MTTC Lower El Subtest 3: Math Practice Exam Question Fully Solved| Graded A+.

A kindergarten teacher conferences with a small group of students after a lesson on addition to check in with the students. The teacher takes notes on each student's response to the following prompt. "Today we learned about addition at the carpet. What are some ways you can already use what we learned about today in your homes or outside of school?" Which of the following statements most effectively describes the rationale for this question? A. The teacher assesses students' knowledge of mathematical vocabulary. B. The teacher checks for accurate solutions to real-world addition examples. C. The teacher measures students' prior mathematical instruction outside of the school day. D. The teacher builds rapport with students and listens for student interests to inform future instruction. - correct answers D. The teacher builds rapport with students and listens for student interests to inform future instruction. -The teacher asks a question to elicit student-generated connections to addition in their lives. This information is important to creating future relevant and meaningful instruction. A student transfers into class. The other students struggle to pronounce the new student's name. As a result, the students avoid talking to the new student, and the student feels left out. Which of the following activities would help the students practice the new name and meet the math goal of comparing measurable attributes? A. Students write down the new name 15 times and then come up with pictures that help them break down and remember the syllables. B. Students play a game in which they pair up and answer questions such as "Whose name is longer?" and "Whose name has more/fewer vowels?" C. The teacher asks each student to tell the class the story behind their name (e.g., who named them, if it has a special meaning) while taking notes on the board. D. The teacher conducts the students in a "repeat after me x times" challenge with the new student's name, "Can you say it one time? Can you say it three times?" - correct answers B. Students play a game in which they pair up and answer questions such as "Whose name is longer?" and "Whose name has more/fewer vowels?" -his activity engages the students in talking with the new student and provides the students with practice with the new name, while also meeting the math goal of thinking about and comparing attributes (e.g., length, quantity). A teacher checks exit tickets after a lesson on multiplication. The teacher discovers that students rely on different strategies to solve multiplication equations. Some students draw circles and marks to show equal groups, some use open number lines, and others show repeated addition with numbers. The teacher plans for group work the next day. Which of the following affords students the opportunity to participate equitably through their various affinities and capacities? A. Mix students randomly. Allow students to use their exit ticket to solve the day's work. B. Group students together by the strategy they used. Visit each group to demonstrate other methods. C. Mix students based on the strategies they used. Have each student explain their strategy to the small group. D. Group students by correct and incorrect answers. Explicitly teach strategies for students who did not answer the exit ticket correctly. - correct answers C. Mix students based on the strategies they used. Have each student explain their strategy to the small group. A first-grade mathematics teacher plans a formative assessment to evaluate student understanding of subtraction within 20. The teacher can most effectively identify evidence of student understanding by assigning which of the following student activities? A. solving a word problem that requires subtraction with more than two numbers B. creating a series of subtraction equations in which the unknown value is the difference C. creating a subtraction equation in which students represent the equation as a picture and a word problem D. solving a word problem involving subtraction that provides some information that is unnecessary to solve the problem - correct answers C. creating a subtraction equation in which students represent the equation as a picture and a word problem A second-grade teacher analyzes student performance on an assessment and concludes that 75% of the class meets or exceeds the standards for proficiency. Which of the following approaches can the teacher plan to provide the most effective instruction? A. designing an out-of-class assignment for students to complete with parents/guardians that provides additional practice on the last unit B. using assessment data to form heterogeneous groups, then implementing a group activity that connects the two units C. delaying the start of the new unit indefinitely and reviewing the concepts until all students have achieved proficiency D. allowing students who have yet to reach proficiency the option to retake the end-of-unit assessment the next day - correct answers B. using assessment data to form heterogeneous groups, then implementing a group activity that connects the two units A teacher plans a lesson to get students talking about the attributes of composite shapes. For the activity, students work independently with tangrams to create a composite shape, trace their shape, list its attributes, and give their shape a name. Then, students work in small groups to create an image or story that uses the composite shapes of all group members. Which of the following modifications would promote participation? A. substituting tracing plastic tangrams with gluing construction paper cutouts onto a piece of posterboard to create the composite shapes B. directing students to work independently so each student gets more say in how their shape is used in the final product C. offering an alternative computational activity for students who are not interested in designing a composite shape D. assigning roles once the students are in groups to ensure that each student makes a meaningful contribution - correct answers D. assigning roles once the students are in groups to ensure that each student makes a meaningful contribution A second-grade teacher plans to conclude a unit on solving word problems involving money. Which of the following approaches can the teacher use to reinforce the concepts while also encouraging students' enjoyment of the mathematics? A. creating an activity in which students use a computer to look up items that can be purchased for a given amount of money B. creating a game in which students compete to earn the greatest amount of