Content Area: Math

 

Index: 4.3C Grade 8 CPI 1

 

Standard: 4.3 - Patterns and Algebra

 

Strand: C - Modeling

 

Cumulative Progress Indicator: 1 - The student will analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.

 

Grade: 8

 

Sample Activities:

 

·        Students investigate how increasing the temperature measured in degrees Celsius affects the temperature measured in degrees Fahrenheit and vice versa. They collect data using water, ice, and a burner. They use their data to develop a formula relating Celsius to Fahrenheit, summarize the formula in a sentence, and graph the values they have generated.

 

·        Students investigate how the temperature affects the number of chirps a cricket makes in a minute.

 

·        Students investigate the effect of changing the radius or diameter of a circle upon its circumference by measuring the radius (or diameter) and the circumference of circular objects. They graph the values they have generated, notice that it is close to a straight line, and describe the relationship they have found in a paragraph. Then they develop a symbolic expression that describes that relationship.

 

·        Students investigate the effect on the perimeters of given shapes if each side is doubled or tripled. They summarize their findings.

 

·        Students investigate how the areas of rectangles change as the length is doubled, or the width is doubled, or both are doubled. They discuss their findings.

 

·        Students work on problems like this one from the New Jersey Department of Education's Mathematics Instructional Guide (p. 7-69): Two of the opposite sides of a square are increased by 20% and the other two sides are decreased by 10%. What is the percent of change in the area of the original square to the area of the newly formed rectangle? Explain the process you used to solve the problem.

 

·        Students investigate how the areas of triangles change if the base is kept the same, but the height is repeatedly increased by one unit.

 

·        Students stack a given number of unit cubes in various ways and find the surface areas of the structures they have built. They sketch their figures and discuss which of the figures has the largest surface area and which has the smallest, and justify their conclusions.

 

·        Students make models of cubes using blocks or other manipulatives, and investigate how the volume changes if the length, width, and height are all doubled.

 

·        Using a spreadsheet, students investigate how adding (or subtracting) values to given data can affect the mean, median, mode, or range of the data. They discuss how various other changes to the data would affect the mean, the median, the mode, or the range.