ALEX | Alabama Learning Exchange

Linear Models

Classroom Resource Information

Title:

Linear Models

URL:

https://aptv.pbslearningmedia.org/resource/our20-math-85910/linear-models/

Content Source:

PBS

Type:

Audio/Video

Overview:

In this video lesson, students use linear functions to model real-world situations. Students are given data for an almost linear relationship and develop a linear model. They use their model to make predictions and discuss the reasonableness of the model. Sometimes it is difficult to tell from the information given if a linear model is appropriate. When none of the given data perfectly fit by a linear function, students have to determine whether a linear approximation is reasonable and for which values it would be reasonable. Students also use piecewise linear graphs to find information about the real-life situation they represent. In situations where a quantity changes at different constant rates over different time intervals, students model the situation with a piecewise linear function.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 8	13. Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs. Unpacked Content Evidence Of Student Attainment: Students: Define a function as a rule assigning each input exactly one output. Identify functions when given a relation as graph, table of values, mapping, or set of ordered pairs. Teacher Vocabulary: Relation Function Input Output Knowledge: Students know: how to interpret a graph, table, mapping, and ordered pairs. Skills: Students are able to: give an accurate definition of a function. Analyze graphs, tables, mappings, and sets of ordered pairs to determine if a relation is a function. Understanding: Students understand that: Functions assign every input one output, but they may see outputs repeat. Diverse Learning Needs: Essential Skills: Learning Objectives: M.8.13.1: Define function, ordered pairs, input, output. M.8.13.2: Demonstrate how to plot points on a Cartesian plane using ordered pairs. M.8.13.3: Recall how to complete input/output tables. M.8.13.4: Recognize numeric patterns. M.8.13.5: Given a function, create a rule. Prior Knowledge Skills: Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection. Demonstrate an understanding of an extended coordinate plane. Draw a four-quadrant coordinate plane. Draw and extend vertical and horizontal number lines. Interpret graphing points in all four quadrants of the coordinate plane in real-world situations. Recall how to graph points in all four quadrants of the coordinate plane. Alabama Alternate Achievement Standards AAS Standard: M.AAS.8.13 Determine whether a relation is a function given a graph or a table.
Mathematics MA2019 (2019) Grade: 8 Accelerated	33. Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 31] Unpacked Content Evidence Of Student Attainment: Students: Engage in the Mathematical Modeling Cycle (Appendix E) to solve contextual problems involving linear, quadratic, exponential, absolute value and linear piecewise function Teacher Vocabulary: Mathematical Modeling Cycle Define a problem Make assumptions Define variables Do the math and get solutions Implement and report results Iterate to refine and extend a model Assess a model and solutions Knowledge: Students know: The Mathematical Modeling Cycle. When to use the Mathematical Modeling Cycle to solve problems. Skills: Students are able to: Define the problem to be answered. Make assumptions to simplify the problem, identifying the variables in the situation and create an equation. Analyze and perform operations to draw conclusions. Assess the model and solutions in terms of the original context. Refine and extend the model as needed. Report on conclusions and reasonings. Understanding: Students understand that: Making decisions, evaluating those decisions, and revisiting and revising work is crucial in mathematics and life. Mathematical modeling uses mathematics to answer real-world, complex problems. Diverse Learning Needs:
Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability	31. Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions. Unpacked Content Evidence Of Student Attainment: Students: Engage in the Mathematical Modeling Cycle (Appendix E) to solve contextual problems involving linear, quadratic, exponential, absolute value and linear piecewise functions. Teacher Vocabulary: Mathematical Modeling Cycle Define a problem Make assumptions Define variables Do the math and get solutions Implement and report results Iterate to refine and extend a model Assess a model and solutions Knowledge: Students know: The Mathematical Modeling Cycle. When to use the Mathematical Modeling Cycle to solve problems. Skills: Students are able to: Make decisions about problems, evaluate their decisions, and revisit and revise their work. Determine solutions to problems that go beyond procedures or prescribed steps. Make meaning of problems and their solutions. Understanding: Students understand that: Mathematical modeling uses mathematics to answer real-world, complex problems. Diverse Learning Needs: Essential Skills: Note: One does not need to move through the modeling cycle in the same order, aspects of the cycle may be repeated. The Mathematical Modeling Cycle: Define the problem. Make assumptions/Define variables. Do the math/Get solutions. Assess the model and solutions. Iterate to refine and extend model. Implement and report results. Prior Knowledge Skills: oes not need to move through the modeling cycle in the same order, aspects of the cycle may be repeated. The Mathematical Modeling Cycle: Define the problem. Make assumptions/Define variables. Do the math/Get solutions. Assess the model and solutions. Iterate to refine and extend model. Implement and report results. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.12.31 Choose the graph of the linear function that represents a solution in a real-world scenario. (Ex: Choose the graph that shows a steady increase or decrease rather than a graph with fluctuating data.)