Title: Make a Conjecture
In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.
Standard(s): [MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]
Title: Whelk-Come to Mathematics
In this four-lesson unit, from Illuminations, students make a conjecture, conduct an experiment, analyze data and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops.
Standard(s): [MA2015] AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama)
Title: Road Trip!
In this Illuminations lesson, students investigate the famous Traveling Salesman Problem by considering the shortest route between five northeastern cities. Three different algorithms for finding the shortest route are explored, and students are encouraged to look for others.
Standard(s): [MA2015] ALT (9-12) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]
Title: Escape from the Tomb Activity
This reproducible activity sheet, from an Illuminations lesson, includes instructions and questions for a mathematical adventure game. In the game, students are given a problem in which two bowls are suspended from the ceiling by springs, and one bowl is lower than the other. Students must work out how many items should be placed in each bowl so that the heights of the bowls are the same.
Standard(s): [MA2015] AL2 (9-12) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]