Adult Learners will review the previous lesson, measuring with a thermometer, to continue their application in horizontal number lines. Learners will use the number line to increase their understanding of integer values as well as apply their understanding to solving real world problems.

Data structures play a central role in modern computer science. You interact with data structures even more often than with algorithms (think Google, your mail server, and even your network routers). In addition, data structures are essential building blocks in obtaining efficient algorithms. This course covers major results and current directions of research in data structure.
Acknowledgments
Thanks to videographers Martin Demaine and Justin Zhang.

This simulation allows you to use a slider to see how positive and negative integers add on a number line.

This lesson will be the first of six lessons guiding students in constructing the abstract concepts necessary to understand adding positive and negative integers.
It is designed for adult learners (or middle school or older) who are not fluent with using numbers. A real life lesson will be included in this series of lessons-Budgeting.

For many adult students, positive and negative integers are an example of when math “keeps changing the rules.” This is the fifth of six lessons guiding students in constructing the abstract concepts necessary to understand adding positive and negative integers.
This lesson will review previous knowledge about negative numbers and teach adding integers with different signs. This is a time when it’s important to stress to students that understanding this lesson will help them in many future lessons.

This is the third of six lessons teaching basic concepts related to positive and negative integers. This lesson will review previous knowledge about negative numbers and teach adding integers with the same sign, with connections to “real life” situations such as gains and losses in football yards or bank account overdraws.

For many adult students, positive and negative integers are an example of when math “keeps changing the rules.” This is the fourth of six lessons guiding students in constructing the abstract concepts necessary to understand adding positive and negative integers.
This lesson will review previous knowledge about negative numbers and teach adding integers with the same sign. The previous lesson focused on “real life situations” and this will teach expressing those real life situations on a number line. The actual problems will still be adding integers of the same sign because of the prevalence of confusion with adding two negative numbers.

This second lesson in negative integers carries the "real life" concept (temperature and debt) to the number line. Students will work with number lines with positive and negative numbers.

This is a three-credit course which covers topics that enhance the students’ problem solving abilities, knowledge of the basic principles of probability/statistics, and guides students to master critical thinking/logic skills, geometric principles, personal finance skills. This course requires that students apply their knowledge to real-world problems. A TI-84 or comparable calculator is required. The course has four main units: Thinking Algebraically, Thinking Logically and Geometrically, Thinking Statistically, and Making Connections. This course is paired with a course in MyOpenMath which contains the instructor materials (including answer keys) and online homework system with immediate feedback. All course materials are licensed by CC-BY-SA unless otherwise noted.

Basic Algebra Operations Notes:Place Value and RoundingIntegers and DecimalsFractions, Decimals, and PercentsFractionsProportionsExponentsAlgebraic Expressions

Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems with positive rational numbers.
Plot positive rational numbers on a number line.
Understand the equal sign.
Use the greater than and less than symbols with positive numbers (not variables) and understand their relative positions on a number line.
Recognize the first quadrant of the coordinate plane.

Lesson Flow

The first part of this unit builds on the prerequisite skills needed to develop the concept of negative numbers, the opposites of numbers, and absolute value. The unit starts with a real-world application that uses negative numbers so that students understand the need for them. The unit then introduces the idea of the opposite of a number and its absolute value and compares the difference in the definitions. The number line and positions of numbers on the number line is at the heart of the unit, including comparing positions with less than or greater than symbols.

The second part of the unit deals with the coordinate plane and extends student knowledge to all four quadrants. Students graph geometric figures on the coordinate plane and do initial calculations of distances that are a straight line. Students conclude the unit by investigating the reflections of figures across the x- and y-axes on the coordinate plane.

Students revise their work on the Self Check based on feedback from the teacher and their peers.Key ConceptsConcepts from previous lessons are integrated into this assessment task: integers, absolute value, and comparing numbers. Students apply their knowledge, review their work, and make revisions based on feedback from the teacher and their peers. This process creates a deeper understanding of the concepts.Goals and Learning ObjectivesApply your knowledge of integers, absolute value, and comparing numbers to solve problems.Track and review your choice of strategy when problem solving.

Students revise their work on the assessment task based on feedback from the teacher and their peers.Key ConceptsConcepts from previous lessons are integrated into this assessment task: the opposite of a number, integers, absolute value, and graphing points on the coordinate plane. Students apply their knowledge, review their work, and make revisions based on feedback from the teacher and their peers. This process creates a deeper understanding of the concepts.Goals and Learning ObjectivesApply knowledge of the opposite of a number, integers, absolute value, and graphing points on the coordinate plane to solve problems.Track and review a choice of strategy when problem solving.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Algebraic Reasoning

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.

Lesson Flow

This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.

Students explore the effects of wind on a plane's time and distance and represent these situations using algebraic expressions and equations. They use terms with positive, negative, and zero coefficients.Key ConceptsIn this lesson, students show what they remember from Grade 6 about writing expressions and solving one-step equations. They use what they learned earlier in Grade 7 about adding and subtracting integers. They extend these concepts to write and interpret an expression with a negative coefficient.Goals and Learning ObjectivesReview addition and subtraction of integers.Review the relationship between distance, time, and speed.Write an algebraic expression for distance in terms of time, t.Write a term with a negative coefficient.Review solving a one-step equation using the multiplication property of equality.

Working With Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Compare and order positive and negative numbers and place them on a number line.
Understand the concepts of opposites absolute value.

Lesson Flow

The unit begins with students using a balloon model to informally explore adding and subtracting integers. With the model, adding or removing heat represents adding or subtracting positive integers, and adding or removing weight represents adding or subtracting negative integers.

Students then move from the balloon model to a number line model for adding and subtracting integers, eventually extending the addition and subtraction rules from integers to all rational numbers. Number lines and multiplication patterns are used to find products of rational numbers. The relationship between multiplication and division is used to understand how to divide rational numbers. Properties of addition are briefly reviewed, then used to prove rules for addition, subtraction, multiplication, and division.

This unit includes problems with real-world contexts, formative assessment lessons, and Gallery problems.