# NUMBER & QUANTITY

Growing IQ focuses on the real number system, comprised of nearly any number that you can think of. They include whole, rational, and irrational numbers. Research has shown that number sense develops gradually, meaning that students require a variety of opportunities to explore numbers, visualize them in varying contexts, and relate numbers in a multitude of ways.

## 8 Categories of Number & Quantity

## 1

## COUNTING

The counting sequence is foundational in mathematics and is connected to the development of the conceptual understandings of quantity, place-value, and arithmetic operations.

## 2

## Cardinality

## The first step in developing number sense awareness is learning the digits that make up the base-ten system. A strong familiarity with these ten digits will enable larger quantities to be derived and are fundamental for place-value understandings.

## 3

## PLACE-VALUE

Place-value is essential to understanding the meaning of numbers. It provides the foundation for regrouping, arithmetic, algebra, inequalities, scientific notation, and developing number facility.

## 4

## Rational Numbers

## A strong understanding of rational numbers (fraction, decimal, ratio, and percentage) provides a foundation for the ability to solve real-life problems and lays the ground work for mastering probability, statistics, measurement, graphing, and more.

## 5

## INTEGERS

Integers are whole numbers that can be positive, negative, or zero. The introduction of negative numbers highlights the concept of opposites and balance. Integer understandings are foundational to economics, statistical analysis, algebra, graphing, and more.

## 6

## Absolute Value

## Absolute value refers to the magnitude or the size of a number. Understanding absolute value is important in real analysis and will be foundational in the study of calculus.

## 7

## INEQUALITY

Used to compare items and indicates limits, working with inequalities increases the ability to think critically about quantities and check assumptions. Inequalities highlight that there can be a range of possibilities in mathematics, not always a single correct answer.