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Content Area: Math
Index: 4.3C Grade 8 CPI 2
Standard: 4.3 - Patterns and Algebra
Strand: C - Modeling
Cumulative Progress Indicator: 2 - The student will use patterns, relations, symbolic algebra, and linear functions to model situations · Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities · Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)
Grade: 8
Sample Activities:
· Groups of students pretend that they work for construction companies bidding on a federal project to build a monument. The monument is to be built from marble cubes, with each cube being one cubic foot. The monument is to have a "triangular" shape, with one cube on top, then two cubes in the row below, then three cubes, four cubes, and so on. The monument is to be 100 feet high. The students make a chart and look for a pattern to help them predict how many cubes they will need to buy so that they can include the cost of the cubes in their bid.
· Students use the constant function on the calculator to determine when an item will be on sale for half price. If the price goes down by a constant dollar amount each week, then they record successive prices, such as 95 - 15 = = = . . . (or 15 - - 95 = = = on other calculators). If the price is reduced by a certain percent each week, then they use the constant function on the calculator to obtain successive discounts as percents by multiplying. For example, if a $95 item is reduced by 10% each week, they key in 95 x .9 = = = . . . (or as .9 x x 95 = = = . . . on other calculators).
· Using a temperature probe and a graphing calculator or computer, students measure the temperature of boiling water in a cup as it cools. They make a table showing the temperature at five-minute intervals for an hour. Then they graph the results and make observations about the shape of the graph, such as the temperature went down the most in the first few minutes or it cooled more slowly after more time had passed, or it's not a linear relationship. The students also predict what the graph would look like if they continued to collect data for another twelve hours.
· Students use coins to simulate boys (tails) and girls (heads) in a family with five children. They make a list of all of the possible combinations, use patterns to help them organize all of the possibilities, and find the probability that all five children are girls or that exactly three are girls. As a question on a test, they are asked to react to an argument between Pam and Jerry, a couple who want to have four children. Jerry thinks that they will probably end up with two boys and two girls, while Pam thinks that they will probably wind up with an unequal number of boys and girls.
· Students make Ferris wheel models from paper plates, with notches representing the cars. They use the models to make a table showing the height above the ground of a person on a ferris wheel at specified time intervals, determined by the time needed for the next chair to move to loading position. After collecting data through two or three complete turns of the wheel, they make a graph of time versus height. In their math notebooks, they respond to questions about their graphs: Why doesn't the graph start at zero? What is the maximum height? Why does the shape of the graph repeat? The students learn that this graph represents a periodic function.
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