Certify Teacher- Math

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

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)

Popular toys for Christmas are on sale for 35% off. Early shoppers on December 20th can take an additional 25% off before 7 a.m. Let f(x) = price with 35% off and let g(x) = price with 25% off. Express the best concept or procedure in mathematical language that describes a method to find the price of the toy before 7 a.m. on December 20th.

(g o f)(x) ~ The composition of functions finds the sale price of the toy with the 35% discount [f(x)] and then finds the sale price of the toy with an additional 25% discount [g(f(x)].

What is the range of the linear correlation coefficient (r) that describes the strength of the linear relationship amongst two variables?

-£ 0 £ 1 The range of the correlation coefficient is between -1 and 1 inclusive with 1 meaning there is a strong positive relationship and with -1 representing there is a strong negative relationship. The correct answer is D.

A sample of 400 college students was asked the following question, "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?

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

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

0.5

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 km2. The individual is lost as to the size of the piece of land. He needs to be able to convert the 1.8 km2 to square miles. Convert 1.8 km2 to square miles for the Texan (using 1 square mile = 2.6 square kilometers).

0.69 Square miles

Which Choice is a real number?

0^1

Given the pattern 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

One family member's monthly salary is $24,000, the other member earns $24,000 per month. The household income is $56,000. The rest is from investment. What is the fraction of the investment?

1/7

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 in. How much area does the new label cover?

1005.31 in2

Tymon is building a bookshelf. He has the entire outside completed. He must purchase wood to make the 5 shelves. Each shelf needs to be 26 3/4 inches long. He can purchase wood up to 16 feet long. He needs to allow 1/8 in for each saw cut, how many feet of wood does he need?

11 3/16

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 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 third-grade class is using 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 1 pound=16 ounces

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

18

The teacher shows the students the following model using algebra tiles.Write an equation that gives the factors and the area of the rectangle.

2(x + 2) = 2x + 4

Order from least to greatest:1/3, 75%, 3/10, 0.8%

3/10, 1/3, 75%, .8%

A baseball team wins 60% of their first 70 games. They have 40 games left. How many more games do they need to win to get a perfect 70%?

35%

Zane on the trip to downtown Orlando traveled 60 mph and arrives 1 minute early. He traveled back at 30 mph and arrived 1 minute late. What was the distance of the trip?

45 miles

Mark's semi-monthly gross pay increased from $2,541.79 to $2,654.65. His net pay increased from $1,589.67 to $1,659.58. He notices that his health insurance and life insurance combined have increased about $16.00 from last year and both of these deductions are tax exempt. Mark wants to determine what percentage he will actually bring home of his extra earnings doing these odd duties. Which of the following is the best estimate Mark will bring home of any extra earning based on the information gathered from his pay increase this year provided he does not move into a higher tax bracket.

76% ~ The difference in gross pay is $112.86. The difference in net pay is $69.91. Add the insurance deduction of $16 back to the $69.91, because this amount is deducted only one time will not effect future deductions when extra money is earned. The percentage of net pay is 85.91/112.86 = .76 or 76%.

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

82.5

A bimodal distribution contains two nonadjacent values that occur more often than the others in a set of data. An example of this would be if the same number of men and women were weighted and their weights recorded using a histogram.

A Gaussian distribution, also called the normal distribution, is bell shaped and symmetric about the mean . ~ Rectangular distribution is correct. In rolling a die a number of times, we expect all the numbers from 1-6 to occur about the same amount of times. The rectangular distribution looks like the following.

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. The teacher is most likely assessing students' understanding of which of the following.

Appropriate representation of real numbers

This prenumeration activity of having young children place similar shapes in columns is laying the foundation for which of the following?

Bar Graphs

Given the following set of data, predict the correlation coefficient.{(1, 2), (2, 4), (3, 4), (4, 5), (5, 8), (6, 9)}:-)

Close to 1 The correlation coefficient is close to 1, because the points almost form a straight line.~ A correlation coefficient of 0 indicates the points are scattered in a way that they do not tend to go up or down in a line

Mrs. Johnson teaches fourth graders with learning disabilities. She asks them to add the following numbers: 15 12 28 +45Jamie responds very quickly with 100. When Mrs. Johnson asks him how he 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. 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.

