# Glossary

- Page ID
- 208539

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Words (or words that have the same definition) | The definition is case sensitive | (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] | (Optional) Caption for Image | (Optional) External or Internal Link | (Optional) Source for Definition |
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(Eg. "Genetic, Hereditary, DNA ...") | (Eg. "Relating to genes or heredity") | The infamous double helix | https://bio.libretexts.org/ | CC-BY-SA; Delmar Larsen |

Word(s) | Definition | Image | Caption | Link | Source |
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Acute triangle | a triangle with all angles measuring less than 90 degrees | ||||

Addition symbol | an operation that combines two or more numbers or groups of objects (component parts: addend + addend = sum) | ||||

Arithmetic patterns | a pattern that changes by the same rate, such as adding or subtracting the same value each time | ||||

Assessment | Conceptual understanding is knowing more than isolated facts and methods; it is understanding mathematical ideas, and having the ability to transfer knowledge into new situations and apply it to new contexts. | ||||

Associative Property of Multiplication | when three or more numbers are multiplied, the product is the same regardless of the grouping of the factors | ||||

Base ten number system | Our everyday number system is a Base-10 system and has 10 digits to show all numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. | ||||

Cardinal numbers | say how many of something there are | ||||

Cardinality | the last number word said when counting, tells how many | ||||

Categorical data | a collection of information that can be divided into specific groups, such as favorite color, types of food, favorite sport, etc. | ||||

Clusters | groups of related standards | ||||

Communication | Mathematics communication is both a means of transmission and a component of what it means to “do” mathematics. | ||||

Commutative Property of Addition | numbers can be added in any order and you will still get the same answer | ||||

Commutative Property of Multiplication | when two numbers are multiplied, the product is the same regardless of the order of the factors | ||||

Computational fluency | using efficient and accurate methods for computing | ||||

Connections | the ability to understand how mathematical ideas interconnect and build on one another | ||||

Conservation of length | if an object is moved, its length does not change | ||||

Contextualize | taking the abstract mathematical representation and putting into context | ||||

Data analysis | processing data to find useful information that will help make decisions | ||||

Decontextualize | taking a context and representing it abstractly | ||||

Defining | attributes that must always be present in order to create that shape | ||||

Denominator | how many equal part in the whole amount | ||||

Difference | the result of subtraction; the inverse of addition | ||||

Distributive Property of Multiplication over Addition | multiply a sum by multiplying each addend separately and then add the products | ||||

Dividend | the amount we want to divide up | ||||

Divisor | the number we divide by | ||||

Domains | larger groups of related standards. Domains are the big idea. | ||||

Emergent mathematics | the earliest phase of development of mathematical and spatial concepts | ||||

Equal sign | a relational symbol used to indicate equality | ||||

Equilateral triangle | a triangle in which all sides are the same length | ||||

Equivalence | equivalent fractions have the same value, even though they may look different. For example 12 and 24 are equivalent, because they are both “half” | ||||

Expanded notation | writing a number and showing the place value of each digit | ||||

Factor | numbers multiplied together | ||||

Flexible | the ability to shift among multiple representations of numbers and problem-solving strategies | ||||

Fluently | accurately (correct answer), efficiently (within 4-5 seconds), and flexibly (using strategies, such as “making 10” or “breaking apart numbers”) finding solutions | ||||

Growth mindset | In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point | ||||

Isosceles triangle | at least two sides of the triangle the same length | ||||

Iteration | use multiple copies of one object to measure a larger object | ||||

Low Floor/High Ceiling Task | a mathematical activity where everyone in the group can begin and then work on at their own level of engagement | ||||

Manipulatives | physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics | ||||

Mass | a measure of how much matter is in an object | ||||

Mathematize | the process of seeing and focusing on the mathematical aspects and ignoring the non mathematical aspects | ||||

Measure | to find a number that shows the size or amount of something | ||||

Measures of central tendency | The “central value” of two or more numbers. Mean, median, and modes are measures of central tendency. | ||||

