Math Standards

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.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = 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; write an equation to express one quantity, thought of as 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.

Use properties of operations to generate equivalent 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.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

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.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities

to solve problems by reasoning about the quantities.

Work with radicals and integer exponents.

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.7 Solve linear equations in one variable.

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal

expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which

repeats eventually into a rational number.

Essential Understandings

Students will understand that…

Essential Questions

Vertical Alignment

Vocabulary

Continuous Data, Dependent Variables, Discrete Data, Independent Variables

ONLINE PRACTICE LINKS

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.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = 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; write an equation to express one quantity, thought of as 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.

Use properties of operations to generate equivalent 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.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

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.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities

to solve problems by reasoning about the quantities.

- 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.

Work with radicals and integer exponents.

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.7 Solve linear equations in one variable.

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal

expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which

repeats eventually into a rational number.

Essential Understandings

Students will understand that…

- solutions to equations are numbers that one can substitute in for the variable to make the equation true.
- equations can represent real-world contexts, and can be used to solve real-world problems.
- if a situation has two variables, the dependent variable is affected by changes in the independent variable.
- equations can be written to show the relationships between independent and dependent variables.
- each side of an equation maintains the same value.
- inverse operations are used to isolate the variable.
- equations can be constructed to represent real-world problems.
- equations may have solutions that require expanding an expression with the distributive property and collecting like terms.
- every number has a decimal expansion.
- rational numbers have decimal expansions that terminate in 0’s or eventually repeat
- numbers that aren’t rational are called irrational
- there is an algorithm for converting a repeating decimal to a fraction.
- squaring a number and taking the square root of a number are inverse operations
- cubing a number and taking the cube root of a number are inverse operations

Essential Questions

- Why are inverse operations used to solve one-step equations?
- How might you justify that a value is a given solution to an equation in a real world context?
- How do you solve equations with variables on both sides of the equal sign?
- How are inverse operations used to maintain equal values while solving for a variable?
- What contexts are usually represented with independent variables? With dependent variables?
- How does rewriting an expression in different forms show how the quantities are related?
- How/Where might square roots and cube roots be used outside of the classroom?
- How do you solve equations with variables on both sides of the equal sign?
- How are inverse operations used to maintain equal values while solving for a variable?
- How are equations and the process of converting a repeating decimal to a fraction related?

Vertical Alignment

- In 5th grade students apply formulas for finding the volume of rectangular prisms.
- Later in this course students write and solve equations to represent proportional relationships and percents.
- Later in this course students write and solve equations to represent geometric situations.
- In CCMI students solve and graph non-linear equations.
- In CCMI students solve two-variable equations and functions.
- To determine additional ways to support and enrich student learning, please access the K-12 progression here -
**Turn on CC Math**

Vocabulary

Continuous Data, Dependent Variables, Discrete Data, Independent Variables

ONLINE PRACTICE LINKS

- Algebra Tiles - interactive tool using algebra tiles to teach solving one step equations
- Balance the Scale - interactive tool to show students how to balance a scale. Can be used to connect to balancing an equation.