TExES Math 4-8 (115) key terms

A number that can be written as a fraction a/b where a and b are integers and b is not zero. Its decimal form either terminates or repeats, as in 3/4, −5, or 0.25.

A real number that cannot be written as a fraction of two integers. Written as a decimal, it neither terminates nor repeats, such as the square root of 2 or pi.

A whole number that is positive, negative, or zero, with no fractional or decimal part. The set continues indefinitely in both directions, as in −2, −1, 0, 1, 2.

The distance of a number from zero on the number line, which is never negative. Written with bars around the number, it changes negative inputs to positive, so the absolute value of −7 is 7.

The largest whole number that divides evenly into every number in a given set. For 12 and 18 the greatest common factor is 6, which is useful when simplifying fractions.

The smallest positive number that is a multiple of every number in a given set. For 4 and 6 the least common multiple is 12, which helps when adding fractions with unlike denominators.

A rate in which the second quantity is exactly one unit, found by dividing one quantity by the other. Everyday examples include 60 miles per hour or $3.50 per pound.

A relationship between two quantities in which their ratio stays constant, so doubling one quantity doubles the other. Its graph is a straight line passing through the origin.

A symbol, usually a letter, that stands for a number whose value is unknown or allowed to change. In the expression 3x + 5, the letter x serves this role.

A mathematical phrase that combines numbers, variables, and operation symbols without an equals sign, such as 4n − 7. It can be simplified or evaluated, but it cannot be solved.

A function whose graph is a straight line and whose rule can be written in the form y = mx + b. Its output changes at a constant rate as the input changes.

A measure of how steep a line is, computed as the vertical change divided by the horizontal change between two points. It is often described as rise over run.

Two or more linear equations considered together, solved by finding values that satisfy all of them at once. On a graph, the solution is the point where the lines intersect.

A function that can be written in the form y = ax² + bx + c, where a is not zero. Its graph is a U-shaped parabola that opens upward when a is positive.

A rule that assigns exactly one output value to each input value, so every input gives a single output. A graph represents a function if no vertical line crosses it more than once.

The domain is the set of all allowable input values of a function, and the range is the set of all output values it produces. Together they describe what a function accepts and returns.

A statement comparing two expressions that are not necessarily equal, using symbols such as <, >, ≤, or ≥. Its solutions form a range of values, often shown on a number line.

Figures that have the same shape but not necessarily the same size. Corresponding angles are equal, and corresponding side lengths are proportional by a constant scale factor.

Figures that have exactly the same size and shape. Their corresponding sides and angles are equal, and one can be carried onto the other using rigid transformations.

The relationship stating that in a right triangle the square of the hypotenuse equals the sum of the squares of the two legs, written a² + b² = c². It is used to find missing side lengths.

The amount of space a three-dimensional figure occupies, measured in cubic units. Formulas depend on the shape, such as length times width times height for a rectangular prism.

The total area of all faces or curved surfaces of a three-dimensional figure, measured in square units. For a rectangular prism it is the sum of the areas of six rectangular faces.

A movement of a figure, such as a translation, rotation, or reflection, that changes its position but not its size or shape. Applying one always produces a congruent image.

The ratio of a length in an image or model to the corresponding length in the original figure. A factor greater than one enlarges the figure; a factor less than one reduces it.

A method of converting units by multiplying by fractions equal to one, arranged so unwanted units cancel. For example, converting 2 hours to minutes uses the fraction 60 minutes over 1 hour.

The arithmetic average of a data set, found by adding all the values and dividing by the number of values. It is pulled strongly toward unusually large or small data values.

The middle value of a data set after the values are arranged in order. When there is an even number of values, it is the mean of the two middle values.

The difference between the third quartile and the first quartile of a data set, written Q3 − Q1. It describes the spread of the middle half of the data and resists outliers.

The ratio of the number of favorable outcomes to the total number of equally likely outcomes in a sample space. For a fair coin, the theoretical probability of heads is one half.

Two events in which the outcome of one does not change the probability of the other occurring. For such events, the probability that both happen is the product of their individual probabilities.

The set of all possible outcomes of a probability experiment. For rolling a standard number cube, the sample space contains six outcomes: 1, 2, 3, 4, 5, and 6.

A straight line drawn through a scatterplot that best models the trend in the data. It can be used to describe the direction of an association and to make predictions.

Presenting the same mathematical idea in different forms, such as a table, graph, equation, or verbal description. Moving among these forms builds understanding and supports problem solving.

Using mathematics to represent and analyze a real-world situation, then interpreting the results in context. The process often requires simplifying assumptions and later revising the model.

A mathematical statement believed to be true based on patterns or examples but not yet proven. Students test and justify conjectures using reasoning and counterexamples.

Ongoing checks of student understanding during instruction, used to adjust teaching and provide feedback. Examples include exit tickets, questioning, and short quizzes that are not heavily graded.

An evaluation of student learning at the end of a unit, course, or grading period, such as a final exam or major project. It measures achievement against standards after instruction is complete.

Planning instruction so that content, process, or product is adjusted to meet varied readiness levels, interests, and learning needs within the same classroom.

A physical object students handle to explore mathematical ideas, such as fraction tiles, base-ten blocks, or algebra tiles. Manipulatives connect concrete actions to abstract symbols and procedures.

Temporary support a teacher provides so students can complete a task they cannot yet do alone, gradually removed as competence grows. Examples include worked examples and guided questioning.