UNIT 8: Building conceptual understanding of expressions
IN THIS UNIT, STUDENTS WILL BE EXPECTED TO:
- Write numerical expressions with rational bases and whole number exponents, adding to their experience with base ten in previous courses.
- Evaluate numerical expressions with rational bases and whole-number exponents.
- Determine the greatest common factor to solve authentic problems.
- Determine the least common multiple to solve authentic problems.
- Read and write expressions with rational numbers and variables that represent real-life situations.
- Evaluate expressions with variables, given values for the variable, especially given realistic situations.
- Apply properties of operations such as the associative property, commutative property, distributive property, and identity properties to generate and evaluate equivalent expressions.
- Write numerical expressions with rational bases and whole number exponents, adding to their experience with base ten in previous courses.
- Evaluate numerical expressions with rational bases and whole-number exponents.
- Determine the greatest common factor to solve authentic problems.
- Determine the least common multiple to solve authentic problems.
- Read and write expressions with rational numbers and variables that represent real-life situations.
- Evaluate expressions with variables, given values for the variable, especially given realistic situations.
- Apply properties of operations such as the associative property, commutative property, distributive property, and identity properties to generate and evaluate equivalent expressions.
LEARNING OBJECTIVES:
6.PAR.6. Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant situations.
6.PAR.6.1. Write and evaluate numerical expressions involving rational bases and whole-number exponents.
6.PAR.6.2. Determine the greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems.
6.PAR.6.3. Write and read expressions that represent operations with numbers and variables in realistic situations.
6.PAR.6.4. Evaluate expressions when given values for the variables, including expressions that arise in everyday situations.
6.PAR.6.5. Apply the properties of operations to identify and generate equivalent expressions.
6.PAR.6. Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant situations.
6.PAR.6.1. Write and evaluate numerical expressions involving rational bases and whole-number exponents.
6.PAR.6.2. Determine the greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems.
6.PAR.6.3. Write and read expressions that represent operations with numbers and variables in realistic situations.
6.PAR.6.4. Evaluate expressions when given values for the variables, including expressions that arise in everyday situations.
6.PAR.6.5. Apply the properties of operations to identify and generate equivalent expressions.
LEARNING TARGETS (I Can Statements):
- I can evaluate numerical expressions that include rational bases with whole-number exponents.
- I can interpret and write numerical expressions.
- I can apply the least common multiple of two whole numbers less than or equal to 12 to solve applicable, mathematical problems.
- I can determine the greatest common factor of 2 whole numbers and use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factors (GCF).
- I can use the order of operations to solve a numerical expression.
- I can identify parts of an expression using mathematical terms (sum, different, term, product, factor, quotient, coefficient, variable, constant).
- I can translate from a word form into a variable expression.
- I understand letters (called variables) represent unknown numbers and the same rules that apply in operations with numbers also apply to operations with variables.
- I can evaluate algebraic expressions for a given value of a variable, using the order of operations.
- I can 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).
- I can apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x.
- I can 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.
- I can identify equivalent expressions by applying properties of operations (associative, commutative, and distributive properties).
- I can apply properties of operations to simplify algebraic expressions.
- I can evaluate numerical expressions that include rational bases with whole-number exponents.
- I can interpret and write numerical expressions.
- I can apply the least common multiple of two whole numbers less than or equal to 12 to solve applicable, mathematical problems.
- I can determine the greatest common factor of 2 whole numbers and use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factors (GCF).
- I can use the order of operations to solve a numerical expression.
- I can identify parts of an expression using mathematical terms (sum, different, term, product, factor, quotient, coefficient, variable, constant).
- I can translate from a word form into a variable expression.
- I understand letters (called variables) represent unknown numbers and the same rules that apply in operations with numbers also apply to operations with variables.
- I can evaluate algebraic expressions for a given value of a variable, using the order of operations.
- I can 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).
- I can apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x.
- I can 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.
- I can identify equivalent expressions by applying properties of operations (associative, commutative, and distributive properties).
- I can apply properties of operations to simplify algebraic expressions.
TEXTBOOK CONNECTIONS:
(Use Georgia Reveal Math - Course 1 - 6th Grade)
Module 5 – Numerical and Algebraic Expressions
Write and evaluate numerical and algebraic expressions.
Lesson 5-1 Powers and Exponents
Students will write and evaluate powers.
Lesson 5-2 Numerical Expressions
Students will write and evaluate numerical expressions.
Lesson 5-3 Write Algebraic Expressions
Students will write algebraic expressions.
Lesson 5-4 Evaluate Algebraic Expressions
Students will evaluate algebraic expressions.
Lesson 5-5 Factors and Multiples
Students will solve problems by finding the greatest common factor and the least common multiple of two whole numbers.
Lesson 5-6 Use the Distributive Property
Students will use the Distributive Property to expand and factor expressions.
Lesson 5-7 Equivalent Algebraic Expressions
Students will identify and generate equivalent algebraic expressions.
(Use Georgia Reveal Math - Course 1 - 6th Grade)
Module 5 – Numerical and Algebraic Expressions
Write and evaluate numerical and algebraic expressions.
Lesson 5-1 Powers and Exponents
Students will write and evaluate powers.
Lesson 5-2 Numerical Expressions
Students will write and evaluate numerical expressions.
Lesson 5-3 Write Algebraic Expressions
Students will write algebraic expressions.
Lesson 5-4 Evaluate Algebraic Expressions
Students will evaluate algebraic expressions.
Lesson 5-5 Factors and Multiples
Students will solve problems by finding the greatest common factor and the least common multiple of two whole numbers.
Lesson 5-6 Use the Distributive Property
Students will use the Distributive Property to expand and factor expressions.
Lesson 5-7 Equivalent Algebraic Expressions
Students will identify and generate equivalent algebraic expressions.
IXL SKILLS: