MAT-HS.A-CED.03

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 and application 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

(advanced)

In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught
  • 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.   Write the system of equations that resemble the following constraints.


  • You have 140 tomatoes and 13 onions left over from your garden.  You want to use these to make jars of tomato sauce and jars of salsa to sell at the farm stand.  A jar of tomato sauce requires 10 tomatoes and 1 onion, and a jar of salsa requires 5 tomatoes and ¼ onion.  The owner of the farm stand wants you to have at least 3 times as many jars of tomato sauce as jars of salsa.  Write the system of inequalities that models this situation.


  • A clothing manufacturers has 1,000 yards of cotton to make shirts and pajamas.  A shirt requires 1 yard of fabric and a pair of pajamas requires 2 yards of fabric.  It takes 2 hours to make a shirt and 3 hours to make the pajamas, and there are 1,600 hours available to make the clothing. Write inequalities for the limits on the constraints.

  • A potter is making cups and plates.  It takes her 6 min. to make a cup and 3 min. to make a plate.  Each cup uses ¾ lb. of clay, and each plate uses 1 lb. of clay.  She has 20 hours available to make the cups and plates and has 250 lbs. of clay. Write inequalities for limits on the constraints.
  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

(beginner)

The student:

  • can write a system of equations and/or inequalities to solve an application problem.

  • can use equations and inequalities to represent problem constraints and objectives (linear programming).

  • can develop equations or inequalities

 

 



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.  

  • Your family is planning a 7 day trip to Texas.  You estimate that it will cost $275 per day in San Antonio and $400 per day in Dallas.  Your total budget is $2300.  (How many days would be spent in each city?  If you want to assess REI.06 as well).  Write a system of equations to model the situation.

  • Andy’s Cab Service charges a $6 fee plus $0.50 per mile.  His twin brother Randy starts a revival business where he charges $0.80 per mile but does not charge a fee.  (Where would Andy and Randy’s rates be the same?  If you want to assess REI.06 as well).  Write the system of equations that models this situation.

  • Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second job, she works as a tutor and makes $12 per hour. One week she worked 30 hours and made $268. (How many hours did she spend at each job? If you want to assess REI.06 as well) Write the system of equations that relate to the situation.


  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:

The student:

  • can recognize and recall terminology such as:

    • equation,

    • inequality
    • operation keywords (sum, difference, more than....)
  • can recognize the constraints in a particular problem, but not use them

  • can identify the variable in a situation


However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

What are the constraints (restrictions) of the following problem:

  • A customer hires a caterer to prepare food for a party for 40 people.  They have $120 to spend on the food and would like for there to be both sandwiches and pasta.  A $40 pan of pasta contains 10 servings and a $10 sandwich tray contains 5 servings.  The caterer must prepare enough food so each person receives one serving of either food.  

Identify the variables in the following situation:

  • The manager of a bookstore in the mall placed some hardcover books and some paperback books on a table for the “sidewalk sale.” Hardcover books cost $14.95 and paperback books cost $4.95. Mary bought 6 books for $49.70.

  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, 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.  

Resources

Web

Vocab

  • linear programming

» MAT-HS: Algebra