Concepts Addressed in Aim for Algebra
Explore the detailed concepts addressed in Aim for Algebra:
- Signed Number Operations — Learning Objectives
- Patterns — Learning Objectives
- Variables and Expressions — Learning Objectives
- The Coordinate Plane — Learning Objectives
- Ratio and Proportion — Learning Objectives
- Inequalities — Learning Objectives
Signed Number Operations — Learning Objectives
Concept 1: Numbers Less Than Zero
- 1. Students identify signed numbers and number order. They plot signed numbers on a number line and compare their values.
- 2. Students become familiar with contextual situations that use integers.
- 3. Students apply knowledge of signed numbers in the context of elevation.
- 4. Students find the absolute value of numbers and compare absolute values.
- 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
- 6. Students explore models that lend meaning to integer operations.
- 7. Students compare signed number operations and whole number operations.
- 8. Students generalize the rules for integer operations by observing the patterns created by doing integer operations.
Concept 3: Applying Signed Numbers
- 9. Students derive the same answer using different operations with signed numbers.
- 10. Students combine like terms and evaluate algebraic expressions using signed numbers Variables and expressions using signed numbers
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Patterns — Learning Objectives
Concept 1: Numerical Patterns and Sequences
- 1. Students identify patterns in numerical sequences.
- 2. Students analyze numerical patterns.
- 3. Students extend/expand numerical patterns and geometric representations of patterns.
- 4. Students understand and can write the recursive rule in words
Concept 2: Patterns Describing Numeric and Geometric Relationships
- 5. Students examine/analyze a t-chart describing a functional relationship arising from a geometric/graphic representation.
- 6. Students complete and create an input/output table based on geometric representations of a pattern.
- 7. Students generalize patterns in words and algebraic symbols.
- 8. Students distinguish between recursive rules and explicit rules to describe patterns.
- 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
- 10. Students examine/analyze and describe the connection between a representation of a geometric pattern of growth and the algebraic symbols describing the pattern.
- 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.
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Variables and Expressions — Learning Objectives
Concept 1: Variables
- 1. Students use numbers from context in various combinations: reviewing units,properties of operations, and order of operations.
- 2. Students define and apply the definitions of variable, algebraic expression, term,constant term, and numerical coefficient.
- 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
- 4. Students use variables to write and interpret algebraic expressions and to translate words into algebraic expressions.
- 5. Students interpret algebraic expressions and translate them into words.
- 6. Students evaluate expressions using substitution.
Concept 3: Creating Algebraic Expressions
- 7. Students use variables to create number games.
- 8. Students use algebraic expressions to set up word problems.
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The Coordinate Plane — Learning Objectives
Concept 1: Parts of the Coordinate Plane/Identifying/Locating
- 1. Students identify the vocabulary terms connected to the coordinate plane.
- 2. Students identify points located on a coordinate grid by naming their location(ordered pair).
- 3. Students locate points on a coordinate plane given the ordered pair.
Concept 2: The Equation of a Line–Graphing/Interpreting/Finding Slope
- 4. Students plot points on a plane that describe a linear pattern (function).
- 5. Students use points located on the graph of a straight line to determine the slope of the line.
- 6. Students identify/determine the equation that defines a line located on a coordinate plane.
- 7. Students use the slope of a line to determine its relation to another line.
- 8. Students graph a line on the coordinate plane given the equation of the line.
Concept 3: Using the Coordinate Plane in Algebra
- 9. Students graph two linear equations on the same grid to explore a solution strategy for systems of equations.
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Ratio and Proportion — Learning Objectives
Concept 1: Ratios – Comparing Quantities
- 1. Students recognize, describe and represent various comparisons in familiar real life situations.
- 2. Students recognize, represent and compute the relationship between two quantities using ratios, including unit ratios.
- 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
- 4. Students recognize similar figures.
- 5. Students use scale factors to compare relative sizes.
- 6.Students identify and find the relationships between similar figures using scale factors.
Concept 3: Proportions
- 7. Students use equivalent ratios to solve problems involving proportions.
- 8. Students determine unit rates to make comparisons.
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Inequalities — Learning Objectives
Concept 1: Basics of Inequalities
- 1. Students interpret and write inequalities using appropriate notation and symbols.
- 2. Using the number line, students represent and interpret solutions to inequalities as continuous intervals or discrete sets.
Concept 2: Inequalities in One Variable
- 4. Students represent and interpret inequalities resulting from combining inequalities including absolute value and other compound inequalities
Concept 3: Inequalities in Two Variables
- 5. Students interpret and sketch graphs of inequalities in two variables.
- 6. Student graph the solution set for a system of inequalities.
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