Expressions, Equations & Inequalities
In this unit the students will learn to recognize that variables are used to represent specific but unknown numbers and are used to make statements that are true for all numbers or a set of numbers. They will learn to read, write and evaluate expressions. The students will identify and generate equivalent expressions.
Essential Outcomes of the Unit
- Recognize that variables are used to represent specific but unknown numbers and are used to make statements that are true for all numbers or a set of numbers.
- Identify and generate equivalent expressions.
- Read, write and evaluate expressions in a variety of real world contexts.
Expressions, Equations, and Inequalities
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers.
6.EE.2b Identify parts of an expression using mathematical terms (term, coefficient, sum, difference, product, factor, and quotient); view one or more parts of an expression as a single entity.
6.EE.2c Evaluate expressions given specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order (Order of Operations).
6.EE.3 Apply the properties of operations to generate equivalent expressions.
6.EE.4 Identify when two expressions are equivalent.
Expressions, Equations, and Inequalities
Reason about and solve one-variable equations and inequalities.
6.EE.5 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? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x – p = q; px = q; and 𝑥𝑥 𝑝𝑝 = q for cases in which p, q, and x are all nonnegative rational numbers.
6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another. Given a verbal context and an equation, identify the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Other Standards Addressed in the Unit
Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.5 Use area and volume models to explain perfect squares and perfect cubes.
Expressions, Equations, and Inequalities
Reason about and solve one-variable equations and inequalities.
6.EE.8 8. Write an inequality of the form x > c, x ≥ c, x ≤ c, or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on a number line.
Essential Questions and Big Ideas
What are exponents?
- Exponents represent repeated multiplication of the same factor.
- The term squared represents an exponent of 2. The term cubed represents an exponent of 3.
How can I write and evaluate expressions and equations?
- Mathematical language such as sum, product, difference, etc. can be used to describe mathematical expressions.
- When the value of a variable is known, it can be substituted into an expression or equation.
How can I identify and create equivalent expressions?
- Like terms, terms with the same variable, can be combined or subtracted.
- The distributive property can be used to simplify an expression with parentheses.
How can I solve equations and inequalities?
- Substitution can be used to solve equations and inequalities.
Download the complete Grade 6 Math Unit 4 framework to customize for your own planning.