Wednesday, May 29, 2024, 3:59 PM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
Glossary: MAT-HS: Algebra

MAT-HS.A-APR.01

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Arithmetic with Polynomials and Rational Expressions
Cluster: Perform arithmetic operations on polynomials

MAT-HS.A-APR.01 Add, subtract, and multiply polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.

 

Student Learning Targets:

Knowledge Targets

  • I can identify polynomials.

Reasoning Targets

  • I can recognize how closure applies under these operations.
  • I can

Skills (Performance) Targets

  • I can add, subtract, and multiply polynomials and recognize how closure applies under these operations.

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. Shannon, a cabinetmaker, started out with a block of wood, and then she hollowed out the center of the block.  The dimensions of the block and the cutout is shown below.
    • Write the volume of the original block, and the volume of the hole. (ignore units for this problem)

    • Write the polynomial for the volume of the wood remaining.

  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:
  • add, subtract, and multiply polynomials.
  • recognize that when two polynomials are added, subtracted, or multiplied, a polynomial is the result.
The student exhibits no major errors or omissions.

Simplify the following:

  • (2x2+3x+5)+(5x3-9x-8)
  • (x4+3x3-x2)-(4x3+8)

  • (x+2)(5x2-7x+10)

  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
    • trinomial
    • binomial
    • term
  • combine like terms.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 

Simplify the following:

  • 2x2+7x-9+3x2+5x-10

  • (2x+3)(4x-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

  • Polynomial

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.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

MAT-HS.A-REI.02

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain the reasoning

MAT-HS.A-REI.02 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can solve simple rational and radical equations in one variable and provide examples of how extraneous solutions arise.

Product Targets

  • I can
  • I can

Alg II Solve Radical Equations 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 the following equation:
  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 a radical equation and identify an extraneous solution.
  • provide examples of how extraneous solutions to a radical equation arise.
The student exhibits no major errors or omissions.

Solve the following equations:

 

 

  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:
    • radical
    • radicand
    • index
    • inverse operations
    • extraneous solution
  • identify an extraneous solution to a radical equation when given possible solutions.
     However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 


Solve the following equations:

 

 

 

 

  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 Solve Rational Equations 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.

 

Describe the error in the following work:

 

  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 a rational equation and recognize an extraneous solution.
The student exhibits no major errors or omissions.

 

Solve the following rational equation for r  and check for extraneous solutions:


 

  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:
    • rational equation
    • denominator
    • extraneous solution
  • solve simple rational equations.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 

Solve the following rational equation for n:

 

 

 

 

  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-REI.03

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain the reasoning

MAT-HS.A-REI.03 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. .

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 check the solution.
  • I can set a polynomial equal to zero and solve by factoring, quadratic formula, graphing, linear combinations, and substitution.
  • I can solve for (isolate) a specific variable.
  • I can write a linear system.
  • I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
  • I can check the solution.
  • I can solve a quadratic.
  • I can multiply and factor polynomials.
  • I can solve a linear inequality.
  • I can graph a linear inequality.
  • I can solve a system of linear inequalities.
  • I can graph a system of linear inequalities.
  • I can check the solution of the system.
  • I can solve a linear system (substitution, linear combination, graphically).
  • I can write a linear system.
  • I can identify the number of solutions of a linear system.
  • I can identify the most efficient method to solve a system.
  • I can check the solution of the system.
  • I can solve linear equations in one variable, including equations with coefficients represented by letters**.
  • I can solve linear inequalities in one variable, including inequalities with coefficients represented by letters**.

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

|3c+4|=6      

|x+3|+2<5
  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:

o solves linear equations with one variable:

    -Additive Inverse

    -Multiplicative Inverse

    -Distributive Property

    -Combine like terms

    -Proportions

**including special cases of no solution, infinitely many solutions

o solve and graph the solution set of linear inequalities with one variable:

    -Apply the properties of linear equation

    -Multiplicative Inverse of negative coefficients


The student exhibits no major errors or omissions.

o  3(h-4)=-1224-6h+2h

o  52c-3=37c+4

o  -67y-642

o  Solve for x: ax+bc=d

o  -4<k+3<8

o   Solve.   3x + 5 = 3x – 8;        2(3x+4) = 6x + 8

o   5y + 7 < -3    or    3y - 2 > 13

  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:

o  demonstrates basics processes (HS.A-REI.01)

    -one-step equations/inequalities

    -two-step equations/inequalities


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

o  3x=14

o  -3x+5-2x=10

o  x2=83

o  4x-17

o  Solve for x: x+y=c

  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

MAT-HS.A-REI.03a

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain the reasoning

MAT-HS.A-REI.03a Solve linear equations in one variable, including equations with coefficients represented by letters. .

