Core Subjects Vocabulary: Math

Culturally Responsive Teaching

teaching that recognizes students' cultural references

Visual Learning

learning through seeing and observing

Symbolic Stage/Representational Stage

Drawing pictures or symbols to represent numbers in an equation

Behaviorism

learning theory rooted in the notion that all behaviors are learned through interaction with the environment

Closure Activity

a time to summarize the learning for the day

Kinesthetic Learning/Tactile Learning

learning through hands-on experiences and movement

Word Problems

a math question written as one sentence or more that requires children to apply their maths knowledge to solve a 'real-life' scenario

Thematic Unit

a unit that has an overarching, uniting idea or topic, and incorporates skills into that theme; it can be within one subject area or support cross-curricular instruction

Concrete Representations

Using physical pieces to represent mathematical problems

Place Value

The value of each digit in a number based on its location, or place

Abstract Thinking

Using numbers or letter variables in an equation

Cognitivism

learning new behaviors by connecting current knowledge with new knowledge

Compartmentalized Teaching

concepts taught one at a time in isolation of other concepts (no longer recommended)

Multimodal Teaching

employing multiple instructional methods, strategies, and modes of communication to support diverse learning styles

Basic Operations

addition, subtraction, multiplication, and division

Manipulatives

objects used by students to illustrate and explore mathematical concepts, such as to represent numbers in an equation

Small Group Instruction

a few members of the class learning together, as opposed to whole-group instruction

Flexible Grouping

grouping students based on their learning needs or interests

Reading/Writing

learning through engaging with texts and writing

Counting

to name or list one-by-one in order to reach the total quantity

Constructivism

Learning new behaviors by adjusting our current view of the world

Integrated Teaching

multiple concepts are used in problem-solving at once (current best practices)

Inquiry-Based Teaching/Student-Centered Learning

students drive instruction by asking questions and creating projects to answer the questions

Auditory Learning

learning through listening and speaking

Benchmark Numbers

Numbers that are easily added, subracted, multiplied, or divided.

Partitioning

A mental math strategy that involves breaking up numbers by place value before adding, subtracting, multiplying or dividing

Compensation

A mental math strategy in which one number is changed to a value that simplifies the computation, such as a multiple of 10

Teacher Wait Time

the silence that often comes after a question has been asked but before students have finished considering their answer and/or find the courage to speak up

Addition Property of Equality

If the quantities on each side of an equal sign have the same amount added to them, the resulting statement will still be equal.

Benchmarking

Using benchmark numbers to estimate a mathematical expression

Decomposing

Breaking up numbers by place value

Subtraction Property of Equality

If the quantities on each side of an equal sign have the same amount subtracted from them, the resulting statement will still be equal.

Deductive Reasoning

using two or more known premises to draw a conclusion

Composing

Recombining numbers broken up by place value

Algorithms

systematic methods that always produce a correct solution to a problem

Conjecture

an inference created without proof

Multiplication Property of Equality

If the quantities on each side of an equal sign are both multiplied by the same amount, the resulting statement will still be equal.

Formal Reasoning

the use of logic and algorithms to reach conclusions

Inductive Reasoning

generalizing knowledge from one area to another

Informal Reasoning

used to answer questions and solve problems that are complex and open-ended (without a definitive solution)

Division Property of Equality

If the quantities on each side of an equal sign are both divided by the same amount, the resulting statement will still be equal.

Estimating

rounding numbers or approximating them to quickly perform math operations

Credit Union

community-based bank owned by its members, offering banking services like savings accounts and loans, with a focus on serving its members' needs rather than making profits for shareholders

Pawn Shop

business where people can bring in items of value as collateral to receive a short-term loan, with the option to reclaim the item by repaying the loan plus interest within a specified period, or forfeit the item if the loan is not repaid

Sales Tax

additional fee added to the price of most goods and some services at the point of sale, collected by governments to fund public services and infrastructure

Bank

financial institution that accepts deposits from the public and creates credit, offering loans and investment products while providing various financial services such as savings accounts, checking accounts, and mortgages

Payday Lender

type of financial institution that offers short-term, high-interest loans, typically due on the borrower's next payday, often targeting individuals with poor credit or financial difficulties

State Income Tax

money collected by state governments from individuals and businesses based on their earnings, which is used to fund various state programs and services

U.S. Income Tax

money that individuals and businesses pay to the government based on how much they earn, which helps fund government programs and services

Tax

contribution to federal or state funds required for individuals or businesses

Property Tax

a tax on the value of a home or land that is paid to local governments by the owner of the real estate

Dependent Variable (in functions)

The output of a function, or the result after solving the function using the independent variable. It commonly represented by the variable y.

