Math Pedagogy Test
A student purchases a ball and a bat for $9.00. The bat costs three times as much as the ball. What is the cost of the ball?
A. $2.25 B. $3.00 C. $6.00 D. $6.75
In a bag of marbles , 2 are blue, 3 are green, and 3 are red. What is the probability that a marble drawn at random from the bag will be blue?
A. 1/8 B. 1/4 C. 1/3 D. 1/2
There is a total of 28 wheels in a store with both bicycles and tricycles. What is the largest number cycles that could be in the store?
A. 11 B. 12 C. 13 D. 14
A school pans to erect a fence around a rectangular playing field that is 120 feet long and 75 feet wide. The fence will be set 6 feet away from each edge of the field. What is the length of fence required?
A. 138 yards B. 142 yards C. 146 yards D. 150 yards
In order to demonstrate the appropriate ratio of feet to yards, how many rulers should be available to compare to a yardstick?
A. 2 B. 3 C. 5 D. 10
A second grade teacher instructs students to show their work for the two digit subtraction problem 42-17. Which of the following depictions of student work indicates procedural fluency?
A. 42, 41, 40, 39, 38, 37, 36, 35- 10= 25 B. 42= 20+22 -17= 5+ 20= 25 C. 42- 2=40- 5=35- 10= 25 D. 42= 30+ 10 + 2 -17= -10 -7 ________________________ 20+ 3 + 2 = 25
In a game, there are eight bowling pins numbered from 1 to 8. A ball is rolled toward the pins, with the score determined by the sum of the pins knocked over. In how many different ways can a person get a score of 8?
A. 9 B. 6 C. 5 D. 3
Use the student work below to answer the question. 17 36 39 + 3 + 3 - 20 ===== ======= ======= 20 39 19 The strategy and concepts used by the student to compute 36- 17 is best described as:
A. Adding up using known addition facts--- thinking of the number that must be added to the smaller number to get the larger number. B. Compensating-- understanding addition and subtraction as inverse operations so that both numbers are increased by the same number before the subtraction occurs. C. Composing and decomposing numbers using place value--- breaking apart the second number into 10s and 1s, subtracting the 10s first, and then subtracting the 1s. D. Subtracting in two steps--- breaking apart the second number so that the 1s place matches the 1s pace in the first number, finding the difference as a multiple of 10, and then subtracting the remaining part.
A preschool teacher is preparing lessons for a class of children who will be four years old at the beginning of the school year. Which of the following activities would be most appropriate to begin development of the concept of number?
A. Asking children to write randomly stated numbers from 1 to 10 in a sand tray. B. Asking children to say numbers in order from 1 to 10 and then back from 10 to 1. C. Asking children to write the number that tells them how many objects are pictured, with totals less than 10. D. Asking children to count how many objects are in a group of up to 10, rearranging the number of objects after each count.
A first-grade teacher wants to introduce the concept of Venn diagrams to students as a way to organize and present data. Which of the following activities would be the most appropriate way to generate data for this purpose?
A. Asking students to record temperature and conditions each day of the week. B. Asking students to sort blocks of various shapes and colors. C. Asking students to order different figures by the number of sides D. Asking students to say whether they buy lunch or bring it to school each day.
First graders have been developing an understanding of adding and subtracting 10 from a given number by using counters, base-ten blocks, number lines, and 100 charts. Their teacher now wants students to mentally add or subtract 10 to a given two-digit number without having to count. Which of the following learning activities would best introduce this concept?
A. At the start of the math class, having students count forwards and backwards by 10 without using a number line or 100 chart. B. Having students use chips to solve equations adding 10 and subtracting 10 from a given number (e.g., 5 + 10 = ?) C. Choosing a number on 100 chart and having the students add 10 or subtract 10 and discuss patterns and observations as a class. D. Demonstrating adding and subtracting 10 using the traditional algorithm and pointing out that the tens digit changes, but the ones digit stays the same.
A kindergarten student enjoys playing with geometric shapes during activity time. The teachers has observed that the student sorting, counting, and naming the shapes. To challenge the student, the teacher chooses two of the triangles. Which of the following questions by the teacher would best further the development of the students spatial sense?
A. Can you join these two triangles to make a rectangle? B. Can you correctly name these two shapes? C. What is the difference between these triangles and a rectangle? D. What is the difference between a two-dimensional and a three-dimensional figure?
Use the student work below to answer the question. 356 + 238= ? 300 + 200= 500 50+ 30= 80 6+ 8= 14 500+ 80 +14= 594 The answer is 594. This work shows that the student is able to add using strategies based on an understanding of the:
A. Concept of place value B. Relationship between addition and subtraction C. Associative Property D. Order of operations.
