Math- Teacher Certification Exam
Bobby is buying gumballs for 7 of his friends. There are 51 gumballs before Bobby makes his purchase at the store. Bobby wants to give each of his friends the same amount of gumballs and not have any gumballs left. Which of the following approaches can Bobby use to find the greatest number of gumballs he can purchase to give his friends?
C
Caitlin knows that all birds have a beak. Adam is a bird. Therefore, Caitlin concludes that Adam has a beak. What type of reasoning is Caitlin using? A informal reasoning B inductive reasoning C deductive reasoning
C
Colin is a child learning about animals. He notices that dogs have four legs and a tail. When he sees a cat he incorrectly calls it a dog. What type of reasoning is Colin using? A inductive reasoning B deductive reasoning C formal reasoning D informal reasoning
A
For a student with strong addition skills, which subtraction algorithm is most suited their skill set? A Counting Up B Trade First C Same Change Rule
A
John made a circular garden in his backyard. The garden has a diameter of 20 feet. He used ⅓ of the garden for tomatoes, his favorite vegetable. He enclosed the entire garden with a picket fence that was 12 inches high. Which of the following questions could NOT be answered with the information provided? A What is the volume of the dirt in the garden? B What is the area of John's garden? C How many feet of fence does John need? D What is the area of the tomato patch?
A
After a lesson on rounding and estimation, a teacher tells students that the football concession stand has purchased 590 candy bars to sell for the 6 football home games this year. The teacher asks the students to estimate the average number of candy bars that will be sold at each home game. Which of the following would be the correct estimation? A 105 B 100 C 98.3 D 90
B
Bill went to the store to purchase new clothes for the upcoming school year. Bill purchased 8 shirts, 4 pairs of shorts, and 2 pairs of pants. If a single outfit consists of one shirt and either one pair of shorts or one pair of pants, how many outfits can Bill create with the clothes he purchased? A 42 B 48 C 16 D 32
B
During a lesson on using models in mathematics, a teacher asks the students to figure out how many hours they spend on homework for all their classes each year. In asking this question, the teacher has asked the class to: A demonstrate their proficiency with the use of proofs. B demonstrate an understanding of the estimation process. C demonstrate their ability to use statistics with data. D demonstrate the use of symbols to represent mathematical quantities.
B
Which situation could best be represented by the equation: 12x = 54? A Marty had 54 minutes left on his cell phone plan. If he uses 12 minutes, what is x, the number of minutes remaining on his cell phone plan? B Marty earns $12 for typing a paper. If her rate is $54 per hour, what is x, the number of hours it actually took to type the paper? C Marty made car payments on her car for 54 months until it was paid off. What is x, the number of years it took Marty to pay off her car?
C
Which of the following is a developmentally appropriate activity for an average sixth grader to establish number sense? A multiplying 2- and 3-digit numbers together B graphing an ordered pair on the coordinate plane where x and y are both positive C placing positive and negative numbers on a number line D using positive and negative numbers to represent financial situations
D
The following word problem was given to Mr. Trout's fourth-grade class: The Hotel Vacay is hosting a Wintertime Brunch for families. Each child that attends gets to decorate a gingerbread house and use the ice slide 3 times. Every family gets 2 snowballs per person. If 108 people can be seated and there are an equal number of adults and children, how many gingerbread houses and snowballs do they need? Morgan solved the problem using this equation: 108/2 + 108 × 2 Julia solved the problem using this equation: 108 × 2 ½ Which child is correct? A Morgan B Julia C Both children D Neither child
C
What learning progression should be used when teaching math concepts to sixth-grade students? A symbolic to abstract to real world B symbolic to concrete to abstract C concrete to symbolic to abstract D concrete to symbolic to real world
C
Which of the following statements is false? A Indirect proof is based on deductive reasoning. B Direct, formal proof is based on deductive reasoning. C Inductive reasoning never leads to a correct conclusion. D Inductive reasoning is the basis of many hypotheses and conjectures.
C
Anytown School District wants all elementary students to be able to use computational strategies fluently and estimate appropriately. Which of the following learning objects best reflects this goal? A Students evaluate the reasonableness of their answers. B Students understand the theoretical reasoning of basic mathematical rules. C Students will memorize multiplication tables. D Students will use calculators to perform their computations and check for accuracy.
A
Before teaching multiplication, a teacher reviews skip counting on a number line. Students use different colored markers to show counting by 2s, 5s, and 10s. After introducing multiplication, they review their number lines and connect the concept to the jumps. Why did the teacher return to the number line as she taught? A This allowed students to connect prior knowledge to new concepts with a visual example. B This tied the warm-up to the exit ticket. C Students could add decorations if they already understood multiplication. D It provided remediation for struggling students.
