8F-Use+functions+to+model+relationships+between+quantities

8.F.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.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. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍Anchor Standard/Mathematical Practice(s) === F.5 F.5 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. || 8.TT.1 Use technology and other resources for assigned tasks. 8.SE.1 Analyze responsible behaviors when using information and technology resources. 8.SI.1 Evaluate information resources based on specified criteria. 8.TT.1 Use technology and other resources for assigned tasks. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinkin****g**=== Understanding Applying Evaluating Creating || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**=== verbal descriptions to write a function (linear equation). Students understand that the equation represents the relationship between the x-value and the y-value; what math operations are performed with the x-value to give the y-value. Slopes could be undefined slopes or zero slopes. Students recognize that in a table the y-intercept is the y-value when x is equal to 0. Using graphs, students identify the y-intercept as the point where the line crosses the y-axis and the slope as the __rise__. run Students need to be given the equations in formats other than y = mx + b, such as y = ax + b (format from graphing calculator), y = b + mx (often the format from contextual situations), etc. Point and Slope: Students write equations to model lines that pass through a given point with the given slope. Students also write equations given two ordered pairs. Note that point-slope form is not an expectation at this level. Students use the slope and y-intercepts to write a linear function in the form y = mx +b. Students interpret the rate of change and the y-intercept in the context of the problem.
 * ===**Common Core Standards**===
 * 1) Make sense of problems and persevere in solving them.
 * 2) Reason abstractly and quantitatively.
 * 3) Construct viable arguments and critique the reasoning of others.
 * 4) Model with mathematics.
 * 5) Use appropriate tools strategically.
 * 6) Attend to precision.
 * 7) Look for and make use of structure.
 * 8) <span style="font-family: Arial,Helvetica,sans-serif;">Look for and express regularity in repeated reasoning.
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**===
 * 8.F.4** Students identify the rate of change (slope) and initial value (y-intercept) from tables, graphs, equations or
 * 8.F.5** Given a verbal description of a situation, students sketch a graph to model that situation. Given a graph of a situation, students provide a verbal description of the situation.

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**
I can identify the slope and y-intercept from tables, graphs, equations or verbal descriptions. I can construct a model of a linear relationship between two quantities. I can sketch a graph to model a verbal description of a situation.
 * 8.F.4**
 * 8.F.5**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**
linear relationship, rate of change, slope, initial value, y-intercept

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Work station: Looking for Lines page 142 Work station for sketching a graph: Teaching Student-Centered Mathematics: page 303 Work station for rate of change: Teaching Student-Centered Mathematics: page 299 and page 304

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
Hands-on activities book page 191 F.4 and page 198 F.5

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
Navigating through Algebra page 27

[[file:fun_websites_for_8th_grade_math.doc]]
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**=== Carnegie Learning chapters 2,3 and 4 Mathematics Stations page 88
 * Quantile F.4**
 * Quantile F.5**

[[file:8_math_F4 FINAL.docx]][[file:8_math_F5 FINAL.docx]]
===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===
 * Refer to NC DPI unpacked content pages 23-25**
 * Refer to Arizona Academic Content standards pages 16 and17**