Unit Summary
Unit Overview: The NCTM Algebra Standards for Grades 9-12 indicate that “All students should generalize patterns using explicitly defined and recursively defined functions and identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships.” This unit will provide students with opportunities to extend various patterns in order to find specific terms in a pattern, by exploring linear, quadratic, and exponential functions. Investigations will include comparing the properties of the functions such as domain and range, parameter changes, and recursive and explicit rules for the functions.
Unit Plan: The student will recognize, name, and analyze recursive and explicit patterns in linear, quadratic, and exponential functions
Essential Questions to Guide the Unit and Focus Teaching and Learning:
1. How do patterns help us represent, analyze, make predictions, and draw and justify conclusions from sets of data?
2. How can we use patterns to communicate mathematical ideas?
3. How do patterns, relations, and functions help us understand our world?
4. How do you use patterns, relations, and functions to solve problems?
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Algebraic Relationships |
2 |
Data & Probability |
2 |
Number and Operations |
Unit Goals and Grade-Level Expectations:
The students will
A1B10: Generalize patterns using explicitly or recursively defined functions.
A1C10: Compare and contrast various forms of representations of patterns.
A1D10: Understand and compare the properties of linear, quadratic and exponential functions (include domain and range)
A1E10: Describe the effects of parameter changes on quadratic and exponential functions.
G4B10: Draw or use visual models to represent and solve problems.
Unit Relationship to Grade-Level Expectations:
In this unit, students develop the mathematics skills listed in the Targeted Learning column below. While supporting students in the development of these skills, teachers should consider students’ previous learning and keep in mind their future learning.
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PREVIOUS LEARNING |
TARGETED LEARNING |
FUTURE LEARNING |
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A1B9 Algebraic Relationships Generalize patterns using explicitly or recursively defined functions.
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A1B10 Algebraic Relationships -Generalize patterns using explicitly or recursively defined functions.
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A1B11 Algebraic Relationships Generalize patterns using explicitly or recursively defined functions.
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A1C9 Algebraic Relationships Compare and contrast various forms of representations of patterns.
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A1C10 Algebraic Relationships -Compare and contrast various forms of representations of patterns.
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A1C11 Algebraic Relationships Compare and contrast various forms of representations of patterns.
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A1D9 Algebraic Relationships Understand and compare the properties of linear and exponential functions (include intercepts)
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A1D10 Algebraic Relationships - Understand and compare the properties of linear, exponential, and quadratic functions (include domain and range)
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A1D11 Algebraic Relationships Understand and compare the properties of linear, quadratic, exponential, logarithmic, and rational functions (include domain and range)
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A1E9 Algebraic Relationships Describe the effects of parameter changes on linear functions.
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A1E10 Algebraic Relationships - Describe the effects of parameter changes on quadratic and exponential functions. |
A1E11 Algebraic Relationships Describe the effects of parameter changes on quadratic and exponential functions.
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