Chapter 4: TE Graphs of Equations and Functions
Overview
Formulas and equations describe the relationships between quantities. Graphs represent them visually. This chapter emphasizes reading and interpreting graphs.
Suggested pacing:
- The Coordinate Plane - \begin{align*}1\;\mathrm{hr}\end{align*}
- Graphs of Linear Equations - \begin{align*}1\;\mathrm{hr}\end{align*}
- Graphing Using Intercepts - \begin{align*}1-2\;\mathrm{hrs}\end{align*}
- Slope and Rate of Change - \begin{align*}1-2\;\mathrm{hrs}\end{align*}
- Graphs Using Slope-Intercept Form - \begin{align*}1/2 \;\mathrm{hr}\end{align*}
- Direct Variation Models - \begin{align*}1\;\mathrm{hr}\end{align*}
- Linear Function Graphs - \begin{align*}1/2 \;\mathrm{hr}\end{align*}
- Problem-Solving Strategies:
- Use a Graph - \begin{align*}2\;\mathrm{hrs}\end{align*}
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Problem-Solving Strand for Mathematics
In this chapter, the problem-solving strategy is to Use a Graph. The examples and review questions encourage students to think about the data presented, to discuss reasonable tolerances for estimates, and to interpret graphs in real-life contexts.
Alignment with the NCTM Process Standards
The NCTM Process Standards in the use of graphs include portions of the communication, connections, and representation standards. One of the key requirements when constructing graphs is to organize and consolidate mathematical thinking in order to display the information accurately (COM.1). Graphing requires recognizing and using connections among mathematical ideas (CON.1) such as independent and dependent variables, appropriate scale when assigning values to the \begin{align*}x-\end{align*} and \begin{align*}y-\end{align*}axes, or patterns and trends in the data displayed.
- COM.1 - Organize and consolidate their mathematical thinking through communication.
- COM.3 - Analyze and evaluate the mathematical thinking and strategies of others.
- CON.1 - Recognize and use connections among mathematical ideas.
- CON.3 - Recognize and apply mathematics in contexts outside of mathematics.
- R.1 - Create and use representations to organize, record, and communicate mathematical ideas.
- R.3 - Use representations to model and interpret physical, social, and mathematical phenomena.
- 4.1.
The Coordinate Plane
- 4.2.
Graphs of Linear Equations
- 4.3.
Graphing Using Intercepts
- 4.4.
Slope and Rate of Change
- 4.5.
Graphs Using Slope-Intercept Form
- 4.6.
Direct Variation Models
- 4.7.
Linear Function Graphs
- 4.8.
Problem-Solving Strategies - Graphs