115 TExES Mathematics 4 - 8 Exam Practice Questions
1. The basics of math include:
A. Addition and division
B. Economics
C. Social Sciences
D. All of the above
2. Areas of mathematics include:
A. History and Social Studies
B. Biology
C. Probability and Statistics
D. All of the above
3. Some important facts about numbers include:
A. Numbers are subjective
B. Numbers do not mean anything
C. Numbers can be shown symbolically
D. All of the above
4. Which of the following is not a common math term?
A. Integer
B. Ratio
C. Consequences
D. Place value
5. Which of the following is not a basic algebraic concept?
A. Patterns
B. Fractions
C. Equivalence
D. Balance
6. Geometry studies the relationship of:
A. Points and lines
B. Angles
C. Surfaces and solids
D. All of the above
7. One step in the statistics process is:
A. Collection of data
B. Memorization of data
C. Classification of data
D. All of the above
8. Probability Theory measures the likelihood of:
A. An event occurring
B. Pluto being a planet
C. The end of the world
D. All of the above
9. Teaching math using the procedural approach means:
A. Providing precise methods
B. Letting students move at their own pace
C. Requiring memorization of advanced math facts
D. All of the above
10. List some reasons for learning math.
A. Improves reasoning ability
B. Hones critical thinking skills
C. Discovering applications in the real world
D. All of the above
ANSWER KEY EXAM 115
1. Answer: A
Math explains the logic of and relationship between numbers. It is used every day in countless ways. In order to minimize potential math phobia, teachers need to make the subject relevant to the students' lives and use examples with which they are familiar and that make sense to them. In order to do that, learning the basics is critical because all math concepts are built on addition, division, fractions and shapes. All mathematical relationships flow from these concepts. It is imperative students understand one concept before moving on to the next. If they fail to grasp the basics, students become confused as they progress to higher levels because they are unable to apply applicable background knowledge when introduced to geometry, algebra, probability and statistics.
2. Answer: C
Mathematics is a formal science of structure, order and relationships and is considered the basic language and foundation of all the other sciences. It evolved from counting, measuring and describing shapes. Some areas and their definitions:
- Arithmetic: A system to count numbers using addition, subtraction, multiplication and division
- Algebra: An abstract form of arithmetic using symbols to represent numbers
- Geometry: The relationship of points, lines, angles, surfaces and solids
- Probability: The chance random events will occur
- Statistics: The collection, organization and analysis of data
- Trigonometry: The relationship of the sides and angles of triangles
- Calculus: The limits, differentiation and integration of the functions of variables
3. Answer: C
Number concepts are the building blocks of all mathematical calculations and representations. Students must understand what a number means, in what ways it can and cannot be used and its relationship to other numbers. They need to be able to depict numbers concretely, pictorially and symbolically. Students need to understand the basic definitions of number concepts in order to use numbers properly in whatever math discipline in which they are working.
4. Answer: C
These definitions of some common math terms are from The American Heritage College Dictionary:
- Integers are the positive and negative whole numbers plus zero.
- Natural Numbers or Counting Numbers are the positive integers.
- Fractions are the result of dividing one quantity by another quantity.
- Prime Numbers are only divisible by one (1) and itself.
- Percentage is a fraction or ratio expressed as a part of one hundred (100).
- Ratio is the relation between two quantities expressed as the result (quotient) of one divided by the other.
- Place Value is the position of a figure in a numeral or series.
5. Answer: B
There are basic concepts in algebra that allow generalizations about "unknowns." Patterns and functions represent change and relationships. Repeating patterns show the same unit over and over again. In growth patterns, each unit is dependent upon the one before it as well as its position in the pattern. The function is the relationship between values, i.e., the second depends on the first. Once functional relationships are understood, symbols are used as an abstract stand-in for the relationships. Equivalence and balance are critical concepts in understanding algebraic equations. The equal sign represents some type of relationship between the numbers and symbols on each side of the sign. If a calculation is performed on one side, the same calculation must be performed on the other side. Each side is equal and they must balance.
6. Answer: D
The American Heritage College Dictionary defines geometry as investigation of "properties, measurements and relationships of points, lines, angles, surfaces and solids." Geometry developed from a practical need to determine land boundaries (survey), figure the size (area) of a field, measure the volume of a silo (cylinder) and where three-dimensional objects are placed and how they fit into a defined space. Studying geometry helps students hone their spatial visualization skills, which helps them function better in the physical world. Points, lines, angles, surfaces and solids are all used in painting, sculpture and architecture. The artist must understand the relationship of these components in order to create in any medium. Various engineering disciplines use geometry to build bridges and dams, design freeway systems, mine for minerals and drill for oil. Geometry is used every day by many professions.
7. Answer: A
Statistics is the collection, organization and interpretation of data. The data can be facts or isolated bits of information, but it all relates in one way or another to a specific topic. This precise, analytical system is used to identify, study and solve various problems. Statistics can help people interpret events and make decisions in uncertain and difficult situations. Statistics infers relationships, measures interactions and predicts outcomes among variables. Descriptive statistics defines and explains the basic components in a study. Exploratory statistics tries to figure out what the collected data is saying. Confirmatory statistics applies general ideas and concepts to an issue or a problem in an effort to answer specific questions.
8. Answer: A
The Probability Theory is the study and analysis of random events and whether those events can predict the behavior of a defined system. It is the possibility of an event happening or something being true. It is used to explain events that do not happen with any certainty. A probability is the numerical measure of the likelihood the event will happen. It is a number from zero (0) to one (1). Zero means it will definitely not happen, one means it definitely will happen and point five (0.5) means it is a draw, i.e., just as likely to happen as not happen. In other words, it has a fifty/fifty chance of happening.
9. Answer: A
Teaching math with a procedural approach or by direct instruction means defining terms and symbols, explaining formulas and giving students a step-by-step method to solve a problem. Definitions are exact and don't allow for creative examples or encourage critical thinking. The problem is solved "by the book." Most students acquire some level of proficiency but are usually unable to apply anything learned in math class in other academic areas or to situations outside of school. Experts agree students need to know the definitions of terms, how to apply formulas and understand the methods used to arrive at the answer to a problem. So even though studies have shown using the procedural approach to teach math can actually inhibit understanding and prohibit integrating new concepts with previously learned data, the basics still need to be acquired.
10. Answer: D
One of the functions of leaning math is improving reasoning ability and honing critical thinking skills and discovering these talents are applicable in all academic disciplines, as well as issues in the real world. To accomplish that goal, the teacher must design lesson plans, compose problems and devise activities that require students to explain their thought process, compare methods and approaches and justify results. Students discover patterns and relationships and the activity becomes a meaningful learning experience rather than a rote exercise in memorization. Using this approach, students learn the definitions, formulas and methods as a natural outcome of understanding and integrating the new concepts. The goal is to help students make sense of math by using examples to which they can relate and making the lesson relevant to their life outside of math class.