Students use the Hot Air Balloon simulation to model integer subtraction. They then move to modeling subtraction on a number line. They use patterns in their work and their answers to write a rule for subtracting integers.Key ConceptsThis lesson introduces the number line model for subtracting integers. To subtract on a number line, start at 0. Move to the location of the first number (the minuend). Then, move in the negative direction (down or left) to subtract a positive integer or in the positive direction (up or right) to subtract a negative integer. In other words, to subtract a number, move in the opposite direction than you would if you were adding it.The Hot Air Balloon simulation can help students see why subtracting a number is the same as adding the opposite:Subtracting a positive number means removing heat from air, which causes the balloon to go down, in the negative direction.Subtracting a negative number means removing weight, which causes the balloon to go up, in the positive direction.The rule for integer subtraction (which extends to addition of rational numbers) is easiest to state in terms of addition: to subtract a number, add its opposite. For example, 5 – 2 = 5 + (–2) = 3 and 5 – (–2) = 5 + 2 = 7.Goals and Learning ObjectivesModel integer subtraction on a number line.Write a rule for subtracting integers.

Lesson OverviewStudents learn the definition of rational number, and they write rational numbers as ratios of integers and as repeating or terminating decimals.Key ConceptsStudents have been working with rational numbers throughout this unit, but the term rational number is formally defined in this lesson. A rational number is a number that can be written in the form pq, where p and q are integers. All the integers, fractions, decimals, and percents students have worked with so far in their math classes are rational numbers. Following are some rational numbers written as ratios of integers:36=361−1.2=−12105%=5100 −12=−12Any rational number can also be written as a decimal that terminates or that repeats forever in a regular pattern. For example, 35 = 0.6 and 711 = 0.63636363… Repeating decimals are often written with a bar over the digits that repeat. For example, 0.63636363… can be written as 0.63¯.There are numbers that are irrational. These numbers include π and the square root of any whole number that is not a perfect square, such as 2. The decimal form of an irrational number does not terminate, and the digits do not follow a repeating pattern. Students will study irrational numbers in Grade 8.Goals and Learning ObjectivesUnderstand the definition of rational number.Write rational numbers as ratios of integers.Write rational numbers as terminating or repeating decimals.SWD: Students with disabilities may have difficulty working with decimals and fractions, especially moving between the two. If students demonstrate difficulty to the point of frustration, provide direct instruction on the basics for finding equivalent fractions and decimals.ELL: Target and model key language and vocabulary. Specifically, focus on the term rational, as well as terms such as terminate. As you’re discussing the key points, write the words on the board or on large sheets of paper and explain/demonstrate what the words mean. Since these are important points that students will be using throughout the module, write them on large poster board so that students can use them as a reference. Have students record new terms, definitions, and examples in their Notebook. 

Provides teaching tips, information on common errors, differentiated instruction, enrichment, and problem solving for teachers to use with the CK-12 Middle School Math - Grade 6, Student Edition.

A work in progress, CK-12's Math 7 explores foundational math concepts that will prepare students for Algebra and more advanced subjects. Material includes decimals, fractions, exponents, integers, percents, inequalities, and some basic geometry.

This lesson discusses how to identify sets of numbers as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

The intention of this curriculum guide is to provide teachers with supplemental materials to use to support students in strengthening their skills in various concept areas that are crucial for understanding beginning algebra. The activities are broken down by skill with links provided below. This is intended as a way to provide students with engaging, primarily computer-based activities to get extra practice with material that is covered elsewhere in the curriculum. This collection focuses on simulations and games using the computer—some resources may be ripe for teachers to develop unique activities to accompany the simulation and some possible suggestions are included with the descriptions. This series is intended to be pick-and-choose.

In this Curriculum Guide:

Activities and practice with: Integers, Exponents, Order of Operations, Distributive Property, Expressions, Equations and Basic Graphing

In this seminar you will explore different types of numbers in math. You will learn to classify numbers into the categories of natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. You will see how some numbers can be classified in a few of these categories. Some important things to consider will be whether or not a decimal number terminates or repeats.StandardsCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems. 

This is an instructional video demonstrating how to subtract integers using colored chips to visually represent the subtraction rule of adding the opposite.