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In Algebra 1, students demonstrate fluency by creating, comparing, analyzing, solving, providing multiple representations, and identifying the structures of exponential & quadratic functions building on the understanding of linear functions from grade 8 to apply linear, quadratic and exponential models to data and unfamiliar problems.
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Learning Progression 1
Understanding Relations
Learning Intention 1: I am learning to understand the concept of a function distinguishing a relation as a function or not a function. (3.2 Explain 1 & 3.2 Explain 2 HMH)
Learning Intention 1: I am learning to understand the concept of a function distinguishing a relation as a function or not a function. (3.2 Explain 1 & 3.2 Explain 2 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
1a. I can explain that a function from one set (the domain) to another set (the range) assigns to each element of the domain exactly one element of the range in a variety of contexts
1b I can distinguish between functions and non-functions. (Procedural, level 2)
1c. I can distinguish a relation as a function or not a function in a mapping diagrams. (Procedural, level 2)
1d. I can distinguish a relation as a function or not a function in a table of values. (Procedural, level 2)
1e. I can distinguish a relation as a function or not a function in a graph by using the vertical line test or context. (Procedural, level 2)
1f. I can distinguish a relation as a function or not a function in an equation. (Procedural, level 2)
Learning Intention 2: I am learning to I am learning to recognize that sequences are functions whose domain is a subset of the integers. (4.1 HMH, 15.1 HMH)
Learning Intention 2: I am learning to I am learning to recognize that sequences are functions whose domain is a subset of the integers. (4.1 HMH, 15.1 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
2a. I can recognize that sequences are functions whose domain is a subset of the integers. (Conceptual, level 3)
2b. I understand the difference between an arithmetic and geometric sequence. (Conceptual, level 3)
[Note: The goal here is not a full understanding of sequences as that is found in the transition from Unit 3 to Unit 4. At this point, the goal is simply to understand what a sequence is and that is has an unstated domain, which makes it a function.]
Learning Progression 2
Identifying Domain & Range
Learning Intention 3: I am learning to identify the domain & range for any given function given a graph. (3.2 Explore HMH & Examples of Graphs listed below.)
Learning Intention 3: I am learning to identify the domain & range for any given function given a graph. (3.2 Explore HMH & Examples of Graphs listed below.)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
3a. I can state the domain given a graph. (Conceptual, level 1)
3b. I can state the range given a graph. (Conceptual, level 1)
3c. I can state the domain and range given a graph of a linear function. (Procedural, level 2)
3d. I can state the domain and range given a graph of an absolute function. (Procedural, level 2)
3e. I can state the domain and range given a graph of an exponential function. (Procedural, level 2) [Exponentials added as a course overview.]
3f. I can state the domain and range given a graph of a quadratic function. (Procedural, level 2)
3g. I can state the domain and range given a graph of a cubic function. (Procedural, level 2)
Learning Intention 4: I am learning to identify the domain & range for any given function in any form presented. (3.2 Evaluate HMH)
Learning Intention 4: I am learning to identify the domain & range for any given function in any form presented. (3.2 Evaluate HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
I can identify the domain and range for any given function presented in any form:
4a. as a graph, (Application, level 3)
4b. as a verbal description (contextual/mathematical)(Application, level 3)
4c. or as a sequence. (Application, level 3)
4d. as an equation
4e. as a mapping diagram
Learning Progression 3
Evaluation, Graphs & Equations of Functions
Learning Intention 5 & 6 (two days): I am learning to use function notation to find inputs and outputs. (3.3 Explore 2 & 3.3 Explain 1 HMH)
Learning Intention 5 & 6 (two days): I am learning to use function notation to find inputs and outputs. (3.3 Explore 2 & 3.3 Explain 1 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
5a. I can use function notation to evaluate a function given in function notation for a particular input. (Procedural, level 3)
6a. I can find the input for a given output when given in function notation. (Application, level 4)
[Note: Instead of spending one day on 5a & one day on 6a; you could do both in a single context each day for comprehension, repetition & retention.]
