How can the infinite nature of the number line broaden the perception of number?

Students investigate magnitude with positive and negative numbers.

Negative numbers are to the left of zero on the number line visualized horizontally, and below zero on the number line visualized vertically.

Positive numbers can be represented symbolically with or without a positive sign (+).

Negative numbers are represented symbolically with a negative sign (−).

Zero is neither positive nor negative.

Negative numbers communicate meaning in context, including

• temperature

• debt

• elevation

Magnitude is a number of units counted or measured from zero on the number line.

Every positive number has an opposite negative number with the same magnitude.

A number and its opposite are called additive inverses.

The set of integers includes all natural numbers, their additive inverses, and zero.

The sum of any number and its additive inverse is zero.

The sum of two positive numbers is a positive number.

The sum of two negative numbers is a negative number.

The sum of a positive number and a negative number can be interpreted as the sum of zero and another number.

Subtracting a number is the same as adding its additive inverse.

Symmetry of the number line extends infinitely to the left and right of zero or above and below zero.

Direction relative to zero is indicated symbolically with a positive or negative sign.

Magnitude with direction distinguishes between positive and negative numbers.

Any number can be expressed as a sum in infinitely many ways.

The difference of any two numbers can be interpreted as a sum.