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    Example and Directions
    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
    (Eg. "Genetic, Hereditary, DNA ...") (Eg. "Relating to genes or heredity") The infamous double helix CC-BY-SA; Delmar Larsen
    Glossary Entries
    Word(s) Definition Image Caption Link Source
    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        
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