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 check the solution.
  • I can set a polynomial equal to zero and solve by factoring, quadratic formula, graphing, linear combinations, and substitution.
  • I can solve for (isolate) a specific variable.
  • I can write a linear system.
  • I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
  • I can check the solution.
  • I can solve a quadratic.
  • I can multiply and factor polynomials.
  • I can solve a linear inequality.
  • I can graph a linear inequality.
  • I can solve a system of linear inequalities.
  • I can graph a system of linear inequalities.
  • I can check the solution of the system.
  • I can solve a linear system (substitution, linear combination, graphically).
  • I can write a linear system.
  • I can identify the number of solutions of a linear system.
  • I can identify the most efficient method to solve a system.
  • I can check the solution of the system.
  • I can solve linear equations in one variable, including equations with coefficients represented by letters**.
  • I can solve linear inequalities in one variable, including inequalities with coefficients represented by letters**.

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

|3c+4|=6      

|x+3|+2<5
  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:

o solves linear equations with one variable:

    -Additive Inverse

    -Multiplicative Inverse

    -Distributive Property

    -Combine like terms

    -Proportions

**including special cases of no solution, infinitely many solutions

o solve and graph the solution set of linear inequalities with one variable:

    -Apply the properties of linear equation

    -Multiplicative Inverse of negative coefficients


The student exhibits no major errors or omissions.

o  3(h-4)=-1224-6h+2h

o  52c-3=37c+4

o  -67y-642

o  Solve for x: ax+bc=d

o  -4<k+3<8

o   Solve.   3x + 5 = 3x – 8;        2(3x+4) = 6x + 8

o   5y + 7 < -3    or    3y - 2 > 13

  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:

o  demonstrates basics processes (HS.A-REI.01)

    -one-step equations/inequalities

    -two-step equations/inequalities


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

o  3x=14

o  -3x+5-2x=10

o  x2=83

o  4x-17

o  Solve for x: x+y=c

  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

MAT-HS.A-REI.03b

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain the reasoning

MAT-HS.A-REI.03b Solve linear inequalities in one variable, including equations with coefficients represented by letters. .

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 check the solution.
  • I can set a polynomial equal to zero and solve by factoring, quadratic formula, graphing, linear combinations, and substitution.
  • I can solve for (isolate) a specific variable.
  • I can write a linear system.
  • I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
  • I can check the solution.
  • I can solve a quadratic.
  • I can multiply and factor polynomials.
  • I can solve a linear inequality.
  • I can graph a linear inequality.
  • I can solve a system of linear inequalities.
  • I can graph a system of linear inequalities.
  • I can check the solution of the system.
  • I can solve a linear system (substitution, linear combination, graphically).
  • I can write a linear system.
  • I can identify the number of solutions of a linear system.
  • I can identify the most efficient method to solve a system.
  • I can check the solution of the system.
  • I can solve linear equations in one variable, including equations with coefficients represented by letters**.
  • I can solve linear inequalities in one variable, including inequalities with coefficients represented by letters**.

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

|3c+4|=6      

|x+3|+2<5
  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:

o solves linear equations with one variable:

    -Additive Inverse

    -Multiplicative Inverse

    -Distributive Property

    -Combine like terms

    -Proportions

**including special cases of no solution, infinitely many solutions

o solve and graph the solution set of linear inequalities with one variable:

    -Apply the properties of linear equation

    -Multiplicative Inverse of negative coefficients


The student exhibits no major errors or omissions.

o  3(h-4)=-1224-6h+2h

o  52c-3=37c+4

o  -67y-642

o  Solve for x: ax+bc=d

o  -4<k+3<8

o   Solve.   3x + 5 = 3x – 8;        2(3x+4) = 6x + 8

o   5y + 7 < -3    or    3y - 2 > 13

  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:

o  demonstrates basics processes (HS.A-REI.01)

    -one-step equations/inequalities

    -two-step equations/inequalities


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

o  3x=14

o  -3x+5-2x=10

o  x2=83

o  4x-17

o  Solve for x: x+y=c

  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

MAT-HS.A-REI.04

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain the reasoning

MAT-HS.A-REI.04 

Solve quadratic equations in one variable.