Learning Intention 7: I understand that the graph of f is the graph of the equation y= f(x). (3.4 HMH)
Learning Intention 7: I understand that the graph of f is the graph of the equation y= f(x). (3.4 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
7a. I understand that the graph of a function f is the graph of the equation y= f(x). (Conceptual, level 2)
I can evaluate a function for a particular input or output in all representations and write my answer in function notation. (Procedural, level 3)
7b. graph
7c. table
7d. equation
7e. mapping diagram
7f. I can translate input and output values between function notation and ordered pairs. (example: (2,3) to f(2) = 3)
Learning Progression 4
Evaluation, Graphs & Equations of Functions
Learning Intention 8: I am learning to interpret linear, exponential & quadratic functions in context. (Draw problems from 5.1, 16.1 Explore & 19.1 HMH)
Learning Intention 8: I am learning to interpret linear, exponential & quadratic functions in context. (Draw problems from 5.1, 16.1 Explore & 19.1 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
8a. I can interpret linear functions in context. (level 1)
8b. I can interpret exponential functions in two variables in context of the situation. (level 2)
8c. I can interpret quadratic functions in two variables in context of the situation. (level 2)
[Note: While you could split this up, taking more time, remember the purpose of this unit is graphing and function notation while providing a course overview. Students will explore each function type in depth in later units. Keeping these together allows students to focus on how the growth differs between functions. For example, you might explore y=2x, y=2^x and y=x^2 (all in context).]
Learning Intention 9 (could be done with LI10 below): I am learning to interpret the key features of a table representing a function modeling the relationship between two quantities. (3.4 Explore & Explain 1 HMH)
Learning Intention 9 (could be done with LI10 below): I am learning to interpret the key features of a table representing a function modeling the relationship between two quantities. (3.4 Explore & Explain 1 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
9a. I can interpret the key features of a table representing a function modeling the relationship between two quantities (Conceptual, level 2)
Learning Intention 10 (could be done with LI9 above): I am learning to interpret the key features of a graph representing a function modeling the relationship between two quantities. (3.4 Explain 2 & Explain 3 HMH)
Learning Intention 10 (could be done with LI9 above): I am learning to interpret the key features of a graph representing a function modeling the relationship between two quantities. (3.4 Explain 2 & Explain 3 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
10a. I can interpret the key features of a graph representing a function modeling the relationship between two quantities (Conceptual, level 2)
10b. Given the key features of a linear graph, I can identify the appropriate graph. (Procedural, level 1)
[Note: This is a chance to reengage the three function types from LI8 above. 9b. can be a formative assessment of 9a even if only as an exit ticket.]
Learning Intention 11: I am learning to sketch graphs showing key features given a verbal description of the relationship between two quantities that can be modeled with a function. (3.1 HMH)
Learning Intention 11: I am learning to sketch graphs showing key features given a verbal description of the relationship between two quantities that can be modeled with a function. (3.1 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
11a. I can sketch graphs showing key features given a verbal description of the relationship between two quantities that can be modeled with a function (Procedural, level 3)
Learning Intention 12: I am learning to relate the domain and range of a function to the quantitative relationship it describes including its graph. (3.2 Explain 1, 3.3 Explain 1 & 3.3 Explain 2)
Learning Intention 12: I am learning to relate the domain and range of a function to the quantitative relationship it describes including its graph. (3.2 Explain 1, 3.3 Explain 1 & 3.3 Explain 2)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
12a. I can relate the domain and range of a function to its graph. (Procedural. level 3).
12b. When applicable, I can relate the domain and range of a function to the quantitative relationship it describes. (Application, level 3)
Learning Intention 13 (one to three days with multiple representations of the same function each day): I am learning to calculate/approximate & interpret the average rate of change (linear, exponential & quadratic). (5.3, 16.1, 19.1 & 15.1 HMH)
Learning Intention 13 (one to three days with multiple representations of the same function each day): I am learning to calculate/approximate & interpret the average rate of change (linear, exponential & quadratic). (5.3, 16.1, 19.1 & 15.1 HMH)
Success Criteria (click link above for the Clarity Cover Sheet with textbook resources, released SBAC items, vocabulary & a self-assessment scale)
13a. I can calculate/approximate & interpret the average rate of change of a function presented on a graph. (Conceptual, level 3).
13b. I can calculate/approximate & interpret the average rate of change of a function presented in a table (Conceptual, level 3).
13c. I can calculate the average rate of change of a function presented symbolically (Procedural, level 3).
13d. I can calculate the average rate of change of a function presented in a table (level 3).
13e. I can specify the average rate of change from an equation of a linear function. (Procedural, level 2)
13f. I can approximate the average rate of change from a graph of a linear function (Application, level 2)
13g. I can estimate a rate of change of a function from a graph (level 3).
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