Rivers twist and turn as they make their way to the sea. Why does this happen and how can this be explained mathematically? In this module we look at the geometry of meandering rivers. In the process we'll discover some fascinating numerical relationships.

Students will learn some basic concepts about the geophysics of how rivers form, but they will focus their analysis on what is called the sinuousity ratio. This is the ratio of the straight-line distance of the river and its meandering distance. This ratio reveals important characteristics of the river. Then, students will develop and examine geometric models involving circular arcs and segments to get a better understanding of the ratio. These models will first involve using a compass and straight edge to model a river. This is followed by an algebraic analysis.

This module is an excellent way of tying real world concepts to geometry and algebra. The real-world application is easy to understand and yet it reveals a wealth of math concepts to be explored.

Another factor in the mortgage crisis was the use of adjustable rate mortgages. Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis.

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-data-analysis-segment-4-what-adjustable-rate-mortgage

A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-what-adjustable-rate-mortgage

Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river’s length to its straight-line distance tell us? In this segment the geological forces that account for a river’s motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to pi.

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-variables-and-equations-segment-3-river-ratios

A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-river-ratios

Another factor in the mortgage crisis was the use of adjustable rate mortgages. Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis. 

A Video Transcript is available for this tutorial at this Link

Note: The download is Media4Math's guide to closed captioned videos.

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Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river’s length to its straight-line distance tell us? In this segment the geological forces that account for a river’s motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to pi.

A Video Transcript is available for this tutorial at this Link

Note: The download is Media4Math's guide to closed captioned videos.

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Video Tutorial: Ratios: Fraction-Percent Conversion. In this video learn how to convert percents to fractions to simplify percent operations. 

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Video Tutorial: Ratios and Proportions: Scale Drawings. In this video, we look at the properties of similar figures and use proportions to find lengths of corresponding sides. 

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Video Tutorial: Ratios and Proportions: Solving Proportions. In this video, we solve proportion problems algebraically. 

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Video Tutorial: Ratios and Proportions: What are Proportions?. In this video, we solve proportion problems using equivalent ratios. 

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Video Tutorial: Ratios and Rates: Converting Measurement Units. In this video, we show how to use conversion rates to convert from one unit of measurement to another. Students are shown how to create a conversion rate. 

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Video Tutorial: Ratios and Rates: Rates and Slopes of Lines. In this video we connect the concept of rate of change for a set of linear data to the concept of slope. We use the slope formula to find the rate of change. 

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Video Tutorial: Ratios and Rates: Rates from Data. In this video, we look at linear data sets that can be used to find the rate of change. 

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Video Tutorial: Ratios and Rates: Ratios as Decimals. In this video, students explore ratios whose terms are decimals. Students are shown techniques for simplifying these types of ratios in ;the context of solving real-world ratio problems. 

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Video Tutorial: Ratios and Percents: Calculating Percents. In this video, students will see the relationship between ratios, proportions, and percents. A percent formula is derived and used to solve several real-world percent problems. 

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In this video, we explore the application of ratio concepts to the pitch of a roof and the slope of a ramp. Several real-world examples are explored. 

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Video Tutorial: Ratios: Equivalent Ratios. In this video we look at equivalent ratios and solve problems that involve the use of equivalent ratios 

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Video Tutorial: Ratios: Fractional Ratios. In this video look at ratios of the form a:b and a:b:c, where the terms in the ratio are fractions. Techniques are shown for converting fractional ratios to whole number ratios. 

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Video Tutorial: Ratios: Rates. In this video we look at rates. 

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Video Tutorial: Ratios: Ratios and Fractions. In this video, students look at at the similarities and differences between ratios and fractions. We also show how to derive fractional relationships from ratios. 

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Video Tutorial: Ratios: Ratios with Three Items. In this video, students look at ratios of the form a:b:c. Analyze pairs of ratios and see how they can be combined into one ratio. 

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Video Tutorial: Ratios: Unit Rates. In this video we look at unit rates. 

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Video Tutorial: Ratios: Visual Models for Ratios. In this video, we look at different visual models for solving ratio problems. 

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Video Tutorial: Visual Models for Ratios and Percents. In this video explore visual models for ratios and fractions that can be used as visual models for percents. Model different ratios and percents using visual models. 

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Video Tutorial: Ratios: What Are Ratios? In this video, students learn what a ratio is and look at examples of different types of ratios. 

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The definition of the term "Rate."

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Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary