EDEL 481 Exam 2 Review
Which of the following is a nonstandard unit of measure? A. One-inch tiles B. Meter stick C. Paper clip D. Measuring cup
paper clip
The radius is blank hypotenuse
1/2
Identify the activity that would yield categorical data to be collected. A. Temperature range in a month B. Favorite TV shows C. Weights of students school lunch box D. Miles to travel to school
Not numbers Favorite TV shows
Research recommends that teachers use one of the following to support students' understanding that fractions are numbers and they expand the number system beyond whole numbers. A. Circular number pieces B. Color counters C. Cuisenaire rods D. Number lines
Number lines
To compare the weights of two objects, which of the following is the best approach? A. Place the two objects in the two pans of a balance. B. Place the objects in water to see if one floats. C. Match each item to a same-sized ball of clay. D. Measure which item is taller or longer than the other, as that object will have the greatest weight.
Place the two objects in the two pans of a balance.
Review number 77, 79,80,92,93,94, 111, 113, 114
Item m cm mm a. Length of a piece of paper 0.310.31 3131 310310 b. Height of a woman 1.671.67 167167 16701670 c. Width of a filmstrip 0.0390.039 3.93.9 3939 d. Length of a cigarette 0.10.1 1010 100100 e. Length of threethree meter-sticks e. laid end to end 33 300300 30003000
Money skip counting and using the hundreds chart to money count support what mental mathematics strategy? A. Place value B. Counting on C. Front-end adding D. Doubles plus one
B. Counting on
Students should explore the area of a triangle after they have a conceptual understanding of the area of a: A. parallelogram. B. prism. C. hexagon. D. circle.
parallelogram.
A collection of uniform objects with the same mass can serve as nonstandard weight units except: A. plastic toys. B. coins. C. wooden blocks. D. paper clips.
A. plastic toys.
What is the cognitive skill that helps students recognize and group shapes according to their attributes and properties? A. Classification B. Proportional thinking C. Conservation D. Decomposition
Classification
All of the following statements are research-based recommendations for teaching and learning about fractions except one. Which one? A. Invest time for students to understand equivalence concretely and symbolically B. Provide a variety of models and context to represent fractions C. Emphasize the meanings of fractions, rather than rote procedures D. Give greater emphasis to specific algorithms for finding common denominators
Give greater emphasis to specific algorithms for finding common denominators
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. Pour rice into the rectangular prism. C. Put one cube in the box and estimate. D. Layer the cubes on the bottom of the box to fit the dimensions and then see how many layers are needed.
Layer the cubes on the bottom of the box to fit the dimensions and then see how many layers are needed.
What would be a determining factor to decide whether to use median versus mean in representing the center? A. Outliers B. Value of data C. Balance point D. Leveling interpretation
Outliers
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. eating dinner. D. a.m. and p.m.
a.m. and p.m.
For students to have a conceptual understanding developing formulas for perimeter and area, they should do all the following except: A. engage in doing the mathematics. B. understand where formulas come from or can be derived. C. notice how all the formula for area is related to the idea of length of the base times height. D. be told the formula.
be told the formula.
When students explore how shapes fit together to form larger shapes, it is called: A. sorting shapes. B. composing shapes. C. finding similarities in shapes. D. decomposing shapes.
composing shapes.
Writing fractions in the simplest terms means to write it so: A. fractions are not improper. B. fractions with larger denominators. C. fractions are reduced. D. fraction numerator and denominator have no common whole number factors.
fraction numerator and denominator have no common whole number factors.
The fundamental law of fractions
shaded regions all equaling 2/3
The following are examples of graphs that are best used to display categorical data except: A. stem plots. B. bar graph. C. continuous data graph. D. pie chart.
A. stem plots.
Which of the following is a good explanation for how to add fractions? A. Join parts and find a common denominator in order to combine correctly. B. Find the common denominator because one only adds the numerators. C. Add equal-sized partslong dash—finding a common denominator can help to solve the problem. D. Put together through combining the numerators.
Add equal-sized partslong dash—finding a common denominator can help to solve the problem.
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 placed without gaps B. Units are measured by the ending point of a ruler C. Units are equal in length D. Units are aligned with the length being measures
B. Units are measured by the ending point of a ruler
Classifying involves making a decision about what part of the data? A. Ordering objects in terms of their size or shape B. Formulating questions for collected data C. Identifying how to group things D. Sorting objects by their attributes into categories
C. Identifying how to group things
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. eating dinner. C. a.m. and p.m. D. doing homework.
C. a.m. and p.m.
What tool would allow students to make an axonometric drawing where scale is preserved? A. Centimeter grid paper B. Centimeter isometric dot paper C. Centimeter graph paper D. Centimeter coordinate grid paper
Centimeter isometric dot paper
Types of graphs are used to show the shape or distribution of data. Which type is best used to show the distribution of numeric data? A. Box plot B. Circle graph C. Bar graph D. Line plot
D. Line plot
What would be a prerequisite to being successful in measuring angles? A. Know than a one-degree angle is StartFraction 1 Over 360 EndFraction 1 360 of a circle B. Knowing a wide angle will have shorter rays and a narrow angle will have longer rays C. Differentiate between angle and ray D. Mental images of angle size
D. Mental images of angle size
Data collection might involve any of the following except: A. a sample that is designed to represent a population. B. data from all students within the school. C. data from all students in a classroom. D. a sample that is exactly like the intended population.
