EDU351 Final
What does a strong understanding of fractional computation rely on? A) Estimating with fractions. B) Iteration skills. C) Whole number knowledge. D) Fraction equivalence.
D) Fraction equivalence.
What statement would be the description of Visualization? A) Positional descriptions- above, below, beside. B) Changes in position or size of a shape. C) Intuitive idea of how shapes fit together. D) Geometry in the minds eye.
D) Geometry in the minds eye.
The estimation questions below would help solve this problem EXCEPT: - A farmer fills each jug with 3.7 liters of cider. If you buy 4 jugs, how many liters of cider is that? A) Is it more than 12 liters? B) What is the most it could be? C) What is double 3.7 liters? D) Is it more than 7 × 4?
D) Is it more than 7 × 4?
The following are all elements of effective early elementary geometry instruction EXCEPT: A) Opportunities for students to examine an array of shape classes. B) Opportunities for students to discuss the properties of shapes. C) Opportunities for students to use physical materials. D) Opportunities for students to learn the vocabulary.
D) Opportunities for students to learn the vocabulary.
The main link between fractions, decimals and percents are A) Expanded notation. B) Terminology. C) Equivalency. D) Physical models.
D) Physical models.
22) Equivalent fraction models are important for students to have in several contexts. Identify two models and an example of how they can be used for teaching equivalence.
1. Area model - Fractions are determined based on how a part of a region or area relates to the whole area or region. Ex. Make a pie and cut into fractions. Put pieces on top to see the fraction relative to the size of the whole. Ex 2. "Pan of brownies" Have students make paper brownies like the pie above and have them put the pieces together on top of the whole making different kinds of fractions.
Name two strategies or methods for helping students to develop estimation skills. Describe how these strategies/methods would contribute to conceptual understanding.
1. Estimates that are not reasonable 2. Estimation should be a classroom activity, do it once a week. Need experience measuring and estimating.
21) Researchers have described a number of reasons that students have a tendency to struggle with fraction concepts. Name two of these reasons, and describe a method a teacher might use to address each.
1. Fractions are very universal. They can be used to measure building supplies or rooms or even used in the kitchen. This can be confusing to kids. Therefore if the teacher were to ensure students get experience with fractions in a variety of different real-life experiences, the students will understand how to apply them to everyday life. 2. Students tend to think that the top (numerator) and bottom (denominator) are two separate numbers. This can be incredibly confusing to kids that can't conceptualize them as a part of a whole number together. If you show the students real life examples, then it'll hep them be able to apply this skill outside of the classroom.
21) Name two methods that could help students develop the connection between fractions and decimals. Then describe how these methods develop conceptual understanding.
1. Have students use food for examples. Such as 40% would be how much of the pizza? 1/5 would be how much of this pie? Breaking it down into these parts can help students visualize what they are doing as well using real life situations will help them relate these problems to reality. 2. Use plant growth to show how a plant grew. If the plant grew more than 100% in a single year, you can show them in decimals and fractions how much the plant grew. This will help students relate decimals and fractions to outside of the classroom experiences.
Identify two common misconceptions and an instructional approach that would redirect student understanding.
1. longer # is larger. Ex. .375 is larger than .80. Use decimal models to show each number and compare. Two 10 x 10 grids with each number shaded will help make accurate comparisons. 2. less than zero. Ex. 0.36 is less than 0. Use context, for instance ask students if they rather have 0 or .50 of a dollar.
Understanding where to put the decimal is an issue with multiplication and division of decimals. What method below supports a fuller understanding? A) Rewrite decimals in their fractional equivalents. B) Rewrite decimals as whole numbers, compute and count place value. C) Rewrite decimals to the nearest tenths or hundredths. D) Rewrite decimals on 10 by 10 grids.
A) Rewrite decimals in their fractional equivalents.
What is it advisable to do when you are exploring decimal numbers? A) 10 to one multiplicative relationship. B) Rules for placement of the decimal. C) Role of the decimal point. D) How to read a decimal fraction.
A) 10 to one multiplicative relationship.
The statements below represent illustrations of various relationships between the area formulas? Identify the one that is NOT represented correctly. A) A rectangle can be cut along a diagonal line and rearranged to form a non-rectangular parallelogram. Therefore the two shapes have the same formula. B) A rectangle can be cut in half to produce two congruent triangles. Therefore, the formula for a triangle is like that for a rectangle, but the product of the base length and height must be cut in half. C) The area of a shape made up of several polygons (a compound figure) is found by adding the sum of the areas of each polygon. D) Two congruent trapezoids placed together always form a parallelogram with the same height and a base that has a length equal to the sum of the trapezoid bases. Therefore, the area of a trapezoid is equal to half the area of that giant parallelogram, h/2 (b1 +b2).