A
Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable. How should Mr. Johns handle this situation? A Agree to meet, listen to their concerns, and then explain that one component of math is understanding reasonable answers. B Offer to send the test home for them to review. C Agree to meet, but let them know in advance that the grade will not be changed. D Offer to call them because a conference is not necessary.
A
Mr. Marlowe wants his students to be able to interpret word problems relating to geometry. He has many ELL students. What is the best way to clarify the meaning of various prepositions such as: above, below, together, apart, inside, etc.? A Give students a visual diagram that explains these terms. B Give students the questions in their native language. C Teach students to underline the confusing words in a question and ask native speakers for clarification. D Give students a dictionary to use while solving word problems.
A
Mr. Meadows is a third-grade teacher in a low performing school. There is a high rate of absenteeism and low rate of students doing homework. He makes a public star chart where students get a sticker for each assignment they complete. Which of the following learning theories best matches the use of a star chart? A behaviorism learning theory B sociocultural learning theory C social learning theory D constructivist learning theory
A
Mr. Romeo wants his students to understand that math is very important and used in the real world all the time. He wants them to understand that math is used outside of school on a regular basis. Which of the following is the best way to have students learn about this? A Have students interview two adults about how they use math in their everyday life. B Make students read a book about famous mathematicians. C Have students teach their younger siblings to use math to solve problems. D Make students do a hands on project that uses math.
A
Mr. Yoder gave each of his students some Starbursts and some Skittles. He instructed the students to use the candy to set-up and solve multi-step equations, using the Starbursts to represent the x's, the Skittles to represent the constants, and different colors to represent positives and negatives. To solve the equations, students must determine how many Skittles are equivalent to one Starburst. Which of the following concepts is Mr. Yoder most likely working on with his students? A order of operations when solving equations B combining like terms C understanding what a solution is D properties of equality
A
Mrs. Herschend decided not to give a test about ratios and instead had her students do a project to display their knowledge. She has decided that she will do this for every unit going forward. What is the main disadvantage to this approach? A Students need to practice test taking skills periodically. B Some students are not creative and projects are more stressful than tests. C Parents can help with projects and the students knowledge may not be displayed. D Projects take more class time than giving a test.
A
Mrs. Hoyt is excited to be teaching fifth-grade math this year. She would like to encourage her students' independent skills. How can she facilitate this in her classroom? A allow for a variety of choices when it comes to assignments B allow students to choose groups for classwork C allow extra recess time D allow homework to be optional
A
Mrs. Marshall grades tests from the last unit and realizes most students are missing word problems because they do not identify the correct operation to use. They did demonstrate mastery on questions that provided the equation. How should she address this issue? A Provide a warm-up question each day and students must underline key terms that help decide what operation to use. B Address it through homework packets. C Add a mini-unit covering math vocabulary and key terms. D Reteach the unit using word problems.
A
Mrs. Rogers is teaching her students about volumes of regular rectangular prisms. She has students work with pieces of wood and measure their length, width, and height to determine volume. She asks students to analyze nets of prisms to determine their volume. While students have been successful using pieces of wood, they seem to be having issues using nets. How should Mrs. Rogers intervene? A She should demonstrate how to cut out and assemble the nets and then ask students to determine area of the nets in 3D form. B She should ask students what measurements they are taking. C She should use nets of cubes instead. D She should teach students how to calculate surface area using nets.
A
Ms. Klein is teaching her students about tessellations. She brings in magnetic tiles for her students to create their own tessellations as an introductory activity. She hands them out to the students and then begins to explain the activity for the day. Students are not paying attention and instead building whatever they want. How can she improve her teaching practice? A Give the students clear instructions and a worksheet that accompanies the activity prior to handing out the tiles. B Give students a picture of a tessellation to color instead. C Take away tiles from the misbehaving students. D Do not use magnetic tiles because they are distracting to the students.
A
Ms. Monroe is teaching her students about counting money and change. In her first period class she gives several word problems as practice. In her second period class she has students run a school store and practice giving change. She finds that students in her second period class perform much better on the unit test. What could explain the difference? A Students found the school store engaging and learned the material better than students given word problems. B Students in her second period class are more intelligent than students in her first period class. C The word problems were easier than giving change in a school store. D Students did not like the word problems.
A
Ms. Nakaroti wants to teach her students about properties of points, lines, planes, and angles. Which of the following should she include in her planning for the unit? A Analyze the standards to determine learning objectives before she starts writing lesson plans. B Use google to find worksheets about the topic. C Ensure that students are engaged in group work every single instructional day. D Make sure students write an essay that uses all of the key terms as their summative assessment.
