December 10, 2012
This teaching unit addresses four standards under the state of Florida’s strand/Big Idea 3 in 6th Grade Mathematics: Write, interpret and use mathematical expressions and equations. In informal terms, the teaching unit will serve as the very first introduction for sixth grade math students to vocabulary, concepts and basic operations with “unknowns” in algebra.
Standards Covered/Assessed Within the Unit
This unit will specifically address four standards under the Big Idea 3. Key learning objectives within the four standards are outlined below:
* Standard 1 - M.A.6.A.3.1: Write and evaluate mathematical expressions that correspond to given situations. * Learning Objective 1 – Students can define and use correctly/conversationally the terms, “variable, constant, algebraic expression and evaluate”. * Learning Objective 2 – Students can translate between words and math, creating mathematical expressions given situations expressed in language. * Learning Objective 3 – Students can evaluate single-variable expressions when given the value for the variable with 100% proficiency. * Standard 2 – MA.6.A.3.2: Write, solve and graph one and two-step linear equations and inequalities. * Learning Objective 1 – Students can determine if values for variables are or are not solutions to equations with 80% proficiency. * Learning Objective 2 – Students can solve one-step equations using inverse operations with 80% proficiency. * Standard 3 – MA.6.A.3.4: Solve problems given a formula. * Learning Objective 1 – Students can substitute values for multiple variables into a multi-variable equation, such as a commonly used formula, to derive the solution with 80% proficiency. * Learning Objective 2 – Students can find the area of a rectangle, given the formula and the measurements of the rectangle’s sides. * Standard 4 – MA.6.A.3.5: Apply the commutative, associative and distributive properties to show that two expressions are equal. * Learning Objective 1 – Students can define the commutative, associative and distributive properties, and can verbalize which properties were used when viewing a set of equivalent expressions. * Learning Objective 2 – Students can use the distributive property to find the product of two numbers. * Learning Objective 3 – Students can use the commutative and associative properties to simplify numerical expressions using mental math.
The Unit will begin with a pretest of students’ background knowledge and familiarity with content in the standards being taught and assessed. The pretest and answer key follow.
Formative assessments are used so frequently in my classroom that they often “feel” like instruction. Following are just several of the “assessments in disguise” (formative assessments) that correspond to the learning objectives, standards and overall “Big Idea #3” of the Introduction to Algebra unit.
Formative Assessment 1
Standard #1 within Big Idea 3: MA.6.A.3.1: Write and evaluate mathematical expressions that correspond to given situations. Measureable objective being formatively assessed within standard #1: 1. Students can define and use correctly & conversationally the terms “variable, constant, algebraic expression and evaluate”. a. Formative Assessment - Assessing this objective will include a “who am I?” exercise, where students will be given stickers on their backs containing the new vocabulary words (one per student). I’ll give the kids about five minutes to walk around and talk to their classmates to try to find out “who they are” (which vocabulary word is on their backs). The students describing the term to the guessers are not allowed to use the term in their definition. Assessment occurs as I circulate & hear the conversations. Also – a...