Level 2 3 Level 4 5 Objective 13. Solve systems of -Limited to 2x2 systems of -No limit to solutions for 2x2 -No limit to coefficients and Topic extensions: equations. systems. solutions. -Solving 3 dimensional systems of linear linear equations -Integer coefficients for all -Extend topic to include 3x3 -Graphical representation of 2x2 equations. equations systems. systems -Graphical representation of the case of -Coefficients are integers and -All solutions to 3x3 systems kept no solution and infinite solutions for 3 solutions limited to integers and as integers. dimensional systems. common fractions (halves, -Systems given are in mixed -Specifying the vector solutions of an quarters, etc) linear formats infinite solution 3x3 system. -Systems are in same linear format 14. Solve real world -feasible regions limited to 3 -Feasible regions limited to 3 Brief diagnostic review of Topic extensions: with only one being oblique oblique lines or 4 lines (at most 2 topic -Modeling real-world scenarios as linear problems using systems -distinguish between points on being oblique) formats presented inequalities (e.g. animal dietary of inequalities. boundary lines and those inside -uniform formats presented requirements). the feasible region 15. Use linear Not Taught -Constraints given -No constraints given -No constraints given -No more than 3 constraints -All integer solutions -Non integer solutions likely programming to -Only one line as oblique -no limit to formats of lines real-world problems** -All integer solutions -compound inequalities often -feasible regions extended to uncommon quadrilaterals and pentagons -extend to discrete math with lattice points 16. Describe and Not Taught -Operations limited to 2x2 - Writing and solving systems of - Writing and solving systems of matrices by hand equations of 3x3 system using equations of 3x3 systems matrices perform operations on -Systems of equations limited to matrices on graphing utility - Use and application of Cramer’s Rule matrices. Solve a 2x2 systems using inverses - Use and application of -See the advantages of using matrices systems through Cramer’s Rule to solve systems Topic extensions:
Objective Level 2 3 Level 4 5 13. Solve systems of linear equations -Limited to 2x2 systems of equations. -Integer coefficients for all equations -Coefficients are integers and solutions limited to integers and common fractions (halves, quarters, etc) -Systems are in same linear format -No limit to solutions for 2x2 systems. -Extend topic to include 3x3 systems. -All solutions to 3x3 systems kept as integers. -Systems given are in mixed linear formats -No limit to coefficients and solutions. -Graphical representation of 2x2 systems Topic extensions: -Solving 3 dimensional systems of linear equations. -Graphical representation of the case of no solution and infinite solutions for 3 dimensional systems. -Specifying the vector solutions of an infinite solution 3x3 system. 14. Solve real world problems using systems of inequalities. -feasible regions limited to 3 with only one being oblique -distinguish between points on boundary lines and those inside the feasible region -Feasible regions limited to 3 oblique lines or 4 lines (at most 2 being oblique) -uniform formats presented Brief diagnostic review of topic formats presented Topic extensions: -Modeling real-world scenarios as linear inequalities (e.g. animal dietary requirements). 15. Use linear programming to real-world problems** Not Taught -Constraints given -No more than 3 constraints -Only one line as oblique -All integer solutions -No constraints given -All integer solutions -no limit to formats of lines -compound inequalities often -feasible regions extended to uncommon quadrilaterals and pentagons -extend to discrete math with lattice points -No constraints given -Non integer solutions likely 16. Describe and perform operations on matrices. Solve systems through Not Taught -Operations limited to 2x2 matrices by hand -Systems of equations limited to a 2x2 systems using inverses - Writing and solving systems of equations of 3x3 system using matrices on graphing utility - Use and application of Cramer’s Rule - Writing and solving systems of equations of 3x3 systems matrices - Use and application of Cramer’s Rule -See the advantages of using matrices to solve systems Topic extensions:
Algebra_2_Level_Distinctions_May_21_2012.docx