A
Put these fractions, decimals and percentages in order from greatest to least: 15%, 0.34, 245%, 2 ¾, 1.5, 1/15 A 2 ¾, 245%, 1.5, 0.34, 15%, 1/15 It is easiest to convert these numbers to decimals and then order them. 15% = 0.15, 0.34 = 0.34, 245% = 2.45, 2 ¾ = 2.75, 1.5 = 1.5, 1/15 = 0.067 B 1/15, 0.34, 15%, 1.5, 245%, 2 ¾, C 2 ¾, 245%, 1.5, 15%, 0.34, 1/15
A
Susan's second-grade class is studying fact families. Each student is purposefully assigned a fact card and asked to find other members of their family. Above are the cards received by 5 students. Students in the same fact family then work in a group to create fact family houses that are displayed at the school's Open House where parents come by to see the classroom and the student's work. Why is this an effective way to group students? A Students are discussing the concept before working on it. B It forces students to get to know people they don't usually work with. C All of the special education students can be grouped together without it being obvious. D It does not show favoritism.
A
The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500? A $500 = $2b - $0.75b B $500 + $2b = $0.75b C $500 = $2b + $0.75b
A
The Trout family just purchased a large table in the shape of a perfect circle. It is 600 cm across. John helps set one side of the table for dinner and walks exactly halfway around the table. Which of the following is closest to how far has he walked? A 950 cm B 1,000 cm C 1,900 cm D 600 cm
A
The west wall of a square room has a length of 13 feet. What is the perimeter of the room? A 52 feet B 48 feet C 169 feet D There is not enough information
A
When teaching geometric shapes, Mr. Gaines challenges his students to prove a statement right or wrong. He writes on the board, "All rectangles are parallelograms and all squares are rectangles; therefore, all squares are parallelograms". What type of thinking is trying to promote? A deductive reasoning B conjectured reasoning C empirical reasoning D inductive reasoning
A
Which of the following best describes a high-stakes assessment, such as state mandated exams? A formal summative assessment B informal formative assessment C informal summative assessment D formal formative assessment
A
Which of the following cannot form a regular tessellation? A pentagon B hexagon C square D triangle
A
Which of the following is the best activity for reviewing percentages with fifth-grade students? A using a variety of methods and scenarios to determine percentage B writing percentages from decimal or fraction conversions C coloring in 100-blocks to represent percent D comparing percentages from their test scores throughout the year
A
Mr. Miller is teaching his students about the volume of rectangular prisms. He writes the formula volume = length × width × height on the board and tells his students to get to work. He notices two of his students arguing over which leg represents length and which represents width. What should he do? Select all answers that apply. A Allow each student to select which means length and which represents width on their own and then do math and compare the volume they compute. B Remind students that multiplication is commutative so it does not matter which leg they select to represent each variable. C Pull the students outside and tell them that arguing is not allowed. D Ignore them, as arguing can be a beneficial part of the learning process.
A and B
Ms. Colon, a new fifth-grade teacher, is planning her math lessons for the grading cycle. She thinks of all of the topics she needs to teach and makes discrete daily lessons. Each unit has an opening pre-test. Each lesson has instruction, guided practice, and independent practice. Which of the following are methods she should incorporate into her lesson planning? Select all answers that apply. A Plan each lesson with a closure activity. B Instead of making single lesson plans, first create a thematic unit around which to frame her lessons. C Plan time each day for students to explain concepts they have learned to their peers. D Instead of pre-testing students before each unit, begin new material as soon as possible
A, B, and C
A sixth-grade teacher is beginning a unit on probability. She utilizes the following steps in planning her unit: Determine the necessary prerequisite skills. Begin planning probability activities that involve the collection of data. Determine what the students already know by using a KWL chart. Plan the final assessment for the unit. What is the best order for the teacher to organize these steps? A I, III, IV, II B IV, I, III, II C I, III, II, IV D I, II, III, IV
B
A student is instructed to draw a four-pointed geometric shape on an xy-plane. After the shape is drawn, the student is instructed to add 5 to each x-coordinate and add 3 to each y-coordinate. Which of the following did the student perform? A refraction B translation C reflection D rotation
B
A tennis ball has a diameter of about 3 inches. The container that holds a stack of three such balls is a right cylinder with a circular base. What is the approximate volume, in cubic inches, of the container that holds three tennis balls? A 82 B 64 C 108 D 27
B
Jemma likes to earn spending money through babysitting her neighbor's child and helping with extra chores at home. The expression 8b + 6c represents the total amount of money (in dollars) that Jemma can earn, where b is the number of hours of babysitting she completes and c is the number of chores she finishes. Which term represents the total amount of money that she earns from babysitting? A (8b=6c)/2 B 8b C 6c D 8b + 6c
