Certify Teacher EC-6 (391) Mathematics (902)

What is the probability of getting at least two tails in tossing three coins?

0.5

Which choice is a real number?

0^1

The teacher shows the students the following model using algebra tiles. 1 1 X X 1 1 The teacher instructs the class to form a rectangle with the tiles. X 1 1 X 1 1 Write an equation that gives the factors and the area of the rectangle.

2(x+2) = 2x + 4

Students are building stair steps using cubic blocks. The diagram below shows how the students are arranging the blocks to build the steps. 1 block = 1 step 3 blocks = 2 steps 6 blocks = 3 steps If the pattern continues, what is the total number of cubic blocks needed to build 6 steps?

21

The following net is for a _____. (Image of a hexagon)

Hexagonal pyramid

Workers at a local factory make $8, $10, or $12.50 per hour. Each receives a $50 weekly gas allowance. Let h=hours and r-rate. Which expression can be used to represent the gross weekly pay of each individual?

hr + 50

Determine the linear inequality represented in the graph. <-----------------o -7 5

x<5

Implicit and explicit rules can describe sequences verbally, numerically, graphically, and symbolically. Which of the following would be an explicit rule of mathematics?

y = x + 2

A shirt costs $49.99 plus 8.25 sales tax. What is the total cost of the shirt? (Use a compatible number for the price of the shirt.)

$54.13

Troy and Rosa want to purchase a house. The bank will approve a loan for a house including property tax and insurance on the house for 24% of their adjusted monthly income. Their combined gross monthly income is $5150. They have a car payment of $320 and pickup payment of $465. Also, they have a furniture payment of $250. What is the maximum payment the bank will approve?

$988.00

Which of the following expresses the commutativity of -3^0 + (a + 4) =?

-3^0 + (4 + a)

Find 1^3 * 1 +2^3 * 2

17

What is the greatest common divisor (GCD) of the following numbers? 630 and 36

18

Jill's current salary is $53,241. She learns the school board has approved a 5% raise for the coming school year. Which of the following is not a method that Jill can use to determine her new salary?

(53241/1.05) + (.05)(53241)

A recent survey reveals that 40% of young people between 15 and 25 years of age will buy an iPod this year. Of those who buy iPods, 35% enjoy listening to country music. If N is the number of young people between 15 and 25, how many people between 15 and 25 this year will enjoy listening to country music on their iPods?

.14N

A sample of 400 students was asked the following questions, "On which of the following occasions are you likely to purchase a gift for your mom (only picking one): her birthday, Christmas, Mother's Day, no special occasion, or Valentine's Day?" What is the probability of one mom of these surveyed receiving a gift for Mother's Day this year? Mother's Day 48 Christmas 180 Birthday 28 No special occasion 92 Valentine's 52

0.12

At Leslie's beauty shop, she has found that a customer will want a color with a probability of 0.53, a haircut with a probability of 0.4, and both with a probability of 0.17. What is the probability that a customer will require a color and not a hair cut?

0.36

An individual from Texas is interested in purchasing land in Canada. The realtor informs him that there is a piece of land that is 1.8 km^2. The individual is lost as to the size of the piece of land. He needs to be able to convert the 1.8 km^2 to square miles. Convert 1.8 km^2 to square miles for the Texan (using 1 square mile = 2.6 square kilometers).

0.69 square miles

Use the diagram below to answer the question that follows. Given that the problem continues in the last two layers, use inductive reasoning to predict the pattern in the bottom layer of the triangle? 1 1+2 1+3+3 1+3+7+4 1+3+7+15+5

1+3+7+15+31+63+7

Sam and Jody are learning about money in their third-grade class. Sam tosses four coins on the table. What is the probability that all four coins will land on heads?

1/16

What is the probability that a couple's first or second child will be a boy?

1/2

What is the probability that both a couple's first two children will be boys?

1/4

What is the value of A/B+C if A/B = 5 and B/C = 2?

10/3

A popcorn company needs to have a new side label printed for their large popcorn holiday can. The side label will cover the entire surface area of the cylinder part from top to bottom. The diameter of the can is 16 inches and the height is 20 inches. How much area does the new label cover?

1005.31 in^2

Use the concept of Combinations to solve the problem. What is the probability of being dealt 4 hearts from a standard 52-card deck if only 4 cards are to be dealt?

11/4165

A third-grade class is under plaster of Paris to make impressions of their hands. Each student needs 12 ounces of plaster to make an impression of their hands. There are a total of 20 students in the class. How many pounds of plaster will the teacher need for the activity?

15 pounds

Find the measure of x. 93(deg) 145(deg) x

52(degrees)

Use the diagram below to answer the question that follows. A D X 10 5 4 B C F E Assume triangle ABC is similar to DEF. If AC is 10, DF is 5 and DE is 4, what is the length of AB?

8

What is the median of the following grades for a math test? 45, 85, 95, 83, 82, 76, 76, 92

82.5

In what context is it important that students be exposed early on to diversity in acquisition of mathematical concepts?