Fifth graders at Smith Elementary were introduced to number bonds as first graders. Which of the following, when applied to fifth grade concepts, would relate back to number bonds?

Diagrams

Tonya is trying to help her 3rd 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

The following is a net for _________ ?

HEXAGONAL PYRAMID

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, and etc, and choose an item they would like to purchase.

Mr. Grant wants his fourth-grade math students to learn to work collaboratively, to discuss alternative approaches to solving tasks, and to justify their solutions. Students are grouped in pairs and Mr. Grant gives his students the following task:Express the ratios below in the lowest forms:15/25 , 18/6 , 9/36 , 18/15Which of the following best describes the level of student engagement expected with the given task?

It will not engage students in high level forms of thinking.

Since the area of a rectangle is A = L × W, what is the area of a triangle?

LW/2

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

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

Midrange

In which distribution would the mean, median, and mode all have the same value?

Normal Distribution ~ A normal distribution is bell shaped and symmetric about the three values of central tendency. ~ bimodal distribution, the mean and median will be together in the center while the two modes will be on both sides of the center ~ rectangular distribution has no mode, because the frequency of the values is the same. The median and the mean would appear in the middle of the distribution.

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.

Mr. Jansen's second-grade students have been working on addition and are now ready to begin learning two-digit subtraction. To introduce this new unit of study, he first has students work on addition problems they are familiar with and then follows up by demonstrating to them how those problems are related to subtraction. Mr. Jansen has been debating whether or not he should allow his students to use calculators to do their math. Some of his students are learning disabled. When considering the use of calculators for math exercises, Mr. Jansen should keep in mind that —

Once students have demonstrated that they know the correct way to perform math calculations, they should be allowed to use a calculator.

Use the figure and information below to answer the question that follows. Three students are playing a game using the spinner above. Each student draws three boxes on a piece of paper. The spinner is spun, and each student writes the number in any one of the three boxes. The spinner is spun two more times, and each time the students write the number in a remaining empty box. The Students then compare numbers, and whoever has the largest three-digit number wins the game. This game would be particularly useful in helping students' understanding of:

Place value

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. 8 -3.5 9⁄2 π 2.1 2.03 √ 2 Based on the exercise the teacher has given, the exercise is most likely trying to assess which of the following number concepts.

Relative Magnitude

Students learn from what they do and the process they go through to acquire knowledge. Their learning of mathematics impacts society and culture. What theory of learning would this statement support?

Situated learning theory

First graders are applying skip counting as they count to 100. The teacher wants to explore common items for the students to use with skip counting. For skip counting by 5s, the teacher will have the students trace their hands and number their fingers then glue the hands on a large poster board to display the number of hands with five fingers it would take to reach 100. What are some things the teacher could use to teach skip counting by 2s?

Socks,shoes,feet

The problem below appears on a sheet of a papyrus text written in Egypt about 650 B.C. This suggests that the ancient Egyptians had developed techniques for which of the following?

Solving algebraic equations in one variable

Calculators, base-ten blocks, attribute blocks and cubes are some of the manipulatives a math teacher has available to teach several mathematical concepts to his class. Attribute blocks is a type of manipulative most effectively used to teach which of the following sets of concepts.

Sorting, classification, investigation of size, shape, color, logical reasoning, sequencing, patterns, symmetry. similarity, congruence, thinking skills, geometry, organization of data.

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. 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?

Summ

A first grade teacher is assessing students' ability to apply strategies to add numbers up to 20. The TEKS list four strategies students should learn in first grade. Which of the following is NOT one of those strategies?

Ten frame

Tesselations Mass Patterns and Symbols changes in population Budgets

Tessellations, while geometric in concept, are seen in many forms of Art, as well as, in nature. Mass, along with other forms of measurement, is taught in Science. Applying the mathematical operations to the science of finding and calculating measurement is important for students to be able to link concepts across disciplines. Patterns and Symbols are taught in Music from reading music notes (symbols) to following the patterns of notes on a written line of music and hearing the patterns within music. Changes in population are important in calculating within the Social Sciences as population trends are studied and data is compared across regions and generations. Budgets are created within Businesses. Students who are be able to connect learning in math and applying it in real-world situations are able to expand to deeper levels of learning.

