Math Methods Final
Exploring properties of quadrilaterals is a rich investigation for students. The following are important concepts that emerge from these investigations except: A. prisms are special cylinders. B. generating definitions. C. learning proper terminology. D. shapes are subcategories of other shapes.
A
Money skip counting and using the hundreds chart to money count support what mental mathematics strategy? A. Counting on B. Doubles plus one C. Place value D. Front-end adding
A
Purposes of conducting experiments (doing simulations) are important for all of the following reasons except: A. Assess whether students have a probability sense B. Provide experiential background for theoretical model C. See ration of outcomes to number of trials D. Model real world problems
A
Rotational symmetry is described as: A. smallest angle required to have shape match its footprint. B. transformation of two-dimensional shapes. C. portion of a shape reflected onto the other side. D. reasoning about the movement of two-dimensional shapes.
A
The following are examples of independent probability events except: A. Drawing a blue cube from a bag of six different colored cubes B. Having a cup and tack land up when each is tossed C. Spinning blue twice on a spinner D. Getting two heads when tossing four coins
A
The following are suggested strategy for estimating except: A. guessing. B. iterating a unit mentally or physically. C. using subdivisions. D. using benchmarks as referents.
A
Students should explore the area of a triangle after they have a conceptual understanding of the area of a: A. hexagon. B. prism. C. parallelogram. D. circle.
C
Which of the following transformations is a nonrigid transformation? A. Rotation B. Translation C. Dilation D. Reflection
C
Which of the following would result in an unequal likelihood versus and equal likelihood? A. Drawing from bag with two colored tiles B. Spinner with 1/2 green and 1/2 red C. Number cube with sides 4,4,4, 5,5,5, 6,6,6 D. Coin Toss
C
A good task to use with students to assess their understanding of the use of a standard ruler is: A. measuring in the customary system only. B. using a chain of paper clips. C. measuring with string. D. measuring with a "broken ruler."
D
Coordinate grids are often used in geometry to explore: A. volume of a prism. B. classifications and sorts. C. probability. D. transformations.
D
Analyze informal arguments Make connections based on logic
Deduction
Students describe what they have learned about the topic in their own words
Explicitation
True or False: All parallelograms have congruent diagonals.
False
True or False: If it has exactly two lines of symmetry, it must be a quadrilateral.
False
True or false: All pyramids have square bases.
False
Students apply the relationships they are learning to solve problems and investigate more open-ended tasks
Free orientation
Students explore the objects of instruction in carefully structured tasks such as folding, measuring, or constructing
Guided orientation
Think about the properties without focusing on a particular object "If then" thinking Classify with a minimum set of characteristics Observes beyond the properties Uses informal reasoning and the value of counterexamples
Informal deduction
The teacher identifies what students already know about a topic and the students become oriented to the new topic
Information
Students summarize and integrate what they have learned, developing a new network of objects and relations
Integration
True or False: All squares are rectangles.
True
True or False: If it's a square, then it's a rhombus.
True
True or False: Some parallelograms are rectangles.
True
Name figures based on global visual characteristics Judge based on appearance See alike and differences
Visualization
Comparison activities guide students understanding of volume and capacity. Identify the activity that would not use volume comparison. A. Provide students with grid paper and rulers to construct different sized rectangular prisms B. Provide a target container and have students sort a collection of containers to determine which holds more, less, or about the same C. Provide students with equal size sheets of paper to make tubes and use beans to fill for a volume measure D. Provide students with two small boxes and unit cubes to find which has greater volume
A
The natural progression for teaching students to understand and read analog clocks includes starting with which of the following steps? A. Begin with a one-handed clock that can be read with reasonable accuracy. B. Use a digital clock and relate it to decimals. C. Focus on a.m. and p.m. D. Start with 60 minutes and discuss the fractional components such as one-quarter after.
A
What are the standard units used to measure capacity? A. Milliliters, centiliters, and liters B. Inches, feet, and yards C. Millimeters, centimeters, and meters D. Spoons, cylinders, and beakers
A
What is a key idea in connecting whole number place value and decimal fraction place value? A. 10 to 1 multiplicative relationship between values of any two adjacent positions B. With base-ten models the small square is the only piece that can be one C. The symmetry on the system is around the tens place D. Decimal point designates the unit in the dollars place value with money
A
When a shape can be folded on a line—so that the two halves match—that fold line is also a line of: A. reflection. B. rotation. C. translation. D. tessellation.
A
Which of the following is a nonstandard unit of measure? A. Paper clip B. Measuring cup C. Meter stick D. One-inch tiles
A
Which of the following is one of the best approaches for teaching elapsed time? A. An empty number line B. Paper plates C. Fraction pieces D. Grid paper
A
Consider all shapes in a class Consider properties of ALL rectangles Focus on what makes a rectangle a rectangle Class corresponds by defining properties
Analysis
Angles are measured by: A. using a ruler to measure the distance between the arrows on the two rays. B. using a smaller angle to fill or cover the spread of the rays. C. using a ruler to measure the length of the two rays—the longer the rays, the larger the angle. D. using a spring scale.
B
Estimation is particularly important for students who have learned the rules of computation but cannot decide about? A. Equivalence B. Reasonable answers C. Place value D. Relative size of decimals
B
How can one obtain an accurate measure of the volume of a rectangular prism when given a set of the same-sized cubes? A. Use a ruler and convert the measurement. B. Layer the cubes on the bottom of the box to fit the dimensions and then see how many layers are needed. C. Put one cube in the box and estimate. D. Pour rice into the rectangular prism.
B
In the real-world decimal fractions are rarely those with exact equivalents to common fractions. Students need to wrestle with the magnitude of decimal fractions. Identify the activity below that addresses magnitude. A. What fraction produces this repeating decimal 3.454545? B. Identify what 7.396 is close to 7, 7 and one half712, or 8 C. Use both a fraction and decimal on a number line D. Write a fraction as a decimal
B
The following statements are true about early experiences in probability except: A. If a spinner is shaded one-fourth blue, it is not obvious that the probability of getting blue is one-fourth. B. Students should begin in middle school when they are developmentally ready. C. Rather than focus on numeric answers, students should decide where events land between impossible and certain. D. Tools such as number lines, spinners, and counters should be used in experiences focused on the question of how likely an event is.
B
The most important factor in moving students up the van Hiele levels is: A. the use of manipulative materials. B. geometric experiences that teachers provide to the students. C. repetition and practice. D. students' background knowledge of shapes.
B
The role of the decimal point in a number is to: A. designate the tenths position. B. designate the units position. C. separate the dollars from the cents. D. separate the big numbers from the small numbers.
B
What mathematical tool(s) would provide students with the opportunity to make a conjecture about how likely an event is? A. Number cubes B. Probability number line 0 impossible to 1 certain C. Color tiles D. Spinners
B
When a figure can be reflected over a line and rotated about a point this combination of transformations is called: A. congruence. B. composition. C. line symmetry. D. similar.
B
When students explore how shapes fit together to form larger shapes, it is called: A. decomposing shapes. B. composing shapes. C. sorting shapes. D. finding similarities in shapes.
B
A collection of uniform objects with the same mass can serve as nonstandard weight units except: A. coins. B. paper clips. C. plastic toys. D. wooden blocks.
C
According to your textbook, which of the following trios of real-world situations represent common uses for estimating percentages? A. Discounts, car loans, and interest on bank accounts B. Tips, car loans, and home mortgages C. Tips, taxes, and discounts D. Taxes, home mortgages, and interest on bank accounts
C
All of the materials below can be used to represent an area model of decimal fractions except: A. base-ten materials. B. 10×10 grid. C. meter stick. D. rational number wheel.
C
An area model that demonstrates how figures can have the same area composed of different shapes is: A. index cards. B. playing cards. C. tangrams. D. newspaper sheets.
C
Angle measurement can be a challenge for some students for the following reason. A. Angle relationships are supplementary, complementary, and vertical B. Attribute of the angle size is the spread of the angle's rays C. Protractors are used to measure angles D. Unit for measuring and angle is an angle
C
Area representations have all of the following features except: A. they illustrate the connection between fractions, multiplication, and probability. B. they are more concrete than tree diagrams. C. they are readily adaptable to situations with three events. D. they are representations that help students examine "and" as well as "or" situations.
C
For students to have a conceptual understanding developing formulas for perimeter and area, they should do all the following except: A. notice how all the formula for area is related to the idea of length of the base times height. B. understand where formulas come from or can be derived. C. be told the formula. D. engage in doing the mathematics.
C
Measurement _______________________ is the process of using mental and visual information to measure or make comparisons without the use of measuring instruments. A. strategy B. procedure C. estimation D. benchmarking
C
Multiplication of decimals is poorly understood for many reasons. Identify the misunderstanding that relates to whole number multiplication. A. Using the powers of ten for counting and shifting the decimal B. Count the decimal places in the problem to decide where to place the decimal in the product C. Multiplying makes the product larger D. Understanding decimal numeration should tell the approximate product
C
One of the main goals of the visualization strand is to be able to identify and draw which of the following? A. Symmetrical shapes B. Tessellations C. Two-dimensional images of three-dimensional shapes D. Rotations
C
Probability is about how likely an event is. A good place to begin is with: A. simulation B. virtual manipulatives C. possible and not possible D. probability continuum
C
Spatial sense includes all the following except: A. recognize spatial relationships. B. mentally visualize objects. C. identifying hierarchy of geometric properties. D. intuition about shapes.
C
Students need to be acquainted with various visual models to help them think flexibly of quantities in terms of tenths and hundredths. Which example below would help students understand the decimal fraction StartFraction 65 Over 100 in terms of place value? A. This decimal fraction could be written as six tenths6/10+5/100 B. This decimal fraction is less than one half. C. This decimal fraction could be thought of as 6 tenths and 5 hundredths D. This decimal fraction could be thought of as 6 dimes and one nickel
C
Students need to learn that time is something that can be measured. All the activities listed help them think in terms of seconds, minutes, and hours except: A. watching TV. B. doing homework. C. a.m. and p.m. D. eating dinner.
C
The following are "place learning" words learned as a position description in kindergarten except: A. below. B. above. C. direction. D. in front of.
C
The value of a collection of coins is best learned by having students: A. write all of the individual coin values down and add them on paper. B. create an equivalent coin collection. C. sort the coins starting with the highest value and skip counting. D. solve word problems involving money.
C
The "place learning" words lay the foundation for students to identify points on what system? A. Graph paper B. Grid paper C. Coordinate plane D. Centimeter dot paper
C
Three of the four important principles of iterating units of length are listed below. Identify the one that is actually a misconception. A. Units are equal in length B. Units are placed without gaps C. Units are measured by the ending point of a ruler D. Units are aligned with the length being measures
C
To answer the question "What is the chance of having triplets being all girls?" the best random device for a simulation would be: A. Calculator B. Six-sided die C. Two color spinner D. Four different colored cubes
C
To compare the weights of two objects, which of the following is the best approach? A. Measure which item is taller or longer than the other, as that object will have the greatest weight. B. Match each item to a same-sized ball of clay. C. Place the two objects in the two pans of a balance. D. Place the objects in water to see if one floats.
C
What activity described below would guide students understanding of halves, thirds, fourths, and eighths as decimal fractions? A. Students are given a list of five decimal fractions and put them in order from least to greatest B. Students use an empty number line to represent placement of decimal fractions C. Students shade in a 10 x 10 grid to illustrate a familiar fraction D. Students use a meter stick to compare size of decimal fractions
C
What event listed below would be an example of known sample space? A. How many girls in the second grade? B. How many minutes of rain in September? C. What is the probability of drawing a red cube from a bag of six different colored cubes? D. What is the probability of lightning striking a house?
C
What is the cognitive skill that helps students recognize and group shapes according to their attributes and properties? A. Proportional thinking B. Conservation C. Classification D. Decomposition
C
What type of scale measures mass from small to large? A. Kitchen scale B. Supermarket scale C. Beam or balance scale D. Spring scale
C
What would be a prerequisite to being successful in measuring angles? A. Differentiate between angle and ray B. Knowing a wide angle will have shorter rays and a narrow angle will have longer rays C. Mental images of angle size D. Know than a one-degree angle is StartFraction 1 Over 360 of a circle
C
When using base-ten materials in developing decimal concepts what is an important idea to be realized? A. The large square in the hundreds piece B. The strip is the tens piece C. Any piece could be effectively chosen as the ones piece D. The small square is the ones piece
C
Which of the following statements is not true about simulations? A. Simulations are important to build in order to test the probability of real-life situations that may not have a theoretical probability. B. Simulations should focus on real-life context and help students identify the key components and assumptions for that real-life context. C. Simulations are important in middle school because they provide an engaging way in which to explore probability and connect to the abstract and difficult concepts related to compound events. D. Simulations engage students in higher-level thinking because students are challenged to design and test a particular simulation they have created.