Dependent Variable

a variable that changes in response to another variable

Function Table

a table that describes a function by displaying inputs and corresponding outputs in a table format

Vertical Line Test

A method for examining the graph of a relation to determine whether or not the relation is a function; pass a vertical line (like a pencil) through all the points of the graph, and if the vertical line passes through more than one point of the graph at the same time, the relation is not a function.

Constant

a number without a variable; value does not change (stays constant)

Term

Each part of an expression that is separated by a + or - sign.

Like Terms

terms with the same variable and exponent combination

Quadratic Equation: Standard Form

The quadratic equation written as y=ax2+bx+cy=ax2+bx+c, where a, b, and c are coefficients.

Combine Like Terms

method of simplifying an algebraic expression by adding or subtracting the coefficients of like terms

Quadratics: ROXS

An acronym (ROXS) used to remember that roots, 0's (zeros), x-intercepts, and solutions all refer to the same characteristic of parabolas.

Equation

A statement that two expressions are equal. It has an equal sign and therefore can be solved.

Slope Formula

a fraction used to calculate slope, with the change in y-values in the numerator, and change in x-values in the denominator

Independent Variable (in functions)

The input into a function, representing the variable that is known. Normally, it is represented by the variable x.

Distributive Property

a number in front of a group of terms will multiply all terms in the grouping individually

Inequality

A statement that 2 expressions are not equal.

Relation (in math)

A relationship between sets of values. In math, the relation is often between x values (inputs) and y values (outputs), and can be represented as a set of ordered pairs, a table of values, a mapping diagram, or a graph.

Variable

a letter or non-numeric symbol that represents an unknown value

Mapping Diagram

A diagram showing a relation's inputs and their corresponding outputs using arrows.

System of Linear Equations

A set of two or more equations with the same set of variables, or unknowns. The solution is the intersection of the lines.

Coefficient

A number that multiplies a variable.

Order of Operations

PEMDAS: the set order in which multi-step equations must be solved: Parenthesis, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)

Rate

a quotient of two quantities

Linear Relationship

a relationship with a constant rate of change that creates a straight line when graphed

Independent Variable

a variable that determines the value of another variable

Function

a special type of relation where each input has only one output

Expression

Numbers, symbols, and operators grouped together to show the value of something. Note that it differs from an equation because there is no equal sign and therefore cannot be solved, only simplified.

Quadratic Equation

a polynomial equation with a degree of 2; written in the form of ax2+bx+c=0ax2+bx+c=0

Algebra

The branch of mathematics in which letters and symbols are used to represent unknown values.

Diagnostic Assessment/Pre-Assessment

assessment administered before instruction to determine students' strengths and weaknesses

Norm-Referenced Tests

tests that compare an individual's performance/achievement to a group called the "norm group"

Progress Monitoring

periodic assessments to monitor student growth and evaluate the effectiveness of instruction

Formative Assessments

ongoing evaluations to monitor student progress

Universal Screener

assessment administered to all students to gather data and form groups, such as intervention groups

Summative Assessments

evaluations at the end of an instructional period

Criterion-Referenced Tests

tests in which a standard has been set for the test taker to achieve in order to pass the test

Curriculum-Based Assessments

testing the curriculum being taught

Portfolio

collection of student's work and achievements that is used to assess past accomplishments and future potential; can include finished work in a variety of media and can contain materials from several courses over time

Informal Assessments

more flexible than formal assessments and can be adjusted to fit the situation and particular needs of the student being tested

Performance-Based Assessment

assessment that requires students to show mastery of specific skills by demonstrating, producing, or performing something

Formal Assessments

a usually post-instruction assessment with the purpose of assessing student knowledge, retention, and application; often involve the use of a standardized rubric or scoring guide based on several criteria

Exit Slips

short formative assessment given by a teacher after completing a lesson to determine the degree to which students have learned the material taught in the lesson

Theoretical Probability

what we expect to happen in theory.

Bias

when incorrect conclusions are made because some parts of the population are over-represented in the sample and some parts are under-represented

Simulation

imitation of a real-world process or system

Sample

a subset of the population

Placebo

something that looks like the actual treatment but designed to have no effect on the subject

Independent Events

two or more events that have no influence on each other.

Probability

the likelihood of an event occurring. Compares the successful outcomes to the total outcomes.

Probability Model

a mathematical representation of a random phenomenon