D. a sample that is exactly like the intended population.
Coordinate grids are often used in geometry to explore: A. volume of a prism. B. probability. C. classifications and sorts. D. transformations.
D. transformations.
Angles are measured by: A. using a spring scale. B. using a ruler to measure the distance between the arrows on the two rays. C. using a ruler to measure the length of the two rayslong dash—the longer the rays, the larger the angle. D. using a smaller angle to fill or cover the spread of the rays.
D. using a smaller angle to fill or cover the spread of the rays.
What is the primary reason to not focus on specific algorithms for comparing two fractions? A. Not the most efficient strategies B. Cross-multiplication is too easy C. Developing number sense about relative size of fractions is less likely D. Common denominators are too hard
Developing number sense about relative size of fractions is less likely
Which of the following transformations is a nonrigid transformation? A. Reflection B. Translation C. Dilation D. Rotation
Dilation
Teaching statistics literacy should begin at what level in school? A. High school B. Upper elementary C. Middle grades D. Early elementary
Early elementary
The goal is to rename a fractional amount. What is the concept that requires the use of many contexts and models? A. Equivalent fractions B. Multiplying by one C. Missing number equivalences D. Magnitude of fractions
Equivalent fractions
What is a problem with learning only designated (standard) algorithms for fraction operations? A. Follow a procedure in a short term, but not retain B. More effective and quicker to learn C. Helps students think conceptually about the operation D. Use it to assess whether answer makes sense
Follow a procedure in a short term, but not retain
There are multiple contexts that can guide students understanding of fractions. Which of the following would involve shading a region or a portion of a group of people? A. Ratio B. Measurement C. Part-whole D. Division
Part-whole
To compare the weights of two objects, which of the following is the best approach? A. Place the objects in water to see if one floats. B. Place the two objects in the two pans of a balance. C. Match each item to a same-sized ball of clay. D. Measure which item is taller or longer than the other, as that object will have the greatest weight.
Place the two objects in the two pans of a balance.
A survey was handed out that asked "How likely are you to go rock climbing question mark How likely are you to go rock climbing?" The choices for the answers were 1. Not very likelyNot very likely 2. Extremely unlikelyExtremely unlikely 3. Not at all3. Not at all. How useful is this rating scale? Choose the best statement below. A. The scale is not useful because there are only negative choices. B. The scale is not useful because there are only positive choices. C. The scale is useful because there is a range of choices. D. The scale is useful because there are three choices.
The scale is not useful because there are only negative choices.
Which of the following is true about the van Hiele levels? A. They are not sequential. B. They are a progression of ways in which students understand geometric ideas. C. They are age dependent. D. They are an idea that all students should memorize.
They are a progression of ways in which students understand geometric ideas.
The benefits of using a rectangular area to represent multiplication of fractions include all the following except which? A. They are a good connection to the standard algorithm and to applying the distributive property. B. They are easy for students to draw. C. They can illustrate fractions multiplied by whole numbers as well as multiplication involving mixed numbers. D. They readily show the concept of multiplication of a part of a part.
They are easy for students to draw.
When adding fractions with like denominators it is important for students to focus which key idea? A. Connect fractions to whole numbers B. Know the meaning of numerator and denominator C. Compare the two quantities D. Units are the same
Units are the same
The following questions focus on interpreting data except: A. How strong is the association between two variables? B. What does the graph tell us? What does it not tell us? C. What type of data would you like to explore? D. How do the population numbers in this graph compare to the population numbers in that graph?
What type of data would you like to explore?
Which of the following questions is statistical in nature? A. What is the cost of an e-reader? B. How many licks does it take to get to the center of a Tootsie Pop? C. Which sport is safest to play? D. What is the typical number of jeans a person owns?
Which sport is safest to play?
Which of the following questions is statistical in nature? A. What is the typical number of jeans a person owns? B. Which sport is safest to play? C. How many licks does it take to get to the center of a Tootsie Pop? D. What is the cost of an e-reader?
Which sport is safest to play?
The following statements are important components of doing mathematics except: A. focusing on the context of the situation. B. analyzing the spread of data, including the variability and the center of the data. C. interpreting data to answer a question. D. being able to accurately compute the mean for a set of data.
being able to accurately compute the mean for a set of data.
All the statements below relate to being a mathematical literate citizen except: A. identifying misleading statistics. B. what can or cannot be interpreted from data. C. determine the center, spread and shape of data. D. what is important to pay attention to from varied graphical representations.
determine the center, spread and shape of data.
The following are "place learning" words learned as a position description in kindergarten except: A. above. B. in front of. C. direction. D. below.
direction
The following are "place learning" words learned as a position description in kindergarten except: A. above. B. in front of. C. below. D. direction.
direction.