 

a.  Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions.

 

(+) Derive the quadratic formula from this form.

 

b.  Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can explain why taking the square root of both sides of an equation can yield two solutions.

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 check the solution.
  • I can solve for (isolate) a specific variable.
  • I can solve a quadratic.
  • I can multiply and factor polynomials.
  • I can solve quadratic equations in one variable.
  • I can transform a quadratic equation to an equation in the form (x-p)2=q by completing the square.
  • I can derive the quadratic formula by completing the square on a quadratic equation.
  • I can solve quadratic equations in one variable by simple inspection, taking the square root, factoring, and completing the square.
  • I can use the quadratic formula to solve any quadratic equation, recognizing the formula produces all complex solutions and write the solutions in the form a ± bi , where a and b are real numbers.

Product Targets

  • I can
  • I can

Algebra II Solving Quadratic Equations Proficiency Scale

Score   Description Sample Activity
4.0 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.

Suppose the quadratic functions

f(x)=ax2+bx+c with f(-2)=0 and -b/(2a) =1. Solve f(x)=0.

  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:

  • solve a quadratic equation using any method.


 

Solve the following quadratic equation using any method:

 

  x2+4x+15=0

 

  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 can:

  • solve simple quadratic equations.

  • recognize and recalls specific terminology, such as:
    • quadratic equation

    • factor

    • complete the square

    • quadratic formula

    • square root

    • imaginary/complex numbers

 
 

Solve the following quadratic equations:

x2+100=0



Perform the given operation:

(3+i)(-6-i)

 

  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, 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

  • completing the square
  • quadratic formula

MAT-HS.A-REI.10

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Represent and solve equations and inequalities graphically

MAT-HS.A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can find any solution to an equation in two variables from the graph of that equation.
  • I can graph the solution(s) of any linear or exponential function.
  • I can verify an ordered pair is a solution to the equation.

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

Given a quadratic function, identify two solutions.

Given more than one function on a graph, determine the solution of the system.  
  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:


  • Find any solution to an equation in two variables from the graph of that equation.

  • Graph the solution(s) of any linear or exponential function.

  • Verify an ordered pair is a solution to the equation.


The student exhibits no major errors or omissions.

Given the following function:  y=3x+2,  create a graph on a coordinate plane to show all solutions of the function.

Determine if the given point (4, ½ ) is a solution to the      

function y=212x


Given the following function, identify three solutions.

  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 can:

  • Recognize and recall basic vocabulary such as:

    • solution

    • ordered pair

    • coordinate plane

  • Graph a function, given a table of solutions or technology.

  • Evaluate using order of operations.

  • Plot ordered pairs on a coordinate plane.



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

MAT-HS.A-REI.11

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Represent and solve equations and inequalities graphically

MAT-HS.A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Note: In Algebra I, only linear and exponential will be the focus.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any combination of linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Skills (Performance) Targets

  • I can use technology to graph the equations and find their points of intersection.
  • I can use tables of values or successive approximations to find solutions.

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

On the graphs of f(x) and g(x), interpret where f(x)>g(x)or where f(x)<g(x)

                                              

      
  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:

  • explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any linear or exponential functions.

  • use technology and tables to graph the equations and find their points of intersection

  • use tables of values or successive approximations to find solutions


The student exhibits no major errors or omissions.

Use a graphing calculator to find and justify the approximate solution(s) to the system below.


f(x)=x+4 g(x)=4-x  


Solutions:   x= 0

      f(0) = 4 and g(0)=4











Given the following system, for what x value(s), is f(x) = g(x)?









Solutions: x=1

Because f(1) = 5 and g(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

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

  • recognize and recall basic vocabulary, such as:

    • function notation

    • solution

    • x-coordinate

    • linear function

    • exponential function

  • evaluate using function notation and order of operations.

  • identify the intersection of two functions.


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

Find the value of f(4). if f(x)=3x+7.

  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

  • intersection

MAT-HS.A-REI.12

MAT-HS Targeted Standards
(A) Concept: Algebra
(REI) Domain: Reasoning with Equations and Inequalities
Cluster: Represent and solve equations and inequalities graphically

MAT-HS.A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane. Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can graph the solutions to a linear inequality in two variables, including dashed or solid boundary lines when appropriate.
  • I can graph the solution set to a system of linear inequalities in two variables as their corresponding intersection.

