UNIT 10: reasoning with expressions, equations, and inequalities
IN THIS UNIT, STUDENTS WILL BUILD UPON THEIR UNDERSTANDING IN GRADE 6:
- Mathematical properties (such as commutative, associative, and distributive properties) and conventions (such as order of operations).
- Use these conventions and properties of operations to rewrite equivalent expressions and interpret expressions in context.
- Extend properties used with whole numbers to rational numbers in multiple formats (fractions and decimals).
- Construct and solve equations and inequalities to solve contextual problems and interpret solutions based on context.
- Mathematical properties (such as commutative, associative, and distributive properties) and conventions (such as order of operations).
- Use these conventions and properties of operations to rewrite equivalent expressions and interpret expressions in context.
- Extend properties used with whole numbers to rational numbers in multiple formats (fractions and decimals).
- Construct and solve equations and inequalities to solve contextual problems and interpret solutions based on context.
LEARNING OBJECTIVES:
7.PAR.2 Use properties of operations, generate equivalent expressions, and interpret the expressions to explain relevant contextual situations.
7.PAR.2.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.PAR.2.2 Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in it are related.
7.PAR.3 Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.
7.PAR.3.1 Construct algebraic equations to solve practical problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Interpret the solution based on the situation.
7.PAR.3.2 Construct algebraic inequalities to solve problems, leading to inequalities of the form px ± q > r, px ± q < r, px ± q ≤ r, or px ± q ≥ r, where p, q, and rare specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.
7.PAR.2 Use properties of operations, generate equivalent expressions, and interpret the expressions to explain relevant contextual situations.
7.PAR.2.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.PAR.2.2 Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in it are related.
7.PAR.3 Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.
7.PAR.3.1 Construct algebraic equations to solve practical problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Interpret the solution based on the situation.
7.PAR.3.2 Construct algebraic inequalities to solve problems, leading to inequalities of the form px ± q > r, px ± q < r, px ± q ≤ r, or px ± q ≥ r, where p, q, and rare specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.
LEARNING TARGETS (I Can Statements):
- I can identify the parts of an algebraic expression.
- I can rewrite an expression in a different form.
- I can use Commutative, Associative, Distributive, Identity, and Inverse Properties to add and subtract linear expressions with rational coefficients.
- I can use Commutative, Associative, Distributive, Identity, and Inverse Properties to factor and expand linear expressions with rational coefficients.
- I can interpret real-world situations using properties and choose the form of an expression that justifies the algebraic property.
- I can rewrite expressions related to math stories in different forms to clarify the math story.
- I can translate words or real-life situations into variable equations.
- I can construct and solve word problems leading to one or two-step equations with rational numbers.
- I can solve one and two-step equations involving variables with positive and negative rational numbers (integers, fractions, decimals).
- I can construct and solve multi-step equations including all rational numbers.
- I can justify my answer by checking my solution.
- I can solve real-world problems involving subtracting rational numbers.
- I can solve one or two-step inequalities with rational numbers.
- I can construct and solve word problems leading to one or two-step inequalities with rational numbers.
- I can graph and interpret the solution set of inequalities in the context of the problem.
- I can justify my answer by checking my solution. I can use Commutative, Associative, Distributive, Identity, and Inverse Properties to factor and expand linear expressions with rational coefficients.
- I can interpret real-world situations using properties and choose the form of an expression that justifies the algebraic property.
- I can rewrite expressions related to math stories in different forms to clarify the math story.
- I can identify the parts of an algebraic expression.
- I can rewrite an expression in a different form.
- I can use Commutative, Associative, Distributive, Identity, and Inverse Properties to add and subtract linear expressions with rational coefficients.
- I can use Commutative, Associative, Distributive, Identity, and Inverse Properties to factor and expand linear expressions with rational coefficients.
- I can interpret real-world situations using properties and choose the form of an expression that justifies the algebraic property.
- I can rewrite expressions related to math stories in different forms to clarify the math story.
- I can translate words or real-life situations into variable equations.
- I can construct and solve word problems leading to one or two-step equations with rational numbers.
- I can solve one and two-step equations involving variables with positive and negative rational numbers (integers, fractions, decimals).
- I can construct and solve multi-step equations including all rational numbers.
- I can justify my answer by checking my solution.
- I can solve real-world problems involving subtracting rational numbers.
- I can solve one or two-step inequalities with rational numbers.
- I can construct and solve word problems leading to one or two-step inequalities with rational numbers.
- I can graph and interpret the solution set of inequalities in the context of the problem.
- I can justify my answer by checking my solution. I can use Commutative, Associative, Distributive, Identity, and Inverse Properties to factor and expand linear expressions with rational coefficients.
- I can interpret real-world situations using properties and choose the form of an expression that justifies the algebraic property.
- I can rewrite expressions related to math stories in different forms to clarify the math story.
