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Define Integer

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Holt Mathematics Course 1 Chapter 11 Lesson 1

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1. Use positive and negative numbers in opposite directions from zero (C) | LearnZillion

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Hot, Cold, Wet, Dry, Off, On... Are you thinking about opposites yet? We see and use opposites in the real world every day, but what about numbers. Do numbers have an opposite? Have you ever thought that about the fact that the number system includes more than just numbers we can actually count? What is the opposite of positive? Negative! We will be working with and using positive and negative numbers in this unit and applying it to how we look at direction and distance.

Essential Questions

What are positive and negative numbers used for?

How are rational numbers represented on a number line?

How are coordinates graphed on a coordinate plane?

How do you order and arrange rational numbers?

What does the absolute value of a rational number represent on the number line?

How does absolute value differ from a statement about order?

What is the distance between two coordinates that have the same first or second coordinate?

Module Minute

Negative numbers are used everywhere like temperature. It is useful for me to know the absolute value of a number when finding distances. Graphing on the coordinate plane is helpful to see how two numbers can relate to a direction and distance. We use positive and negative numbers in everyday life like when we take a test and the teacher deducts points for incorrect answers. We place positive rational numbers on the right side of zero on the number line and negative rational numbers to the left of zero on the number line. We use positive and negative numbers to represent quantities in real-world contexts like figuring out how much we have left after we buy something. Opposites are numbers that have the same absolute value. Opposites are shown on a number line by being the same distance on each side of zero. Statements of inequality help me place numbers on a number line when comparing two numbers to each other. We can use coordinates to find the distances between points by finding the absolute value between points with the same first coordinate or the same second coordinate. We can use number lines to find the distances between points by plotting both points and counting the distance between the points. We can use absolute value to find the lengths of the sides of polygons on the coordinate plane.

Key Words

Absolute value: The distance between a number and zero on the number line. The symbol for absolute value is shown in the equation |−8| = 8.

Coordinates: An ordered pair, (, ), that locates a point in a plane.

Inequality: Any mathematical sentence that contains the symbols > (greater than), < (less than), < (less than or equal to), or > (greater than or equal to).

Integers: The set of whole numbers and their opposites {... − 3, −2, −1, 0, 1, 2, 3, ... }

Negative numbers: The set of numbers less than zero

Opposite number: Two different numbers that have the same absolute value. Example: 4 and −4 are opposite numbers because both have an absolute value of 4.

Ordered Pair: A pair of numbers, (, ), that indicate the position of a point on the Cartesian Plane.

Origin: The point of intersection of the vertical and horizontal axes of a Cartesian plane. The coordinates of the origin are (0, 0).

Positive number: The set of numbers greater than zero.

Rational number: The set of numbers that can be written in the form where a and b are integers and b ≠ 0.

Sign: a symbol that indicates whether a number is positive or negative. Example: in −4, the (−) sign shows this number is read "negative four".

x-axis: The horizontal number line on the Cartesian coordinate plane.

x-coordinate: The first number of in ordered pair; the position of a point relative to the vertical axis

y-axis: The vertical number line on the Cartesian coordinate plane

y-coordinate: The second number in an ordered pair; the position of a point relative to the horizontal axis

Solve the crossword puzzle. There are no spaces for 2 or more words. You can click re-start and get a new puzzle.

A handout of these key words and definitions is also available in the sidebar
What To Expect

Representing Numbers on a Number Line Assignment

Absolute Value Assignment

Rational Explorations Quiz 1

Opposites Assignment

Rational Explorations Discussion

Coordinate System Assignment

Rational Explorations Quiz 2

Rational Explorations Task

Rational Explorations Test

To view the standards from this unit, please download the handout from the sidebar.

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Rational Explorations: Numbers and Their Opposites

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Hot, Cold, Wet, Dry, Off, On... Are you thinking about opposites yet? We see and use opposites in the real world every day, but what about numbers. Do numbers have an opposite? Have you ever thought that about the fact that the number system includes more than just numbers we can actually count?