certify teacher math

Ambers dog, Bob, eats apporoximately 85$ of dog food in 2 weeks. How much will Amber spend on dog food in a year?

$2210

a shirt cost $49.99 plus 8.24% sales tax. what is the total cost of the shirt?

$54.13 50* .0825=4.125 4.125+50=54.125

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 $5150-320-465-250=4115 4115x.024= $988

which of the following expresses the commutativity of -3^0+(a+4)=/

-3^0+(4+a)

a recent survey reveals that 40% of young people between 15 and 25 years of age will buy an iPod this year. of this 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 .40x.35=.1400

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 0.53-0.17 = 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 theres 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 connect the 1.8km2 to square miles. Convert 1.8km2 to square miles for the texan. (using 1 square mile =2.6 square kilometers)

0.69 square miles 1.8 / 2.6 = 0.69

which could be used to find two consecutive even numbers whose some is 80?

0= no solution

what is the solution, if any, to the expression: 1^n=?

1

which of the following is not a prime number?

1

find the sum of the following: 2/9+ 1/4+ 1/6

23/36

the teacher ask the students to investigate the following pattern and write a mathematical fact about the pattern

24/4=6

which is a factor of 125

25

three times the width of a rectangle plus five is the same as seven more than four times the width. if W is used to represent the width of the rectangle, which of the following expresses this relationship?

3w+5=4w+7

Express 4 3/8 as a decimal

4.375 Find 3÷8 = 0.375 add this to the whole number ( 4 )

BLUE GEOBOARD: students in a fourth grade class are working with geoboards. each geoboard has a grid drawn on it and peg at each intersection of the grid. Students stretch the rubber bands around the pegs to create shapes. One students shape is shown below. The teacher shows the students 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 wold best promote the students understanding of which of he following geometry concepts?

Area

students were assigned to work in groups of two to investigate probability and its properties as it relates to flipping two coins. prior to flipping the first pair of coins, partners were to predict the outcomes of 10 flips. Pairs were assigned to flip two pennies and to record their findings of HH, HT, TH or TT in a frequency chart. the teacher observes some students skipping prediction step. what approach should the teacher take with the students who opted to ship the prediction step?

stop to observe the students and correct the behavior before they move on to flipping coins and collecting data: the observe them making the prediction and working through the flipping part of the activity

mr. jacobs fifth graders will work in small groups to solve addition and subtraction of fractions with like and unlike denominators. when solving addition and subtraction of fractions with unlike denominators what will be important for students to remember and apply?

students will need to make equivalent factions using LCD prior to solving problems with unlike denominators

mathematics revision and reform is an ongoing debate to reach a conclusion as to what is "best practice" to improve mathematics education. "it is clear that the work of reform requires large investments of time and energy to enact critical change in mathematics education. what is one way teachers can work towards reform in mathematics education?

teachers can design learning environments to allow for mathematical discussion and the connection of mathematical ideas

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

johnny is solving the following word problem with a classmate. Elyse is 26 years younger than her mom. If Elyse's mom is 32, how old is Elyse? the students find the solution to be 26. How could Johnny and his classmate check for reasonableness?

the can conclude that Elyse must be younger than her mom, so they could subtract 32-26 = Elyse's age or 6, and then check by plugging in Elyse's age to see if 32-6=26.

which of the following response supports 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 based carriers in the twenty first century

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

the students would model the algebraic expression with cubes

the students in homeroom 304 were asked to bring in illustrations of real-world forms of symmetry in tessellation. students had previously learned about symmetry and tessellation through visual representation 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 of their environment and applying what they are learning in the classroom to what they experience and see around them.

a first grade teacher is teaching algebraic reasoning through problems which present to the students as if they are puzzles. one way the teacher could do this is to introduce students to a card game in which they must find the missing addend. what could be the teacher's goal with this method?

the teacher's goal is to use the concept of learning through play in order to strengthen the students number sense and introduce algebraic reasoning

mrs. whites students are exploring graphing on a coordinate plane. students are asked to describe the x-axis and y-axis in terms of parallel lines, perpendicular lines, origin of intersection of lines and ordered pair. which of the following describes the coordinate plane illustrated below?

the x-axis and y-axis form intersecting, perpendicular lines whereby the ordered pair indicated here is (4,3)

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 x-axis and y-axis. which of the following would NOT be a characteristics the students would have explored when being introduced to coordinate planes?