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


  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:


  • graph the solutions to a linear inequality in two variables, including dashed or solid boundary lines when appropriate.

  • graph the solution set to a system of linear inequalities in two variables as their corresponding intersection.



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 can:

  • recognize and recall basic vocabulary, such as:

    • linear inequality.

    • linear equation.

  • understand when to use a solid line vs a dashed line.

  • understand that there is a region of solutions and how to identify it.

  • graph a linear equation as the boundary line.

  • solve for Y in a linear equation or inequality.





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, 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

  • half-plane

MAT-HS.A-SSE.01

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Interpret the structure of expressions

MAT-HS.A-SSE.01 Interpret expressions that represent a quantity in terms of its context.

  • a. Interpret parts of an expression,such as terms, factors, and coefficients.
  • b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
    For example, interpret P(1+r)n as the product of P and a factor not depending on P.

Student Learning Targets:

Knowledge Targets

  • I can identify the different parts of an expression and explain their meaning within the context of a problem.

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can use algebraic expressions, equations or inequalities involving one or two variables to represent geometric relationships.
  • I can interpret expressions that represent a quantity in terms of its context.
  • I can interpret expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts.

Product Targets

  • I can
  • I can

Proficiency Scale:

Score   Description Sample Activity
4.0 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 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  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 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  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, 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:

What is a variable?

Vocabulary:

expression term factor coefficient

MAT-HS.A-SSE.02

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Interpret the structure of expressions

MAT-HS.A-SSE.02 Use the structure of an expression to identify ways to rewrite it.

For example, see x4 – y4 as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

Student Learning Targets:

Knowledge Targets

  • I can recall the order of operations.
  • I can understand and identify a power and its parts (base and exponent).
  • I know the properties of exponents (i.e. product of powers, power of a power, power of a product).
  • I can recognize a zero or negative exponent.
  • I can recall the order of operations.
  • I can understand and identify a power and its parts (base and exponent).
  • I know the properties of exponents (i.e. product of powers, power of a power, power of a product).
  • I can recognize a zero or negative exponent.

Reasoning Targets

  • I can analyze an algebraic expression.
  • I can decide what to do next based on my knowledge of the order of operations.
  • I can analyze an algebraic expression.
  • I can decide what to do next based on my knowledge of the order of operations.

Skills (Performance) Targets

  • I can factor algebraic expressions.
  • I can combine like terms to simplify an algebraic expression.
  • I can perform basic operations.
  • I can simplify algebraic expressions.
  • I can apply order of operations.
  • I can simplify an algebraic expression.
  • I can rewrite algebraic expressions in equivalent forms such as factoring or combining like terms.
  • I can use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor an expression completely.
  • I can simplify expressions by combining like terms, using the distributive property and using other operations with polynomials.

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.

Factor the following algebraic expressions.

  • x3+2x2-4x-8

  • 6x3-14x2-12x

  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:

  • uses the structure of an expression to identify ways to rewrite it, using the following techniques to factor:

    • factor by grouping.

    • difference of perfect squares.

    • greatest common factor.

    • factor a trinomial.


The student exhibits no major errors or omissions.

Factor the following algebraic expressions.

  • 4x2-8x+3

  • 2x2-15x+18

  • 3x2-5x-2

  • x3+8x2+6x+48

  • 9x2-49

  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:

  • combines like terms to simplify an expression. (A.SSE.1) & (A.APR.1)

  • uses the following techniques to factor:

    • greatest common factor.

    • factor a trinomial with a leading coefficient of 1.


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

Simplify the following algebraic expressions.

  • 3x2+2x-6x2+4y+6+2x


Factor the following algebraic expressions.

  • 6x2+3x

  • x2+4x+3

  • x2-3x-4

  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 Equivalent Expressions 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. Describe the error in each of the following: 
  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:
  • recognize a suitable factoring technique given the structure of the expression.
  • use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor an expression completely.
  • rewrite algebraic expressions in equivalent forms such as factoring or combining like terms.  

The student exhibits no major errors or omissions.
 
Factor: x3+3x2-4x-12
Factor and Simplify:
  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:
  • simplify expressions by combining like terms, using the distributive property and using other operation with polynomials.

  • understand that like terms can be combined using the distributive property and using other operations with polynomials.

  • understand factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor an expression completely.  

  • recognize equivalent forms of the same expression.  

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


 

Factor: x2+5x-6 

Factor and Simplify:

 

  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-SSE.03

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Write expressions in equivalent forms to solve problems

MAT-HS.A-SSE.03 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

  • a. Factor a quadratic expression to reveal the zeros of the function it defines. See: MAT-HS.A-SSE.03a
  • b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Student Learning Targets:

Knowledge Targets

  • I can recall the order of operations.
  • I can understand and identify a power and its parts (base and exponent).
  • I can recognize the properties of exponents (i.e. product of powers, power of a power, power of a product).
  • I can recognize a zero or negative exponent.
  • I can identify a radical.
  • I can identify if a radical expression is in simplest form.
  • I can recognize the properties of radicals, i.e., product, quotient, and sum of radicals.
  • I can identify perfect squares.
  • I can define a logarithm.
  • I can recall properties of logarithms and exponents.
  • I can recognize common logarithms and natural logarithms.
  • I can identify an asymptote.
  • I can recall the change of base formula.

Reasoning Targets

  • I can apply the distributive property.
  • I can analyze what type of factoring technique that should be used for a given expression. (i.e. factor trinomials, factor difference of squares, factor sum and difference of cubes, factor by grouping, factor out the greatest common factor)
  • I can combine like terms in an expression or equation.
  • I can analyze an algebraic expression.
  • I can decide what to do next based on my knowledge of the order of operations.
  • I can distinguish the difference of when to use each property of radicals.
  • I can evaluate the properties of radicals.
  • I can convert from a logarithm to exponential expressions.
  • I can identify an asymptote.
  • I can expand and condense logarithms.
  • I can evaluate logarithms and exponential expressions.
  • I can distinguish between a natural log and common log.

Skills (Performance) Targets

  • I can simplify a polynomial expression.
  • I can multiply polynomials.
  • I can justify the steps taken in manipulating an expression.
  • I can complete all necessary steps in order to simplify the expression.
  • I can distribute and factor an expression.
  • I can simplify an algebraic expression.
  • I can apply factor using perfect square.
  • I can do prime factorization.
  • I can rationalize a denominator.
  • 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 check the solution.
  • I can set a polynomial equal to zero and solve by factoring, quadratic formula, graphing, linear combinations, and substitution.
  • I can write a linear system.
  • I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
  • I can check the solution.
  • I can solve a quadratic.
  • I can multiply and factor polynomials.
  • I can solve a linear inequality.
  • I can graph a linear inequality.
  • I can solve a system of linear inequalities.
  • I can graph a system of linear inequalities.
  • I can check the solution of the system.
  • I can solve a linear system (substitution, linear combination, graphically).
  • I can write a linear system.
  • I can identify the number of solutions of a linear system.
  • I can identify the most efficient method to solve a system.
  • I can check the solution of the system.
  • I can apply basic properties of exponents and logarithms to rewrite algebraic expressions.
  • I can graph logarithmic and exponential functions.
  • I can solve logarithmic and exponential equations.
  • I can apply the change of base formula to evaluate a logarithmic expression.
  • I can apply basic properties of exponents and logarithms to rewrite algebraic expressions.
  • I can graph logarithmic and exponential functions.
  • I can solve logarithmic and exponential equations.
  • I can apply the change of base formula to evaluate a logarithmic expression.
  • I can graph and determine the equation of an asymptote.
  • I can choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • I can write expressions in equivalent forms by factoring to find the zeros of a quadratic function and explain the meaning of the zeros.
  • I can complete the square in a quadratic expression to convey the vertex form and determine the maximum or minimum value of the quadratic function, and to explain the meaning of the vertex.
  • I can use properties of exponents (such as power of a power, product of powers, power of a product, power of a quotient) to write an equivalent form of an exponential function to reveal and explain specific information about its approximate rate of growth or decay.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 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 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  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 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  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, 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-SSE.04

MAT-HS Targeted Standards
(A) Concept: Algebra
(SSE) Domain: Seeing Structure in Expressions
Cluster: Write expressions in equivalent forms to solve problems

MAT-HS.A-SSE.04 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

For example, calculate mortgage payments.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can develop the formula for the sum of a finite geometric series when the ratio is not 1.
  • I can use the formula to solve real world problems.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 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 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  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 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  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, 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.C-DDD.00.z

MAT-HS Targeted Standards
(C) Concept: Algebra
(DDD) Domain: DDDName
Cluster: CCC

PASTE STANDARD HERE.

MAT-HS.C-DDD.00.z SUB-STANDARD HERE.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 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 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  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 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  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, 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