Students solve a problem about a salesperson's compensation. They solve the problem first by arithmetic and then by writing and solving an inequality.Key ConceptsIn Lesson 11, students learned how to solve inequalities using the addition and multiplication properties of inequality. In this lesson, they solve word problems by writing and solving inequalities.To help students make connections and see how problems can be solved in different ways, students first solve the same problem using arithmetic.Goals and Learning ObjectivesWrite and solve an algebraic inequality to solve a word problem.

Students extend what they learned about solving equations in Grade 6. They learn to solve equations that require them to use both the addition and the multiplication properties of equality. They use what they know about solving equations such as 2x = 6 and x + 3 = 7 to solve equations such as 2x + 3 = 8. They connect solving problems using arithmetic to solving problems using equations. They solve equations containing both positive and negative rational numbers.Key ConceptsAddition property of equality: If a = b, then a + c = b + c.Multiplication property of equality: If a = b, then ac = bc.For any equation, add or subtract the same value from both sides of the equation and the equation will still be true.For any equation, multiply or divide both sides of the equation by the same value and the equation will still be true.In this lesson, students use both properties to solve equations. They then solve equations that contain both positive and negative rational numbers.Goals and Learning ObjectivesSolve equations using both the addition and multiplication properties of equality.Relate solving problems using arithmetic to solving problems using equations.Solve equations containing both positive and negative rational numbers.

Students explore the relationship between the flapping frequency, the amplitude, and the cruising speeds of a variety of animals to calculate their Strouhal numbers.Key ConceptsStudents are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills. Students will:Try a variety of strategies to approaching different types of problems.Devise a problem-solving plan and implement their plan systematically.Become aware that problems can be solved in more than one way.See the value of approaching problems in a systematic manner.Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.Make connections between previous learning and real-world problems.Create efficacy and confidence in solving challenging problems in a real-world setting.Goals and Learning ObjectivesAnalyze the relationship between the variables in an equation.Write formulas to show how variables relate.Communicate findings using multiple representations including tables, charts, graphs, and equations.

Students first create a diagram that represents the distance a ship drops in each of a series of locks. Students create their diagrams based on a video of an actual ship traveling through the locks. Students need to use contextual clues in order to determine the relative drops in each of the locks.Key ConceptsStudents are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills.Students will:Try a variety of strategies to approaching different types of problems.Devise a problem-solving plan and implement their plan systematically.Become aware that problems can be solved in more than one way.See the value of approaching problems in a systematic manner.Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.Make connections between previous learning and real-world problems.Create efficacy and confidence in solving challenging problems in a real-world setting.Goals and Learning ObjectivesRead and interpret maps, graphs, and diagrams.Solve problems that involve linear measurement.Estimate length.Critique a diagram.

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.

This resource is designed to assist students understanding of real-world applicaitono f mathematical concepts.  Students will complete their investigation over the course of 4-5 days, following the multi-segment program "Mathnet" from the PBS series "Square One Television" While watching the day's segment, students will be recording in their notebooks the following information: math concepts used/referred to, important clues about the investigation, and individuals who they believe are "persons of interest."  Following the last video segmnet, students will complete their I"Investigation Report" for submission to their supervisor (a.k.a the teacher).

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: explore relationships between variables in everyday situations; find unknown values from known values; find relationships between pairs of unknowns, and express these as tables and graphs; and find general relationships between several variables, and express these in different ways by rearranging formulae.

This a remix from original author Nancy Hetrick. The original resource did not have a practive video that worked so I made a 5 question Quizlet to review.As students prepare to work with algebraic expressions, either with operations (add, subtract, multiply, or divide) or when making connections to constant, linear, and/or quadratic functions, it is important that students can name basic polynomial expressions as monomials, binomials, or trinomials, During this activity students will learn how to name these polynomials through watching a video and then practice naming polynomials through a Quizlet.

As students prepare to work with algebraic expressions, either with operations (add, subtract, multiply, or divide) or when making connections to constant, linear, and/or quadratic functions, it is important that students can name basic polynomial expressions as monomials, binomials, or trinomials, During this activity students will learn how to name these polynomials through watching a video, practice naming polynomials through a sorting activity, and then complete five-formative assessment questions.

8.EE.7 Solving Equations Quiz. Version A is standard with complex equations. Version B is a modified version with simplified use of integers and smaller multi-step equations. Both versions contain fractional problems. Each quiz provides directions including the tip Don't Call Me After Midnight to remind students of the steps for solving equations.

NCM1.A-REI.3 Solving linear equations and inequalities in one variable to include fractions.

8.EE.7 Solving Equations Quiz. Two versions. M is the standard version M1 is the modified version with simplified negatives and smaller multi-step equations. Both versions contain fractional problems too.

NCM1.A-REI.3 Solving linear equations and inequalities in one variable to include fractions.

8.EE.7 Solving Equations Quiz. Two versions. M is the standard version M1 is the modified version with simplified negatives and smaller multi-step equations. Both versions contain fractional problems too.

8.EE.7 Solving Equations Quiz. Two versions. M is the standard version M1 is the modified version with simplified negatives and smaller multi-step equations. Both versions contain fractional problems too.

NCM1.A-REI.3 Solving linear equations and inequalities in one variable to include fractions.

This lesson was created by Shameeka Wilson as part of her undergraduate student teaching at the North Carolina School of the Deaf in Morganton N.C.

Students will practice measuring the diameter and radius of food themed circular objects. Next, they will discover that finding the ratio of circumference and diameter is the value of approximately 3.14 or pi.
Then, using the number 3.14 for Pi, students will find the area of the various circular objects.

Students will practice measuring the diameter and radius of various circular objects. Next, they will discover the ratio of pi to about 3.
Then, using the number 3.14 for Pi, students will find the area of the various circular objects.

Students will practice measuring the diameter and radius of various circular objects. Then using the number 3.14 for Pi, will find the area of the various circular objects.

Students will practice measuring the diameter and radius of various circular objects. Next, they will discover the ratio of pi to about 3.
Then, using the number 3.14 for Pi, students will find the area of the various circular objects.

Students to enter and compare numeric or algebraic expressions in this interactive pan balance, from Illuminations, . They can "weigh" the expressions they want to compare by entering them on either side of the balance, allowing them to practice arithmetic and algebraic skills, as well as to investigate the concept of equivalence.