Use the Diagram below to answer the question that follows. 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.

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

The order of operations

Which choice below will best help the student use technology to check his answer and relate the answer to real application? A. Have the student check his answer using a calculator. B.Have the student use an Excel spreadsheet to lay the supports out one by one using functions provided by Excel as needed. C. Have the students work in pairs using calculators. D. Have the student draw the supports on a piece of paper and label each support with its appropriate length and find the sum with his calculator.

The student can be assisted in creating formulas in Excel.. He can use the sum function of Excel to total what is in the column. ~ This also gives him a visual format to connect to the real-life application of this problem.

An early childhood teacher is planning a lesson series on addition. The teacher introduces the concept of addition through recalling prior knowledge of patterns using cubes or different colors. The teacher then moves to having the students model 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 students would model the algebraic expression with cubes

A fifth-grade classroom has 30 students consisting of 17 boys and 13 girls. There are 6 rows and 5 students in each row. The principal asks the teacher to randomly select 5 students to send to the library. Which method below is a random sample?

The teacher rolls a die and selects the row that corresponds to the outcome and sends all the students on that row.

The students in homeroom 304 were asked to bring in illustrations of real-world forms of symmetry in tessellations. Students had previously learned about symmetry and tessellations through visual representations of honeycombs. What does the teacher understand about the importance of students finding other examples of tessellations in the world around them?

The teacher understands the importance of students being aware of their environment and applying what they are learning in the classroom to what they experience and see around them.

Fifth graders learning about coordinate planes and graphing ordered pairs were put into teams of two to design a board game in which their fellow classmates would be able to play to practice graphing and finding the x-axis and y-axis. Which of the following would NOT be a characteristic the students would have explored when being introduced to coordinate planes?

There are four quadrants in a coordinate plane, and quadrant 2 and quadrant 3 are positive.

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 basketball 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?

A first-year math teacher visiting Mrs. Wilson's classroom quickly observes the tasks have "real world" context, require an explanation, involve multiple-steps, are "text-like" but require no manipulatives and show no connection to meaning. Which of the following best describe 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 • 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.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 dismeter?

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. 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.

Determine the choice that illustrates the commutative property for (a + b) + c =

c+(a+b)

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

c/a

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

The teacher would like for her students to find the area of the following polygon. What steps must the students take in order to solve for the area?

partition the polygon into two rectangles, find the area of each rectangle, add the two areas together

Mrs. Jones is preparing her fourth grade students for their field trip to the farmers' market. While at the farmers' market, students will have the opportunity to meet local farmers from their community, incorporate concepts they are learning in science about plants and purchase some locally grown fruits and vegetables. Mrs. Jones obtained a price list from several of the vendors at the farmers' market and will guide students to create a budget prior to the field trip to know how much they can spend. Which instructional strategy could Mrs. Jones be implementing with her students to maximize their time and efforts at the farmers' market?

real-world situations with budgeting and building meaningful connections

Determine the linear inequality represented in the graph. <———————————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

So, the next 50 people leaving the mall become his population. He draws one of the pieces of paper to see which person he needs to interview. The first time he draws a 10, so he stops the 10th person leaving the mall to interview. Once this interview is over, the next 50 people leaving the mall become his population, and he proceeds in the same manner until 200 individuals have been interviewed. Describe the type of sampling procedure the cola company is using to collect their data.

~ Random sampling is sampling in a way that each item in the population has an equal chance of being selected. ~ Cluster sampling is a random selection of groups, so an example of this would be drawing the #3 and the 3rd, 4th, 5th, 6th, and 7th individuals are selected and pulled aside to interview. ~Convenience sampling uses data that is readily and easily obtained, ~ Systematic sampling is selecting every nth one.

Mark's semi-monthly gross pay increased from $2,541.79 to $2,654.65. His net pay increased from $1,589.67 to $1,659.58. He notices that his health insurance and life insurance combined have increased about $16.00 from last year and both of these deductions are tax exempt. Mark makes an additional $167.35 in a semi-monthly period doing bus duty. After finding out what Marks % after taxes take home is how much can Mark estimate his next check will be?

~$1,787 Estimating 76% * 167.35 = 127. Adding this to his next check gives approximately $1,787.00

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

−3^0 + (4 + a)