Math Standards

6.EE.5Understand 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.7Solve 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.

7.EE.2Understand 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.

7.EE.3Solve 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.4Use 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.

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?

8.EE.2Use 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.

8.EE.7bSolve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

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

Math Practice Standards

Essential Understandings

Students will understand that…

Essential Questions

Vertical Alignment

Vocabulary is in packet (linked at top)

6.EE.5Understand 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.7Solve 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.

7.EE.2Understand 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."*7.EE.3Solve 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.

*For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.*7.EE.4Use 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.

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?

8.EE.2Use 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.

8.EE.7bSolve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

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

Math Practice Standards

**MP.1**Make sense of problems and persevere in solving them**MP.3**Construct viable arguments and critique the reasoning of others**MP.4**Model with mathematicsEssential Understandings

Students will understand that…

- equations are composed of expressions
- the solution set of an equation is limited
- inverse operations are used to solve equations
- equations must be simplified before solving
- repeated decimals can be written in the form of a fraction
- defining a variable is essential to writing algebraic equations from word problems
- inverse operations also apply to equations with squares, cubes and roots
- formulas can be manipulated to solve for a specific variable

Essential Questions

- What is an equation and how is it similar/different from an expression?
- How can you prove if a solution to an equation is correct?
- If x is a negative number, then what would -x equal?
- What strategies can I use to solve equations?
- Can equations be simplified like expressions?
- How can everyday situations be represented in the form of an equation?
- How can you use equations to convert repeating decimals into fractions?
- What are common misconceptions when solving an equation containing squares, cubes or roots?
- How can you rearrange an equation to solve for a specific variable?

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 is in packet (linked at top)