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MAT-HS.A-CED

Domains are larger groups of related standards. So the Domain Score is a calculation of all the related standards. So click on the standard name below each Domain to access the learning targets and proficiency scales for each Domain's related standards.

Domain (CED)

Creating Equations

  • Create equations that describe numbers or relationships

Domain Description

An equation is a statement of equality between two expressions, often viewed as a question asking for which values of the variables the expressions on either side are in fact equal. These values are the solutions to the equation. An identity, in contrast, is true for all values of the variables; identities are often developed by rewriting an expression in an equivalent form.

The solutions of an equation in one variable form a set of numbers; the solutions of an equation in two variables form a set of ordered pairs of numbers, which can be plotted in the coordinate plane. Two or more equations and/or inequalities form a system. A solution for such a system must satisfy every equation and inequality in the system.

An equation can often be solved by successively deducing from it one or more simpler equations. For example, one can add the same constant to both sides without changing the solutions, but squaring both sides might lead to extraneous solutions. Strategic competence in solving includes looking ahead for productive manipulations and anticipating the nature and number of solutions.

Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of x + 1 = 0 is an integer, not a whole number; the solution of 2x + 1 = 0 is a rational number, not an integer; the solutions of x² – 2 = 0 are real numbers, not rational numbers; and the solutions of x² + 2 = 0 are complex numbers, not real numbers.

The same solution techniques used to solve equations can be used to rearrange formulas. For example, the formula for the area of a trapezoid, A = ((b1+b2)/2)h, can be solved for h using the same deductive process. Inequalities can be solved by reasoning about the properties of inequality. Many, but not all, of the properties of equality continue to hold for inequalities and can be useful in solving them.

Connections to Functions and Modeling. Expressions can define functions, and equivalent expressions define the same function. Asking when two functions have the same value for the same input leads to an equation; graphing the two functions allows for finding approximate solutions of the equation. Converting a verbal description to an equation, inequality, or system of these is an essential skill in modeling.

Standards in this Domain

  • MAT-HS.A-CED.01 - Create equations and inequalities in one variable and use them to solve problems.  Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
  • MAT-HS.A-CED.02 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • 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.
  • 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.

MAT-HS.A-CED.01

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

MAT-HS.A-CED.01 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

 

This standard is divided into parts.  Click on these links to see specific proficiency scales.

MAT-HS.A-CED.01.a

MAT-HS.A-CED.01.b

MAT-HS.A-CED.01.c

MAT-HS.A-CED.01.d

 

MAT-HS.A-CED.01.a

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

MAT-HS.A-CED.01.a Create and solve linear equations in one variable.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can create a linear equation or inequality given a situation or set of data.

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

  • Write an equation of a parabola that has two x-intercepts and a minimum vertex.

  • Create a rational equation given a situation or set or data
  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

Can create equations and inequalities in one variable and use them to solve problems (linear only)


The student exhibits no major errors or omissions.

  • An online music club sells compact discs for $13.95 each plus $1.95 shipping and handling per order.  Maria’s total bill was $85.65.  Create an equation to model this situation.  Solve your equation to determine how many compact discs were sold.

  • Suppose you are working for a trucking company. Your job is to load a truck with at least 5000 lb of freight. You have loaded 2395 lb of freight, but you have to unload 50 lb that was loaded by mistake. Write and solve an inequality to find how many more pounds you need to load.

  • Which kind of function best models the data in the table? Write an equation to model the data.  

x

y

0

5

1

7

2

9

3

11
  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

  • correctly identifies whether the relationship is linear or  exponential.

  • writes the general equations for linear and exponential functions.

  • pick out relevant information in a contextual problem.

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).

 

Resources

Web

Vocab

  • linear equations
  • quadratic equations
  • rational equations
  • exponential
  • equations
  • inequalities

MAT-HS.A-CED.01.b

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

MAT-HS.A-CED.01.b Create and solve exponential equations in one variable

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can 

Product Targets

  • 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.

