EC-6 MATH
Shirt cost $49.99 plus 8.25% sales tax. What is the total cost 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
Jills current salary is $53,241. She learns the school board has approved a 5% raise this coming school year. Which of the following is NOT a method Jill can use to determine her new salary?
(53241/1.05) + (.05)(53241)
Which of the following expresses the commutativity of -3^0 + (a + 4) = ?
-3^0 + (4 + 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
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: 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 .53f, a haircut with a probability of .4 and both with a probability of .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 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 1.8^2 to square miles for the Texan.
0.69 square miles
Which choice is a real number?
0^1
Given the pattern shown above continues in the last two layers, use inductive reasoning to predict the pattern in the bottom layer of the triangle.
1 + 6 + 15 + 20 + 15 + 6 +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+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
Use the picture below as a stimulus material that relates to the question below. The area enclosed by the rubber band can be calculated by using which of the following expressions?
1/2 bh
What is the probability that 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
Popcorn company needs to have a new side labeled 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 of the can is 20 inches. How much area does the new label cover?
1005.31 in^2
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
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 am 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?
11:00 am the same day
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
Find 1^3*1+2^3*2
17
What is the greatest common divisor of the following numbers? 630 and 36
18
Tymon is cooking biscuits. The recipe calls for the following ingredients. If he wants to triple the recipe, how much baking soda will he need to put in the biscuit mix? 3/4 tsp baking soda
2 1/4 teaspoons
Teacher shows the students the following model using algebra tiles. XX. 1111. The teacher instructs the class to form a rectangle with the tiles. X11 and X11. 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. If the pattern continues, what is the total number of cubic blocks needed to build 6 steps?
21
Find the sum of the following: 2/9 + 1/4 + 1/6
23/36
The teacher asks the students to investigate the following pattern and write a mathematical fact about the pattern.
24 '/. 4 = 6
Calclate the area of the following figure. 3, 3, 5, 2.5
35
Find the mean of rainfall for 2011 by using the chart below. 3, 3.5, 4.5, 4, 4.9, 6.7, 6.9, 7.3, 4.7, 4.6, 4.8, 3.5
4.87
Use the bar graph below to answer the questions that follows. How many home runs were hit during the entire week?
50
Find the measure of X: 145*, 93* and X
52*
Walter looks forward to Fridays because his teacher plays his favorite math game during the math period. She gives the class a number, and the students write an expression to equal that number. The object is to see some unusual methods to calculate the number because the class wants to get as many different answers as possible. Today the teacher gives the number 24. Which of the following is the correct expression to equal 24?
60 '/. 3 + 6 - 2 x (-1)^0
Assume triangle ABC is similar to DEF. If AC is 10 and DF is 5 and DE 4f, what is the length of AB?
8
What is the median of the following grades for a math test? 45, 95, 82, 76, 85, 83, 76, 92
82.5
Mr. Brown's kindergarten students are classifying geometric figures by their attributes to determine which figures may be classified together as three-dimensional figures. Which attribute would be helpful for Mr. Brown to introduce to his class before the proceeding with the activity?
Ability to roll, number of corners, numbers of sides, number of flat surfaces
Teacher has students match each numerical value in Column A with the description it corresponds to in Column B. 3.25% - Distance to the bottom of a canyon 18* - Freezing point 1/3 - Percent the bank is charging on a car loan 0 - Money 3 5/8 - Measurement of an ingredient in a recipe 13.24 - Measurement on a ruler -220 - Temperature outside The teacher is most likely assessing student's understanding of which of the following?
Appropriate representation of real numbers
Students in a fourth-grade class are working with geoboards. Each geoboard has a grid drawn on it and a peg at each intersection of the grid. Students stretch rubber bands around the pegs to create shapes. One student's shape is show below. The teacher shows the student how to add the squares and fractions of squares enclosed by the rubber band to count the total number of squares within the triangle. This activity would BEST promote the student's understanding of which of the following geometry concepts?
Area
Students in Mrs. Lima's kindergarten class are exploring patterns. Mrs. Lima has led through clapping patterns, color patterns and shape patterns. The goal of the lesson is for the students to learn to name patterns in terms of ABC. Which of the following would follow an AABBABC pattern?
