| - Slope
- Rate of Change
- Linear Functions/Equations
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ComCore: Literacy in History/Social Studies, Science, & Technical Subjects 6-12 |
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ComCore: Grades 6-8 |
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Capacities of the Literate Individual |
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Students Who are College and Career Ready in Reading, Writing, Speaking, Listening, & Language | | Students establish a base of knowledge across a wide range of subject matter by engaging with works of quality and substance. They become proficient in new areas through research and study. They read purposefully and listen attentively to gain both general knowledge and discipline-specific expertise. They refine and share their knowledge through writing and speaking. | | | Students cite specific evidence when offering an oral or written interpretation of a text. They use relevant evidence when supporting their own points in writing and speaking, making their reasoning clear to the reader or listener, and they constructively evaluate others’ use of evidence. | | ComCore: Mathematics |
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ComCore: Grade 8 |
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Functions |
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8.F.A. Define, evaluate, and compare functions. | | Function notation is not required in Grade 8. | | | 8.F.A.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | | | For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | | 8.F.B. Use functions to model relationships between quantities. | | 8.F.B.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | | | 8.F.B.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | |
| Students understand that . . . - Change is constant (8.F.A.1)
- Change can be positive or Negative (Zero and Undefined). (8.F.A.2) (8.F.A.3)
- Change can be predicted.(8.F.A.2)
- Change can be Linear or Nonlinear. (8.F.A.3)
- Change can be translated among verbal tabular, graphic, and algebraic representation of functions.(8.F.B. 4) (8.F.B.5)
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Essential Concept: The Rate of Change expressed as a ratio between a change in one variable relative to a corresponding change in another, thus, the effect of change of a dependent variable in relation to the independent variable. Critical Content: Slope is the 'steepness' of the line, also commonly known as rise over run. We calculate slope by dividing the change in the x-value between two points over the change in the y-value. Academic Vocabulary: Non-linear Slope-intercept form Rate of change Output Input Y-intercept Linear | 8 Mathematical Practices MP 1 Make sense of problems, & persevere. MP 2 Reasoning abstractly & quantitatively. MP 3 Critiquing reasoning of others & justifying own work. MP 4 Model with mathematics. MP 5 Use tools of appropriately. MP 6 Attend to precision. MP 7 Seeing Structure. MP 8 Seeing regularity in repeated reasoning & patterns. Process #1: (Connects to MP 1,2,3,6,7) Explain reasoning and justify mathematical choices. Strategies: Identify what information is required. Create a plan to present information verbally or visually in a logical fashion. Using AVID tutorials Skills: Use content specific vocabulary. Show work to reflect the use of mathematical properties & structure. |
FACTUAL: CONCEPTUAL: - What makes a linear function linear?
- Why is a vertical line undefined?
- How does the numerical value of slope affect the steepness of a line?
PROVACATIVE: | Videos, Review Game, Lab, Presentation, Homework, Coordinates Planes, RAFT, TI-83/73 graphing calculators |
| | | Quiz: Graphing Linear Functions Formative: Other: Quiz 8.F.B.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 8.F.B.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
| | | | Rate of Change RAFT Formative: Written: Informative 8.F.A.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
| | Quiz Formative: Other: Quiz 8.F.A.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
| | | | Unit Test Summative: Test: Benchmark 8.F.A.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 8.F.A.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.A.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. 8.F.B.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 8.F.B.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
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P21: 21st Century Student Outcomes |
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P21: K-12 |
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Core Subjects & 21st Century Themes |
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| | Using 21st century skills to understand and address global issues | | | Learning from and working collaboratively with individuals representing diverse cultures, religions and lifestyles in a spirit of mutual respect and open dialogue in personal, work and community contexts | | Financial, Economic, Business and Entrepreneurial Literacy | | Using entrepreneurial skills to enhance workplace productivity and career options | |
| READING: - Students will summarize the steps in setting up and evaluating/solving expressions, equations and inequalities as described in their textbooks using the words first, second, third, etc.
- Students will identify words, or phrases, in word problems that help them solve them using a causative structure such as: The following words "evaluate" and "solution," and "solution set" help me solve the problem.
WRITING: - Students will write a constructed response to a word problem using logically ordered reasons that are supported by facts and details and using the appropriate mathematic vocabulary
- Students will list possible reasons for their conclusions, using verbs such as explain, demonstrate, justify and because)
LISTENING & SPEAKING: - Students will explain how to set up and solve/evaluate equations, expressions, and inequalities to a partner using the words first, second, third, etc.
- Students will describe the difference between an equation, an expression, and an inequality using the words solution, simplify, solution set
TECHNOLOGY: - Students will use digital tools to create work product for the RAFT assessment & viewing videos
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| For students who need more support: - Provide step by step instructions.
- Provide examples or models.
- Teach self-questioning skills to help target "point of confusion".
- Teach how to articulate "point of confusion" or request for help.
- Provide ways for students to self-check.
- Reduce number of problems or stimuli to be worked with at one time.
For students who need more challenge: - Reduce the number of directions, making the tasks more open ended.
- Allow students to generate questions to be answered or investigated.
- Request that students use multiple models or representations & articulate the connections.
- Encourage the students to find patterns, generalizations or "short cuts" and prove that they work for all numbers.
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