Saturday, April 20, 2024, 8:37 AM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
Glossary: MAT-HS: Function

MAT-HS.F-LE.01

MAT-HS Targeted Standards
(F) Concept: Function
(LE) Domain: Linear, Quadratic and Exponential Models
Cluster: CCC

MAT-HS.F-LE.01 Distinguish between situations that can be modeled with linear functions and with exponential functions.

  • a. Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.
  • b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
  • c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can determine a situation as linear or exponential by examining rates of change between data points.

Skills (Performance) Targets

  • I can show there is a constant difference in a linear function over equal intervals.
  • I can show there is a constant multiplier in an exponential function over equal intervals.
  • I can describe situations where one quantity changes at a constant rate per unit interval relative to another.
  • I can describe situations where one quantity grows or decays by a constant multiplier per unit interval relative to another.

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

  • constant difference
  • constant multiplier

MAT-HS.F-LE.02

MAT-HS Targeted Standards
(F) Concept: Function
(LE) Domain: Linear, Quadratic and Exponential Models
Cluster: Construct and compare linear and exponential models and solve problems

MAT-HS.F-LE.02 Construct linear functions given a graph, table, a description or two input-output pairs given their relationship.

**Algebra will focus on point-slope and intercepts as relationships.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can write the equation of a line given a relationship given two characteristics.

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.

Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86.  The cost of the call and the length of the call are related.  The cost of each minute is constant.

        A.  What is the cost, c, of a call of m minutes duration?

       B.  How long can you talk on the phone if you have $12 to spend?
  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:

  • Write linear functions given...
    • point/slope
    • 2 points
    • parallel/perpendicular lines and a slope
  • Write an equation in point-slope form for the line that has the given slope and that passes through the given point.
    • m = 3  (0, -2)
    • m = -2  (5,1)
  • Write an equation in slope-intercept form that passes through the given points.
    • (2,3) & (1,5)
    • (5, -2) & (-16, 4)
  • Write an equation in slope-intercept form for the line that passes through the given point and is PARALLEL to the given line.
    • (4,5)  y = -2x + 4
    • (-7,3)  x = 4
  • Write an equation in slope-intercept form for the line that passes through the given point and is PERPENDICULAR to the given line.
    • (5, -1)  y = 4x - 7
    • (4, -2)  y = 3
  • Write the equation of the function represented by the graph in slope-intercept form.

  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)

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).

 

  • Can find slope between 2 points

  • Write the equation of a line given the slope and y-intercept

  • Find parallel/perpendicular slopes from an equation

 

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

 

 

 

Write the equation of the line given a slope of 4 and a y-intercept of -5.


Find the slope of the line that goes through  (-2, 5) and (3, 8).


What is the slope of the line parallel to y=3x + 8


What is the slope of the line perpendicular to y=-4x - 6

 

  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.F-LE.03

MAT-HS Targeted Standards
(F) Concept: Function
(LE) Domain: Linear, Quadratic and Exponential Models
Cluster: Construct and compare linear and exponential models and solve problems

MAT-HS.F-LE.03 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can use graphs and tables to make the connection that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any other polynomial function.

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.F-LE.04

MAT-HS Targeted Standards
(F) Concept: Function
(LE) Domain: Linear, Quadratic and Exponential Models
Cluster: Construct and compare linear and exponential models and solve problems

MAT-HS.F-LE.04 Use logarithms to express the solution to abct=d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

 

 

 

Student Learning Targets:

Knowledge Targets

  • 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 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 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 graph and determine the equation of an asymptote.
  • I can express the solution to an exponential function as a logarithm.
  • I can evaluate logarithms using technology.

Product Targets

  • I can
  • I can

Alg II Solve Exponential 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 an exponential equation using logarithms.

The student exhibits no major errors or omissions.

Solve the following 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 :
    • exponent
    • logarithm
    • Euler number (e)
    • base
  • identify an exponential equation.
  • use inverse operations.
  • evaluate a logarithmic expression.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Which of the following is an exponential equation?

  1.    43x-2=1

  2.    2x+1=8

    3.   3x2-2=45
  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.F-LE.05

MAT-HS Targeted Standards
(F) Concept: Function
(LE) Domain: Linear, Quadratic and Exponential Models
Cluster: Interpret expressions for functions in terms of the situation they model.

MAT-HS.F-LE.05 Interpret the parameters in a linear, quadratic, or exponential function in terms of a context.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can explain the meaning of the coefficients, constants, factors, exponents, and intercepts in a linear, quadratic or exponential function in terms of a context.

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

  • coefficient
  • constant
  • parameter