B
Miss Kelly has been teaching fractions and believes her students understand composing and decomposing fractions through the activities they have done. What activity would be best to informally assess their knowledge before moving on to the next lesson? A Lead a discussion on fractions in the real world B Provide a warm-up question that asks them to write one way to decompose 3/4 C Give a short pop quiz with fraction composition and decomposition D Include fraction composition and decomposition in the homework tonight
B
Miss Wilson's class is learning about unit rates. They are comparing costs from the grocery store to see if the store brand is a better deal than the name brand. Douglas and Kaitlyn are volunteering to answer questions during class, but few others are. What should Miss Wilson do? A Reteach the lesson as most students must not be understanding it B Provide wait time before calling on someone to answer C Call on students who have not volunteered and help them to the right answer D Give a few more practice problems to see if other students begin picking up on the concept
B
Mr. Chappel hangs posters in each corner of the room with different names of number categories. One corner has a sign that says integers, another has a sign that says rational numbers, another says irrational numbers, and the last says whole numbers. Students are assigned a corner to start and on the first rotation they must add a definition to the sign. On the second rotation, they must add numbers that are examples to the sign. What should be the third rotation task? A editing the definition contributed by the first group B adding a picture that helps students remember what is included in the number set C adding non-examples D beginning a worksheet related to the number group in their corner
B
Mr. Erikson has his friend Ted, who is an architect, come present to the class about how he uses math in his job. What is Ted likely to talk about? A How he uses calculators daily. B How geometric figures are a part of most buildings. C How he measures in yards. D How he did not need to attend college to be an architect.
B
Mr. Miller has taught addition with two-digit numbers and rounding. His students are beginning to use this concept in word problems. He teaches them 3 methods to simplify the process: guess and check, make a list, and draw a picture. Is teaching 3 different strategies a good practice? A No, because it is overwhelming to students to have 3 choices. B Yes, because this allows students to develop a strategy that works for them. C Yes, because students like to have choices as this gives them a sense of control. D No, because these are all visual methods of learning and does not help auditory and kinesthetic learners.
B
Mr. Stiles is introducing measurement to his third-grade class. He has rulers, stopwatches, scales, and graduated cylinders available for them to use. Based on previous lessons, he knows that most students do not know how to use these tools correctly. What is the best introductory lesson for this unit? A a pre-quiz that requires the use of each of the tools B providing students time to explore the items and then creating a K-W-L chart C a demonstration on how to use each tool D stations that go with a worksheet packet
B
Mr. Swan wants to ensure that his students truly understand the material he is teaching. When students get questions incorrect on a test, he presents them the opportunity to correct their answers for half credit. He asks students questions such as "what if I changed this number?" and "why did you do this?" What process is Mr. Swan trying to get his students to engage in? A auditory learning B metacognition C kinesthetic learning D integrative learning
B
Mrs. Brooks is a first-grade mathematics teacher. She wants to incorporate workstations into her lesson. She sets up the following stations: Station 1: Students toss two dice and record the numbers on each die and the sum of the two dice. They repeat the process ten times. Station 2: Students build a tower consisting of nine cubes and each cube must have either a red or blue color on a side. Students then count the number of red sides and blue sides on each side of the tower. Station 3: Two students place 13 marbles on the table. The students take turns removing from 1-12 marbles from the table and the other student has to figure out how many marbles the other student removed. The students then record the two numbers. Which of the following concepts should Mrs. Brooks teach her class before they start work at the stations? A one more and one less B part-part-whole C benchmarking numbers D spatial concepts
B
Mrs. Johnson lets her students choose between two word problems: Problem A: If you are digging for dinosaurs and need to fence off your dig site, what's the biggest site you can fence off with 40 ft. of fence? Problem B: What is the largest area you can create with 20 inches of rope? Mrs. Johnson finds a significant majority of her students chose to work Problem A. Which of the following is the most likely reason more students chose Problem A instead of Problem B? A Students who work Problem A get a greater reward from Mrs. Johnson than students who work Problem B. B Problem B is less interesting than Problem A. C Problem A requires a lower mathematical knowledge. D Problem B is harder than Problem A.
