lack of automaticity will not impede more advanced math learning later on.

Option C is correct because the teacher should introduce a variety of strategies such as flash cards and math games to suit the student’s learning style and provide math fact sheets as an accommodation to help the student solve more advanced math problems.

Question 6

27. In general, math instruction for students with learning disabilities in mathematics should be characterized by
    A. the development of cognitive strategies rather than a mastery of facts.
    B. the development of math process skills.
    C. instructional activities limited to hands-on operations with concrete objects.
    D. a balanced program of concepts, skills and problem solving.

Answer 6

D. a balanced program of concepts, skills and problem solving.

Option D is correct because the general education curriculum consists of a balanced program of concepts, skills, and problem solving, so students with learning disabilities should have access to the same curriculum as their nondisabled peers.

Question 7

28. Joyce and Tyrone, two third graders, are counting how many gallon and quart milk containers have been collected for a class science project. As they count, Tyrone tells Joyce that the gallon container is twice as big as the quart container. Based on his comment, Tyrone needs instruction in understanding the concept of capacity. The teacher can best teach him by
A. asking him if he can think of some method of measurement that will test his statement.
B. pointing out to him that the word “quart” sounds like the word “quarter” and asking him what that suggests about the relative sizes of the two containers.
C. explaining to him that doubling the linear dimensions of a rectangular solid quadruples the volume.
D. having him use a computer to generate two- and three-dimensional models of the containers in question and then identify similarities and differences among the models generated.

Answer 7

A. asking him if he can think of some method of measurement that will test his statement.

Option A is correct because letting the student measure liquid using various methods will allow the student to learn the concept of measurement through hands-on experiments.

Question 8

29. Which of the following is the most appropriate reason to use curriculum-based assessments?
    A. To confirm the students’ grade level
    B. To identify skills that need reteaching
    C. To compare with last year’s test scores
    D. To determine the students’ intellectual ability

Answer 8

B. To identify skills that need reteaching

Option B is correct because a curriculum-based assessment is a direct assessment that links instruction with assessment. It is used to help teachers develop goals for instruction and to evaluate the students’ progress in the curriculum.

Question 9

30. Which of the following is the best activity for reviewing the concept of fractions with fourth-grade students?
    A. Using pictures to model unit fractions of a whole
    B. Drawing pictures of fractions from memory
    C. Writing fractions using numbers
    D. Comparing fractions using a variety of materials

Answer 9

D. Comparing fractions using a variety of materials

Option D is correct because using a variety of concrete materials to reinforce the concept of fractions helps students develop a better understanding of the concept.

Question 10

31. Which of the following is a developmentally appropriate activity for a kindergartner to establish basic number sense?
    A. Completing one-to-one correspondence exercise
    B. Generalizing skills and applying them to new situations C. Arranging ten objects from smallest to largest
    D. Using a calculator to solve simple mathematics problems

Answer 10

A. Completing one-to-one correspondence exercise

Option A is correct because by the age of five, children are able to link the number of objects to the numeral.

Question 11

45. While reading a story, students notice that the wheels on a space vehicle look like the figures shown. A special education teacher can use this teachable moment to have students use tiles to make similar figures.
    Which of the following can the students use to make the figures?
    A. A set of squares
    B. A set of trapezoids
    C. A set of rectangles
    D. A set of hexagons

Answer 11

B. A set of trapezoids

Option B is correct because each of the figures can be made using only trapezoids. The center hexagon can be made from two trapezoids.