MAT-HS Targeted Standards (A) Concept: Algebra (CED) Domain: Creating Expressions Cluster: Create equations that describe numbers or relationships
MAT-HS.A-CED.03* Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Student Learning Targets:
Knowledge Targets
I can
I can
Reasoning Targets
I can
I can
Skills (Performance) Targets
I can write and use a system of equations and/or inequalities to solve a real world problem.
I can use equations and inequalities to represent problem constraints and objectives (linear programming).
Product Targets
I can
I can
Proficiency Scale
Score
Description
Sample Activity
4.0
In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught
-
3.5
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
The student:
can write and use a system of equations and/or inequalities to solve a real world problem
can use equations and inequalities to represent problem constraints and objectives (linear programming)
The student exhibits no major errors or omissions.
Zach is a student, and he can work for at most 15 hours a week. He needs to earn at least $100 to cover his weekly expenses. His dog-walking job pays $5 per hour and his job as a car wash attendant pays $4 per hour. Write a system of inequalities to model the situation.
Solve the system: y ≤ 3x + 1, y > 4x –2
2.5
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0
There are no major errors or omissions regarding the simpler details and processes as the student:
The student:
can recognize and recall terminology such as:
equation, inequality
can graph a system, but can not interpret the results
can develop equations or inequalities, but do not understand what to do next
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
-
1.5
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
-
0.5
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
Alg II Solving Systems of Equations & Inequalities Proficiency Scale
Score
Description
Sample Activity
4.0
(advanced)
In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.
There are four boxes labeled A, B, C, and D. A is 3 times as heavy as B, B is 3 times as heavy as C, and C is 3 times as heavy as D. The weight of D is 12 times less than the combined weight of B and C. What are the weights of the four boxes?
Write your own linear programming situation where the solution point for maximum profit is (8,10).
3.5
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
(proficient)
The student can:
express the constraints (restrictions or limitations) on the variables in a contextual problem.
represent a contextual problem using an appropriate system of equations and/or inequalities.
determine whether the solution is reasonable, given the situation.
solve a problem using an appropriate system of equations and/or inequalities.
The student exhibits no major errors or omissions.
3x3 System:
A pizza shop sells combo meals. Two small pizzas, a liter of soda and a salad cost $14. One small pizza, a liter of soda, and 3 salads cost $15. Three small pizzas and a liter of soda cost $16. What is the cost of each item? (pizza, soda and salad)
Linear Programming:
Bob the Builder builds sheds. He uses 10 sheets of drywall and 15 pieces of lumber for a small shed and 15 sheets of drywall and 45 pieces of lumber for a large shed. He has available 60 sheets of drywall and 135 pieces of lumber. If Bob makes $390 profit on a small shed and $520 on a large shed, how many of each type of building should Bob build to maximize his profit?
2.5
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0
(progressing)
There are no major errors or omissions regarding the simpler details and processes as the student can:
recognize and recall specific terminology, such as:
linear equation
linear inequality
constraint
maximum/minimum
solution
feasible region
system of equations/inequalities
linear programming
solve a system when the graphs of the equations are given.
solve a system of equations using the substitution or elimination method.
determine the solution given a feasible region for a system of inequalities (Linear Programming)
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
A linear programming situation has been graphed below and a feasible region has been shaded. Use the following profit formula to determine which point will give the maximum profit. P=12x+15y
Solve the following system by using elimination/linear combination. (Check solution)
3x+4y=-3
2x+y=8
1.5
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0
(beginning)
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).
0.5
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0
Even with help, the student demonstrates no understanding or skill.