TEXTBOOK CONNECTIONS:
(Use Georgia Reveal Math - Course 2 - 7th Grade)
Module 5 – Simplify Algebraic Expressions
Write and solve one-step equations and two-step equations.
Lesson 5-1 Simplify Algebraic Expressions
Students will simplify algebraic expressions by combining like terms and using the Distributive Property.
Lesson 5-2 Add Linear Expressions
Students will add linear expressions and express the sum in the simplest form.
Lesson 5-3 Subtract Linear Expressions
Students will subtract linear expressions and express the difference in simplest form.
Lesson 5-4 Factor Linear Expressions
Students will find the GCF of monomials and factor algebraic expressions.
Lesson 5-5 Combing Operations with Linear Expressions
Students will combine operations to simplify linear expressions.
Module 6 – Write and Solve Equations
Students will combine operations to simplify linear expressions.
Lesson 6-1 Write and Solve One-Step Equations
Students will write and solve one-step equations with rational numbers.
Lesson 6-2 Solve Two-Step Equations: px +q = r
Students will solve two-step equations of the form px + q = r.
Lesson 6-3 Write and Solve Two-Step Equations: px + q = r
Students will write and solve two-step equations of the form px + q = r.
Lesson 6-4 Solve Two-Step Equations: p(x + q) = r
Students will solve two-step equations of the form p(x + q) = r.
Lesson 6-5 Write and Solve Two-Step Equations: p(x + q) = r
Students will write and solve two-step equations of the form p(x +q) = r.
Module 7 – Write and Solve Inequalities
Write and solve one-step inequalities and two-step inequalities.
Lesson 7-1 Solve One-Step Addition and Subtraction Inequalities
Students will solve and graph one-step addition and subtraction inequalities.
Lesson 7-2 Write and Solve One-Step Addition and Subtraction Inequalities
Students will write and solve one-step addition and subtraction inequalities.
Lesson 7-3 Solve One-Step Multiplication and Division Inequalities with Positive Coefficients
Students will solve and graph one-step multiplication and division inequalities with positive coefficients.
Lesson 7-4 Solve One-Step Multiplication and Division Inequalities with Negative Coefficients
Students will solve and graph one-step multiplication and division inequalities with negative coefficients.
Lesson 7-5 Write and Solve One-Step Multiplication and Division Inequalities
Students will write and solve one-step multiplication and division inequalities.
Lesson 7-6 Write and Solve Two-Step Inequalities
Students will write and solve two-step inequalities.
(Use Georgia Reveal Math - Course 2 - 7th Grade)
Module 5 – Simplify Algebraic Expressions
Write and solve one-step equations and two-step equations.
Lesson 5-1 Simplify Algebraic Expressions
Students will simplify algebraic expressions by combining like terms and using the Distributive Property.
Lesson 5-2 Add Linear Expressions
Students will add linear expressions and express the sum in the simplest form.
Lesson 5-3 Subtract Linear Expressions
Students will subtract linear expressions and express the difference in simplest form.
Lesson 5-4 Factor Linear Expressions
Students will find the GCF of monomials and factor algebraic expressions.
Lesson 5-5 Combing Operations with Linear Expressions
Students will combine operations to simplify linear expressions.
Module 6 – Write and Solve Equations
Students will combine operations to simplify linear expressions.
Lesson 6-1 Write and Solve One-Step Equations
Students will write and solve one-step equations with rational numbers.
Lesson 6-2 Solve Two-Step Equations: px +q = r
Students will solve two-step equations of the form px + q = r.
Lesson 6-3 Write and Solve Two-Step Equations: px + q = r
Students will write and solve two-step equations of the form px + q = r.
Lesson 6-4 Solve Two-Step Equations: p(x + q) = r
Students will solve two-step equations of the form p(x + q) = r.
Lesson 6-5 Write and Solve Two-Step Equations: p(x + q) = r
Students will write and solve two-step equations of the form p(x +q) = r.
Module 7 – Write and Solve Inequalities
Write and solve one-step inequalities and two-step inequalities.
Lesson 7-1 Solve One-Step Addition and Subtraction Inequalities
Students will solve and graph one-step addition and subtraction inequalities.
Lesson 7-2 Write and Solve One-Step Addition and Subtraction Inequalities
Students will write and solve one-step addition and subtraction inequalities.
Lesson 7-3 Solve One-Step Multiplication and Division Inequalities with Positive Coefficients
Students will solve and graph one-step multiplication and division inequalities with positive coefficients.
Lesson 7-4 Solve One-Step Multiplication and Division Inequalities with Negative Coefficients
Students will solve and graph one-step multiplication and division inequalities with negative coefficients.
Lesson 7-5 Write and Solve One-Step Multiplication and Division Inequalities
Students will write and solve one-step multiplication and division inequalities.
Lesson 7-6 Write and Solve Two-Step Inequalities
Students will write and solve two-step inequalities.
IXL SKILLS: