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A-SSE

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.03.a

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.a 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.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills (Performance) Targets

  • I can solve a quadratic equation by factoring methods and the zero product property.

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.

Solve the following polynomials by factoring:
  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 by factoring

  • can use the zero product property


The student exhibits no major errors or omissions.

Solve the following polynomials by factoring.

  • x2+8x+7=0

  • 2x2-15x+18=0

  • 3x2+2x+1=7x+3

  • 4x2-8x+3=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:

The student:

  • can solve a quadratic equation using the zero product property


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

Solve the following polynomials by the zero product property.

  • (x+5)(x-3)=0

  • 7x(x-1)=0

  • (3x-5)(x-9)=0
  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-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

MODELING

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.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-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-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.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

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