Measurement _______________________ is the process of using mental and visual information to measure or make comparisons without the use of measuring instruments. A. strategy B. benchmarking C. estimation D. procedure
estimation
One of the purposes of the interpreting phase of a lesson is to: A. design another data collection. B. examine other graphs. C. compute to find measures of center. D. make inferences.
make inferences
A good task to use with students to assess their understanding of the use of a standard ruler is: A. using a chain of paper clips. B. measuring in the customary system only. C. measuring with string. D. measuring with a "broken ruler."
measuring with a "broken ruler."
When a shape can be folded on a line—so that the two halves match—that fold line is also a line of: A. translation. B. reflection. C. tessellation. D. rotation
reflection
When you are measuring an object using a tool and choosing the attribute to be measured, then you must: A. consider which tool gives the largest measurement. B. only use tools with metric units. C. select a tool with the same attribute to measure with. D. use a tool that aligns with a benchmark on your body.
select a tool with the same attribute to measure with.
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. select a tool with the same attribute to measure with. D. consider which tool gives the largest measurement.
select a tool with the same attribute to measure with.
The four major content goals in geometry for all grade levels are: A. shapes and properties, transformation, location, and visualization. B. two-dimensional shapes, three-dimensional shapes, Pythagorean Theorem, and symmetry. C. shapes, properties, conjectures, and proof. D. polygons, solids, lines, and spatial sense.
shapes and properties, transformation, location, and visualization.
The four major content goals in geometry for all grade levels are: A. polygons, solids, lines, and spatial sense. B. shapes, properties, conjectures, and proof. C. shapes and properties, transformation, location, and visualization. D. two-dimensional shapes, three-dimensional shapes, Pythagorean Theorem, and symmetry.
shapes and properties, transformation, location, and visualization.
Using contextual problems with fraction division works in providing students with an image of what is being: A. computed. B. compared to unit divisors. C. shared or partitioned. D. proportional to size.
shared or partitioned.
One of the basic ideas of length measurement is that when the unit is longer, the measure is: A. either smaller or larger. B. the same. C. smaller. D. larger.
smaller
An area model that demonstrates how figures can have the same area composed of different shapes is: A. index cards. B. newspaper sheets. C. playing cards. D. tangrams.
tangrams
A critical aspect of understanding divisions of fractions is: A. the numerator is the unit. B. the partitive situations. C. the divisor is the unit. D. inverted and multiplied.
the divisor is the unit.
A fraction by itself does not describe the size of the whole. A fraction tells us only: A. the denominator is the size of the piece being counted. B. the relationship between part and whole. C. the sharing of equal size groups. D. the numerator is the counting number.
the relationship between part and whole.
The following are examples of attribute objects that can be sorted and classified except: A. pattern blocks. B. leaves. C. yellow centimeter cubes. D. seashells
yellow centimeter cubes.
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. Rotations D. Two-dimensional images of three-dimensional shapes
Two-dimensional images of three-dimensional shapes
One of the main goals of the visualization strand is to be able to identify and draw which of the following? A. Two-dimensional images of three-dimensional shapes B. Tessellations C. Symmetrical shapes D. Rotations
Two-dimensional images of three-dimensional shapes
Teaching fractions involves using strategies that may not have been part of a teacher's learning experience. What is a key recommendation to teachers from this chapter? A. Use symbols early and focus on numerator and denominators definitions B. Use algorithms and procedures to address student misconceptions C. Use multiple representations, approaches, explanations, and justifications D. Use recognized modelsdash-that is, circular and rectangular
Use multiple representations, approaches, explanations, and justifications
Tell whether each of the following questions is biased or fair. Why? a. Given the dangers of firearms, do you support increased gun control? b. Do you think the school day should be lengthened? a. Choose the correct answer below. A. Fair because the question does not make an unjustified assumption and does not make some answers appear better than others. B. Biased because the question does not make an unjustified assumption and does not make some answers appear better than others. C. Biased because the question makes an unjustified assumption or makes some answers appear better than others. D. Fair because the question makes an unjustified assumption or makes some answers appear better than others. b. Choose the correct answer below. A. Biased because question does not make an unjustified assumption and does not make some answers appear better than others. B. Biased because the question makes an unjustified assumption or makes some answers appear better than others. C. Fair because the question does not make an unjustified assumption and does not make some answers appear better than others. D. Fair because the question makes an unjustified assumption or makes some answers appear better than others.
1. C. Biased because the question makes an unjustified assumption or makes some answers appear better than others. 2. Fair because the question does not make an unjustified assumption and does not make some answers appear better than others.
