The study of geometry includes all of the following EXCEPT:
Reasoning skills about space and properties.
Visualization
Transformation.
Time.
Identify what a student operating at van Hiele's geometric thought level one would likely be doing.
Making and testing hypothesis.
Classifying shapes based on properties.
Looking at counter examples.
Generating property lists.
What statement below applies to the geometric strand of location?
Study of shapes in the environment
Study of the relationships built on properties
Study of translations
Study of coordinate geometry.
Identify what a student product of thought at van Hiele level zero visualization would be.
Shapes are alike
Grouping shapes that are alike
Classifying shapes that are alike
Identifying attributes of shapes that are alike
The following are appropriate activities for van Hiele level one analysis EXCEPT:
Classifying quadrilaterals into special categories according to certain characteristics
Discovering pi by measuring the circumference and diameter of various circular objects and calculating their quotient.
Sorting pattern blocks by their number of sides
Determining which shapes will create tessellations.
What would be a signature characteristic of a van Hiele level 2 activity?
Students can use dot or line grids to construct tessellations
Students can classify properties of quadrilaterals
Students can use logical reasoning about properties of shapes.
Students can prepare informal arguments about properties of shapes
The following are all elements of effective early elementary geometry instruction EXCEPT:
Opportunities for students to examine an array of shape classes.
Opportunities for students to discuss the properties of shapes.
Opportunities for students to use physical materials
Opportunities for students to learn the vocabulary
Tangrams and pentominoes are examples of physical materials that can be used to do all of the following EXCEPT:
Create tessellations
Sort and classify
Compose and decompose
Explore two-dimensional models
Categories of two-dimensional shapes include the following EXCEPT:
Triangles
Cylinders
Simple closed curves
Convex quadrilaterals
The study of transformations includes all of the categories below EXCEPT:
Line symmetry
Translations
Compositions
Dilations
The activities listed below would guide students in exploring the geometric content of location. Identify the one that can also be used with transformations
Pentomino positions
Paths
Coordinate reflections
Coordinate slides
What statement would be the description of Visualization?
Positional descriptions- above, below, beside.
Changes in position or size of a shape.
Intuitive idea of how shapes fit together.
Geometry in the minds eye
What would be an advantage of dynamic geometry programs over the use of paper pencil and geoboards?
Shapes can be stretched and more examples of the class of that shape
Construct visual model of shapes.
Construction of points, lines and figures
Shapes can be moved about and manipulated
What is the purpose of the activity “Minimal Defining Lists”?
To list the many properties of shapes.
To list the classes of shapes.
To list the subset of the properties of a shape
To list the relationships between the properties of shapes
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 as rigid.
Reflections
Translations.
Tessellations.
Rotations.
What is the name given to a set of completely regular polyhedrons?
Polyhedron solid.
Platonic solids.
Polyominoid figures
Polydron shape.
What do statistics and mathematics have in common?
About numbers and operations
About numbers.
About generalizations and abstractions
About variables and cases
Which statistical literacy activity below is appropriate for early elementary students?
How data can be categorized and displayed
How data can be collected and represented.
How data can be represented in frequency tables and bar graphs
How data can be analyzed with measure of center.
The following are categorical data EXCEPT:
Food groups served for lunch.
The students’ favorite things.
Count of boys and girls in the fifth grade.
Different color cars in the parking lot.
Complete this statement, “When students create data displays themselves...”
They become less familiar with the structure of different graphs
They are usually more invested and, therefore, interested in the data analysis.
They have less time to discuss how to interpret the data.
They are usually required to construct them with paper pencil
Which of these options is the best way to display continuous data?
Stem-and-leaf plot
Circle graph
Line graph
Venn diagram
These are true statements about the measures of center EXCEPT:
The median is easier for students to compute and not affected by extreme values like the mean is.
The context of a situation determines which measure would be most appropriate.
When one hears the word “average,” he or she can assume that the mean is being referred to.
The mode is the value in a data set that occurs most frequently.
