MAT-HS.F-LE.01
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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.
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Student Learning Targets:
Knowledge Targets
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
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 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. |
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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. |
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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). |
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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). |
- |
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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. |
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Resources
| Web |
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Vocab
- constant difference
- constant multiplier
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MAT-HS.F-LE.02
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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.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills (Performance) Targets
- I can write the equation of a line given a relationship given two characteristics.
Product Targets
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Proficiency Scale
| Score |
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Description |
Sample Activity
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4.0
(advanced)
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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?
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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. |
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3.0
(proficient)
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The student can:
- Write linear functions given...
- point/slope
- 2 points
- parallel/perpendicular lines and a slope
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- 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.
- 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.
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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). |
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2.0
(progressing)
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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).
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Can find slope between 2 points
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Write the equation of a line given the slope and y-intercept
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Find parallel/perpendicular slopes from an equation
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
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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
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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). |
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1.0
(beginning)
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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). |
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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. |
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Resources
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MAT-HS.F-LE.03
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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.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
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
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Proficiency Scale
| Score |
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Description |
Sample Activity
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| 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. |
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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. |
- |
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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). |
- |
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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). |
- |
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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. |
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Resources
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MAT-HS.F-LE.04
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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.
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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
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Alg II Solve Exponential Equations Proficiency Scale
| Score |
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Description |
Sample Activity
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4.0
(advanced)
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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:
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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. |
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3.0
(proficient)
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The student can:
The student exhibits no major errors or omissions.
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Solve the following equation.
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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). |
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2.0
(progressing)
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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.
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Which of the following is an exponential equation?
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43x-2=1
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2x+1=8
3. 3x2-2=45
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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). |
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1.0
(beginning)
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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). |
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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. |
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Resources
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MAT-HS.F-LE.05
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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.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
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
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Proficiency Scale
| Score |
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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). |
- |
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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. |
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Resources
| Web |
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Vocab
- coefficient
- constant
- parameter
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