Which van Hiele level is it when students are considering classes of shapes and focusing on properties of shapes? A. Analysis B. Informal deduction C. Deduction D. Visualization
A. Analysis
The "place learning" words lay the foundation for students to identify points on what system? A. Coordinate plane B. Graph paper C. Grid paper D. Centimeter dot paper
A. Coordinate plane
Research findings support all of the following fraction teaching ideas but one. Which of the following is the unsupported method? A. Give students area models that are already partitioned and ask them to record the fractional amount shaded. B. Ask students to partition rectangles, collections of counters, and paper strips. C. Ask students to use partitioning and describe where on a number line a particular fraction is (such as seven eighths 7 8). D. Ask students to connect the symbols to the visuals (showing sixths and writing one sixth 1 6).
A. Give students area models that are already partitioned and ask them to record the fractional amount shaded.
Identify which statement below would not be considered a common or limited conception related to fractional parts? A. Knowing that answers can be left as fractions rather than writing them as mixed numbers B. Knowing that fractional parts must be the same size and/or that they do not have to be the same shape C. Knowing that fractions are numbers in and of themselves (not a number over another number). D. Knowing and being able to locate fractional parts on the number line, including using incorrect notation or incorrectly counting tick marks.
A. Knowing that answers can be left as fractions rather than writing them as mixed numbers
Which of the following options would be misleading for student understanding of fractions? A. Tell students that fractions are different from whole numbers, so the procedures are also different. B. Emphasize conceptual understanding by connecting to visuals. C. Use examples that are not just part-whole, but are also measurement and operator situations. D. Design situations to address student misconceptions and help them make distinctions between whole numbers and fractions.
A. Tell students that fractions are different from whole numbers, so the procedures are also different.
The mean is all of the following definitions except: A. a value in the data set that is in the center of the data. B. an evening-out or leveling of data. C. a balance point of the data. D. one measure that describes the center of the data.
A. a value in the data set that is in the center of the data.
The following activities support students learning about two-dimensional shapes in different orientations except: A. constructing figures with centimeter cubes. B. sketching shapes that have been show for only five seconds. C. cutting shapes with five squares on grid paper. D. constructing shapes with given number of simple tiles.
A. constructing figures with centimeter cubes.
As students progress in their ability to categorize it is important to introduce labels that will widen their classification schemes such as: A. negative attributes. B. attribute names. C. measurement terms. D. conjectures.
A. negative attribute
The following are money ideas and skills typically required in primary grades except: A. reading and writing number and word money amounts. B. recognizing coins and identifying their value. C. creating equivalent coin collections (same amount, different coins). D. counting and comparing coins.
A. reading and writing number and word money amounts.
The value of a collection of coins is best learned by having students: A. sort the coins starting with the highest value and skip counting. B. solve word problems involving money. C. create an equivalent coin collection. D. write all of the individual coin values down and add them on paper
A. sort the coins starting with the highest value and skip counting.
Which of the following is a good explanation for how to add fractions? A. Add equal-sized partslong dash—finding a common denominator can help to solve the problem. B. Put together through combining the numerators. C. Join parts and find a common denominator in order to combine correctly. D. Find the common denominator because one only adds the numerators.
Add equal-sized partslong dash—finding a common denominator can help to solve the problem.
A seventh-grade class wants to determine if the students on one floor of the school are more boringboring than those on another floor. What are some types of questions to consider? Choose the correct answer below. A. What does it mean to be boring question mark What does it mean to be boring? B. In a typical school, would one expect the students on one floor to be more boringboring than those on a different floor? C. Where could you find a baseline of "normal" so that you know what boringboring means and what it means to be less boringboring? D. Both Upper A and C.Both A and C. E. All of the above.All of the above. F. None of the above.
All of the above (E)
Steve asks what an exit poll is and whether they are effective at predicting results in an election. What do you tell him? Choose the correct answer below. A. An exit poll attempts to determine who or what voters in an election cast their ballot for as soon as they leave their polling station. An exit poll may not be great at predicting results since data collected are only from one state. B. An exit poll attempts to determine who or what voters in an election cast their ballot for as soon as they leave their polling station. An exit poll is never great at predicting results because people of one party affiliation tend to never respond. C. An exit poll attempts to determine who or what voters in an election cast their ballot for as soon as they leave their polling station. An exit poll may not be great at predicting results since the data is collected by asking for volunteers' opinions. D. An exit poll attempts to determine who or what voters in an election cast their ballot for as soon as they leave their polling station. An exit poll is excellent at predicting results since the data collected is a great representative sample.
An exit poll attempts to determine who or what voters in an election cast their ballot for as soon as they leave their polling station. An exit poll may not be great at predicting results since the data is collected by asking for volunteers' opinions
A student says, "My answer must be wronglong dash—my answer got bigger." Which of the following responses will best help the student understand why the answer got bigger? A. Show the student a picture of a rectangle partitioned into eighths; tell the student that you are dividing by eighths and they are small, like one-digit numbers, so the answer is bigger. B. Ask them to explain the meaning of 8 ÷ 2, using cutting ribbon as a context, and then ask them to re-explain to you using 8 ÷ one half 1 2, still using cutting ribbon as a context. C. Tell the student that fractions work the opposite of whole numbers, so with division, the answer gets bigger. D. Ask the student to round the numbers to the nearest whole number and estimate.
