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.

Additional content to be taught:

Recognizing the relationships between numerical patterns in tables and their respective graphs in the coordinate plane

Example: recognizing the pattern illustrated in both the table and graph as y = 2x

Determining if a constant rate of change exists in a pattern

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.

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

Counting on a Formula
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.

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.

## Table of Contents

## ACOS Objective 4

Express a pattern shown in a table, graph, or chart as an algebraic equation.ARMT Possible Points = 4 (MC)

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.Additional content to be taught:- Recognizing the relationships between numerical patterns in tables and their respective graphs in the coordinate plane

Example: recognizing the pattern illustrated in both the table and graph as y = 2x## 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 equationTechnology skills:Presentation (web page, PowerPoint, poster, video), searchesInterdisciplinary:Geography (capital cities around the world, latitude and longitude)## Cool Problems

Counting on a FormulaThe 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.## 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.