Monday, May 20, 2024, 4:34 PM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
Glossary: MAT-HS: Algebra

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