money by answering questions correctly C. creating a game in which students show the same amount of money using different combinations of coins and bills D. creating an activity in which students count amounts of money using different currency - correct answers C. creating a game in which students show the same amount of money using different combinations of coins and bills A kindergarten teacher meets with a small group of students. The teacher shows them models of three-dimensional shapes. One student explains that the cube is flat compared to the round cone and sphere, so it must be two-dimensional. The teacher can most effectively clarify the student's partial understanding of two- and three-dimensional shapes by using which of the following instructional strategies? A. reviewing a list of common two-dimensional shapes B. explaining that they are only using three-dimensional shapes today C. formatively assessing students on the names of the three-dimensional shape models D. providing two-dimensional shapes for students to compare with the three-dimensional models - correct answers D. providing two-dimensional shapes for students to compare with the three-dimensional models A first-grade teacher distributes bins of small cubes to their class. The teacher expects students to engage in discussion with each other and discover which three-dimensional shapes can be composed by iterating the cubes. Which of the following questions is most effective to elicit student thinking and encourage discussion? A. "Can you make a sphere out of the cubes?" B. "Is it possible to make a big cube using eight smaller cubes?" C. "What do you notice about the shapes you are able to compose out of cubes?" D. "How many cubes does it take to make a rectangular prism that is two cubes wide, six cubes long, and three cubes high?" - correct answers C. "What do you notice about the shapes you are able to compose out of cubes?" A small group in a kindergarten classroom is building two-dimensional shapes using sticks and clay. Teacher: What could we do to change a square into a triangle? Student: We could just take away a side! Then it would have three sides. Which of the following responses should the teacher use to clarify and accurately understand the student's thinking? A. "What do you have to do after you take away the side?" B. "Is there another way you can think of to make a triangle?" C. "Does everyone else agree? Anything else you might add?" D. "Will you please show me your strategy with sticks and clay?" - correct answers D. "Will you please show me your strategy with sticks and clay?" A second-grade teacher plans a lesson on understanding subtraction as an unknown-addend problem. Which of the following tasks affords students the opportunity to strengthen their understandings of this concept? A. Students decompose numbers from 11 to 20 using place value. B. Students count on a number line to find the distance between numbers. C. Students check to see if equations involving addition or subtraction are true or false. D. Students simplify differences by using easier numbers, such as expressing 13 − 4 as 13 - 3 − 1. - correct answers B. Students count on a number line to find the distance between numbers. A kindergarten teacher places five cups on a table and asks a group of students, "How many cups are here?" After a minute talking quietly with each other, the students announce, "There are five cups.'" The teacher then adds a sixth cup to the table and asks the students, "How many cups are here now?" Again, the students talk quietly together and then announce, "There are six cups." Which of the following questions can the teacher ask to determine whether the students counted up from five, recounted all the cups, or subitized to come up with their answer? A. "Can you draw for me how you count to six?" B. "How did you figure out that there are six cups?" C. "How many cups will be on the table if I take away two cups?" D. "Did you count on, count all, or subitize to get the answer?" - correct answers B. "How did you figure out that there are six cups?" Which of the following teacher explanations best supports a first-grade student's ability to identify, name, and use an equal sign? A. "An equal sign looks like two dashes written on top of each other, like this (draws an equal sign). It means that both sides of an equation are equal." B. "Notice than when we do math, we often put this symbol (points to an equal sign) on our papers. This symbol indicates that the values on both sides of it are equivalent." C. "This symbol (points to an equal sign) is called an equal sign. Unlike the plus and minus symbols, which tell us how to combine values, the equal sign tells us how the two values relate." D. "When you have two values that are the same, like 5 and 1 + 4, you can put this symbol between them (draws an equal sign), which is called an equal sign, to show that they are the same." - correct answers D. "When you have two values that are the same, like 5 and 1 + 4, you can put this symbol between them (draws an equal sign), which is called an equal sign, to show that they are the same." Which of the following questions can help students to think about comparing the fractions 3/4 and 7/8? A. "Are fourths or eighths larger pieces?" B. "Which fraction has a larger denominator?" C. "If you draw both, which one is closer to a whole?" D. "Would you rather eat 3/4 of a pizza or 7/8 of a pizza?" - correct answers C. "If you draw both, which one is closer to a whole?" A third-grade teacher selects manipulatives to promote students' ability to understand how fractions can describe parts of a set. Which of the following manipulatives best promotes this interpretation? A. paper strips B. number lines C. grid-paper regions D. two-color counters - correct answers D. two-color counters A first-grade teacher conferences with a student about addition within 20. The teacher asks the student to use ten frames to show the addition problems. The student accurately places counters on the ten frames for each number, then counts the total counters one by one to find the answer. Which of the following tools would best support the student's understanding of addition? A. a timed assessment to ensure that the student can solve the problems quickly B. a sequence of tasks that helps the student construct more efficient strategies for adding C. a pair of addition problems in which the order of the two numbers being added is reversed D. a series of equations of addition within 20 that increase in difficulty to challenge the student - correct answers B. a sequence of tasks that helps the student construct more efficient strategies for adding A kindergarten teacher plans instruction for a small group of students. The learning target for the group is to compose numbers 11 through 19 and record them as a ten plus a group of ones. Which of the following materials would be most appropriate for the learning target of this activity? A. a set of two ten frames, counters, and writing materials B. a collection of random dominos with pips and a whiteboard C. addition flash cards of equations with sums of 11 through 19 D. a math game in which students roll six-sided dice and add the results - correct answers A. a set of two ten frames, counters, and writing materials What is the CRA order for teaching math? - correct answers 1. Concrete- Manipulatives 2. Representational- Pictures and/or symbols 3. Abstract- Numbers and mathematical notations Mrs. Joseph is planning on teaching his students about adding fractions. Which is the most appropriate first activity? A. Give students each a different sheet with fractions to add. Have students swap papers to check each other's work. B. Give students pattern blocks to manipulate while adding different unit fractions. C. Ask students to draw pictures representing fractions being added. D. Give students word problems relating to proportional reasoning. - correct answers B. Give students pattern blocks to manipulate while adding different unit fractions. -Giving students pattern blocks as the first activity follows the guidelines for CRA (Concrete, representational, and abstract). Pattern Blocks - correct answers Pattern blocks are sets of six different shapes: hexagons, parallelograms, trapezoids, rhombuses, squares, and triangles. While pattern blocks are used in lower elementary grades for patterns and shape attributes, they can also be used in upper elementary classrooms to teach concepts related to fractions. For example, a student can use pattern blocks to show that six triangles are equal to one hexagon, so 6/6 equals 1 whole. Base 10 blocks - correct answers Base 10 blocks represent the different place value amounts in our base 10 number system. Cubes are used to represent the ones place. Rods or "tens sticks" are used to represent the tens place because they are made of 10 fused cubes. Flat squares are used to represent the hundreds place, and blocks or cubes represent the thousands place. Students can continue to use base 10 blocks in upper elementary grades to reinforce place value concepts and to model regrouping with addition and subtraction. They can also be used to model the process of multiplication and division, and the regrouping that occurs in these processes. Cuisenaire rods - correct answers Cuisenaire rods consist of 10 rods, each a different length and color. They are used in a variety of different concepts including addition, subtraction, multiplication, and fractions. For example, Cuisenaire rods can be used to find the missing addend in the equation 4 + __ = 7. Students would place the 4 Cuisenaire rod above the 7 rod, discovering that the 3 rod fills in the gap. Attribute Blocks - correct answers Attribute blocks are models of different 2D shapes, such as squares, triangles, and rectangles. In upper elementary grades, attribute shapes can be used to review shape attributes and to teach concepts such as perimeter and area. Geometric Solids - correct answers Geometric solids are similar to attribute shapes, but they are models of 3D solids instead of 2D shapes. Geometric solids can be used in upper elementary grades to review the attributes of 3D shapes and to introduce surface area and volume. Geoboards - correct answers Geoboards are used to teach concepts such as area, perimeter, and angles. Geoboards have pegs arranged in a grid pattern. Rubber bands are stretched around the pegs to create various geometric shapes. Money Models - correct answers Money models are similar to base 10 blocks but represent the value of each coin. For example, the penny is one unit and the nickel is five units fused together. Upper elementary students might use money models to practice adding and subtracting different amounts of money. Tangrams - correct answers A tangram is a set of seven tiles that can be arranged in various ways to create different shapes. Students are typically given an outline of a shape or "puzzle" that needs to be filled in with all seven of the tangram pieces. Tangrams can be an enjoyable activity for students while promoting spatial reasoning and problem-solving skills. Fraction tiles - correct answers Fraction tiles are color-coded strips that are used to represent different fractions. They are sometimes called fraction strips. can help students get a visual representation of equivalent fractions or help them compare two or more fractions. Related, fraction circles are sets of circles divided into different numbers of equal parts to represent different fractions. Algebra Tiles - correct answers Algebra tiles are square and rectangle-shaped tiles that are used to represent integers and variables. Typically, the rectangles represent variables (x) and the squares represent constants (1). Different colors are used to distinguish positive and negative values. Algebra tiles are used to help students gain a deeper understanding of algebraic processes. In the upper elementary grades, algebra tiles would be used with very basic algebraic equations. Concrete Operational Stage - correct answers in Piaget's theory, the stage of cognitive development (from about 6 or 7 to 11 years of age) during which children gain the mental operations that enable them to think logically about concrete events Non-proportional manipulatives - correct answers objects that are not proportional to each other with respect to shape and size. Often all of the items are the same size. counting tokens Proportional Manipulatives - correct answers objects that are proportional to each other with respect to shape and size tangrams Mr. Burke is a second-grade teacher working on counting sets of coins with a small group of students. Students are each given a set of play coins and asked to find the total. Mr. Burke watches one student, Elijah, as he counts a set of 3 dimes, 2 nickels, and 2 pennies. Elijah separates the coins into two sets: a row of dimes and nickels and a separate row of pennies. He then begins counting the row of dimes and nickels by saying, "five, ten, fifteen, twenty, twenty-five." Next, he moves to the pennies and continues to count on, saying "twenty-six, twenty-seven." Based on this observation, which of the following skills should Mr. Burke plan on reviewing with Elijah? A. skip counting B. mnemonic devices for coin values C. coin identification