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Descriptive Statement: Patterns, relationships, and functions constitute a unifying theme of mathematics. From the earliest age, students should be encouraged to investigate the patterns that they find in numbers, shapes, and expressions, and by doing so, to make mathematical discoveries. They should have opportunities to analyze, extend, and create a variety of patterns and to use pattern-based thinking to understand and represent mathematical and other real-world phenomena. These explorations present unlimited opportunities for problem-solving, making and verifying generalizations, and building mathematical understanding and confidence.
 

Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Patterns, Relationships, and Functions     Timeline 2nd Q 2nd Q	Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8, students will: Represent and describe mathematical relationships with tables, rules, simple equations, and graphs.	Investigate and describe functions with rules and tables Investigate and describe functions with equations and graphs	See Lesson 6-2. See Lesson 6-3.	Math journal, Investigations software "Measuring Elephant Populations in Africa" Spreadsheet software, math journal, Hot Page software, graph paper	"On Your Own" examples, teaching resources provided by the publisher "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet
Timeline 3rd Q 2nd Q	Understand and describe the relationships among various representations of patterns and functions.	Give the rule for a pattern based on the values in a table Give the equation for a function based on the values in a table or a graph	See Work Together activities on pages 297, 328, and 354. See Think and Discuss activity on page 369. See Lesson 6-3.	See teacher’s edition for a list of materials needed for these activities Spreadsheet software, math journal, Hot Page software, graph paper	Group assessment "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet
Timeline 1st Q 4th Q	Use patterns, relationships, and functions to model situations and to solve problems in mathematics and in other subject areas.	Construct solutions to word problems by looking for a pattern Construct solutions to word problems by making a table	See Lesson 2-3. See Lesson 10-9.	Calculator Investigations software "Mission: Mars"	Self assessment Same as #1

 

Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Patterns, Relationships, and Functions  Timeline 2nd Q 2nd Q	Analyze functional relationships to explain how a change in one quantity results in a change in another.	Explore how a change in one quantity in a function results in a change in another Describe the effect on the output of changing the value of one of the input values in a formula	See Lesson 6-2. See Lesson 4-8.	Math journal, Investigations software "Measuring Elephant Populations in Africa" Spreadsheet software, Investigations software "Hazard City Messengers", math journal	"On Your Own" examples, teaching resources provided by the publisher Same as #1
Timeline 2nd Q 2nd Q	Understand and describe the general behavior of functions.	Explore rule, tabular, and graphical representations of functions Distinguish between linear and quadratic functions	See Lessons 6-2 and 6-3. See Lesson 6-7.	Math journal, Investigations software "Measuring Elephant Populations in Africa", spreadsheet software, Hot Page software, graph paper Spreadsheet software, math journal	"On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet "On Your Own" examples, teaching resources provided by the publisher

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Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Patterns, Relationships, and Functions  Timeline 3rd Q 2nd Q	Use patterns, relationships, and linear functions to model situations in mathematics and in other areas.	Explore the sine, cosine, and tangent ratios Create a plausible explanation of the situation depicted by a graph without numbers	See Lessons 8-7 and 8-8. See Lesson 6-5.	Math Tools software "Geometry", math journal Graph paper, stopwatch, Hot Page software, math journal	"On Your Own" examples, teaching resources provided by the publisher "On Your Own" examples, teaching resources provided by the publisher, Hot page record sheet
Timeline 2nd Q All year	Develop, analyze, and explain arithmetic sequences.	Continue a sequence Verify the pattern in a sequence	See Lesson 6-1. These are found throughout the text. For example, see pages41 #18, 59 #6, 148 #35, 253 #24, 259 #10, 303 #9, 314 #13.	Math journal See teacher’s edition for the materials needed for these examples	"On Your Own" examples, teaching resources provided by the publisher Group assessment

 

Resources What’s My Rule?  -For this game you will be given a set of x values which will be put into a function machine which will                                      process the numbers and spit out y values. Your job is to guess the rule of the function machine. Patterns and Exponents  -Lesson on Patterns and Exponents Traffic Jam Activity  -an interactive lesson Locker Problem Activity  -an interactive lesson The Global Sun/Temperature Project  -Join schools from around the world as they try to figure out how proximity to the                                                                                  equator affects average daily temperature and hours of sunlight. The International Boiling Point Project  -students can analyze data to reach an answer to the question: What causes a                                                                                      pot of water to boil? It's that simple!