A) A rectangle can be cut along a diagonal line and rearranged to form a non-rectangular parallelogram. Therefore the two shapes have the same formula.
Tangrams and pentominoes are examples of physical materials that can be used to do all of the following EXCEPT: A) Create tessellations. B) Sort and classify. C) Compose and decompose. D) Explore two-dimensional models.
A) Create tessellations
All of the models listed below support the understanding of fraction equivalence EXCEPT: A) Graph of slope B) Shapes created on dot paper. C) Plastic, circular area models. D) Clock faces.
A) Graph of slope
What language supports the idea that the area of a rectangle is not just measuring sides? A) Height and base B) Length and width C) Width and Rows D) Number of square units
A) Height and base
The term improper fraction is used to describe fractions greater than one. Identify the statement that is true about the term improper fraction. A) Is a clear term, as it helps students realize that there is something unacceptable about the format. B) Should be taught separately from proper fractions. C) Are best connected to mixed numbers through the standard algorithm. D) Should be introduced to students in a relevant context.
A) Is a clear term, as it helps students realize that there is something unacceptable about the format.
Young learners do not immediately understand length measurement. Identify the statement below that would NOT represent a misconception about measuring length. A) Measuring attribute with the wrong measurement tool. B) Using wrong end of the ruler C) Counting hash marks rather than spaces. D) Misaligning objects when comparing.
A) Measuring attribute with the wrong measurement tool.
A common set model for decimal fraction is money. Identify the true statement below. A) Money is a two-place system. B) One-tenth a dime proportionately compares to a dollar. C) Money should be an initial model for decimal fractions. D) Money is a proportional model.
A) Money is a two-place system.
The activities listed below would guide students in exploring the geometric content of location. Identify the one that can also be used with transformations. A) Pentomino positions. B) Paths. C) Coordinate reflections. D) Coordinate slides.
A) Pentomino positions.
What is the name given to a set of completely regular polyhedrons? A) Polyhedron solid. B) Platonic solids. C) Polyominoid figures. D) Polydron shape.
A) Polyhedron solid.
What would be an advantage of dynamic geometry programs over the use of paper pencil and geoboards? A) Shapes can be stretched and more examples of the class of that shape. B) Construct visual model of shapes. C) Construction of points, lines and figures. D) Shapes can be moved about and manipulated.
A) Shapes can be stretched and more examples of the class of that shape.
Identify the statement that is NOT a part of the sequence of experiences for measurement instruction. A) Using measurement formulas. B) Using physical models. C) Using measuring instruments. D) Using comparisons of attributes.
A) Using measurement formulas.
What is a method teachers might use to assess the level of their students understanding of the decimal point placement? A) Ask them to show all computations. B) Ask them to show a model or drawing. C) Ask them to explain or write a rationale. D) Ask them to use a calculator to show the
B) Ask them to show a model or drawing.
Identify what a student operating van Hiele's geometric thought level one would likely be doing. A) Making and testing hypothesis. B) Classifying shapes based on properties. C) Looking at counter examples. D) Generating property lists.
B) Classifying shapes based on properties.
Categories of two-dimensional shapes include the following EXCEPT: A) Triangles. B) Cylinders. C) Simple closed curves. D) Convex quadrilaterals.
B) Cylinders.
Understanding that when decimals are rounded to two places (2.30 and 2.32) there is always another number in between. What is the place in between called? A) Place value. B) Density. C) Relationships. D) Equality.
B) Density.
Decimal multiplication tends to be poorly understood. What is it that students need to be able to do? A) Discover the method by being given a series of multiplication problems with factors that have the same digits, but decimals in different places. B) Discover it on their own with models, drawings and strategies. C) Be shown how to estimate after they are shown the algorithm. D) Use the repeated addition strategy that works for whole number.
B) Discover it on their own with models, drawings and strategies.
Comparing fractions involves the knowledge of the inverse relationship between number of parts and size of parts. The following activities support the relationship EXCEPT: A) Iterating. B) Equivalent fraction algorithm. C) Estimating. D) Partitioning
B) Equivalent fraction algorithm.
Using precise language can support students' understanding of the relationship between fractions and decimal fractions. All of the following are true statements EXCEPT: A) 0.75 = 3/4. B) Five and two-tenths is the same as five point two. C) Six and three-tenths = 6 3/10. D) 7. 03 = 7 30/100.
B) Five and two-tenths is the same as five point two.