 

 
  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:

The student exhibits no major errors or omissions.

  
  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:

  •  

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

(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

MAT-HS.A-CED.01.c

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

MAT-HS.A-CED.01.c Create and solve linear inequalities in one variable.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can create a linear equation or inequality given a situation or set of data.

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

  • Write an equation of a parabola that has two x-intercepts and a minimum vertex.

  • Create a rational equation given a situation or set or data
  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

Can create equations and inequalities in one variable and use them to solve problems (linear only)


The student exhibits no major errors or omissions.

  • An online music club sells compact discs for $13.95 each plus $1.95 shipping and handling per order.  Maria’s total bill was $85.65.  Create an equation to model this situation.  Solve your equation to determine how many compact discs were sold.

  • Suppose you are working for a trucking company. Your job is to load a truck with at least 5000 lb of freight. You have loaded 2395 lb of freight, but you have to unload 50 lb that was loaded by mistake. Write and solve an inequality to find how many more pounds you need to load.

  • Which kind of function best models the data in the table? Write an equation to model the data.  

x

y

0

5

1

7

2

9

3

11
  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

  • correctly identifies whether the relationship is linear or  exponential.

  • writes the general equations for linear and exponential functions.

  • pick out relevant information in a contextual problem.

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).

Resources

Web

Vocab

  • linear equations
  • quadratic equations
  • rational equations
  • exponential
  • equations
  • inequalities

MAT-HS.A-CED.01.d

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

MAT-HS.A-CED.01.d Create and solve exponential inequalities in one variable

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can 

Product Targets

  • 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.

 

 
  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:

The student exhibits no major errors or omissions.

  
  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:

  •  

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

(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

MAT-HS.A-CED.01.e

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

MAT-HS.A-CED.01.e Create quadratic equations

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can 

Product Targets

  • 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.  
  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 one variable and use them to solve problems.       
The student exhibits no major errors or omissions.		  

A square has an unknown side length of x.  A rectangle has a side length that is four feet longer than the square and a width that is two feet shorter than the square.  The areas of both the square and the rectangle are equal.  Find the side length of the square.

 
  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
    • equation
  • create the equation; however, is unable to solve.
  • solve a quadratic equation.
 
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

What is the expression that represents the volume of the following prism?


 
  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

MAT-HS.A-CED.01.f

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

MAT-HS.A-CED.01.e Create simple rational equations

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can 

Product Targets

  • 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.  
  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 simple rational equations in one variable and use them to solve problems.
The student exhibits no major errors or omissions.		   

Source  Illustrative Math: Basketball

Chase and his brother like to play basketball. About a month ago they decided to keep track of how many games they have each won. As of today, Chase has won 18 out of the 30 games against his brother.

  1. How many games would Chase have to win in a row in order to have a 75% winning record?
  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:
    • Solution
    • Equation
    • Rational Equation
    • Inverse operations
  • solve a linear equation.
  • solve a quadratic equation.
  • solve a simple rational equation.
 However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Solve:  




Solve: 0.25(x+10)=14

 
  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

MAT-HS.A-CED.01.g

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

MAT-HS.A-CED.01.g Create exponential equations

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can 

Product Targets

  • 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.  
  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 one variable and use them to solve problems.
The student exhibits no major errors or omissions.		  

During normal breathing, about 12% of the air in the lungs is replaced after one breath. Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL. How much of the original air is present after 240 breaths?

The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?

 
  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
    • Decay
    • Growth
    • Rate
    • Equation
    • Annually
    • Semi-Annually
    • Quarterly
    • Compounded
  • create the equation; however, is unable to solve.
  • solve a quadratic equation.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Solve:

50 = 2(3)x
  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

MAT-HS.A-CED.02

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

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

 

This standard is divided into parts.  Click on these links to see specific proficiency scales.

MAT-HS.A-CED.02.a

MAT-HS.A-CED.02.b

 

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

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