B
A fifth-grade teacher is beginning a unit on equivalent fractions with her students. If this is an introductory lesson, which of the following activities would be the most effective in helping the students understand the concept of equivalent fractions? A begin with the concept that 50¢ is ½ of $1; 25¢ is ½ of 50¢; 5¢ is ½ of 10¢ B compare pictures showing ½ of a variety of different objects C find as many fractions as possible equivalent to ½ in one minute D use pattern blocks to model fractions equivalent to ½ of the hexagon
C
Mrs. Peters teaches a class with native English speakers and English language learners (ELL). She needs to introduce new mathematics terminology for the upcoming instructional unit. Which of the following would be the best strategy for implementing the new terminology? A Have students practice using the terminology with each other using English in their conversation. B Mrs. Peters explains each term to the class and then uses the term in a variety of sentences. C Because mathematics terminology can be difficult, have students create their own spelling for the new terminology. D Have each student write down the new word with the corresponding definition.
B
Mrs. Summer's students are having difficulty with the concept of multiplication. She wants to use calculators to help students better understand the concept of multiplication. Which of the following would be the most appropriate activity for Mrs. Summer to provide her class? A Have students add together the ages of each of their classmates to find the average age of the class. B Have students type 8 + 8 + 8 + 8 + 8 and then 8 x 5 and then write down why the values of the two equations are equal. C Calculators cannot be used to enhance the students' conceptual understanding of multiplication. D Have students race against the other classmates to answer equations that Mrs. Summer writes on the board.
B
Mrs. Wheelan is teaching geometric shapes and wants to use informal reasoning questions for discussion. What question is best to start with? A What geometric shape does not have any edges? B How do geometric shapes play a role in daily life? C What is a quadrilateral? D What is your favorite shape and why?
B
Ms. Trask wants to create an authentic assessment to test her students about angles in triangles. Which of the following should she do first? A Ask students what they would like to learn about angles. B Look at the standards to determine what a meaningful task that students could complete to demonstrate their knowledge. C Write all of her lesson plans for the unit. D Create a secondary multiple choice exam to validate her assessment.
B
Rather than give a unit test, Mrs. Kirby decides to assign a major project to her students. They are provided a rubric that sets the expectations and guidelines. Students will be given 2 class periods to work on it and the rest must be completed at home. Students will then present their projects in class. What is the main advantage to giving a project rather than a test? A Parents can help their children with the project and parental involvement is key to academic success. B Projects require higher level thinking and can demonstrate greater concept mastery than tests. C There are usually fewer answers to grade on a project than a test so it saves time. D It lowers students anxieties as they do not have to prepare for a test.
B
Sheila has a large collection of stickers. She gives ½ of her collection to Sue, ½ of what is remaining to Sandra, and then gave ⅓ of what was left over to Sarah. If she has 30 stickers remaining, how many stickers did she begin with? A 90 stickers B 180 stickers C 270 stickers D 120 stickers
B
The cement pipe used in a storm drain system is an 8-foot long right circular cylinder with a wall thickness of 3 inches and an outside diameter of 24 inches. Which of the values below best approximates the volume, in cubic feet, of the interior of the pipe? (The formula for the volume, V, of a right circular cylinder with radius r and height h is V = πr2h.) A 25.1 B 14.1 C 2,034.7 D 113.0
B
Which expression can be used to solve the following word problem? John and Jose want to buy a pizza for dinner and then head to a movie. They will each pay for their movie ticket, which costs $12 each, and they will split the pizza cost of $9. John has $17 and Jose has $20. How much will Jose have left at the end of the evening? A 20 + 17 - 9 - 12 B 20 - (9/2 + 12) C 17 - (9/2 + 12) D 9/2 + 12
B
Which of the following has the least value? A 4 thousands B 483 ones This is the same as multiplying 483 × 1 which equals 483. C 44 hundreds
B
Which of the following is the best way for elementary students to be introduced to rectangular arrays? A Giving them sample problems with arrays B Using manipulatives such as 10-blocks to create their own arrays C Watch an online video over arrays D During math games, use an array as part of a question
B
Ms. Smith gives a unit exam on transformations of geometric figures. It is a 20-question multiple-choice exam. All but one student gets a 100 percent on the exam. What can be said about her assessment? Select all answers that apply. A She clearly taught the material very well since so many of her students got a 100 percent. B She probably should have added some open ended questions to give her students more opportunity to demonstrate mastery. C Her students are very good at answering multiple choice questions pertaining to transformations. D Her exam was too difficult.
B and C
A math teacher plans her instructional delivery method on resolving the difficulty students have distinguishing between mode and median. She plans to have students first work alone calculating the mode and median of sets of performance results from the school track team. Next, her students will work in groups of 2 or 3 to discuss and interpret their results, and record a summary of the significance of the results on whiteboards. Finally, the groups will present their summaries to the class, along with a teacher-led discussion of the findings. By planning such an activity, the teacher demonstrates that she understands: A how to use a variety of questioning strategies that encourage mathematical discourse and help students analyze and evaluate their mathematical thinking. B how technological tools and manipulatives can be used to assist students in developing mathematical thinking. C how to apply a variety of instructional delivery methods that can help students develop their mathematical thinking. D how students' prior mathematical knowledge can be used to build conceptual links to new knowledge.
C
A sixth-grade teacher discovers that each student in his class receives an allowance from their parents. Which of the following examples would best demonstrate to the students the power of saving their allowance instead of spending all of their allowance? A Have students set aside 10% of their allowance each week. B Have students calculate the amount of federal tax owed on their allowance if it was taxed. C Show students the expected return of 5% allowance savings over a 10-year period. D Have students research a charity and ask how their allowance money could impact those whom the charity serves.
C
A student asks the teacher, "Why is the area of a triangle formula ½bh?" Which of the following would be the most appropriate answer for the teacher to provide? A The base of a triangle is usually half its height, so dividing the area by two gives an accurate measurement of the area. B The formula ½bh applies only to isosceles triangles. C A parallelogram is the combination of two congruent triangles. Since the area of a parallelogram is bh, one half of the area of a parallelogram equals the area of a triangle. D Since a trapezoid can always be divided into two equal triangles, dividing the area of a trapezoid in two equals the area of one triangle.
C
A teacher is monitoring her class while the students are involved in a group activity exploring the size of angles in a set of triangles. She moves from group to group, pausing and watching the group dynamics. What the teacher is doing can best be described as: A informal summative assessment. B formal summative assessment. C informal formative assessment. D formal formative assessment.
C
A teacher provides students a table on the historical populations of the United States during the 19th century, divided by decade. Which of the following would be the most appropriate display for the information? A a pie chart B a Venn diagram C a line graph D a histogram
C
A teacher wants her students to demonstrate mastery of combining and dissecting figures. Which of the following is the best activity to determine if they have mastered this concept? A Give students a challenging irregularly shaped object and have them determine the area. B A multiple choice test that asks for the area of various irregularly shaped polygons. C A project where students determine the area of 10 oddly shaped objects they have encountered in the last week and describe the process. D Have students write an essay about geometry in their lives.
C
Adam wants to determine how much to charge for an event. He looks through his records from old events to determine a reasonable price for the venue, the average price of catering, and thinks about other incidentals. He then solicits quotes from several people and places before setting a price for the event. What process is he using to create this budget? A informal reasoning B deductive reasoning C formal reasoning D inductive reasoning
C
Anytown School District provides a 50 multiple-choice question mathematics assessment to all students. The students complete the assessment, the tests are scored, and the scores are compared throughout the school district. Which of the following mathematics component is most likely the goal of this type of assessment? A automaticity B rate C accuracy D flexibility
C
It took Julie ¾ of an hour to run 3½ miles. What is her average speed in miles per hour? A 3 ⅔ miles per hour B 4 ⅓ miles per hour C 4 ⅔ miles per hour D 4 ½ miles per hour
C
Maria has recently moved from Mexico City to the U.S. She is a secondary student who speaks little English, but who came from her school in Mexico City with excellent grades. Which of the following would be the most appropriate accommodation for Maria's math teacher to use with Maria? A Repeat the instructions that are given to the rest of the class more slowly and privately to Maria. B Make sure that Maria has all the materials she needs to complete the assigned tasks. C Pair Maria with another student who speaks Spanish, to clarify instructions in Spanish as needed. D Allow Maria to be an observer in math class for a few days until she feels a bit more at ease.
C
Mr. Feeny has been teaching fifth-grade math for thirty years. He will only accept answers from his students that follow his algorithmic procedures. If a student determines a correct solution by any method other than the way they were taught in class they will not receive credit. How could Mr. Feeny improve his teaching practice? A Give half credit if a student determines the correct solution not using his method. B Give students credit as long as they get the right answer, regardless of how they found it. C Teach students multiple varied ways to achieve the right answer and accept any correct answer as long as there is mathematically reasonable supporting work. D His teaching methods are appropriate as they are.
C
Mr. Harris is planning to teach a unit on division to students for the first time. Which of the following would be the best first instructional lesson for Mr. Harris to present to his students? A presenting and solving a division problem using an abstract form or concept B having students memorize their multiplication tables C solving a division problem using a concrete manipulative D asking students their understanding of division prior to presenting the concept
C
Mr. Marshall is a math teacher and a student council sponsor. He has encouraged student council to do a service project, but they are struggling with ideas. He decides to assign his math class a project where they research local non-profits. How can he align this project with the curriculum? A Require students to write 3 words problems about the agency they research B Have students review the budget for the agency C Teach a lesson on how math can be used to inform people about social issues and have students find numbers that can help tell the story of the agency D Ask for a numbers sheet that has 10 numerical facts about the agency
C
Mr. Sexton has been trying a variety of teaching methods to engage his class, but it seems to make things more out of control. How can he increase engagement while maintaining an orderly classroom? A Incorporate more activities that allow students to move around and burn energy. B Use a louder voice that commands attention. C Establish a daily procedure for class and vary the activities used for instruction. D Rearrange the seating chart to separate disruptive students.
C
Mrs. Adamson's student asks her how much space a cube takes up. Mrs. Adamson said to answer this question, the student would need to calculate the volume of the cube. Which of the following measurable attributes is the formula for a cube based upon? A intensity B mass C length D capacity
C
Mrs. Campbell is teaching a lesson on slope-intercept form. She requires each student to create a formula that represents a graph they find visually interesting. Once each student creates a formula, she has the student present and explain his equation and graph to the class. Which of the following learning theories best matches the activity Mrs. Campbell uses with her students? A behaviorism learning theory B sociocultural learning theory C constructivist learning theory D social learning theory
C
Ms. Miller is a student teacher in a fourth-grade classroom. She has heard that group work is important so she wants to plan for group activities. On her first day student teaching, she briefly says "today we'll be doing group work about fractions" before she sends the students to stations. How could she best improve her teaching? A Her lesson plan is effective as it is. B Give students a behavior based participation grade to ensure they engage in the small group activity. C Give a whole group lesson on fractions before breaking into groups. D Ensure that each workstation addresses only one mode of learning.
C
Students are working to solve the following question: ½ - x = ¼. The teacher then gives the following as an example: "If you are sharing a pizza with somebody and there is half a pizza left, how much must the other person eat so that you only have one quarter of the pizza left?" As the teacher engages with several students, the teacher observes students are still having difficulty understanding the concept of fractions. The teacher then uses a pie chart to help explain the concept. Which of the following types of assessments has the teacher used? A formal B summative C formative D criterion
C
A student asks a teacher when calculating percentages of numbers will be useful in real life. Which of the following examples would be the most appropriate response for the student? A a builder cutting materials for a house B a architect designing a building C a pharmacist measuring the correct amount of medication D a mother going shopping at a store sale
D
A student asks a teacher when would knowing the likelihood of a six being rolled on a dice be useful in real life. Which of the following examples would be the most appropriate response for the student? A a teacher averaging a student's grade for the semester B a farmer measuring the length of the fields to determine area C a builder cutting materials for a house D a casino estimating the expected number of jackpot payouts over the next fiscal year
D
A student asks the teacher who invented the number system we use today. Which of the following answers would be most appropriate? A The current number system was developed by the Greek and Roman empires. B The current number system has evolved over a period of thousands of years and each culture contributed to its development. C The base-ten number system was invented by Isaac Newton in the late 17th century. D The base-ten number system was developed by the Hindu-Arabic civilizations.
D
A survey is taken of students in a math class to determine what pets the students have. 7 students have birds; 15 students have cats; 18 students have dogs. Some students have more than 1 animal. For example, 3 students have cats and dogs and 4 students have cats, dogs, and birds. All students have at least one of these three types of pets. Which of the following would be the best strategy to use to answer a question about how many total students are in the class? A work a simpler problem B work backwards C simply add all of the given numbers D draw a Venn diagram
D
A teacher wants to introduce her students to three dimensional figures. Which of the following is the best first activity to do? A Draw images of three dimensional figures on the board and ask students to determine the number of faces, edges, and vertices in each. B Define the essential key terms: faces, edges, and vertices. Make a word wall to display these terms for the entire unit with the students. C Give students a reading about three dimensional figures and have them define the key terms: faces, edges, and vertices in their own words. D Give students models of various three dimensional figures and have them write what they observe about the figures.