Identify what a student product of thought at van Hiele level zero visualization would be. A) Shapes are alike. B) Grouping shapes that are alike. C) Classifying shapes that are alike. D) Identifying attributes of shapes that are alike.
B) Grouping shapes that are alike.
All of these statements are true about reasons for including estimation in measurement activities EXCEPT: A) Helps focus on the attribute being measured. B) Helps provide an extrinsic motivation for measurement activities. C) Helps develop familiarity with the unit. D) Helps promote multiplicative reasoning.
B) Helps provide an extrinsic motivation for measurement activities.
Counting precedes whole-number learning of addition and subtraction. What is another term for counting fraction parts? A) Equalizing. B) Iterating. C) Partitioning. D) Sectioning.
B) Iterating
What is a common misconception with fraction set models? A) There are not many real-world uses. B) Knowing the size of the subset rather than the number of equal sets. C) Knowing the number of equal sets rather than the size of subsets. D) There are not many manipulatives to model the collections
B) Knowing the size of the subset rather than the number of equal sets.
The following decimals are equivalent 0.06 and 0.060. What does one of them show that the other does not show? A) More place value. B) More hundreds. C) More level of precision. D) Closer to one.
B) More hundreds.
As students move to thinking about formulas it supports their conceptual knowledge of how the perimeter of rectangles can be put into general form. What formula below displays a common student error for finding the perimeter? A) P = l + w + l + w B) P = l + w C) P = 2l + 2w D) P = 2(l + w)
B) P = l + w
Teaching considerations for fraction concepts include all of the following EXCEPT: A) Iterating and partitioning. B) Procedural algorithm for equivalence. C) Emphasis on number sense and fractional meaning. D) Link fractions to key benchmarks.
B) Procedural algorithm for equivalence.
Volume and capacity are both terms for measures of the "size" of three-dimensional regions. What statement is true of volume but not of capacity? A) Refers to the amount a container will hold. B) Refers to the amount of space of occupied by three-dimensional region. C) Refers to the measure of only liquids. D) Refers to the measure of surface area
B) Refers to the amount of space of occupied by three-dimensional region.
Identify the attribute of an angle measurement. A) Base and height. B) Spread of angle rays. C) Unit angle. D) Degrees.
B) Spread of angle rays.
The 10-to-1 relationship extends in two directions. There is never a smallest piece or a largest piece. Complete the statement, "The symmetry is around..." A) The decimal point. B) The ones place. C) The operation being conducted. D) The relationship between the adjacent pieces.
B) The ones place.
When using a nonstandard unit to measure an object, what is it called when you use many copies of the unit as needed to fill or match the attribute? A) Iterating. B) Tiling. C) Comparing. D) Matching.
B) Tiling.
Estimation of many percent problems can be done with familiar numbers. Identify the idea that would not support estimation. A) Substitute a close percent that is easy to work with. B) Use a calculator to get an exact answer. C) Select numbers that are compatible with the percent to work with. D) Convert the problem to one that is simpler.
B) Use a calculator to get an exact answer.
The way we write fractions is a convention with a top and bottom number with a bar in between. Posing questions can help students make sense of the symbols. All of the questions would support that sense making EXCEPT: A) What does the denominator in a fraction tell us? B) What does the equal symbol mean with fractions? C) What might a fraction equal to one look like? D) How do know if a fraction is greater than, less than 1?
B) What does the equal symbol mean with fractions?
What is the most common model used for decimal fractions? A) Rational number wheel B) Base ten strips and squares. C) 10 × 10 grids. D) Number line.
C) 10 × 10 grids.
The concept of conversion can be confusing for students. Identify the statement that is the primary reason for this confusion. A) Basic idea if the measure is the same as the unit it is equal. B) Basic idea that if the measure is larger the unit is longer. C) Basic idea that if the measure is larger the unit is shorter. D) Basic idea that if the measure is shorter the unit is shorter.
C) Basic idea that if the measure is larger the unit is short
There are three broad goals to teaching standard units of measure. Identify the one that is generally NOT a key goal. A) Familiarity with the unit. B) Knowledge of relationships between units. C) Estimation with standard and nonstandard units. D) Ability to select and appropriate unit.
C) Estimation with standard and nonstandard units.
Complete this statement, "Comparing two fractions with any representation can be made only if you know the..." A) Size of the whole. B) Parts all the same size. C) Fractional parts are parts of the same size whole. D) Relationship between part and whole.
C) Fractional parts are parts of the same size whole.