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

a 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

mrs. jones first graders are learning how to write equations. the students have previously learned to write equations with addends and minuends, but today they are learning to write an equation when an addend is missing. for missing values, mrs. jones has introduced that a symbol can be out in the place of a missing addend. what is the proper mathematical term for the symbol in this equation? 13+____=18

variable

personal financial literacy was added to the TEKs in 2012 so that students might learn to apply "mathematical process standards to manage one's financial resources effectively for lifetime financial security." which of the following would NOT relate to one's financial security?

volunteer jobs

which of the following would not be considered an acceptable form of mathematical representation?

written sentence

if the price 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)

x(300-x)

which is not a proper way to denote multiplication

x9

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

the third graders in homeroom 302 are working collaboratively to find the perimeter of the schools garden to determine the number of feet of edging they will need o put a boarder around one section of the garden. the picture of the garden is shown below. complete the formula for the perimeter.

formula: P=2(12)+2(5)=34

a teacher decides to assign 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

(blue statment with activity 1 and 2)based on the descriptions above, these activities will promote development of map skills to second graders mainly because they

help students learn abstract map concepts through involvement in concrete experiences related to a familiar location

pat and her sister returned home 2 hours 45 minutes after they had left a movie. they returned home at 4:30 pm. what time did they leave for the movie? shortly after, ms. jones was dismayed to see that the students were not making much progress. some were already off-task and many others were complaining that the task was too difficult. not knowing where to begin, the students began to urge her to give some help. wanting them to feel successful and stay engaged.

her discourse cut off opportunities for discovery by giving the students the information they needed rather than asking probing questions to get them to the solution of the task.

mrs. jones students are using principles of inductive reasoning to solve for mossing numbers in patterns. mrs. jones gave her students the patter 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 to 4, but if i add 4+2, it equals to 6. So, I can multiply 2x2=4 and 4x2=8. the pattern is to multiply by 2

during math work stations, the students are to use the Math talk posters to guide their thinking in solving the given problems. as the teacher walks around the room helping different students, the teacher hears johnny ask joe how he solved the problems of five times nine. which response from joe may have appeared on the math talk poster as a way to explain his thinking?

i multiplied five times nine by counting by five nine times

Mr. jansen's second grade students have been working on addition and are now ready to being 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 demonstrated Mr. jansen's understanding that

instruction in math should build on existing knowledge of math

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?

least common multiple

since the area of a rectangles is A=L*W, what is the area of a triangle?

lw/2

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?

Chart C correlates to the t-chart

mr. williams is preparing a lesson on counting money with coins and bills for his second grade students. he has set up a store in his classroom whereby students will shop for school supply items then pay for them with play money. Mr. williams is hoping the students will learn to make change correctly by applying the concept to a real-world situation which many of his students experience in purchasing their own school supplies. which of the following instructional strategies could mr. williams be hoping to achieve with his lessons?

math language and discovery activity

what is another way to say average in mathematics

mean

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

midrange

learning to skip count forward in lower grades in preparation for which of the following mathematical operations

multiplication

joelle and her friends replanting to visit the zoo in the neighboring town. they know the price of each student ticket is $5 and each adult is $7. if joelle and 7 of her friends visit the zoo with two parents, what will be the final costs of the zoo tickets? what method could the student use to most efficiently solve this problem?

multiply five times eight then multiply seven times two then add the two products together.

mr brown introduced his class to solving missing angles within triangles. He provided his students with graphic representation of triangles and asked them to solve for them missing angle. for which representation of the triangles is mr. brown asking his students to solve?

numeric

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

in order to teach the relationship of number of dimes to the value of the dims. the teacher introduces the following input-output table to the class. which algebraic express would show the relationship between the input and the output?

Number x 10= value

a teacher is introducing the concept of elapsed time to a third grade class. the teacher understands that some of the students are able to read an analog clock while others are only familiar with a digital clock. the teacher realizes it will be important to use different manipulative aids the teacher chooses to use?

T chart, number line, judy clock

Mr. jansen's second grade students have been working on addition and are now ready to being 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 calculation, they should be allowed to use a calculator

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, and add the two areas together

which method below does not define a function

passes the horizontal line test

the teacher is gathering data on the students from the past three assessments given in her class. in order to analyze and draw conclusions on the data in the most efficient manner, the teacher has decided it would be best to plot the assessment scores for each student to determine the probability with which the students will pass future assessments. in looking for patterns and relationships within the data, for which variables will the teacher be looking?

patterns in assessment grades over time and within similar concepts

a 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 students 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 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 blocks as she checks for understanding with the students?

pictorial models and blocks

second graders will be introduced to fractional parts through the use of shaded regions. the teacher will introduce that more fractional parts used to make a whole, the smaller the part, and the fewer the parts, the larger the part. the teacher will guide students to apply the concepts to halves, fourths, and eights, in order for students to see the difference in the fractional parts, how might the teacher represent this with the shaded regions?

provide students with three rectangles: one cut in halves, one in fourths and one in eights. then have the students shade the parts and compare the size of each part to a whole

the greatest benefit of providing elementary students with mathematical tools such as geoboards is that these tools

provide students with visual representation that promote their conceptual understanding

the fourth grade teachers at XYZ elementary school have planned the next three units in the math scope and sequence. during their planning time. the teachers set learning goals, developed the delivery of the lessons and designed the assessments. they delegated responsibilities for preparing copied of needed materials and set deadlines for when assessments needed to be graded. which of the following would need to take place to determine if goals were met?