In statistics, _________ is essential to analyzing and interpreting the data
Type of graphical representation
Context
Range
Mean absolute deviation
The full process of doing meaningful statistics involves all of these EXCEPT:
Clarify the problem at hand.
Employ a plan to collect the data.
Interpret the analysis.
Randomly sample.
What are Box plots most suited for displaying?
The mean of a data set.
The mean and mode of a data set.
The median of a data set
The median and range of a data set
Analyzing or interpreting data is a function of organizing and representing data. Identify the question that would NOT foster a meaningful discussion about the data.
What does the graph not tell us?
What other graphical representations could we use?
What kinds of variability do we need to consider?
What is the maker of the graph trying to tell us?
Identify the graphical representation that works well for comparisons.
Dot plot
Scatter Plot
Object graph
Stem and leaf plot
Data collection should be for a purpose and to answer a question. Identify the question below that would NOT generate data.
How much change do you have in your pocket?
How much loose change does a person typically carry in their pocket?
How do people choose gum?
How long does a piece of gum keep its flavor?
What type of graphical representation can help make sense of proportion by having students convert between degrees and percents?
Histogram
Pie Chart
Box Plot
Stem and Leaf
The graphical representations listed can be used to display continuous data EXCEPT:
Bar graph.
Stem and Leaf.
Line Plot.
What do bivariate data representations show?
Spreading and bunching of each quarter of data.
Number of data elements falling into an interval
Covariation of two data.
Two sets of data extending in opposite directions
These are components of creating a box plot graphical representation EXCEPT:
Data located on one-fourth to the left and right of the median
A line inside at the median of the data
A line to show the lower extreme and upper extreme
A line with Xs or dots to correspond with the data.
Scatter plots can indicate a relationship. Complete this statement, “The value of this statistic is to create a model that will..."
Predict what has not been observed
Define the quartiles.
Represent rational number data
Convert between percents and degrees
Existing data can be found in print and web resources. All of the activities below would be reasons to use and discuss them in a classroom EXCEPT:
Difference between facts and inference.
Message intended by the person who made the graph.
Effectiveness of the graph in communicating the findings
Process of gathering data to answer questions.
Assessing young students on probability knowledge, what would the expectation be that they would be able to do?
Explain their confidence in a theory result
Determine the probability of an experiment.
Tell whether an event is likely or not.
Write reports about the probability of a real situation.
Tools that could be used by young students to model probability experiments include all of the following EXCEPT:
Spinners (virtual and manual).
Weather forecasts.
Coin tosses
Marbles pulled out of bag
Identify the term that is used to for the measure of the probability of an event occurring
Experimental probability.
Theoretical probability.
Relative frequency
An observed occurrence.
This phenomenon refers to a probability experiment being carried out more and more times so that the recorded results get close to theoretical probability.
The law of averages.
The law of likelihood
The law of large numbers.
A law of small numbers.
Conducting experiments and examining outcomes in teaching is important. All of these help address student misconceptions EXCEPT:
Provide a connection to counting strategies
Helps students learn more than students who do not engage in doing experiments.
Model real-world problems
It is significantly more intuitive and fun
All of the following can be used to model and record the results of two independent events EXCEPT:
Tree diagram
Table
Pair of Dice
Stem and Leaf Plot
Identify the description of an experiment of dependent events.
The probability of drawing a certain marble out of a bag on two different tries, replacing the first marble before drawing out a second.
Drawing two cards from a deck, if, when you draw the first, you leave it out, then draw the second.
The probability of getting an even number after rolling a die, then rolling it again
The probability of obtaining heads after flipping a coin once, then a second time.
What is the mathematical term that describes probability as the comparison of desired outcomes to the total possible outcomes?
Fraction
Ratio.
Students can often determine the number of outcomes on some random devices than others. Identify the random device that is challenging and students need more experience
Coin toss
8- sided die
Spinners
Two color counters
Probability has two distinct types. Identify the event below that the probability would be known
What is the possibility of Luke H. making all his free throws?
What is the chance of a snowstorm in Minnesota in January?
