Patterns+as+Algebraic+Equations


 * toc**

=ACOS Objective 4=


 * Express a pattern shown in a table, graph, or chart as an algebraic equation.**
 * Recognizing the relationships between numerical patterns in tables and their respective graphs in the coordinate plane
 * Determining if a constant rate of change exists in a pattern

ARMT Possible Points = 4 (MC)
 * Determining an algebraic equation for a pattern shown in a table, graph, or chart will be required.
 * Any representation of a rational number may be used as values in tables or charts.
 * Any representation of a rational number may be included in the algebraic equation as a coefficient of a variable or a constant.
 * Word problems/real-life situations may be used.

Sample problems from Item Specs

Prerequisites from Curriculum Guide

 * Objective 7.4.1:** Solve problems using numeric and geometric patterns.
 * Objective 7.4.2:** Determine a verbal rule for a function given the input and output.

Example: recognizing the pattern illustrated in both the table and graph as y = 2//x//
 * Additional content to be taught:**
 * Recognizing the relationships between numerical patterns in tables and their respective graphs in the coordinate plane
 * Determining if a constant rate of change exists in a pattern

Resources
[|Navigating Through Algebra in Grades 6-8], published by NCTM is full of activities that develop the ideas of relating patterns and functions.

CMP units, "Variables and Patterns" and "Moving Straight Ahead" explores linear relationships and students develop a rule for a pattern from a table or a graph. Interesting experiments. There is also an investigation of slope.

Using Calculator Based Rangers

Webquest: [|The Wide World of Soccer]

Soccer fans, get up on your feet! You've been selected by an elite committee to join us on a world-wide soccer adventure. Along the way, you'll be gathering data about the geography of countries where soccer is the favorite sport. You'll also make some predictions about the future of soccer in the United States. We will be leaving on our adventure very shortly, so pack your math tools and your thinking cap. This is one adventure you don't want to miss.

//Soccer Goal 1:// First, find and graph the location of the capital cities of 10 different countries in which soccer is the country's favorite sport. A printable map for your use is found in the [|Process] section. //Soccer Goal 2:// Second, research and describe some of the international rules of the game of soccer. //Soccer Goal 3:// Third, gather data about the growth of college and professional soccer in the United States. Graph this data, and use your graphs to predict the future of soccer in the United States.
 * Math Content:** graphing, inequalities, scatter plots, determine which equation best fits the data, make a prediction based on that equation
 * Technology skills:** Presentation (web page, PowerPoint, poster, video), searches
 * Interdisciplinary:** Geography (capital cities around the world, latitude and longitude)

Cool Problems
The numbers below are arranged according to a particular formula: 1 11 21 1211 111221 312211 Can you figure out the formula? What is the next term in the sequence? Answer: //The Daily Spark Critical Thinking,// p. 9.
 * Counting on a Formula**

Follow the Sequence
What is the next number in this sequence? 1, 1, 2, 3, 5, 8, ... Do you know the name of this type of sequence? Answer: //The Daily Spark Critical Thinking//, p. 26.