All students need to be exposed so that more women and minorities will pursue mathematical careers and broaden the field of experts across cultures.

Sea-tac Airport in Seattle, WA, has a flight leaving for Dallas, TX every 2 hours and a flight leaving for Washington, D.C. every 45 minutes. At 5:00 A.M., on Monday, a flight to Dallas and a flight to Washington, D.C. leave at the same time. What is the next time that flights to Dallas and Washington, D.C. will leave at the same time?

Answer: 11:00 A.M. the same day.

The teacher has students match each numerical value in Column A with the description it corresponds to in Column B. Column A: 3.25%, 18(degrees), 1/3, 0, 3 & 5/8, 13.24, and -220 Column B: Distance to the bottom of a canyon, Freezing point, percent the bank is charging on a car loan, money, measurement of an ingredient in a recipe, measurement on a ruler, temperature outside. The teacher is most likely assessing students' understanding of which of the following?

Appropriate representation of real numbers.

Mrs. Sanders is introducing multiplication to her second graders. She would like to integrate the children's learning of multiplication into other subject areas to demonstrate to her students how they will use multiplication in real life. Which of the following would be an appropriate activity for integrating multiplication into the second-grade science curriculum?

Asking the children to calculate how much food the class pet will need for the week.

The prenumeration activity of having young children place similar shapes in columns is laying the foundation for which of the following? (Chart Column with rectangles/squares, triangles, circles, and stars)

Bar Graph

The letter a, b, and c represent whole numbers greater than zero with a<b<c. Which of the following numbers is greatest?

C/A

Use the information below to answer the question that follows. Mrs. Johnson teaches fourth graders with learning disabilities. She asks them to add the following numbers: 15+12+28+45 = Jamie responds very quickly with 100. When Mrs. Johnson asks him how to solved it he replies: "I added 15 and 45 and got 60 and then I added 12 and 28 and got 40. Next, I added 60 and 40 together and got 100." Which of the following two properties of numbers did Jamie use to solve this problem?

Commutative and associative

Use the information below to answer the question that follows. Students in Mr. Stephen's fourth-grade class are working on a project for the cross-country team involving motion in one dimension. The graph below illustrates the velocity of a member of the cross-country team running in a straight line. The data was collected at 2-second intervals for 20 seconds. (Image of Graph) If Mr. Stephen's students wanted to provide an estimate of the total distance the runner has run between 0 and 12 seconds which of the following approaches should they use?

Determine the area that is under the curve between 0 and 12 seconds.

Tanya is trying to help her third grade student understand how to check for mathematical reasonableness. The student has calculated 8+7=21. What is a technique she might suggest to help her student learn estimation?

Doubling

A teacher decides to assign students a project where they will develop an amortization schedule of a purchase so they can apply a lesson using the future value formula and observe the details line by line as payments are made. What would be the best approach in assigning a purchase?

Have the class research products online such as stereos, game stations, etc, and choose an item they would like to purchase.

Since the area of a rectangle is A = l*W, what is the area of a triangle? (Image of rectangle with Length and width and line in diagonal)

LW/2

The teacher creates the following word problem. Word problem: Troy and Walter are neighbors. They both have mowed their grass today. Troy mows his grass every 3 days. Walter mows his grass every 5 days. How many days will it be before they both mow their grass on the same day? Based on the word problem, the lesson will most likely cover which of the following?

Least common multiple

Use the letters below to answer the question that follows. E T V D Students are classifying the letters of the alphabet according to the type of symmetry they have. Which of the following letters has the same kind of symmetry as the letters shown above?

M

Average daily temperatures are most likely calculated using which method of central tendency?

Midrange

Mrs. Ramirez and her second graders have been engaged in a math unit focusing on measuring length. In the classroom math center, Mrs. Ramirez has put a set of objects including a book, a photograph, a pencil, a notebook, an index card, and a ruler. She instructed her students to individually visit the center at some time during the week and to use the ruler to measure each of the objects and record the lengths on the worksheet provided. Mrs. Ramirez is observing the children to collect formative assessment data for the children's mastery of the following mathematics TEKS: (9) Geometry and measurement. The student applies mathematical process standards to select and use units to describe length, area, and time. The student is expected to: (A) find the length of objects using concrete models for standard units of length; Mrs. Ramirez observes carefully as Emma comes to the math center an begins to measure each object. She notes that Emma does not place the ruler evenly with the base of the object she is measuring and so the lengths that she is recording are significantly shorter than the objects. What action should Mrs. Ramirez take next?

Mrs. Ramirez should plan and present a re-teach activity on using a ruler to measure length for Emma and any other children who did not successfully complete the math center activity.

Which of the following approaches and initiatives used by a math teacher will best assist with planning, delivery, and reevaluating instruction to ensure that every student is learning sound and significant mathematics and is developing a positive disposition toward mathematics?

Observing, listening to and gathering other information about the students to assess what they are learning.

Manipulatives, as concrete objects of a mathematical expression, can be labeled as symbolic mathematics. In order to learn mathematics from the manipulatives, what must students perceive from the manipulatives?

