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