Overview
Students apply their knowledge about linear equations to solve real-world problems. They use linear regression methods to fit lines to the data provided and make predictions.
Suggested pacing:
- Linear Equations in Slope-Intercept Form -
- Linear Equations in Point-Slope Form -
- Linear Equations in Standard Form -
- Equations of Parallel and Perpendicular Lines -
- Fitting a Line to Data -
- Predicting with Linear Models -
- Problem Solving Strategies:
- Use a Linear Model -
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Problem-Solving Strand for Mathematics
In this chapter, the problem solving technique Use a Linear Model builds directly on lesson material, particularly in “Fitting a Line to Data” and “Predicting with Linear Models.” Within the context of this chapter, linear modeling is defined as using linear interpolation, linear extrapolation, or a line of best fit as a method of predicting trends and/or obtaining reasonable data.
Alignment with the NCTM Process Standards
Being able to approximate or estimate well (R.2) is a valuable skill in mathematics as well as real life. When younger students are asked to estimate, they often follow the rules for rounding rather than truly estimating with regard to the magnitude of a quantity (CON.1). Sometimes teachers unintentionally contribute to this issue because it is difficult to correct estimations; several estimations could be acceptable given different scenarios or different priorities. Taking a few moments to discuss significant digits in real-life situations, such as the cost of a house, a car, or a meal at a restaurant, can really improve students’ number sense and their ability to make appropriate approximations (COM.2; COM.3).
Informal scale drawings can be very helpful whenever geometric shapes are part of a class exercise, and, when done attentively, can internalize the notion of scale (R.1). Free-hand enlargements or miniatures, which many students love to do, can develop an instinct for proportional reasoning (RP.4) and engage artistically inclined students. Displaying attractive, correct student work around the room reinforces the concept of scale and inspires others to think proportionately (R.3).
The question of the reasonableness of a solution is something that must be addressed repeatedly. Teachers should ask students to reflect on the reasonableness of their answers on a regular basis (PS.4).
- COM.2 - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
- COM.3 - Analyze and evaluate the mathematical thinking and strategies of others.
- CON.1 - Recognize and use connections among mathematical ideas.
- PS.4 - Monitor and reflect on the process of mathematical problem solving.
- RP.4 - Select and use various types of reasoning and methods of proof.
- R.1 - Create and use representations to organize, record, and communicate mathematical ideas.
- R.2 - Select, apply, and translate among mathematical representations to solve problems.
- R.3 - Use representations to model and interpret physical, social, and mathematical phenomena.
Chapter Outline
- 5.1. Linear Equations in Slope-Intercept Form
- 5.2. Linear Equations in Point-Slope Form
- 5.3. Linear Equations in Standard Form
- 5.4. Equations of Parallel and Perpendicular Lines
- 5.5. Fitting a Line to Data
- 5.6. Predicting with Linear Models
- 5.7. Problem Solving Strategies: Use a Linear Model