13 Glossary
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