Saturday, July 13, 2024, 12:11 PM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
Glossary: MAT-HS: Algebra

MAT-HS.A-CED.02.a

MAT-HS Targeted Standards
(A) Concept: Algebra
(CED) Domain: Creating Expressions
Cluster: Create equations that describe numbers or relationships

MAT-HS.A-CED.02.a Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can create an equation in two or more variables to represent relationships between quantities.
  • I can graph equations in two variables on a coordinate plane and label the axes and scales.

Product Targets

  • 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 including

  • construct linear functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (A.F.LE.2)
-
  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:

  • create linear equations in two or more variables to represent relationships between quantities  

  • graph equations on coordinate axes with labels and scales



The student exhibits no major errors or omissions.

Suppose $15 US is worth $150 Mexican pesos. What is an equation that relates US dollars x to Mexican pesos y?


The cost to rent a car is $50 plus $0.25 per mile driven.  Write and graph an equation to represent 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

There are no major errors or omissions regarding the simpler details and processes as the student:

  • recognizes and recalls specific terminology, such as:  (A.SSE.1)

               linear


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 Create and Graph Quadratic Functions 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.

Given two parabolic graphs, create the equations for both functions, graph them, and describe the similarities and differences.


Function 1:  the turning point is (2,-3) and another random point on the graph is (4,5)  

Function 2:  the turning point is (2,-3) and another random point on the graph is (5,6)

 

  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:
  • create quadratic equations in two variables given information about the function.

The student exhibits no major errors or omissions.
Given the x-intercepts of 6 and -2, write a quadratic function that would also pass through the point (1,5).

 

  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:
    • quadratic
  • identify the graph and/or equation of quadratic functions two variables on a coordinate plane and label the axes and scales.

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

 

Given the graph below, write the quadratic function.

 

 

 

  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.  

Alg II Create and Graph Exponential Functions 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.

Given two exponential graphs, create the equations for both functions, graph them, and describe the similarities and differences.
Function 1:  contains the point (0, 4) and (1, 12)  

Function 2:  contains the point (0, 4) and (1, 2)

 

  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:
  • create exponential equations in two variables given information about the function.

The student exhibits no major errors or omissions.
 

Given the points (0, 3) and (-1, 6), create the exponential equation.

 

  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:
    • exponential
  • identify the graph and/or equation of exponential functions in two variables on a coordinate plane and label the axes and scales.

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

 

Given the graph below, write the exponential function.

 

 

  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. -

Alg II Create and Graph Polynomial Functions 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.  

Given two polynomial graphs, create the equations for both functions, graph them, and describe the similarities and differences.


Function 1:  the zeros are  1, 2, 3, and another random point on the graph is (0,-6)

 

Function 2:  the zeros are 1, 2,3, and another random point on the graph is (0,18)

 

  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:
  • create polynomial equations in two variables on a coordinate plane and label the axes and scales.
The student exhibits no major errors or omissions.
 

Given the x-intercepts of -4, -1 and 2, write a polynomial function that would also pass through the point (0,-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

(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:
    • polynomial
  • identify the graph and/or equation of polynomial functions in two variables on a coordinate plane and label the axes and scales.

 

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

Given the graph below, write the polynomial function.

 


 

  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

  • coordinate plane
  • scale

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 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.  

Resources

Web

Vocab

  • linear programming

MAT-HS.A-CED.04

MAT-HS Targeted Standards
(A) Concept: Algebra
(CED) Domain: Creating Expressions
Cluster: Create equations that describe numbers or relationships

MAT-HS.A-CED.04 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

For example, rearrange Ohm’s law V = IR to highlight resistance R.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can solve for (isolate) a specific variable.
  • I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
  • I can solve multi-variable formulas or literal equations for a specific variable.

Product Targets

  • I can
  • I can

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.

Solve for h:  

3h+g=5h-hg

 

  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:

  • solve multi-variable formulas or literal equations for a specific variable.

The student exhibits no major errors or omissions.

Solve the following equation for b:

A = 1/2h (b+c)


Solve the following equation for a:

Solve the following equation for b:

  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:
  • identify appropriate inverse operations.
  • solve a simple linear equation for y.

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


Solve the following equation for y:

2x - 3y = 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

  • literal equation