Relationships between manipulatives and other forms of mathematical expressions.

The teacher tells the class to put the following numbers in order from smallest to largest. 2.03, 8 square root of 2, -3.5, 9/2, pi, 2.1 Based on the exercise the teacher has given, the exercise is most likely trying to assess which of the following number concepts.

Relative magnitude

The problem below appears on a sheet of a papyrus text written in Egypt about 650 B.C. Divide 100 loaves among 10 men. Three of the men, a boatman, a foreman, and a doorkeeper, should each receive double portions. How many loaves does each of the 10 men receive? This suggest that the ancient Egyptians had developed techniques for which of the following?

Solving algebraic equations in one variable

The second-grade math teachers assessed their students over several concepts including problem solving with addition and subtraction. After grading a benchmark summative assessment, the teachers met to review the data and determine which students struggled most with which concepts. The teachers put the students into groups according to each student's weakest concept. The teachers then formulated a plan to re-teach the concepts. Which of the following could be part of the plan to re-teach?

Spend a few days with the students grouped by what they struggled with the most and re-teach the corresponding concept to that group.

Use the diagram below to answer the question that follows. Number Step 1 A 42 cubes B 27 cubes Number Step 2 A 42 cubes B 27 cubes The diagram shows the first two steps in modeling a computation involving numbers. A and B using base-ten blocks. Which type of computation is being modeled with the blocks?

Subtraction with regrouping.

A teacher begins a new lesson on multiplication on Monday. She would like to identify which concepts of the new lesson are most difficult for students to comprehend, so that she can adjust her lesson plans for Tuesday as the lesson progresses. Which of the following assessment methods would be least appropriate for achieving this goal?

Summative

Use the diagram below to answer the question that follows. 5 3 1 0 Alex makes the target board shown above and places it on the floor. Alex makes a conjecture that is possible to obtain any score from 0 to 15 by dropping exactly three coins on the board, assuming all the coins land somewhere inside the square. Which of the following statements best evaluates Alex's conjecture?

The conjecture is invalid, since it is impossible to obtain a score of 12 or 14.

Which of the following responses support this statement? "As our need for mathematically literate workers and citizens increases, our economic security will depend on how well we have educated other individuals and incorporated them into full participation in the economy of the twenty-first century." (Herzig 2005)

The need for trained workers will continue to rise in mathematically based careers in the twenty-first century.

Mrs. Johnson teaches fourth graders, some with learning disabilities. Many of them are having trouble with expressions similar to this one: 12 + (7 X 2) - 2(5 + 3). Students' trouble is most likely the result of misunderstanding —

The order of operations

An early childhood teacher is planning a lesson series on addition. The teacher introduces the concept of addition through recalling prior knowledge of pattern using cubes of different colors. The teacher then moves to having the students do what she models with adding cubes of two different colors. The next day the teacher models adding cubes of different colors with a written algebraic expression. What would be the next step for the students?

The student would model the algebraic expression with cubes.

Which choice best describes an explanation a teacher could give a student to help him/her judge the reasonableness of the solution in the following scenario. Evaluate: -7-12 The student gives an answer of 5.

Think of a baseball game where you had missed your first 7 shots, and then you go on to miss your next 12 shots as well. How many shots have you missed in total?

Mrs. Wilson is preparing her fourth graders for Mathematical TEKS. Four math problems similar to the one shown below fill up the blackboard. The cost of a sweater at Sears was $75.00. At the Back-to-school sale it was marked $13.50 off of the original price. What was the price of the sweater during the sale? Explain the process you used to find the sale price. A first-year math teacher visiting Mrs. Wilson's classroom quickly observes the tasks have "real world" context, require an explanation, involve multiple-steps, and are "text-like" but, require no manipulatives and show no connection to meaning. Which of the following best describes the reason Mrs. Wilson most likely chose the tasks for her students?

To increase students' speed and accuracy in solving problems.

Using the Present Value Formula, students have calculated a house payment for a loan set up on an annuity. The principal is $127,000 and the monthly payments are $583.56. The students want to know how much interest over the period of the note (30 years) will accrue. They decide the first step is to calculate the total amount to be invested in the house. For this, they determine the following equation should be used. Payment amount x Number of payments = Total amount invested What should the next step of the algorithm be?

Total amount invested - principal

The teacher helps a student draw a horizontal line 3 inches with a straightedge and a perpendicular line 2 inches connecting the edge of these lines at a point as shown in the graph below. (image) The teacher should use several questions to help the student critically think about this graph. Determine the question below that the teacher should not include in these statements.

What is the length of the diameter?

A sample of 500 men leaving the mall was asked the following question: "On which of the following occasions are you likely to purchase a gift for your wife: her birthday, Christmas, Mother's Day, her anniversary, or Valentine's Day?" The graph below shows the percent of responses for each of the occasions. Christmas 45% Birthday 10% Anniversary 35% Valentine 15% Mother's Day 15% Is this graph misleading? Determine the correct choice of whether the graph is misleading or not and the best reason for your choice.

Yes. The sum of the percentages is more than 100.