build on their understanding of order of operations.

use the properties of operations to rewrite equivalent numerical expressions.

understand that the properties of operations hold for integers, rational, and real numbers.

use variables to represent real-world situations and use the properties of operations to generate equivalent expressions for these situations.

experience expressions for amounts of increase and decrease.

use substitution to understand that expressions are equivalent.

use and understand the properties of operations which include: the commutative, associative, identity, inverse properties of addition and of multiplication, and the zero property of multiplication.

understand the connections between performing the inverse operation and undoing the operations.

show their steps in their work and explain their thinking using the correct terminology for the properties and operations.

build upon their understanding and application of writing and solving one-step equations from a problem situation in order to understand and solve multi-step equations from a problem situation.

practice using rational numbers including: integers, and positive and negative fractions and decimals.

analyze a situation and identify what operation should be completed first, and then find the values for that computation.

work with multi-step problem situations that have multiple solutions and therefore can be represented by an inequality.

understand that values can satisfy an inequality but may not be appropriate for the situation, therefore limiting the solutions for that particular problem.

Vocabulary

* Variable: A symbol, usually a letter, which is used to represent one or more numbers.

Numerical expression: An expression consisting of numbers and operations.

Algebraic expression: An expression consisting of at least one variable and also consist of numbers and operations.

Term: A number, a variable, or a product and a number and variable.

Coefficient: The number part of a term that includes a variable. For example, 3 is the coefficient of the term 3x.

Constant: A quantity having a fixed value that does not change or vary, such as a number. For example, 5 is the constant of x + 5.

Equation: A mathematical sentence formed by setting two expressions equal.

Inequality: A mathematical sentence formed by placing inequality symbol between two expressions.

October-November Lessons 7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Video: Add linear expressions by combining like terms Video: Expand linear expressions using the distributive property Video: Expand linear expressions with fractions using the distributive property Video: Factor linear expressions

7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Video: Write an expression to find the cost of an item with tax Video: Write an expression to find the cost of a discounted item Video: Write a percent markup expression

7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. Video: Approach a multi-step problem using steps Video: Solve problems using a chart Video: Solve problems by writing and solving equations

7.EE.4a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. Video: Use a bar model to write and solve equations Video: Solve an equation using inverse operations Video: Convert a real-world situation into an equation

7.EE.4b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Video: Write an inequality from a word problem Video: Solve inequalities with inverse operations Video: Represent an inequality solution set on a number line

## Overview

Students will:

## Vocabulary

*: A symbol, usually a letter, which is used to represent one or more numbers.Variable: An expression consisting of numbers and operations.Numerical expression: An expression consisting of at least one variable and also consist of numbers and operations.Algebraic expression: A number, a variable, or a product and a number and variable.Term: The number part of a term that includes a variable. For example, 3 is the coefficient of the term 3x.Coefficient: A quantity having a fixed value that does not change or vary, such as a number. For example, 5 is the constant of x + 5.Constant: A mathematical sentence formed by setting two expressions equal.Equation: A mathematical sentence formed by placing inequality symbol between two expressions.InequalityChapter 1: Foundations of AlgebraChapter 2: EquationsChapter 3: InequalitiesChapter 4: FunctionsChapter 5: Linear FunctionsChapter 6: Systems of Equations and InequalitiesChapter 7: Exponents and PolynomialsChapter 8: Factoring PolynomialsChapter 9: Quadratic Functions and EquationsChapter 10: Data Analysis and ProbabilityChapter 11: Exponential and Radical FunctionsChapter 12: Rational Functions and EquationsOctober-November Lessons7.EE.1.Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Video: Add linear expressions by combining like termsVideo: Expand linear expressions using the distributive property

Video: Expand linear expressions with fractions using the distributive property

Video: Factor linear expressions

7.EE.2.Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.Video: Write an expression to find the cost of an item with tax

Video: Write an expression to find the cost of a discounted item

Video: Write a percent markup expression

7.EE.3.Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.Video: Approach a multi-step problem using steps

Video: Solve problems using a chart

Video: Solve problems by writing and solving equations

7.EE.4a.Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.Video: Use a bar model to write and solve equations

Video: Solve an equation using inverse operations

Video: Convert a real-world situation into an equation

7.EE.4b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.Video: Write an inequality from a word problem

Video: Solve inequalities with inverse operations

Video: Represent an inequality solution set on a number line