What is the probability of rolling a 4 with a fair die?
What is the probability of dropping a rock in water and it will sink?
A number line with 0 (impossible) to 1(possible) is purposeful when students are learning about probability. All of the statements would be examples of benefits of a number line EXCEPT:
Provides a visual representation.
Connects to the likelihood of an event occurring.
Reference for talking about probability.
Experimental random device.
Truly random events occur in unexpected groups, a fair coin may turn up heads five times in a row; a 100-year flood may hit a town twice in 10 years. This imperfect probability is called:
Distribution of randomness.
Probability inequality
Sampling size error
Measure of chance
The following experiments are examples of probabilities with independent events EXCEPT:
Rolling two dice and getting a difference that is not more than 3
Having a tack or cup land up when each is tossed once
Drawing a certain marble out of a bag on two different tries, replacing the first marble before drawing out a second.
Spinning blue twice on a spinner
The process for helping students connect sample space to probability includes all of the steps EXCEPT:
Conduct an experiment with a large number of trials.
Create a comparison experiment.
Predict the results of the experiment
Compare the prediction with the experiment.
What type of probability recording method is less abstract and accessible to a larger range of learners?
Area representation
Equation
What is the probability misconception called when students think that an event that has already happened will influence the outcome of the next event?
Law of small numbers
Possibility counting
Commutativity confusion
Gambler’s fallacy
When students begin to work with exponents they often lack conceptual understanding. Identify the method that supports conceptual versus procedural understanding.
Explore growing patterns with physical models
Explore with whole numbers before exponents with variables
Instruction on the order of operations
Instruction should focus on exponents as a shortcut for repeated multiplication
Order of operations extends working with exponents. What part of the order of operations is a convention?
The meaning of the operation
Multiplying before computing the exponent changes the meaning of the problem
Working from left to right, using parenthesis
PEMDAS
The ideas below would guide student understanding of the concept behind scientific notation EXCEPT:
Examining patterns that arise when inputting very large and small numbers into a calculator.
Researching real-life examples of very large and small numbers.
Asking them to perform computation on very large and small numbers that are not in scientific notation, so they can see how difficult it is
Instructing them only on the movement of the decimal point “the exponent with the 10 tells how many places to move the decimal point”
Real-world contexts with negative numbers provide opportunities for discussion of integer operations. What statement below would represent a quantity?
Timeline of Roman Empire rule.
Altitude above sea level
Golf scores.
Gains and lost football yardage.
When using the number line method for the addition of integers, the following statements relate to the number line method EXCEPT:
Each addend's magnitude needs to be presented on the number line
The position of the arrow indicates positive or negative integers.
A line segment pointing to the right could indicate a positive or negative number.
A line segment pointing to the left would indicate a negative number.
Identify the example of an irrational number
3.5
-2
π
1/2
Learning about exponents can be problematic. These are common misconceptions EXCEPT:
Think of the two values as factors
Hear “five three times” and think multiplication
Write the equation as 5 x 3 rather than 5 x 5 x 5
Use repeated addition versus multiplication.
What is the primary reason to teach and use Scientific Notation?
Convenient way to represent very large or small numbers.
A number is changed to be the product of a number greater or equal to 1 or less than 10 multiplied by a power of 10.
Easiest way to convey the value of numbers in different contexts
To determined by the level of precision appropriate for that situation.
The contexts below would support learning about very, very large numbers EXCEPT:
Distance from the planet Mercury to Mars.
Number of cells in the human body.
The estimated life span of a Bengal tiger.
Population of the European countries in 2011.
When students are learning and creating contexts for integer operations. Ask them to consider the following questions EXCEPT:
Where am I now?
Where am I going?
Where did you start?
How far did you go?
For students to be successful in the division of integers they should competence in the following concept?
Whole number division
Division of fractions
Relationship between multiplication and division
Rules for dividing negative numbers
The term rational numbers relates to all of the examples below EXCEPT:
Fractions
Decimals and percents
Square roots
Positive and negative integers