reevaluate the learning goals and delivery of lessons to determine if the students met the goals through the assessments

manipulative, as concrete objects of mathematical expression, can be labeled as symbolic mathematics. ignorer to learn mathematics from the manipulative, what must students perceive from the manipulative

relationships between manipulative and other forms of mathematical expressions

in order to relate rounding numbers to a real life situation, the teacher is taking the class in a virtual field trip of a grocery store. the class has been divided into groups and given a list of items to purchase with a set budget. the students are to shop the store and use mental math with rounding to assess if the budget they have been given is adequate to purchase the needed items. The students have a set amount of time to complete assignment. which mathematical process would be applicable in this activity?

rounding to the whole number, addition of while numbers, subtraction of whole numbers

mr williams teachers a 3rd grade math class specifically for english language learners. his students are representative of four different culture and country backgrounds. some of the students do no currently speak english fluently. while this does present a challenge for mr. villains when communicating with the class as a whole, he designs his instruction in such a way that each student feels values and understood. which approach may be most beneficial to mr. williams students as he assesses them over a current concept

scaffold the assessment to the level of conceptual comprehension-concrete, semi-abstract, abstract-to assess each students ability and knowledge of the concept

fifth graders are learning about linear functions and how to best model a set of data. what kind of graph could best be used to model a set data representation years and average income in those years

scatterplot

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 ship 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 20s?

socks, shoes, feet

Determine the choice that does NOT relate to the following: 10x + 5

solve for the value of x

calculators, base-ten blocks, attribute blocks and cubes are some of the manipulative a math teacher has available to tach 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, classifications, investigations of size, shape, color, logical reasoning, sequencing, patterns, symmetry, congruence, thinking skills, geometry, organizations of data.

the teacher instructs the students to use their knowledge of place value to describe a number in more than one form. which of the following indicates different forms of a number a student could use?

standard form. word form, expanded form, expanded notation

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

BLUE GEOBOARD: 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 both a couples 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 in. How much area does the new label cover?

1005.31 in^2 C=2x3.14x8(R)x20

what is the probability of being dealt 4 heart from a standard 52-card deck if only 4 cards are to be dealt?

11/4165

which of the following answer choices is divisible by 6?

12960

arrange the following from smallest to largest 14 inches, 1 foot, 0.4 yard, 15 cm

15 cm, 1 foot, 14 inches, 0.4 yard

a third grade class is using a 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 20*12=240ounces 1 pd=16 oz 240/16= 15lb

find 1^3*1+2^3*2

17

what is the greatest common divisor (gcd) of the following numbers? 630 and 36

18

walter looks forward to Fridays because his teacher plays his favorite math game during the math period. she gives the class number and the students write an expression to equal that number. The object is to use 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+6-2x(-1^0)

given that a, b, c, are whole numbers, if a/b=4 and b/c=2 what is the value of a/b+c?

8/3

Nissa and alex are picking apples in the orchard. they had picked enough apples to fill two buckets. they knew they had picked 53 apples and that there were 32 apples in the second bucket. which expression will help nissa and alex determine how many apples are in the first bucket?

?+32=53

(blue statement with activity 1 and 2) as the class creates the model in activity 1, the teacher asks questions designed to help students develop particular map skills and understandings. which of the following question best promote students' ability to apply the concept of relative location?

Is the book shelf or the piano closer to the aquarium?

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

given two even integers, a and b, determine what could be the least common multiple (LCM)?

ab/2

which basic operation has commutativity

addition

sea-tac airport in Seattle, WA, has a flight leaving dallas, tx every 2 hours and a flight leaving Washington, D.C. every 45 minutes. At 5:00am, on midday, a flight to dallas and a flight to washington leave at the same time. what is the next times that flights to dallas and washington will leave at the same time?

answer: 11:00 am the same day

which choice is a real number? a. 3/0 b. 0^1 c. 0^0 d. 0/0

b. 0^1

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 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/representation such as tally marks or T-charts

which of the following is NOT a prerequisite for children to recognize patterns?

compare sets

the teacher has designed several situation within the classroom for students to practice measuring objects based upon length and distance. some of the stations require the students to use standard units of measurements and other stations require the students to use non-standard units of measurements, such as paper clips. the teacher will monitor and move about the classroom while students work in small groups to solve the task cards at each station. what approach to learning is the teacher implementing in this lesson?

constructivist theory

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

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

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 in 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

In order to push the students to a higher level of thinking, which question would be appropriate for the teacher to ask if the math problem to be solved was 650*45?

explain how to solve for the product of 650*45