Measurement | also called repeated subtraction division, a way of understanding division in which you divide an amount into groups of a given size | ||||

Measurement division | also called repeated subtraction division, a way of understanding division in which you divide an amount into groups of a given size | ||||

Mindset | a person’s usual attitude or mental state | ||||

Multiplicative Identity Property | the product of any number and zero is zero | ||||

Multiplicative reasoning | a recognition and use of grouping in the underlying pattern and structure of our number system | ||||

Non-defining | attributes that do not always have to be present in order to create the shape | ||||

Numerator | how many parts you have | ||||

Numerical data | data that is expressed in numbers rather than word descriptions | ||||

Object permanence | understanding that objects exist and events occur in the world independently of one’s own actions | ||||

Obtuse triangle | a triangle with one angle that measures more than 90 degrees | ||||

One-to-one correspondence | numbers correspond to specific quantities | ||||

Open number line | A number line that has no numbers. Students fill in the number line based on the problem they are solving. | ||||

Ordinal numbers | tell the position of something in the list, such as first, second, third, fourth, fifth, etc | ||||

Parallelogram | opposite sides parallel and opposite sides are the same length | ||||

Partition | a problem where you know the total number of groups, and are trying to find the number of items in each group | ||||

Partitive division | a problem where you know the total number of groups, and are trying to find the number of items in each group | ||||

Place value | the value of a digit in its position; for example, the value of the 3 in 236 is 3 tens or 30. | ||||

Principles | statements reflecting basic guidelines that are fundamental to a high-quality mathematics education | ||||

Problem | any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method | ||||

Problem solving | engaging in a task for which the solution method is not known in advance (Bahr & Garcia, 2010) | ||||

Product | the result when two or more numbers are multiplied together | ||||

Quotient | the answer to a division problem | ||||

Rational counting | the ability to assign a number to the objects counted | ||||

Reasoning and proof | developing an idea, exploring a phenomena, justify results, and using mathematical conjectures | ||||

Rectangle | a quadrilateral with opposite sides parallel and equal length and all angles right angles | ||||

Representation | visible or tangible products – such as pictures, diagrams, number lines, graphs, manipulatives, physical models, mathematical expressions, formulas, and equations that represent mathematical ideas or relationships | ||||

Rhombus | a parallelogram with all sides equal | ||||

Right triangle | a triangle with one 90 degree angle | ||||

Rote counting | the ability to say the numbers in order | ||||

Round | making a number simpler but keeping its value close to what it was | ||||

Scalene triangle | no sides that are the same length | ||||

Seriation | the process of putting objects in a series | ||||

Spatial sense | an intuition about shapes and the relationships between them | ||||

Square | a quadrilateral with opposite sides parallel and all 4 sides equal length and all angles right angles | ||||

Standards | define what students should understand and be able to do | ||||

Standard notation | writing a number with one digit in each place value | ||||

Subitize | visually recognizing the number of items in a small set without counting | ||||

Subtraction | an operation that gives the difference or comparison between two numbers (component parts: minuend – subtrahend = difference) | ||||

Sum | the result of addition | ||||

Technology | calculators, computers, mobile devices like smartphones and tablets, digital cameras, social media platforms and networks, software applications, the Internet, etc. | ||||

Transitivity | the ability to indirectly measure objects by comparing the length of two objects by using a third object | ||||

Trapezoid | a quadrilateral with opposite sides parallel. The sides that are parallel are called “bases” and the other sides are “legs.” Trapezoids are also called trapeziums. | ||||

Unit fraction | when a whole is divided into equal parts, a unit fraction is one of those parts. A unit fraction has a numerator of one. | ||||

Unitize | a concept that a group of 10 objects is also one ten | ||||

Variable | a letter or symbol that stands for a number | ||||

Verbal counting | learning a list of number words | ||||

Volume | the amount of 3-dimensional space something takes up, or the capacity | ||||

Wait time | 20 seconds to 2 minutes for students to make sense of questions | ||||

Worthwhile problems | problems that should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning |