Beat Ratios and Juggling Proportions

Juggling is analyzed from a mathematical point of view. Initially, timelines are used to represent juggling. The timelines are developed based on the concepts of period, frequency, and phase shift. This analysis leads to development of the juggling ratio. The juggling ratio is then used to solve problems of scheduling machines in a factory and employees in the work place. Throughout the module, the student applies math concepts of least common multiple, greatest common factor, adding and multiplying fractions, setting up ratios, and the principles of periodicity. Lesson 1 Juggling and Mathematics Students interpret and create timelines for people and machines. Temporal patterns are represented using timelines, ratios, and verbal descriptions. Lesson 2 Timelines Students watch a video of a juggler in slow motion and create a timeline for the juggling ball and a timeline for the hand of the juggler. Lesson 3 Juggling Timelines Students investigate period and frequency of drumbeat timelines.  Then, period and frequency of juggling timelines from Lesson 2 are calculated. Lesson 4 Phase Shifts Pairs of timelines are used to calculate phase shifts. Students use the timelines from the juggling video to calculate phase shifts of the ball and hand timelines. Lesson 5 In Sync Students discover the relationship between common period for pairs of timelines and the concept of least common multiple. This synchronization concept is then applied to coordinating factory outputs. Lesson 6 Frequencies in Sync Students discover the relationship between common frequency for pairs of timelines and greatest common factor. Lesson 7 Applications Scheduling problems are solved using timelines.  Problems include scheduling employee work shifts for three employees on two machines, and determining how many crews are needed for servicing a given airline flight schedule. Lesson 8 The Juggling Proportion Scheduling problems are solved using the juggling proportion. Nitty Gritty: Order of operations. Lesson 9 Fractions Fraction related concepts that have been explored throughout the module are addressed formally. Lesson 10 Unit Analysis and Multiplying Fractions Fractions are used to solve unit analysis problems and rate problems. Lesson 11 Work and Adding Fractions Addition and Subtraction of fractions is done visually as well as by using least common multiple of the denominators. Compare this module to traditional course topics in the Matrix of Course Competencies. If one of the lessons has a link, you can preview that lesson. Other modules: Beat Ratios Functions Exp. Growth Data & Graphs Representing Data Finance Geometry Sampling Non-linear Behavior Linear Behavior Sets and Logic Patterns Probability Systems Right Tri. Trig.