Unpacked Content
Knowledge
Students know:
- Correct usage of mathematical symbolism to model the terms sum, term, product, factor, quotient, variable, difference, constant, and coefficient when they appear in verbally stated contexts.
- Conventions for order of operations.
- Convention of using juxtaposition (5A or xy) to indicate multiplication.
Skills
Students are able to:
- Translate fluently between verbally stated situations and algebraic models of the situation.
- Use operations (addition, subtraction, multiplication, division, and exponentiation) fluently with the conventions of parentheses and order of operations to evaluate expressions for specific values of variables in expressions.
- Use terminology related to algebraic expressions such as sum, term, product, factor, quotient, or coefficient, to communicate the meanings of the expression and the parts of the expression.
Understanding
Students understand that:
- The structure of mathematics allows for terminology and techniques used with numerical expressions to be used in an analogous way with algebraic expressions, (the sum of 3 and 4 is written as 3 + 4, so the sum of 3 and y is written as 3 + y).
- When language is ambiguous about the meaning of a mathematical expression grouping, symbols and order of operations conventions are used to communicate the meaning clearly.
- Moving fluently among representations of mathematical situations (words, numbers, symbols, etc.), as needed for a given situation, allows a user of mathematics to make sense of the situation and choose appropriate and efficient paths to solutions.
Vocabulary
- Expressions
- Term
- Coefficient
- Sum
- Product
- Factor
- Quotient
- Variable
- Constant
- Difference
- Evaluate
- Order of Operations
- Exponent
- Absolute Value