How do you know that = ? Identify the statement below that demonstrates a conceptual understanding. A) They are the same because you can simplify and get B) Start with and multiply the top and bottom by 2 and you get C) If you have 6 items and you take 4 that would be . You can make 6 groups into 3 groups and 4 into 2 groups and that would be D) If you multiply 4 × 3 and 6 × 2 they're both 12.
C) If you have 6 items and you take 4 that would be . You can make 6 groups into 3 groups and 4 into 2 groups and that would be
What is it that students can understand if they can express fractions and decimals to the hundredths place? A) Place value. B) Computation of decimals. C) Percents. D) Density of decimals.
C) Percents.
What is the most conceptual method for comparing weights of two objects? A) Place objects in two pans of a balance. B) Place objects on a spring balance and compare. C) Place objects on extended arms and experience the pull on each. D) Place objects on digital scale and compare.
C) Place objects on extended arms and experience the pull on each.
Comparing area is more of a conceptual challenge for students than comparing length measures. Identify the statement that represents one reason for this confusion. A) Area is a measure of two-dimensional space inside a region. B) Direct comparison of two areas is not always possible. C) Rearranging areas into different shapes does not affect the amount of area. D) Area and perimeter formulas are often used interchangeably.
C) Rearranging areas into different shapes does not affect the amount of area.
The following are appropriate activities for van Hiele level one analysis EXCEPT: A) Classifying quadrilaterals into special categories according to certain characteristics. B) Discovering pi by measuring the circumference and diameter of various circular objects and calculating their quotient. C) Sorting pattern blocks by their number of sides. D) Determining which shapes will create tessellations.
C) Sorting pattern blocks by their number of sides.
What would be a signature characteristic of a van Hiele level two activity? A) Students can use dot or line grids to construct tessellations. B) Students can classify properties of quadrilaterals. C) Students can use logical reasoning about properties of shapes. D) Students can prepare informal arguments about properties of shapes.
C) Students can use logical reasoning about properties of shapes.
There are several common errors and misconceptions associated with comparing and ordering decimals. Identify the statement below that represents the error with internal zero. A) Students say 0.375 is greater than 0.97. B) Students see 0.58 less than 0.078. C) Students select 0 as larger than 0.36 D) Students see 0.4 as not close to 0.375
C) Students select 0 as larger than 0.36
Movements that do not change the size or shape of the object are called 'rigid motions. Identify the movement below that would NOT be considered rigid. A) Reflections. B) Translations. C) Tessellations. D) Rotations.
C) Tessellations.
What is the purpose of the activity "Minimal Defining Lists"? A) To list the many properties of shapes. B) To list the classes of shapes. C) To list the subset of the properties of a shape. D) To list the relationships between the properties of shapes.
C) To list the subset of the properties of a shape.
The following are guidelines for instruction on percents EXCEPT: A) Use terms part, whole and percent B) Use models, drawings and contexts to explain their solutions. C) Use calculators. D) Use mental computation.
C) Use calculators.
Locating a fractional value on a number line can be challenging but is important for students to do. All of the statements below are common errors that students make when working with the number line EXCEPT: A) Use incorrect notation. B) Change the unit. C) Use incorrect subsets. D) Count the tick marks rather than the space.
C) Use incorrect subsets.
Instruction on decimal computation has been dominated by rules. Identify the statement that is not rule based. A) Line up the decimal points. B) Count the decimal places. C) Shift the decimal point in the divisor. D) Apply decimal notation to properties of operations.
D) Apply decimal notation to properties of operations.
Approximation with compatible fractions is one method to help students with number sense with decimal fractions. All of the statements are true of 7.3962 EXCEPT: A) Closer to 7 than 8. B) Closer to 7 3/4 than 7 1/2. C) Closer to 7.3 than 7 1/5. D) Closer to 7.4 than 7.5.
D) Closer to 7.4 than 7.5.
Challenges with students' use of rulers include all EXCEPT: A) Deciding whether to measure an item beginning with the end of the ruler. B) Deciding how to measure an object that is longer than the ruler. C) Properly using fractional parts of inches and centimeters. D) Converting between metric and customary units.
D) Converting between metric and customary units.
The study of transformations includes all of the categories below EXCEPT: A) Line symmetry. B) Translations. C) Compositions. D) Dilations.
D) Dilations.
What does it mean to write fractions in simplest term? A) Finding equivalent numerators. B) Finding equivalent denominators. C) Finding multipliers and divisors. D) Finding equivalent fractions with no common whole number factors
D) Finding equivalent fractions with no common whole number factors
All of the statements below are true of this decimal fraction 5.13 EXCEPT: A) 5 + 1/10 + 3/100. B) Five and thirteen-hundredths. C) 513/100. D) Five wholes, 3 tenths and 1 hundredth.
D) Five wholes, 3 tenths and 1 hundredth.
What is an early method to use to help students see the connection between fractions and decimals fractions? A) Show them how to use a calculator to divide the fraction numerator by the denominator to find the decimal. B) Be sure to use precise language when speaking about decimals, such as "point seven two." C) Show them how to round decimal numbers to the closest whole number. D) Show them how to use base-ten models to build models of base-ten fractions.
D) Show them how to use base-ten models to build models of base-ten fractions.
All of these are ideas and skills for money that students should be aware of in elementary grades EXCEPT: A) Making change. B) Solving word problems involving money. C) Values of coins. D) Solving problems of primary interest.
D) Solving problems of primary interest.
The Common Core State Standards and the National Council of Teachers of Mathematics agree on the importance of what measurement topic? A) Students focus on customary units of measurement. B) Students focus on formulas versus actual measurements C) Students focus on conversions of standard to metric. D) Students focus on metric unit of measurement as well as customary units.
D) Students focus on metric unit of measurement as well as customary units.
What statement below applies to the geometric strand of location? A) Study of shapes in the environment. B) Study of the relationships built on properties. C) Study of translations. D) Study of coordinate geometry.
D) Study of coordinate geometry.
What is the definition of the process of partitioning? A) Equal shares. B) Equal-sized parts. C) Equivalent fractions. D) Subset of the whole.
D) Subset of the whole.
Steps for teaching students to understand and read analog clocks include all of the following EXCEPT: A) Begin with a one-handed clock. B) Discuss what happens with the big hand as the little hand goes from one hour to the next. C) Predict the reading on a digital clock when shown an analog clock. D) Teach time after the hour in one-minute intervals.
D) Teach time after the hour in one-minute intervals.
The study of geometry includes all of the following EXCEPT: A) Reasoning skills about space and properties. B) Visualization. C) Transformation. D) Time.
D) Time.
All of the ideas below support the reasoning behind starting measurement experiences with nonstandard units EXCEPT: A) They focus directly on the attribute being measured. B) Avoids conflicting objectives of the lesson on area or centimeters. C) Provides good rational for using standard units. D) Understanding of how measurement tools work.
D) Understanding of how measurement tools work.
Estimating with fractions means that students have number sense about the relative size of fractions. All of the activities below would guide this number sense EXCEPT: A) Comparing fractions to benchmark numbers. B) Find out the fractional part of the class are wearing glasses. C) Collect survey data and find out what fractions of the class choose each item. D) Use paper folding to identify equivalence.
D) Use paper folding to identify equivalence.
When a teacher assigns an object to be measured students have to make all of these decisions EXCEPT: A) What attribute to measure? B) What unit they can use to measure that attribute? C) How to compare the unit to the attribute? D) What formulas they should use to find the measurement?
D) What formulas they should use to find the measurement?
Discuss the strategies or methods for supporting the conceptual learning of the formulas for areas of various figures.
In order to understand area, students need to understand square x square. Need to understand the process of multiplication. B x H. Draw with a picture. Use b x h instead of L x W. Always start with area of a rectangle. Then move into harder things.
A _______ is a significantly more sophisticated length model than other models. a) Number line. b) Cuisenaire rods. c) Measurement tools. d) Folded paper strips.
a) Number line.
The part-whole construct is the concept most associated with fractions, but other important constructs they represent include all of the following EXCEPT: a) Measure. b) Reciprocity. c) Division. d) Ratio.
b) Reciprocity.
The following visuals/manipulatives support the development of fractions using the area model EXCEPT: a) Pattern blocks .b) Tangrams. c) Cuisenaire rods. d) Geoboards.
c) Cuisenaire rods.
All of the following are fraction constructs EXCEPT: a) Part-whole. b) Measurement. c) Iteration. d) Division.
c) Iteration
Models provide an effective visual for students and help them explore fractions. Identify the statement that is the definition of the length model. a) Location of a point in relation to 0 and other values. b) Part of area covered as it relates to the whole unit. c) Count of objects in the subset as it relates to defined whole. d) A unit or length involving fractional amounts
d) A unit or length involving fractional amounts
Fraction misconceptions come about for all of the following reasons. The statements below can be fraction misconceptions EXCEPT: a) Many meanings of fractions. b) Fractions written in a unique way. c) Students overgeneralize their whole-number knowledge d) Teachers present fractions late in the school year.
d) Teachers present fractions late in the school year.
