Mathematics 7 (Grade 6/7)
Unit 3: Expressions & Equations (7.EE)
In this unit, students use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. Students will understand and use properties of operations to generate equivalent expressions. Students use and solve reallife mathematical problems using numerical and algebraic expressions and equations. Also, students will use variables to represent quantities in a realworld or mathematical problem to construct and solve simple equations and inequalities in one and two step. In gaining the understanding of solving the one and twostep equations and inequalities, students will reason about the quantity of their solutions. In preparation for work on congruence and similarity in Grade 8 they gain familiarity with the relationships between angles formed by intersecting lines and solve for unknowns in a figure.
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What will my child learn?
Students will:
Use properties of operations to generate equivalent expressions.
7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.A.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. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."
Solve reallife and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.4
Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
7.EE.B.4.A
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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
7.EE.B.4.B
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. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
7.G.B.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
Students will:
Use properties of operations to generate equivalent expressions.
7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
 Background Info. & Guided Practice
 Check for Understanding: Combining Like Terms with Negative Coefficients and Distribution  Combining Like Terms with Rational Coefficients
 Review/Rewind: Combining Like Terms  Distributive Property with Algebraic Expressions
 Enrichment Tasks: Writing Expressions*  TV Sales  Equivalent Expressions?*
7.EE.A.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. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."
 Check for Understanding: Interpreting Linear Expressions
 Review/Rewind: Simplifying Expressions  Expanding Expressions
 Enrichment Tasks: Ticket to Ride  Miles to Kilometers*
Solve reallife and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.4
Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
 Check for Understanding: TwoStep Equation Word Problems  TwoStep Equations
 Review/Rewind: Modeling with one step equations
 Enrichment Tasks: Bookstore Account
7.EE.B.4.A
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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
 Check for Understanding: TwoStep Equation Word Problems  TwoStep Equations
 Review/Rewind: Solve Equations By Performing the Same Operations on Both Sides
 Enrichment Tasks: Guess My Number*
7.EE.B.4.B
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. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
 Check for Understanding: OneStep Inequalities  TwoStep Inequalities  Twostep Inequality Word Problems
 Review/Rewind: Understand that an expression doesn't have to be equal to another
 Enrichment Tasks: Fishing Adventures 2*  Sports Equipment Set*
7.G.B.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
 Check for Understanding: Complementary and Supplementary Angles  Vertical Angles  Quadrilateral Angles  Unknown Angle Problems (with algebra)
 Review/Rewind: Use Veritical and Adjacent Angles To Find Unknown Angles  Complementary & Supplementary Angles  Vertical Angles
What are some signs of student mastery?

Tools & Technology
NCTM's online Algebra Tiles are tools that can be used to represent variables and constants, solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra! Note: Handson [physical] versions of Algebra Tiles are also used in math classrooms. Combining Like Term Space Invaders: Space invaders game, where the player must shoot ships with the like terms. Integers, exponents, and multiple variables are added as the player progresses. Expanding Expressions with Distributive Property: Students simplify expressions, using the distributive property. The questions alternate between multiple choice and fill in the blank formats. Exploring Algebra Game: This interactive mathematics resource allows the user to explore and interpret word problems by evaluating expressions and solving equations in a variety of different contexts. 