Ask them to explain the meaning of 8 ÷ 2, using cutting ribbon as a context, and then ask them to re-explain to you using 8 ÷ one half 1 2, still using cutting ribbon as a context.
Which of the following best describes how to teach multiplication involving a whole number and a fraction? A. A "fraction times a whole number" and a "whole number times a fraction" are conceptually the same, so they are best taught together. B. Multiplication is commutative, so these two situations should be taught together using arrays. C. A "fraction times a whole number" and a "whole number times a fraction" are conceptually different, so they should be taught separately. D. Both should be taught by applying the idea that any number can be written with a one under it and then you have a fraction times a fraction—this helps students see all types of multiplication problems as the same.
A "fraction times a whole number" and a "whole number times a fraction" are conceptually different, so they should be taught separately.
A student writes StartFraction 15 Over 53 EndFraction 15 53less than<one third 1 3 because 3 times 15 less than 53 times 13•15<53•1. Another student writes StartFraction 1 CrossOut 5 EndCrossOut Over CrossOut 5 EndCrossOut 3 EndFraction 15 53equals=one third 1 3. Where is the fallacy? A. The second student's approach is correct. What the first student has done is to treat the problem as if it had been StartFraction 15 Over 53 EndFraction 15 53, when in reality, the problem is left parenthesis one fifth right parenthesis left parenthesis five thirds right parenthesis 1 5 5 3equals=one third 1 3. One cancels digits not factors. B. The first student's approach is correct. What the second student has done is to treat the problem as if it had been left parenthesis one fifth right parenthesis left parenthesis five thirds right parenthesis 1 5 5 3equals=one third 1 3, when in reality, the problem is StartFraction 15 Over 53 EndFraction 15 53. One cancels factors not digits. C. The first student's approach is correct. What the second student has done is to treat the problem as if it had been left parenthesis one fifth right parenthesis left parenthesis five thirds right parenthesis 1 5 5 3equals=one third 1 3, when in reality, the problem is left parenthesis one fifth right parenthesis left parenthesis three fifths right parenthesis 1 5 3 5.
B (question 67)
Formulating questions can be an opportunity to interdisciplinary learning experiences. Identify the question below that engages science and mathematics inquiry. A. How many different types of restaurants are located near our school? B. How many days does it take for different seeds to germinate? C. How many pets do our classmates have? D. How many TV shows have children in lead roles?
B. How many days does it take for different seeds to germinate?
Angle measurement can be a challenge for some students for the following reason. A. Unit for measuring and angle is an angle B. Protractors are used to measure angles C. Attribute of the angle size is the spread of the angle's rays D. Angle relationships are supplementary, complementary, and vertical
B. Protractors are used to measure angles
A student argued that a pizza cut into 44 pieces was more than a pizza cut into 22 pieces. How would you respond? Choose the correct answer below. A. The student is wrong. A pizza cut into 22 pieces was more than a pizza cut into 44 pieces. B. The student was probably thinking that more pieces meant more pizza. The amount of pizza did not change and only the number of pieces changed. C. The student is wrong. The amount of pizza decreases as the number of pieces increases. D. The student is correct. A pizza cut into 44 pieces was more than a pizza cut into 22 pieces.
B. The student was probably thinking that more pieces meant more pizza. The amount of pizza did not change and only the number of pieces changed.
The following statements are important components of doing mathematics except: A. interpreting data to answer a question. B. being able to accurately compute the mean for a set of data. C. focusing on the context of the situation. D. analyzing the spread of data, including the variability and the center of the data.
B. being able to accurately compute the mean for a set of data.
Spatial sense includes all the following except: A. recognize spatial relationships. B. identifying hierarchy of geometric properties. C. mentally visualize objects. D. intuition about shapes.
B. identifying hierarchy of geometric properties.
Rotational symmetry is described as: A. transformation of two-dimensional shapes. B. smallest angle required to have shape match its footprint. C. reasoning about the movement of two-dimensional shapes. D. portion of a shape reflected onto the other side.
B. smallest angle required to have shape match its footprint.
The way we write fractions with a top and bottom number is a convention. What method focuses on making sense of the parts rather than the symbols? A. Begin by discussing the probability of an event occurring B. Begin by measuring length C. Begin by using words (i.e., one-fourth) D. Begin by talking about fractions as an operator
Begin by using words (i.e., one-fourth)
Which data source could yield data on environmental issues? A. Better World Flux B. U.S. Census Bureau C. Olympic records D. CIA World Fact Book
Better World Flux
95 A. Bonnie is correct since a rectangular prism consists of three congruent and adjacent rectangular faces that could all be a base depending on orientation. B. Bonnie is correct since a rectangular prism consists of a rectangular face as a base. C. Bonnie is assuming that since the rectangle is a base that this is a rectangular prism, however this is a rectangular pyramid. D. Bonnie is assuming that the rectangle is a base, however the bases of a prism must be two congruent, parallel faces.
Bonnie is assuming that the rectangle is a base, however the bases of a prism must be two congruent, parallel faces.
