Concepts Addressed in AIM for Algebra

Explore the detailed concepts addressed in AIM for Algebra:

  1. Signed Number Operations — Learning Objectives
  2. Patterns — Learning Objectives
  3. Variables and Expressions — Learning Objectives
  4. The Coordinate Plane — Learning Objectives
  5. Ratio and Proportion — Learning Objectives
  6. Inequalities — Learning Objectives

Signed Number Operations — Learning Objectives

Concept 1: Numbers Less Than Zero

  1. 1. Students identify signed numbers and number order. They plot signed numbers on a number line and compare their values.
  2. 2. Students become familiar with contextual situations that use integers.
  3. 3. Students apply knowledge of signed numbers in the context of elevation.
  4. 4. Students find the absolute value of numbers and compare absolute values.
  5. 5. Students identify the uses of the dash (-) in relation to subtraction and numbers less than zero.

Concept 2: Models to Illustrate Signed Number Operations

  1. 6. Students explore models that lend meaning to integer operations.
  2. 7. Students compare signed number operations and whole number operations.
  3. 8. Students generalize the rules for integer operations by observing the patterns created by doing integer operations.

Concept 3: Applying Signed Numbers

  1. 9. Students derive the same answer using different operations with signed numbers.
  2. 10. Students combine like terms and evaluate algebraic expressions using signed numbers Variables and expressions using signed numbers
  3. [↑ top ]

Patterns — Learning Objectives

Concept 1: Numerical Patterns and Sequences

  1. 1. Students identify patterns in numerical sequences.
  2. 2. Students analyze numerical patterns.
  3. 3. Students extend/expand numerical patterns and geometric representations of patterns.
  4. 4. Students understand and can write the recursive rule in words

Concept 2: Patterns Describing Numeric and Geometric Relationships

  1. 5. Students examine/analyze a t-chart describing a functional relationship arising from a geometric/graphic representation.
  2. 6. Students complete and create an input/output table based on geometric representations of a pattern.
  3. 7. Students generalize patterns in words and algebraic symbols.
  4. 8. Students distinguish between recursive rules and explicit rules to describe patterns.
  5. 9. Students examine number sequences or tables containing input and output values showing the relationship of the numbers and recognize a pattern.

Concept 3: Connecting Geometric and Algebraic Patterns

  1. 10. Students examine/analyze and describe the connection between a representation of a geometric pattern of growth and the algebraic symbols describing the pattern.
  2. 11. Students model figures of the pattern, create/complete tables with the pattern data, determine recursive rules and generalize the pattern (explicit rule) with algebraic notation and/or words.
  3. [↑ top ]

Variables and Expressions — Learning Objectives

Concept 1: Variables

  1. 1. Students use numbers from context in various combinations: reviewing units,properties of operations, and order of operations.
  2. 2. Students define and apply the definitions of variable, algebraic expression, term,constant term, and numerical coefficient.
  3. 3. Students write and simplify expressions by combining like terms, using the order of operations and the commutative, associative, and distributive properties.

Concept 2: Writing, Translating and Evaluating Algebraic Expressions

  1. 4. Students use variables to write and interpret algebraic expressions and to translate words into algebraic expressions.
  2. 5. Students interpret algebraic expressions and translate them into words.
  3. 6. Students evaluate expressions using substitution.

Concept 3: Creating Algebraic Expressions

  1. 7. Students use variables to create number games.
  2. 8. Students use algebraic expressions to set up word problems.
  3. [↑ top ]

The Coordinate Plane — Learning Objectives

Concept 1: Parts of the Coordinate Plane/Identifying/Locating

  1. 1. Students identify the vocabulary terms connected to the coordinate plane.
  2. 2. Students identify points located on a coordinate grid by naming their location(ordered pair).
  3. 3. Students locate points on a coordinate plane given the ordered pair.

Concept 2: The Equation of a Line–Graphing/Interpreting/Finding Slope

  1. 4. Students plot points on a plane that describe a linear pattern (function).
  2. 5. Students use points located on the graph of a straight line to determine the slope of the line.
  3. 6. Students identify/determine the equation that defines a line located on a coordinate plane.
  4. 7. Students use the slope of a line to determine its relation to another line.
  5. 8. Students graph a line on the coordinate plane given the equation of the line.

Concept 3: Using the Coordinate Plane in Algebra

  1. 9. Students graph two linear equations on the same grid to explore a solution strategy for systems of equations.
  2. [↑ top ]

Ratio and Proportion — Learning Objectives

Concept 1: Ratios – Comparing Quantities

  1. 1. Students recognize, describe and represent various comparisons in familiar real life situations.
  2. 2. Students recognize, represent and compute the relationship between two quantities using ratios, including unit ratios.
  3. 3. Students distinguish between the numeric value of a ratio and what it represents and use values to compare ratios.

Concept 2: Similarity and Scale

  1. 4. Students recognize similar figures.
  2. 5. Students use scale factors to compare relative sizes.
  3. 6.Students identify and find the relationships between similar figures using scale factors.

Concept 3: Proportions

  1. 7. Students use equivalent ratios to solve problems involving proportions.
  2. 8. Students determine unit rates to make comparisons.
  3. [↑ top ]

Inequalities — Learning Objectives

Concept 1: Basics of Inequalities

  1. 1. Students interpret and write inequalities using appropriate notation and symbols.
  2. 2. Using the number line, students represent and interpret solutions to inequalities as continuous intervals or discrete sets.

Concept 2: Inequalities in One Variable

  1. 4. Students represent and interpret inequalities resulting from combining inequalities including absolute value and other compound inequalities

Concept 3: Inequalities in Two Variables

  1. 5. Students interpret and sketch graphs of inequalities in two variables.
  2. 6. Student graph the solution set for a system of inequalities.
  3. [↑ top ]