Tennessee Curriculum Center

Standard 3: Algebra > Mathematical Models Thread | Grade 8

Associated Tennessee Learning Expectations
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
Use slope to analyze situations and solve problems.

Developing a Clear Learning Target

About This Topic Thread
One of the most powerful uses of mathematics is the mathematical modeling of phenomena. Students at all levels should have opportunities to model a wide variety of phenomena mathematically in ways that are appropriate to their level. In the lower elementary grades, students can use objects, pictures, and symbols to model situations that involve the addition and subtraction of whole numbers. In grades 3–5 students should use their models to make predictions, draw conclusions, or better understand quantitative situations. These uses of models will grow more sophisticated. High school students should be able to develop models by drawing on their knowledge of many classes of functions—to decide, for instance, whether a situation would best be modeled with a linear function or a quadratic function—and be able to draw conclusions about the situation by analyzing the model. Using computer-based laboratories (devices that gather data, such as the speed or distance of an object, and transmit them directly to a computer so that graphs, tables, and equations can be generated), students can get reliable numerical data quickly from physical experiments. This technology allows them to build models in a wide range of interesting situations.
Preceding Grade Level
Recognize and generate equivalent forms for simple algebraic expressions.
Use function notation where f(x) represents the output that the function f assigns to the input x.
Understand and graph proportional relationships.
Conceptualize the meanings of slope using various interpretations, representations, and contexts.
Use mathematical models involving linear equations to analyze real-world phenomena.
This Grade Level
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
Use slope to analyze situations and solve problems.
Next Grade Level
Understand and use relations and functions in various representations to solve contextual problems.
Graph and compare equations and inequalities in two variables. Identify and understand the relationships between the algebraic and geometric properties of the graph.
Use mathematical models involving equations and systems of equations to represent, interpret and analyze quantitative relationships, change in various contexts, and other real-world phenomena.
Use analytic geometry tools to explore geometric problems involving parallel and perpendicular lines, circles, and special points of polygons.
Scaffolded (Unpacked) Ideas
  1. Situations often can be described using mathematics which allows students to form elementary notions of mathematical modeling.
  2. Computer technologies today can produce graphs of functions, perform operations on symbols, and instantaneously do calculations on columns of data.
  3. Students now need to learn how to interpret technological representations and how to use the technology effectively and wisely.
  4. Students at all levels should have opportunities to model a wide variety of phenomena mathematically in ways that are appropriate to their level.
  5. In middle school slope represents the constant rate of change in linear functions and by high school students understand there are classes of functions that have nonconstant rates of change.
Academic Vocabulary

Tennessee Academic Vocabulary for Mathematical Models | Grade 8

* Terms not included on the TDOE Academic Vocabulary list
Questions to Focus Instruction
  1. How can mathematical models be used to represent and understand quantitative relationships?
  2. How does the language of mathematics represent change in real world situations?
  3. How does technology allow students to build models in a wide range of interesting situations?