When a figure can be reflected over a line and rotated about a point this combination of transformations is called: A. line symmetry. B. congruence. C. composition. D. similar.
C. composition.
The following are all examples of different kinds of variability that should be explored in elementary and middle school except: A. natural. B. induced. C. differential. D. measurement.
C. differential.
A common misconception with set models is: A. partitioning and Iterating. B. exploring with a variety of models. C. focusing on the size of the subset rather than the number of equal sets. D. determining the relative size of the numbers.
C. focusing on the size of the subset rather than the number of equal sets.
Exploring properties of quadrilaterals is a rich investigation for students. The following are important concepts that emerge from these investigations except: A. generating definitions. B. learning proper terminology. C. prisms are special cylinders. D. shapes are subcategories of other shapes.
C. prisms are special cylinders.
What are the standard units used to measure capacity? A. Inches, feet, and yards B. Spoons, cylinders, and beakers C. Milliliters, centiliters, and liters D. Millimeters, centimeters, and meters
C. Milliliters, centiliters, and liters
Which of the following strategies would you like students to use when determining which of these fractions is greater seven eighths 7 8 or five sixths 5 6? A. Compare how far from 1 B. Find cross products C. Compare to benchmark of one half 1 2 D. Find a common denominator
Compare how far from 1
All of the methods below would work to support students' knowledge about what is happening when multiplying a fraction by a whole number except: A. Equal jumps of length on a ruler B. Use equal sets to Iterate C. Compute with a calculator D. Skip counting by fractional parts i.e. one third 1 3plus+one third 1 3plus+one third 1 3plus+one third 1 3
Compute with a calculator
Locating a fraction on a number line can be challenging but is very important. Which is a common error that students make in working with the number line? A. Count the tick marks that appear without noticing any missing ones B. Visuals show all of the partitions C. Parts should be the same shape and size D. Fractions are numbers
Count the tick marks that appear without noticing any missing ones
Locating a fraction on a number line can be challenging but is very important. Which is a common error that students make in working with the number line? A. Fractions are numbers B. Count the tick marks that appear without noticing any missing ones C. Parts should be the same shape and size D. Visuals show all of the partitions
Count the tick marks that appear without noticing any missing ones
Which of the following is important to do before students learn the formal algorithms? A. Ensure that students have multiple experiences with various contexts. B. Use models such as area grids and counters that illustrate the operation. C. Include estimation as well as different ways in which to find the exact answer. D. Address misconceptions.
D. Address misconceptions.
Which of the following is one of the best approaches for teaching elapsed time? A. Fraction pieces B. Grid paper C. Paper plates D. An empty number line
D. An empty number line
What type of scale measures mass from small to large? A. Kitchen scale B. Supermarket scale C. Spring scale D. Beam or balance scale
D. Beam or balance scale
The natural progression for teaching students to understand and read analog clocks includes starting with which of the following steps? A. Use a digital clock and relate it to decimals. B. Focus on a.m. and p.m. C. Start with 60 minutes and discuss the fractional components such as one-quarter after. D. Begin with a one-handed clock that can be read with reasonable accuracy
D. Begin with a one-handed clock that can be read with reasonable accuracy
All the following are recommendations for effective fraction computation instruction except: A. Variety of models for each operation B. Contextual tasks C. Estimation and invented methods D. Carefully introduce procedures
D. Carefully introduce procedures
The teachers have identified three manipulatives to use when teaching fractional concepts. Each teacher intended to select one manipulative to show each fraction model. Which teacher succeeded in selecting manipulatives for each type? A. Bart selected fraction strips, Cuisenaire rods, and number lines. B. Carla selected number lines, geoboards, and fraction circles. C. Denise selected tangrams, color tiles, and number lines. D. Angela selected 2-color counters, fraction circles, and grid paper.
Denise selected tangrams, color tiles, and number lines.
What description below describes a visualization activity? A. Rotate, reflect, and dilate shapes B. Classify shapes by properties C. Draw and recognize objects for different viewpoints D. Identify and place objects in a coordinate plane
Draw and recognize objects for different viewpoints
Consider the set of all fractions equal to one half 1 2. If you take any 10 of those fractions, add their numerators to obtain the numerator of a new fraction and add their denominators to obtain the denominator of a new fraction. How does the new fraction relate to one half 1 2? Generalize what was found and explain. How does the new fraction relate to one half 1 2? A. The new fraction is greater than one half 1 2. B. The new fraction is less than one half 1 2. C. The new fraction is equal to one half 1 2. Your answer is correct. Generalize what was found in the previous step. Let StartFraction a Over b EndFraction a b be any fraction and r a non-zero integer. Let StartFraction ar 1 Over br 1 EndFraction ar1 br1, StartFraction ar 2 Over br 2 EndFraction ar2 br2,...,StartFraction ar Subscript n Over br Subscript n EndFraction arn brn be equivalent fractions to StartFraction a Over b EndFraction a b. Choose the correct generalization below. A. The sum of the numerators gives a times •r1plus+a times •r2plus+...plus+a times •rnequals=a left parenthesis r 1 plus r 2 plus ... plus r Subscript n right parenthesisar1+r2+...+rn. Adding the denominators gives b times r 1 plus b times r 2 plus ... plus b times r Subscript nb•r1+b•r2+...+b•rnequals=b left parenthesis r 1 plus r 2 plus ... plus r Subscript n right parenthesisbr1+r2+...+rn. The new fraction is StartFraction a left parenthesis r 1 plus r 2 plus ... plus r Subscript n Baseline right parenthesis Over b left parenthesis r 1 plus r 2 plus ... plus r Subscript n Baseline right parenthesis EndFraction ar1+r2+...+rn br1+r2+...+rn and it is greater than StartFraction a Over b EndFraction a b. B. The sum of the numerators gives a times •r1plus+a times •r2plus+...plus+a times •rnequals=a left parenthesis r 1 plus r 2 plus ... plus r Subscript n right parenthesisar1+r2+...+rn. Adding the denominators gives b times r 1 plus b times r 2 plus ... plus b times r Subscript nb•r1+b•r2+...+b•rnequals=b left parenthesis r 1 plus r 2 plus ... plus r Subscript n right parenthesisbr1+r2+...+rn. The new fraction is StartFraction a left parenthesis r 1 plus r 2 plus ... plus r Subscript n Baseline right parenthesis Over b left parenthesis r 1 plus r 2 plus ... plus r Subscript n Baseline right parenthesis EndFraction ar1+r2+...+rn br1+r2+...+rn and it is equal to StartFraction a Over b EndFraction a b. Your answer is correct.C. The sum of the numerators gives a times •r1plus+a times •r2plus+...plus+a times •rnequals=a left parenthesis r 1 plus r 2 plus ... plus r Subscript n right parenthesisar1+r2+...+rn. Adding the denominators gives b times r 1 plus b times r 2 plus ... plus b times r Subscript nb•r1+b•r2+...+b•rnequals=b left parenthesis r 1 plus r 2 plus ... plus r Subscript n right parenthesisbr1+r2+...+rn. The new fraction is StartFraction a left parenthesis r 1 plus r 2 plus ... plus r Subscript n Baseline right parenthesis Over b left parenthesis r 1 plus r 2 plus ... plus r Subscript n Baseline right parenthesis EndFraction ar1+r2+...+rn br1+r2+...+rn and it is less than
EQUAL
The goal is to rename a fractional amount. What is the concept that requires the use of many contexts and models? A. Multiplying by one B. Magnitude of fractions C. Equivalent fractions D. Missing number equivalences
Equivalent fractions
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. benchmarking D. estimation
Estimation
In the video, Felisha was asked to share one cookie among four people. What was Felisha's problem solving strategy? Choose the correct answer below. A. Felisha determined how many groups of one-fourth were in one by drawing a picture. B. Felisha used a fair share model by splitting the cookie into four parts. C. She used the invert-and-multiply rule for dividing fractions. D. She did not use any of these strategies.
Felisha used a fair share model by splitting the cookie into four parts.
All the items listed below would be good resources for data related questions except: A. Picture books B. A local newspaper C. Field trip D. Classmates
Field trip
What is a problem with learning only designated (standard) algorithms for fraction operations? A. More effective and quicker to learn B. Follow a procedure in a short term, but not retain C. Use it to assess whether answer makes sense D. Helps students think conceptually about the operation
Follow a procedure in a short term, but not retain
All of the following statements are research-based recommendations for teaching and learning about fractions except one. Which one? A. Provide a variety of models and context to represent fractions B. Invest time for students to understand equivalence concretely and symbolically C. Give greater emphasis to specific algorithms for finding common denominators D. Emphasize the meanings of fractions, rather than rote procedures
Give greater emphasis to specific algorithms for finding common denominators
Research findings support all of the following fraction teaching ideas but one. Which of the following is the unsupported method? A. Ask students to connect the symbols to the visuals (showing sixths and writing one sixth 1 6). B. Ask students to use partitioning and describe where on a number line a particular fraction is (such as seven eighths 7 8). C. Give students area models that are already partitioned and ask them to record the fractional amount shaded. D. Ask students to partition rectangles, collections of counters, and paper strips.
Give students area models that are already partitioned and ask them to record the fractional amount shaded.
Determining the best way to represent the data should focus on what component? A. Categorical or numerical data B. Details of graph construction C. Determining scale and labels D. Graph will answer the posed question
Graph will answer the posed question
Which of the following best describes the relationship between iterating and partitioning? A. Iterating and partitioning are inverses of each other. B. Partitioning is finding the parts of a whole, whereas iterating is counting the fractional parts. C. Partitioning is the denominator (the size of the parts) and iterating is the numerator (how many parts). D. Iterating is counting by unit fractions and partitioning is grouping unit fractions together.
Partitioning is finding the parts of a whole, whereas iterating is counting the fractional parts.
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. Unit for measuring and angle is an angle D. Protractors are used to measure angles
Protractors are used to measure angles
Comparison activities guide students understanding of volume and capacity. Identify the activity that would not use volume comparison. A. Provide students with two small boxes and unit cubes to find which has greater volume 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 grid paper and rulers to construct different sized rectangular prisms D. Provide students with equal size sheets of paper to make tubes and use beans to fill for a volume measure
Provide students with grid paper and rulers to construct different sized rectangular prisms
Which model below would not provide a clear illustration of equivalent fractions? A. Show an algorithm of multiplying the numerator and denominator by the same number B. Cut a paper strip, shade part of the strip, and ask students to use paper folding to describe what fraction of the strip is shaded C. Draw a rectangle on grid paper with part of it shaded and ask students to determine the fraction that is shaded while giving different possible answers D. Place a pile of 24 two-color counters with 1/4 showing red under the document camera and ask students to tell you different ways to tell what fraction is red
Show an algorithm of multiplying the numerator and denominator by the same number
Explain whether a circle graph would change if the amount of data in each category was doubled. Choose the correct answer below. A. Since each category doubled its count, each interior angle in the circle will increase in size. B. Since each category doubled its count, a second circle is needed to display all the data. C. Since each category doubled its count, the count labels on the graph will change but the size and percentage for each section will not. D. Since each category doubled its count, the circle graph will double in size.
Since each category doubled its count, the count labels on the graph will change but the size and percentage for each section will not.
Providing students with many contexts and visuals is essential to their building understanding of equivalence. More examples of linear situations are needed to make comparisons more visible. Which of the following would not be best to model on a number line? A. Height of plants growth B. Distance walked C. Slices of pizza eaten D. Length of hair
Slices of pizza eaten
For each of the following four squares, write a fraction to describe the shaded portion. What property of fractions does the diagram illustrate? Bold a.a. A square is divided into 2 equally sized rectangles. One rectangle is shaded. Bold b.b. A square is divided into 4 equally sized rectangles. Two rectangles are shaded. Bold c.c. A square is divided into 6 equally sized rectangles. Three rectangles are shaded. Bold d.d. A square is divided into 8 equally sized rectangles. Four rectangles are shaded. a. The fraction illustrated by the shaded region is one half 1 2. (Type an integer or a simplified fraction.) b. The fraction illustrated by the shaded region is one half 1 2. (Type an integer or a simplified fraction.) c. The fraction illustrated by the shaded region is one half 1 2. (Type an integer or a simplified fraction.) d. The fraction illustrated by the shaded region is one half 1 2. (Type an integer or a simplified fraction.) What property of fractions does this illustrate? The definition of simplest form The definition of rational numbers The Fundamental Law of Fractions Equality of fractions
The Fundamental Law of Fractions
What is the important idea in data analysis when students are reading and interpreting graphs? A. The measures of center B. The difference between actual facts and inferences C. The range of the data set D. The measures of variability
The difference between actual facts and inferences
What is the important idea in data analysis when students are reading and interpreting graphs? A. The range of the data set B. The measures of variability C. The measures of center D. The difference between actual facts and inferences
The difference between actual facts and inferences
A student argued that a pizza cut into 1616 pieces was more than a pizza cut into 88 pieces. How would you respond? Choose the correct answer below. A. The student is correct. A pizza cut into 1616 pieces was more than a pizza cut into 88 pieces. B. The student was probably thinking that more pieces meant more pizza. The amount of pizza did not change and only the number of pieces changed. C. The student is wrong. A pizza cut into 88 pieces was more than a pizza cut into 1616 pieces. D. The student is wrong. The amount of pizza decreases as the number of pieces increases.
The student was probably thinking that more pieces meant more pizza. The amount of pizza did not change and only the number of pieces changed.
Mixed numbers: A. can be changed into fractions or "improper" fractions and added. B. should be added using columns, adding whole number parts and fractional parts separately (similar to place value). C. are easier to subtract than fractions less than 1. D. are best introduced after students understand fractions less than 1.
can be changed into fractions or "improper" fractions and added.
The most important factor in moving students up the van Hiele levels is: A. geometric experiences that teachers provide to the students. B. repetition and practice. C. students' background knowledge of shapes. D. the use of manipulative materials.
geometric experiences that teachers provide to the students.
The following are suggested strategy for estimating except: A. using subdivisions. B. iterating a unit mentally or physically. C. guessing. D. using benchmarks as referents.
guessing
All of the following statements are correct except: A. picture graphs can be created so that the picture represents one piece of data or a group of data. B. box plots are used to display both measures of center and the spread of data. C. line plots are graphs in which a line connects data points on a coordinate axis. D. histograms are different from bar graphs because they display continuous data.
line plots are graphs in which a line connects data points on a coordinate axis.
Choose an appropriate metric unit to measure the height of a semi dash trailerthe height of a semi-trailer. Choose the correct answer below. meters . kilometers centimeters millimeters
meters
The following are examples of attribute objects that can be sorted and classified except: A. yellow centimeter cubes. B. pattern blocks. C. leaves. D. seashells.
yellow centimeter cubes.
