Mathematics 17 ) 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. [6-EE6]
NAEP Framework
NAEP Statement:: ax + b = c or ax + b = cx + d or ax + b > c ).
NAEP Statement::
Alabama Alternate Achievement Standards
AAS Standard: x + 3").
Mathematics 15. Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.
a. Interpret a variable as an unknown value for any number in a specified set, depending on the context.
b. Write expressions to represent verbal statements and real-world scenarios.
c. Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient , and coefficient .
d. Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given contextual or mathematical problems both when known models exist (for example formulas) or algebraic models are unknown,
Interpret the parts of the model in the original context.
Create the algebraic model of the situation when appropriate.
Use appropriate mathematical terminology to communicate the meaning of the expression.
Evaluate the expressions for values of the variable including finding values following conventions of parentheses and order of operations. Teacher Vocabulary:
Expressions
Term
Coefficient
Sum
Product
Factor
Quotient
Variable
Constant
Difference
Evaluate
Order of Operations
Exponent
Absolute Value 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. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.6.15.1: Define algebraic expression and variable.
M.6.15.2: Convert mathematical terms to mathematical symbols and numbers.
M.6.15.3: Translate verbal and numerical expression using all operations.
M.6.15.4: Define coefficient, constant and term.
M.6.15.5: Match mathematical terms with correct mathematical symbols.
M.6.15.6: Convert mathematical terms to mathematical symbols and numbers.
M.6.15.7: Calculate an expression in the correct order. with or without a calculator (Ex. exponents, mult./div. from left to right, and add/sub. from left to right).
M.6.15.8: Choose the correct value to replace each variable in the algebraic expression (Substitution).
M.6.15.9: Calculate a numerical expression, with or without a calculator (Ex. V=4x4x4).
M.6.15.10: Recognize the correct order to solve expressions with more than one operation.
Prior Knowledge Skills:
Recognize key terms to solve word problems.
Recognize key terms to solve word problems.
Define simple expression.
Recall simple equations.
Recognize properties of addition and multiplication.
Recall addition, subtraction, multiplication, division symbols.
Define parentheses, braces, and brackets.
Define numerical expression.
Recognize expressions.
Apply properties of operations as strategies to add and subtract.
Recall properties of operations as strategies to add and subtract.
Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
Use addition, subtraction, multiplication and division to solve one- and two-step word problems.
Recognize key terms to solve word problems.
Apply properties of operations as strategies to multiply and divide.
Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
Recall the formula for area (L × W).
Recognize that unit squares are equal.
Recall the formula for perimeter (P= L+L+W+W or P=2L + 2W).
Recall basic addition and multiplication facts.
Alabama Alternate Achievement Standards
AAS Standard:
