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Descriptive Statement: The conceptual building blocks of calculus are important for everyone to understand. How quantities such as world population change, how fast they change, and what will happen if they keep changing at the same rate are questions that can be discussed by elementary school students. Another important topic for all mathematics students is the concept of infinity – what happens as numbers get larger and larger and what happens as patterns are continued indefinitely. Early explorations in these areas can broaden students’ interest in and understanding of an important area of applied mathematics.
 

Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Calculus Timeline 2nd Q 2nd Q 2nd Q	Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8, Students will: Recognize and express the difference between linear and exponential growth.	Illustrate linear growth graphically Illustrate exponential growth graphically Express the difference between linear and exponential growth	See Lesson 6-2. See Lesson 6-6. See Lesson 6-7.	Math journal, Investigations software "Measuring Elephant Populations in Africa", graphing calculator Spreadsheet software, graph paper, math journal, Investigations software "Unidentified Flying Cubes", graphing calculator Spreadsheet software, math journal, graphing calculator	"On Your Own" examples, teaching resources provided by the publisher Same as #1 Same as #1
Timeline 1st Q 4th Q	Develop an understanding of infinite sequences that arise in natural situations.	Explore a Fibonacci-like sequence that arises in nature Explore the infinite sequences in Pascal’s triangle	See "Students discuss how…" activity on page 504 of the Mathematics Curriculum framework. See Lesson 9-6.	Whatever is appropriate to the problems under study Math journal	Group assessment "On Your Own" examples, teaching resources provided by the publisher

 
 

Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Calculus     Timeline 3rd Q 1st Q 3rd Q	Investigate, represent, and use non-terminating decimals.	Explore the relationship between the denominator of a fraction and the repetend in the equivalent repeating decimal Investigate the use of pi in calculating the circumference and area of circles Differentiate between the decimal form of rational and irrational numbers	See Lesson 7-3. See Lesson 2-2. See Lesson 7-11	Spreadsheet software, math journal Math journal, Math Tools software "Geometry" Math journal	"On Your Own" examples, teaching resources provided by the publisher Same as #1 Same as #1
Timeline 2nd Q 4th Q	Represent, analyze, and predict relations between quantities, especially quantities changing over time.	Analyze graphs which represent relations between quantities that change over time Predict a future value given the percent of change	See Lesson 6-5. See Lesson 10-6.	Stop watch, graph paper, math journal, Hot Page software Math journal, spreadsheet software	"On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet "On Your Own" examples, teaching resources provided by the publisher
Timeline 4th Q 1st Q	Approximate quantities with increasing degrees of accuracy.	Find area of irregular shapes using grid paper Investigate various systems of measurement and discuss the degree of accuracy	See page 473. See the Investigation for chapter 3.	See teacher’s edition for a list of materials needed for this activity Same as #1	Group assessment Same as #1

 
 

Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Calculus Timeline 1st Q All year	Understand and use the concept of significant digits.	Decide how many places to use in answers resulting from computation with pi Generalize a way of determining how accurate an answer needs to be	See Lesson 2-2. Examples are found throughout the text and the process is continuous throughout the program.	Math journal, Math Tools "Geometry" See teacher’s edition for a list of materials needed for each problem	"On Your Own" examples, teaching resources provided by the publisher Group assessment
Timeline 4th Q 4th Q	Develop informal ways of approximating the surface area and volume of familiar objects and discuss whether the approximations make sense.	Explore ways to find the surface area of solid geometric shapes Develop ways to find the volume of solid geometric shapes.	See Lesson 11-3. See Lesson 11-5.	Math journal Same as #1	"On Your Own" examples, teaching resources provided by the publisher Same as #1
Timeline 4th Q 4th Q	Express mathematically and explain the impact of the change of an object’s linear dimensions on its surface area and volume.	Express mathematically the effect of changing the dimensions of a prism on its surface area  Explain the change in the volume of a solid geometric shape when its dimensions are doubled	See Lesson 11-6. See Lesson 11-9.	Math journal Spreadsheet software, Hot Page software, math journal	"On Your Own" examples, teaching resources provided by the publisher, group assessment "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet, group assessment

 

Resources Fibonacci Numbers and the Golden Section  - introduction on the Fibonacci numbers and where they appear in Nature.                                                                                                Includes a brief introduction to the other Fibonacci and Golden Section                                                                                                web pages at this site. Pascal's Triangle  -great lessons and links to activities and resources on Pascal's Triangle Calculus Problem of the Week I Love Calculus  -calculus LINKS- So Hot they'll Make Your T-1 Line Sizzle.