3-29-2012 Dependent and Independent Variables

Teching the CCCS for Grade 6 Mathematics

STRAND	CPI	SKILLS	Resources
Expressions & Equations	The goal: Students will be able to apply and extend previous understandings of arithmetic to algebraic expressions, reason about and solve one-variable equations and inequalities, and represent and analyze quantitative relationships between dependent and independent variables.	More specifically, students will understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students will understand that expressions in different forms can be equivalent, and they will use the properties of operations to rewrite expressions in equivalent forms. Students will learn that the solutions of an equation are the values of the variables that make the equation true. Students will use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students will construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.	Algebraic Reasoning Algebra Algebra Games Math By Design Maths Masters Algebra Virtual Manipulatives Exploriments
Apply and extend previous understandings of arithmetic to algebraic expressions.			Pre-Algebra on Shmoop  Algebra: The Supplement
	Write and evaluate numerical expressions involving whole-number exponents.		Powers and Roots Base and Exponent Evaluate Squares Evaluate Cubes Evaluating Exponents Exponents Scientific Notation practice site
	Write, read, and evaluate expressions in which letters stand for numbers.	Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.	Function Machine Formulas and More on Formulas
		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.	Translate Sentences into Equations Writing Equations The Mystery Number Song Escape from Planet X
		Evaluate expressions at 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 = 1/2.	Evaluating Expressions w/ 1 variable Evaluating Expressions w/ 2 variables Balancing Equations Evaluate Expressions
	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.	Properties of Operations Properties Practice Solving with Inverse Operations Order and Zero Properties of Addition Properties
	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.	Algebra Four