A first grade teacher identifies a student who appears to have , according to the state standards, above-grade level number sense. Which of the following skills would best demonstrate the students progress toward a standard from grade 2?
A. Counting forward and backwards by 2's, 3's, 4's, and 5's to and from 200 without a 100 chart B. Performing with consistent accuracy on timed fact tests with mixed addition and subtraction combinations to 18. C. Dividing a number such as 23 into groups of 20 and 3, 10, and 13, and 8 and 15; then writing corresponding number sentences. D. Using counting-on and counting-back strategies to find sums and differences of two-digit and one-digit numbers such as 21- 5 and 18 + 7.
First graders have been solving addition problems with sums less than 20. Their teacher assigns several problems and asks the students to explain their thinking using numbers, pictures, or words. When finding the sum of 7 + 8, a student reasoned as follows: I already know that the sum of 7 + 7 is 14 because its a double. Then you just add 1 more on. So 7 + 8 equals 15. This student shows an understanding of which of the following addition strategies.
A. Decomposing a number leading to 10 B. Counting on from a given value. C. Applying the commutative property of addition. D. Creating an equivalent equation from a known fact.
A kindergarten teacher gives pairs of students a bag of yellow and green blocks. The teacher then poses the follow problem: You have 10 blocks. Some are yellow. Some are green. How many of each could you have? How many yellow? How many green? The teacher then asks the students to find as many combinations as they can and record their solutions. This learning activity would be most appropriate for teaching which of the following mathematical standards?
A. Find the number that makes 10 when added to a given number for any number 1 through 9. B. Understand that 10 can be thought of as a group of 10 ones called a ten. C. Decompose numbers less than or equal to 10 into pairs in more than one way. D. Recognize and label sets of 1 to 10 objects in patterned arrangements.
A pair of first grade students uses a 2 1/2 inch block to measure the length of a table. The students then use a 5 inch block to measure a different table of the same length. They announce to the teacher that the first table is longer than the second table. The teacher then measures the two tables with a ruler and shows the students that the two tables are the same length. This situation could be most appropriately used for introducing the students to which of the following mathematical concepts?
A. Geometric Shapes B. Standard units of measure C. Conservation of number D. Perimeter and Area
The first and second grade teachers are introducing a routine activity in support IN process standard 7: "Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. They step back for an overview and shift perspective. They recognize and use properties of operations and equality." Which of the following activities would best accomplish this goal for both grade levels?
A. Giving each students a math journal to record the big ideas learned that week. B. Asking students to use counting patterns, forward and backward, while lining up for lunch. C. Suggesting that students reflect on how each new topic relates to content or skills already learned. D. Posting a number of the day for students to break apart and put back together with number sentences.
A kindergarten teacher often uses blocks as learning tools in various areas of the curriculum. The teacher is currently planning activities to promote the students' problem solving skills. Which of the following activities with blocks would best support this objective?
A. Having students work in small groups to build a block structure that will support a heavy book. B. Showing students assorted blocks on a tray, then removing one block secretly and asking children to identify which one was removed. C. Distributing a variety of blocks to pairs of students and asking the students to sort the blocks by shape. D. Giving groups of students multicolor blocks and challenging them to make a colorful design.
A teacher wants to establish classroom routines that will both develop children's independence and self-reliance and promote their ability to practice important mathematical skills. Which of the following classroom routines would be most effective in developing students ability to use one-to-one correspondence?
A. Independently counting and laying out napkins and milk for a table of five children at snack time. B. Finding their own cubby space, book box, and sleep mat by finding corresponding number. C. Counting down from five to one orally as they quietly pick up their own center materials. D. Identifying without counting small quantities of items such as scissors, crayons, and markers.
Second graders have learned how to use yardstick and foot-long rulers. In addition, the teacher talks to them about the cubit, an ancient unit of measurement described as the length of a persons forearm from the elbow to the tip of the fingers. The students will then work in pairs and measure the length of a particular table in yards, feet, and cubits. The students will compare their results and try to decide how long the table really is. This activity will provide and introduction to the:
A. Need to use standardized units when measuring objects. B. Advantage of using a yardstick over shorter measurement tools. C. Occurrence of errors regardless of the measurement tool used. D. Reason that the scale of the measurement unit to the object is important.
Which of the following behaviors by a child demonstrates an understanding of one-to-one correspondence?
A. Placing blue and red balls in separate containers. B. Identifying objects in a room that come in pairs. C. Counting a group of ten objects by touching each object while saying the number aloud. D. Matching a puzzle piece with the number five to a puzzle piece with the five apples on it.
A kindergarten teacher wants students to describe the positions of objects using terms such as above, below, in front of, and next to. To ensure mastery, the teacher wants to integrate mathematics vocabulary into lessons throughout the day. Which of the following activities would be most effective in helping students describe the positions of objects using appropriate vocabulary.
A. Playing a game in which the teacher gives verbal directions (e.g., place the block on top of the bookcase), and having students use objects to follow the directions. B. Including position words on the class word wall (e.g., between, below, under), and having students read the words together, from left to right, at the beginning of reading. C. Giving students a list of position words and having them circle the correct word as the teacher describes the position of objects in the room using words from the list. D. When reading a picture book aloud, having the students discuss the structure of the book (e.g., the cover is on the outside, the pages are between the cover)
According to the Indiana Academic Standards and Core Standards for Mathematics, kindergarten students are expected to understand concepts of time including the following: today, yesterday, tomorrow, day, week, month, and year. A teacher plans to teach and review these concepts daily throughout the year. Which of the following class routines would be most effective in teaching the concepts of time to kindergarten students?
A. Posting a list of the vocabulary used to describe time, and having students recite the words as a student points to each on. B. Modeling and encouraging the students to use time vocabulary as they change the date on the class's daily calendar. C. Using the class calendar to determine how many days are in the current month and how many days remain. D. Writing the full date (Month, day, year) on the whiteboard each day and having students copy it to their journals.
Use the example of student work below to answer the question that follows. Express the following words as numbers. Fifty-six 506 Twenty-five 205 A student who made the errors shown would benefit most from which of the following activities?
A. Practicing basic math facts B. Reviewing the concept of "0" as a placeholder when writing numerals. C. Using unit cubes to represent numbers in base 5 D. Arranging groups of base-ten blocks and writing the numerals represented
Which of the following would likely be the most appropriate activity for promoting the development of basic mathematical concepts in 36 month old children?
A. Sorting yellow blocks and blue blocks into two groups by color. B. Buying an item at a pretend store using a specified number of pennies. C. Measuring the length of a familiar object using a nonstandard unit of measure. D. Using one-to-one correspondence to count 20 objects accurately.
At back to school night, a parent questions the standard for measurement at grade 1 that reads: "Use.... a nonstandard unit to compare and order objects according to length." Which of the following explanations of the standard best reflects research on how students learn to measure?
A. Standard measuring tools require understanding the concept of a partial unit as a fraction B. The fine-motor skills required for proper alignment of a ruler develop at a later stage. C. Measuring is comparing one object to another object, so the unit used is not important. D. Young students have limited skill with one-to-one counting and so require larger measuring skills.
A kindergarten teacher brings a basket of apples for a class snack. She has 16 students but brought only 8 apples. She first places the apples on a table and asks the students to each take one. When they observe that there are too few apples, she tells the students to stand in pairs behind the apples. She then cuts the apples in half and puts the halves side by side on the table. She asks the students if there are now enough apple pieces for everyone to take one piece. Finally, she asks the students to observe and discuss why there are now enough apple pieces for everyone. Which of the following mathematical concepts is the teacher demonstrating at snack time?
A. Symmetry B. Spatial Sense C. Additive identity D. Proportional thinking
A preschool teacher is working individually with children to assess their counting skills. The teacher arranges five red cubes, in a random order, in front of a child. The teacher asks, "How many cubes are there on the table?" The child counts, while touching each cube with a finger, "One, two, three, four, five." The teacher then asks. "How many cubes are there?" The child counts again, "One, two, three, four, five," while pointing to each cube and then answers, "Three." Based on this dialogue, the child does not yet understand:
A. That the last number said names the number of the objects counted. B. That the count remains the same regardless of the arrangement of the objects. C. How to apply one-to-one correspondence with objects or people. D. How to identify small quantities of objects in an irregular pattern without counting.
Which of the following activities performed by a second-grade student best demonstrates that the student is using mathematical reasoning?
A. The student measures the length of an object by selecting and using appropriate measurement tool. B. The student uses a vertical subtraction method that requires borrowing. C. The student makes a drawing to show that equal shares of identical wholes do not always have the same shape. D. The student reads the time on an analog clock and writes it in the digital form.
A first grade teacher wants to have students apply flexible thinking while looking for structural relationships in order to formulate and solve mathematical problems. Which of the following activities would best meet this goal?
A. Using a list of fact families to work with children on identifying known facts in computational problems and developing strategies for learning unknown facts. B. Using two digit with one digit numbers to work with children on describing their strategies. C. Using single colored counters to work with children on creating strategies for solving written word problems in real-world situations. D. Using two sided counters to work with children on listing addition and subtraction facts in problems for numbers up to 18.