D
After reviewing a student's math assessment, the student's teacher has determined that the student is not following the order of operations when solving problems. Which of the following is the most appropriate remedial intervention? A use of manipulatives B reduced answer choices C math drills D mnemonic device
D
In a unit on personal finance, a sixth-grade teacher wants students to be able to identify the difference between fixed and variable costs. Which of the following examples would best highlight this difference? A looking at the differences between a tax deduction and a tax credit B having students ask their parents what fixed costs they pay each month C analyzing the money spent on gas each month of an average American and looking at how much a person drives impacting the price they will pay in gas D categorizing the expenses of a local restaurant into expenses that depend on the number of customers and expenses that do no not depend on the number of customers
D
Janine is trying to determine who to vote for in the class president race. She thinks that candidate A is friendlier to her, but candidate B is better at convincing adults to do things. What type of reasoning is she using when she decides who to vote for? A formal reasoning B deductive reasoning C inductive reasoning D informal reasoning
D
Joshua is learning about volumes of three-dimensional figures. First, his teacher explains what volume is. Then, she writes the formula for area of a cube on the board v = s3. Next, she has the students recite "the volume of a cube is the side length cubed". Finally, she has students take six-sided dice of various sizes and measure them to determine their volume. Which best describes the teaching method is the teacher attempting to use? A visual learning B auditory learning C small group instruction D task variety
D
Juan is 5 feet tall and casts a shadow that is 10 feet long. If the flagpole casts a shadow that is 30 feet long, how tall is the flagpole? A 30 feet B 10 feet C 5 feet D 15 feet
D
Mrs. Dobbs is teaching students to skip-count by 2s, 5s, and 10s in her second-grade class. Earlier in the year, she evaluated her students learning style and assigns them one task based on this evaluation. Visual learners have been given a number line and they are to draw the hops across the top. Auditory learners have been given a list of the even number to 20, numbers divisible by 5 to 50 and numbers ending in 0 up to 100. They are told to say them over and over aloud to memorize the skips. Kinesthetic learners have been given a large number line on the floor. They are jumping to the next number as they skip-count. What can Mrs. Dobbs do to improve her teaching? A Allow for more creativity by letting students make an art project out of drawing or write a song as they recite numbers. B Require them to participate in the jumping activity first to burn off some energy and then choose one of the other activities. C Allow students to choose which activity they participate in. D Allow all students to participate in all three activities by rotating through them.
D
Mrs. Doloff's third-grade class has learned about ordering people according to age when given a word problem such as "John is older than Mei and Mei is older than JD. Who is oldest?" What is the next concept for Mrs. Doloff to teach about ordering? A adding algebraic terms so that each person is represented by a letter such as person A, B, C B teaching them to order based on height without numbers C teaching them to order based on height with numbers D adding numbers to the problem to solve for exact age
D
Mrs. Matthews is teaching her sixth-grade class about areas of regular geometric figures. How should she best introduce this topic to her students? A Ask students to draw pictures and then trace those figures onto graph paper to estimate the number of squares inside the figure. B Take students to the gym and have them measure parts of the floor to determine area. C Give students a list of formulas to determine area of figures. D Give students pattern blocks to manipulate. Tell them the area of the smallest figure is one and ask them to determine the area of the larger figures.
D
Mrs. Nadir's students are great at determining the surface area of cubes. They struggle with determining the surface area of rectangular prisms. What should she do to help her students be successful? A Determining the surface area of cubes is sufficient content knowledge. B Teach students to determine length, width, and height. Then go over the surface area formula. C Move on to teaching them about the surface area of spheres. D Reinforce how to determine the area of rectangles and then procedurally add the areas of the faces of a block.
D
Ms. Miles is teaching her students about circles. Students are having problems with determining area because many of them are confusing the formulas for circumference and area. What should she do to address the problem? A Give students half credit if they tabulate the circumference instead of the area. B Have students write an essay about the similarities and differences between circumference and area. C Continue to the next topic. Circles are not generally an important part of the statewide assessment. D Create an activity where students determine area and circumference in a hands on way to activate a concrete level of understanding.
D
The Payday Lending industry has faced increased criticism and scrutiny for which of the following practices? A making cash available on short notice B supporting local economies in depressed cities C increasing the credit scores of low-rated borrowers D charging high interest rates
D
The mathematics teacher and art teacher work together to create an interdisciplinary lesson using tessellations, which are basic geometric shapes set to a repeating pattern. The students cover a large piece of poster board with the patterns they create. Which of the following mathematical concepts is most closely reflected in this activity? A number sense B perimeter C conservation D infinity
D
Which of the following activities is most effective in helping kindergarten students understand measurement of the lengths of small items, such as juice boxes or lunch boxes? A listening to a teacher explain how to use a ruler to measure the objects B watching the teacher estimate the length of the item using a student's arm or leg C tracing the items on construction paper and cutting the construction paper to have a two-dimensional replica of the item D placing same-size objects, such as Legos or cubes, next to the object and counting the number of objects
D
Mrs. Luna tried flipping her classroom to teach common denominators, having students watch a lecture at home and then doing the homework practice during class. Many students did not watch the entire video because they thought they had the concept down after the first example. If she tries this again, how should she change her approach? A Have students create the video. B Provide a notes outline that needs to be filled in as they watch the video. C Give prizes for those who watch the entire video. D Keep students inside during recess if they did not watch the entire video so they can catch up.
b