B
This prenumeration activity of having young children place similar shapes in columns is laying the foundation for which of the following?
Bar graphs
Second graders are learning how bar-type graphs apply to real-world situations. The students were presented with the following T-chart and asked to graph the data on a bar-type graph. Which graph would support the data in the T-chart?
C
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
Each student has been given a small package of colored chocolate candies. The students will sort and classify their candies by color and the number of candies of each color. Students will then make a chart and a graph to show the number of each color in their packages. This activity supports which of the following TEKS?
Collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-Charts
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 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 additive identity
After a lesson in finding the area and the domain of the length of a side of a rectangle given the perimeter of the rectangle, the teacher finds that ALMOST all the students have answered the following question this way. What would be the BEST approach for the teacher to respond to the answers?
Congratulate the students on their efforts of critical thinking through a tough question and their ability to calculate the area correctly. Follow up with a mini-lesson on multiplication property of zero. Let students work in pairs to analyze if they want to change their answer for the domain
The teacher could BEST help the students understand that the triangle is equivalent to half a square by showing them how to:
Create a reflection of the triangle along its longest side
Tanya 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
Students in first grade are expected to organize data to make it useful for interpreting information and solving problems. Ms. Chen has designed a project for her first graders to collect data from the second graders about favorite ice cream flavors. Ms. Chen has provided three options of flavors for students to choose from. The first graders will interview the second graders and ask their favorite flavors then bring the data back to class. Once the data arrives back to class, Ms. Chen will facilitate the collection of the data and guide students to make a bar-type graph. For what could this bar-type graph be useful?
Drawing conclusions and generating and answering questions about the data
Teacher decides to assign students a project where they will develop an amortization schedule of a purchase so they can apply a lesson sing the future value formula and observe the details line by line as payments are made. What should 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
Following net is for a
Hexagonal pyramid
Mrs. Jones' students are using principles of inductive reasoning to solve for missing numbers in patterns. Mrs. Jones gave her students the pattern below and asked them to complete the pattern. What might a student reason in order to apply deductive reasoning to complete the pattern? 2, 4, 8, 16, 32, 64
I can see the pattern increases, so I must need to add or multiply. If I add 2+2, it equals 4, but if I add 4+2, it equals 6. So, i can multiply 2x2=4 and 4x2=8. The pattern is to multiply by 2
I. Whole numbers II. Integers III. Rational numbers IV. Irrational numbers
I, II, and III
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. This approach best demonstrates Mr. Jansen's understanding that -
Instruction in math should build on existing knowledge of math
Mrs. Frankie plans to assess her third - grade math students over two-digit by one digit multiplication. After introducing the concept and allowing students a few days to become familiar and comfortable with the steps. Mrs. Frankie will assess the students through a daily work assignment then a test. She has also planned a project for the students in which she has prepared rubric by which the students will be graded. How does using a variety of assessment tools aid Mrs. Frankie in knowing her students' understanding of the concept?
It allows Mrs. Frankie to evaluate mathematical understanding and discover misconceptions and error patterns.
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, 18/15. Which 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 triangle is A = L X W, what is the area of the 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 cove which of the following?
Least Common Multiple
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? E T V D
M
What is another way to say average in mathematics?
Mean
Average daily temperatures are MOST likely calculated using which method of central tendency?
Midrange
Congruent triangles can be used to explore geometric relationships. Which of the following is NOT representative of a position of congruent triangles?
Mirror
Is the graph of a circle a function? Describe why or why not.
No. It does not pass the vertical line test.
In order to teach the relationship of number of dimes to the value of the dimes, the teacher introduces the following input-output table to the class. 2 = 20 3 = 30 4 = 40 5 = 50 Which algebraic expression would show the relationship between the input and the output?
Number X 10 = Value
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 math?
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
First grade teacher is planning a lesson to engage algebraic reasoning for the students. The teacher will first model two sides of an equation using base ten blocks then write the equation for the stdents to see the relationship between the model and the expression. What other model would be beneficial for students in making connections between the concrete and the abstract in algebraic reasoning?
Pictorial model
Mrs. Green is introducing subtraction to her kindergarten students. Mrs. Green will provide blocks for her students to use to indicate separating to represent subtraction. The lesson sequence will follow a whole group lesson, small group lessons, partner work and independent student work. During the initial small group lessons, which of the following will be important for Mrs. Green to link to the concrete representation of the blocks as she checks for understanding with the students?
Pictorial models and blocks
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 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
Which choice represents an element whose only factors are itself and 1?
Prime numbers
1st-grade students, including ELL Students, at Rice Elementary will be assessed over their understanding of U.S. coins and the value of each coin. During class instruction, all students were able to concretely work with play money to make connections with coins and values. The teacher must determine the best way to assess students over the values of the U.S. coins. Which would be an appropriate method to do so?
Provide pictures of each U.S. coin and have students match the picture with the value of the coin
Greatest benefit of providing elementary students with mathematical tools such as geoboards is that these tools -
Provide students with visual representations that promote their conceptual understanding
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
Teacher tells the class to put the following numbers in order from smallest to largest. 8, -3.5, 9/2, 3.14, 2.1, 2.03, square root of 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
Determine the choice that does NOT relate to the following: 10x + 5
Solve for the value of X
Divide 100 loaves among 10 men. Three of the men, a boatman, a foreman, and a doorkeeper, should eachf receive double portions. How many loaves does each of the 10 men receive? 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
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 formulate 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 the struggled with the most and re-teach the corresponding concept to that group
Mr. Chen has asked his students to solve for the number of square feet of carpet needed to cover his living room floor with carpet. Students were given the following the image from the blueprint. How should the students solve for the area of the room?
Students should multiply the length by the width to find the number of square feet
2nd grade teachers at Red Elementary are planning to teach financial literacy concepts through the method of role play. This lesson series will be introduced by a visit to a local bank where students will learn the role of bank employees and how they handle money and assist customers. Students will continue the lesson series as they role play the roles of the bank employees in handling money, accepting and making deposits and withdrawals and discover examples and reasons for lending money. Identify the example of how students will be able to apply mathematics in this workplace scenario.
Students will use addition and subtraction to make deposits and withdrawals
The diagram shows the first two steps in modelling a computation involving numbers A and B using Base-Ten Blocks. Which type of computation is being modeled with the blocks?
Subtraction with regrouping
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
According to National Council Teachers of mathematics, "technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. Teachers' attitudes play an important role in using technology in teaching and learning mathematics". Which of these would NOT be an effect of technology on math curriculum?
Technology will make math less important
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 0-15 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."
The need for trained workers will continue to rise in mathematically cased 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 * 2) - 2(5 + 3). Students trouble 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 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
Fifth-grade math class, the teacher will be introducing representing real numbers as percentages. What prior knowledge of the students could the teacher draw on to relate percentages to real life situations?
The teacher should implement an activity relating fractions and decimals to percentages
What 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 and the student answers 5.
Think of a basketball game where you had missed your first 7 shots, and then you go on to miss you next 12 shots as well. How many shots have you missed in total?
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
Figure 2 represents a __________________ of figure 1
Translation
Class of second grade students are classifying two-dimensional polygons. Students are given a rectangle and asked to decompose it to form new two-dimensional polygons. Which of the following identifies the geometric parts that could NOT be formed from decomposing the rectangle?
Two congruent rectangles, 1 circle
Bob and Lucas keep track of how many home runs are hit in the major leagues during the previous several days. The bar graph below shows the number of home runs hit during one week. On which day were the MOST home runs hit?
Wednesday
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 diameter
Determine the linear inequality represented in the graph.
X<5
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 the 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
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 betweenf 0-12 seconds, which of the following approaches should they use?
determine the area that is under the curve between 0-12 seconds
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
If the price of selling a pair of shoes is represented by the expression (300-x) where x is the number of shoes sold, the REVENUE FUNCTION is R(x) = _______?
x(300-x) or 300x - x^2
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