Use the chart below to answer the question Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Twenty three students in a kindergarten class are given a day of the week card. The students then tape the cards to the board in sequence: Monday Tuesday Wednesday Thursday Friday Saturday Sunday, Monday, Tuesday, etc. After the cards have been on the wall for several days, the teacher moves the cards into rows, aligning the days in columns as shown. This activity is appropriate for demonstrating that:
A. Weeks follow a pattern that repeats every seven days B. Time is a relationship among days, weeks, and months. C. Months are made up of weeks, and weeks are made up of days. D. Calendars are tools that measure time in days, months, and years.
A second grade teacher wants students to understand that the digits of a three digit number represent hundreds, tens, and ones. To support their understanding, the teacher plans to have students explore this concept by representing three digit numbers using concrete materials. Which of the following materials would be most appropriate for this purpose?
A. a 100 chart B. geoboards C. base-ten blocks D. a number line
Which of the following would be the most effective method to use for monitoring the progress of second-grade students in mathematics?
A. administering norm-referenced assessment midway through the school year B. conducting frequent curriculum based assessments. C. administering a dynamic skills assessment at the beginning of each instructional unit D. conducting a portfolio assessment at the end of the school year.
A teacher wants to introduce geometric shapes to a group of 4 year old children who have not been previously attending preschool. Which of the following activities would best foster these children's understanding of the vocabulary and characteristics of basic geometric shapes?
A. arranging tangram pieces to build shapes that are shown on puzzle cards. B. Identifying and coloring similar shapes on an activity sheet when given the name of the shape C. Making triangles with rubber bands on pegboards and describing how they are the same or different. D. Contributing patterns made with attribute blocks and describing the attribute used to make the pattern.
Kindergarten students have collected red, yellow, and brown leaves on the playground and are wondering how many of each color they have. The most appropriate way for the teacher to help the students organize and present their information is to suggest that they create a:
A. circle graph B. scatterplot C. bar graph D. box plot
A kindergarten teacher keeps a large calendar on the classroom wall. Each morning, the teacher and the students discuss the weather, and the students decide whether they should place a sun or cloud on the calendar. Which of the following teacher-led activities would be most effective and developmentally appropriate for integrating math into this science activity?
A. creating a weather picture graph and updating it daily. B. asking the students to decide each morning whether it is sunnier or cloudier than the day before C. adding a yellow marble to a jar for every day it is sunny. D. Recording the daily temperature and correlating it to cloudy and sunny days.
A kindergarten teacher prepares a chart listing five routine school activities. The teacher hands each student a sticker and instructs the students to place the sticker on the line next to their favorite activity. The teacher then invites the student to explain the reason for his or her choice of activity. Following this sharing, the teacher asks the students to describe the activity graph by writing number sentences that compare how many stickers are on each line. The learning objective addressed through this activity is best described as relating mathematics to:
A. literacy, by describing a simple graph of favorites with oral expressions of why an activity is liked or disliked. B. Cognitive development, by making sense of quantities up to 20 and using numbers to sort and classify groups. C. Oral communication, by using words and symbols to compare objects in organized groups--- most, least, more than, less than, and equal to. D. Social Development, by discussing a simple graph of favorites in terms of "most liked", "least liked", and "how many more like" using words or numbers.
A preschool teacher is introducing patterns to a small group of three-year-old children during center time. Each child is given a container of large wooden beads and a shoe lace. The teacher demonstrates how to string the beads using the shoe lace, and then creates a red, blue, red, blue, repeating pattern with the beads. The teacher stops and asks the children which colored bead should come next. The children then copy the pattern and finish the necklace using the same pattern. Which of the following learning experiences would be the most effective for the children to engage in next to increase their understanding of the repeating ABAB pattern?
A. observing the teacher make another ABAB patterned necklace and recreates the pattern. B. Creating and extending an ABAB pattern independently using different colored beads. C. Representing the ABAB pattern by drawing the necklace and coloring it with red and blue crayons. D. Labeling the beads on drawing of red and blue necklace with the letter A B A B.
When conducting a end of the unit test, it is most important for the teacher to ensure that the test questions:
A. require students to use varied levels of thinking from recall analysis in relation to unit content B. are aligned with the unit's defined instructional objectives C. reflect a range of difficulty levels from relatively easy to highly challenging. D. Prompt students to apply unit content in new ways.
Which of the following expressions represents a unit of speed?
A. s= time/distance B. s= time x distance C. s=distance/time D. s= 1/distance x time
A third grade student has solved a word problem correctly but has not shown any of the work. The teacher best assess the students conceptual understanding of the problem by asking the student to:
A. solve additional similar problems. B. determine if the answer is reasonable C. explain the steps to arrive at the answer D. create a similar type of word problem