Poyen School
Poyen School Curriculum K - 12 2007-2008

Mathematics - Algebraic Connections


Probability/Statistics

    Counting techniques: Number of outcomes
The learner will be able to apply counting techniques to determine the number of outcomes: 1. Tree diagram 2. Fundamental Counting Principle 3. Permutations (with and without repetition) 4. Combinations.
Strand Bloom's Scope Hours Source
Data: Evaluate, Predict, Probability Master 1.0 2004 Arkansas Mathematics Frameworks PS.1.AC.1
Instructional Resources
- Add to lesson, Teacher made worksheets [Teaching Strategies].  
  
    Simple probability experiments
The learner will be able to conduct and interpret simple probability experiments using: 1. Manipulatives (spinners, dice, cards, coins) 2. Simulations (Using random number tables, graphing calculators, or computer software).
Strand Bloom's Scope Hours Source
Data: Evaluate, Predict, Probability Master 1.0 2004 Arkansas Mathematics Frameworks PS.1.AC.2
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 2.6 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 2.7 [Textbook].  
- Activity, Class experiments [Teaching Strategies].  
  
    Theoretical & Experimental Probabili
The learner will be able to compute and display theoretical and experimental probability including the use of Venn diagrams. 1. Simiple 2. Complementary 3. Compound (mutually exclusive, inclusive, independent and dependent events).
Strand Bloom's Scope Hours Source
Data: Evaluate, Predict, Probability Master 1.0 2004 Arkansas Mathematics Frameworks PS.1.AC.3
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 2.6 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 2.7 [Textbook].  
  
    Apply probability theory
The learner will be able to apply probability to real-world situations such as weather prediction, game theory, fair division, insurance tables, and election theory.
Strand Bloom's Scope Hours Source
Data: Evaluate, Predict, Probability Master 1.0 2004 Arkansas Mathematics Frameworks PS.1.AC.4
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 2.6 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 2.7 [Textbook].  
  
    Graphical and Tabular Data Display
The learner will be able to interpret and evaluate, with and without appropriate technology, graphical and tabular data displays for 1. Consistency with the data 2. Appropriateness of type of graph or data display. 3. Scale 4. Overall message.
Strand Bloom's Scope Hours Source
Data: Evaluate, Predict, Probability Master 1.0 2004 Arkansas Mathematics Frameworks PS.1.AC.5
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 1.1 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 1.4 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 1.6 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 8.5 [Textbook].  
  

Linear Functions

    Relationship: independent/dependent
The learner will be able to create, given a graph without an explicit formula, a written or oral interpretation of the relationship between the independent and dependent variables.
Strand Bloom's Scope Hours Source
Analyze functions Master 1.0 2004 Arkansas Mathematics Frameworks LF.2.AC.1
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 8.3 [Textbook].  
  
    Graph:Independent/Dependent Relationship
The learner will be able to create, given a situation, a graph that models the relationship between the independent and dependent variables.
Strand Bloom's Scope Hours Source
Analyze functions Master 1.0 2004 Arkansas Mathematics Frameworks LF.2.AC.2
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 8.4 [Textbook].  
  
    Domain/range/independent/dependent
The learner will be able to determine the independent and dependent variables, domain and range of a relation from and algebraic expression, graph, set of ordered pairs, or table of data.
Strand Bloom's Scope Hours Source
Analyze functions Master 1.0 2004 Arkansas Mathematics Frameworks LF.2.AC.3
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Independent/dependent variables; lesson 8.3 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Domain/range: lesson 8.1 [Textbook].  
  
    Interpret: Slope and intercepts
The learner will be able to interpret the rate of change (slope) and intercepts within the context of everyday life (Example: Telephone charges based on base rate (y-intercept) plus rate per minute (slope)).
Strand Bloom's Scope Hours Source
Analyze functions Master 1.0 2004 Arkansas Mathematics Frameworks LF.2.AC.4
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 5.1 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 4.6 [Textbook].  
  
    Calculate slope
The learner will be able to calculate the slope given: 1. Two points 2. A graph of a line 3. An equation of a line.
Strand Bloom's Scope Hours Source
Analyze functions Master 1.0 2004 Arkansas Mathematics Frameworks LF.2.AC.5
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 5.1 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 5.2 [Textbook].  
  
    Lines: Parallel/perpendicular,/neither
The learner will be able to determine, using slope, whether a pair of lines are parallel, perpendicular, or neither.
Strand Bloom's Scope Hours Source
Analyze functions Master 1.0 2004 Arkansas Mathematics Frameworks LF.2.AC.6
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 11.1 [Textbook].  
  
    Write an equation
The learner will be able to write an equation given: 1. Two points 2. A point and y-intercept 3. An x-intercept and y-intercept 4. A point and slope 5. A table of data 6. The graph of a line.
Strand Bloom's Scope Hours Source
Analyze functions Master 1.0 2004 Arkansas Mathematics Frameworks LF.2.AC.7
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 5.2 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Lesson 5.3 [Textbook].  
  
    Piece-wise and step functions
The learner will be able to graph, with and without appropriate technology, functions defined as piece-wise and step.
Strand Bloom's Scope Hours Source
Analyze functions Master 1.0 2004 Arkansas Mathematics Frameworks LF.2.AC.8
Instructional Resources
- Add to lesson, Algebra 2 book: lesson 2.7 [Teaching Strategies].  
  

Solving Equations & Inequalities

    Multi-step equations/inequalities
The learner will be able to solve, with and without appropriate technology, multi-step equations and inequalities with rational coefficients numerically, algebraically, and graphically.
Strand Bloom's Scope Hours Source
Equations, Inequalities & their Sys Master 1.0 2004 Arkansas Mathematics Frameworks SEI.3.AC.1
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Solve equations: lesson 4.2; lesson 4.8 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Solve inequalities: lesson 6.5 [Textbook].  
  
    Systems of equations/inequalities
The learner will be able to solve, with and wtihout appropriate technology, systems of two linear equations and systems of two inequalities numerically, algebraically, and graphically.
Strand Bloom's Scope Hours Source
Equations, Inequalities & their Sys Master 1.0 2004 Arkansas Mathematics Frameworks SEI.3.AC.2
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Systems of equations [Textbook].  lesson 6.1, lesson 6.2, lesson 6.3, lesson 6.4
- Discovering Algebra, Key Curriculum Press, Systems of inequalities: lesson 6.6, lesson 6.7 [Textbook].  
  
    Literal equations
The learner will be able to solve linear formulas and literal equations for a specified variable.
Strand Bloom's Scope Hours Source
Equations, Inequalities & their Sys Master 1.0 2004 Arkansas Mathematics Frameworks SEI.3.AC.3
Instructional Resources
- Add to lesson, Algebra I book: section 3.7 [Teaching Strategies].  
  
    Distance, midpoint, Pythagorean Theorem
The learner will be able to use, with and without appropriate technology, coordinate geometry to represent and solve problems including midpoint, length of a line segment and Pythagorean Theorem.
Strand Bloom's Scope Hours Source
Equations, Inequalities & their Sys Master 1.0 2004 Arkansas Mathematics Frameworks SEI.3.AC.4
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Distance formula: lesson 11.6 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Midpoint formula: lesson 11.2 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Pythagorean theorem: lesson 11.4 [Textbook].  
  
    Affects of changing dimensions
The learner will be able to determine and describe, with and without appropriate technology, the resulting change in the perimeter, area, and volume when one or more dimensions change (apply this idea in solving real world problems).
Strand Bloom's Scope Hours Source
Equations, Inequalities & their Sys Master 1.0 2004 Arkansas Mathematics Frameworks SEI.3.AC.5
Instructional Resources
- Add to lesson, Teacher made worksheet [Teaching Strategies].  
  
    Apply linear/piece-wise/step functions
The learner will be able to apply linear, piece-wise and step functions to real world situations that involve a combination of rates, proportions, and percents such as sales tax, simple interest, social security, constant depreciation and appreciaton, arithmetic sequences, constant rate of change, income taxes, postage, utility bills, commission, and traffic tickets.
Strand Bloom's Scope Hours Source
Equations, Inequalities & their Sys Master 1.0 2004 Arkansas Mathematics Frameworks SEI.3.AC.6
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Rates: lesson 3.1 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Proportions: lesson 2.1; lesson 2.3 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Percent: lesson 2.2 [Textbook].  
  

Non-Linear Functions

    Factor polynomials
The learner will be able to factor polynomials: 1. Greatest common factor 2. Binomials (difference of squares) 3. Trinomials 4. Combinations of above.
Strand Bloom's Scope Hours Source
Nonlinear: solve, compare, transform Master 1.0 2004 Arkansas Mathematics Frameworks NF.4.AC.1
Instructional Resources
- Discovering Algebra, Key Curriculum Press, GCF: lesson 5.4 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Difference of squares: [Textbook].  Algebra A/B book lesson 10.7
- Discovering Algebra, Key Curriculum Press, Trinomials: lesson 10.4 [Textbook].  
- Add to lesson, Combinations of factoring: teacher made worksheet [Teaching Strategies].  
  
    Operations with radical expressions
The learner will be able to simplify, add, subtract and multiply radical expressions.
Strand Bloom's Scope Hours Source
Nonlinear: solve, compare, transform Master 1.0 2004 Arkansas Mathematics Frameworks NF.4.AC.2
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 11.5 [Textbook].  
  
    Solve quadratic equations
The learner will be able to solve, with and without appropriate technology, quadratic equations with real number solutions using factoring and the quadratic formula.
Strand Bloom's Scope Hours Source
Nonlinear: solve, compare, transform Master 1.0 2004 Arkansas Mathematics Frameworks NF.4.AC.3
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Solve quadratic equations: lesson 10.1 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Quadratic formula: lesson 10.7 [Textbook].  
  
    Domain/range/independent/dependent
The learner will be able to determine the independent and dependent variables, domain and range of a relation from algebraic equations, graphs, sets of ordered pairs, or tables of data.
Strand Bloom's Scope Hours Source
Nonlinear: solve, compare, transform Master 1.0 2004 Arkansas Mathematics Frameworks NF.4.AC.4
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Independent/dependent: lesson 8.3 [Textbook].  
- Discovering Algebra, Key Curriculum Press, Domain/range: lesson 4.4 [Textbook].  
  
    Apply nonlinear functions
The learner will be able to identify and apply nonlinear functions to real world situations such as acceleration, area, volume, population, bacteria, compound interest, percent depreciation and appreciation, amortization, geometric sequences, etc.
Strand Bloom's Scope Hours Source
Nonlinear: solve, compare, transform Master 1.0 2004 Arkansas Mathematics Frameworks NF.4.AC.5
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 8.5 [Textbook].  
  
    Function families
The learner will be able to recognize function families including vertical shifts, horizontal shifts, and reflections over the x-axis.
Strand Bloom's Scope Hours Source
Nonlinear: solve, compare, transform Master 1.0 2004 Arkansas Mathematics Frameworks NF.4.AC.6
Instructional Resources
- Discovering Algebra, Key Curriculum Press, Lesson 9.2 [Textbook].  
  

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