C
Which of the following statements is true? A. Teach theoretical probability first, and then engage students in doing experiments, because they will be able to confirm the theoretical probability (expected value) through the experiment. B. Teach experiments first because they are more concrete, then engage students in learning about theoretical probability. C. Teach experiments and theoretical probability together, focusing on the number of trials needed for experiments to reflect the theoretical probability. D. Teach experiments and theoretical probability together, using small numbers of trials so that students do not get bogged down.
C
Base-ten models, the rational number wheel with 100 markings around the edge, and a 10-by-10 grid are all models for linking which three concepts together? A. Addition, subtraction, and decimals B. Area, perimeter, and volume C. Fractions, decimals, and percents D. Multiplication, division, and fractions
C
A good teaching option for developing a full understanding of computation with decimals is to focus on: A. computation with whole numbers alone. B. delivering a set of rules that should be practiced. C. detaching and reattaching decimal points for multiplication and division. D. concrete models, drawings, place value knowledge, and estimation.
D
Following steps to set up a successful simulation involve three of the following. Which one would not be useful? A. Select a random device for the key components B. Conduct and record a large number of trials C. Define a real trial D. Select an expensive method to manipulate the real situation
D
It is important for students to experience and explore percent relationships in realistic contexts. Three of the statements below are guidelines to follow for presenting percents. Identify the one that does not support best practices. A. Use terms, part, whole, and percent to connect to fractions B. Require students to use models, drawing and contexts to explain solutions C. Initially use numbers compatible to familiar fractions D. Use the following sentences in their solutions "____ is ____ percent of _____"
D
One of the basic ideas of length measurement is that when the unit is longer, the measure is: A. larger. B. either smaller or larger. C. the same. D. smaller.
D
Physical models provide the main link between fractions, decimals, and percents. Identify the one model that is suitable for all three because they all represent the same idea. A. Three-part model to represent original, decrease, and increase B. 10×10 grid C. Percent necklaces D. Base-ten models
D
The following activities support students learning about two-dimensional shapes in different orientations except: A. cutting shapes with five squares on grid paper. B. sketching shapes that have been show for only five seconds. C. constructing shapes with given number of simple tiles. D. constructing figures with centimeter cubes.
D
The following are money ideas and skills typically required in primary grades except: A. counting and comparing coins. B. recognizing coins and identifying their value. C. creating equivalent coin collections (same amount, different coins). D. reading and writing number and word money amounts.
D
The four major content goals in geometry for all grade levels are: A. two-dimensional shapes, three-dimensional shapes, Pythagorean Theorem, and symmetry. B. shapes, properties, conjectures, and proof. C. polygons, solids, lines, and spatial sense. D. shapes and properties, transformation, location, and visualization.
D
The process of concrete-semi-concrete-abstract (CSA) described earlier in this text can refer to the phases of teaching probability. Which of the following would match with semi-concrete? A. Construction B. Analysis C. Exploration D. Representation
D
What description below describes a visualization activity? A. Rotate, reflect, and dilate shapes B. Classify shapes by properties C. Identify and place objects in a coordinate plane D. Draw and recognize objects for different viewpoints
D
What tool would allow students to make an axonometric drawing where scale is preserved? A. Centimeter grid paper B. Centimeter coordinate grid paper C. Centimeter graph paper D. Centimeter isometric dot paper
D
When you are measuring an object using a tool and choosing the attribute to be measured, then you must: A. use a tool that aligns with a benchmark on your body. B. only use tools with metric units. C. consider which tool gives the largest measurement. D. select a tool with the same attribute to measure with.
D
Which of the following is shown through research to be a common error or misconception when students are comparing or ordering decimals? A. The decimal with a 0 in the tenths position is the smallest. B. The decimal that does not have a whole number is the smallest. C. The decimal with a 9 in any place is the largest. D. The decimal that is the shortest is the largest.
D
Which of the following is true about the van Hiele levels? A. They are not sequential. B. They are age dependent. C. They are an idea that all students should memorize. D. They are a progression of ways in which students understand geometric ideas.
D
Which term refers to an event whose results depend on the results of the first event? A. Sample spaces B. Compound event C. Independent event D. Dependent event
D
Which van Hiele level is it when students are considering classes of shapes and focusing on properties of shapes? A. Informal deduction B. Deduction C. Visualization D. Analysis
D
Axiomatic systems Math majors!!!
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