Common Core Standards

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two

whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a

common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8

as 4 (9 + 2).

Apply and extend previous understanding of arithmetic to algebraic expressions.

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

a. Write expressions that record operations with numbers and with letters standing for numbers.

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

c. Evaluate expressions as specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = ½.

6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the

expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to

produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression

3y.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value

is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number

regardless of which number y stands for.

Reason about and solve one-variable equations and inequalities.

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.

Use properties of operations to generate equivalent expressions.

7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

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.

Math Practice Standards

Standard 1: Make sense of problems and persevere in solving them.

Standard 2: Reason abstractly and quantitatively.

Standard 3: Construct viable arguments and critique the reasoning of others.

Standard 4: Model with mathematics.

Standard 5: Use appropriate tools strategically.

Standard 6: Attend to precision.

Standard 7: Look for and make use of structure.

Standard 8: Look for and express regularity in repeated reasoning.

Vertical Alignment

Understanding(s)

Students will understand that…

Essential Vocabulary

Equations, Exceed, Inequalities, Profit, Quantity, Quotient, Term

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two

whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a

common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8

as 4 (9 + 2).

Apply and extend previous understanding of arithmetic to algebraic expressions.

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

a. Write expressions that record operations with numbers and with letters standing for numbers.

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

c. Evaluate expressions as specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = ½.

6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the

expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to

produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression

3y.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value

is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number

regardless of which number y stands for.

Reason about and solve one-variable equations and inequalities.

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.

Use properties of operations to generate equivalent expressions.

7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

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.

Math Practice Standards

Standard 1: Make sense of problems and persevere in solving them.

Standard 2: Reason abstractly and quantitatively.

Standard 3: Construct viable arguments and critique the reasoning of others.

Standard 4: Model with mathematics.

Standard 5: Use appropriate tools strategically.

Standard 6: Attend to precision.

Standard 7: Look for and make use of structure.

Standard 8: Look for and express regularity in repeated reasoning.

Vertical Alignment

- In 5th grade students write and evaluate simple expressions with parenthesis, brackets and braces.
- In 5th grade students explore the distributive property.
- In CCMI students interpret linear expressions, exponential expressions with integer exponents and quadratic expressions.
- Previous in this course student learn the algorithm for how to perform operations with integers and rational numbers.
- In CCMI students compare and analyze graphs by isolating expressions within functions.
- In CCMI students factor expressions.
- To determine additional ways to support and enrich student learning, please access the K-12 progression here -
**Turn on CC Math**

Understanding(s)

Students will understand that…

- algebraic expressions have different parts (terms, variables, coefficients, constants).
- properties are used to rewrite and simplify mathematical expressions.
- there are a variety of ways to write equivalent expressions, including the distributive property.
- algebraic expressions and verbal expressions can be translated and evaluated in real life situations.
- rewriting an expression in different forms can show how the quantities in it are related.
- verbal expressions can be converted into algebraic expressions.

- When can you change the order of the numbers in a problem without changing the outcome?
- Why are some properties only used for addition and multiplication?
- How and when can we simplify expressions?
- How is translating expressions applied in the real world?
- How could you use variables to represent numbers and write expressions when solving a real world problem?
- How does rewriting an algebraic and verbal expression in equivalent forms show how the quantities are related?
- How can the GCF and distributive property be used to rewrite a number?

Essential Vocabulary

Equations, Exceed, Inequalities, Profit, Quantity, Quotient, Term

**UNIT 3 ONLINE PRACTICE LINKS**- Khan Academy Writing Expression Word Problems - notes/videos on writing expressions with word problems - https://www.khanacademy.org/math/pre-algebra/pre-algebra-equations-expressions/pre-algebra-alg-expression-word-problems/v/writing-basic-expressions-from-word-problems-examples
- Khan Academy Equivalent Expressions - notes/videos on equivalent expressions - https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-equivalent-expressions/v/equivalent-algebraic-expressions-exercise
- Translating word phrases to algebraic expressions - online game that can be used as a review http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html