Focus: Covariational Reasoning Using Bottles of Different Shapes

Directions

Have students first explore rates of change with dynamic software such as GeoGebra. Some pre-made files already exist (https://www.geogebra.org/o/LevmWZj1, https://www.geogebra.org/o/RctGlhsY). Then have students do some reading on rates of change and also explore adding water to different shaped bottles. Eventually, provide students with different shaped bottles and ask them to imagine that you are adding water at a constant rate and to draw a graph of the volume of water with respect to height of water. This can lead to discussions on rates of change and ultimately derivative (see https://www.geogebra.org/o/pBiYaUxR and https://www.geogebra.org/o/QSUFdCGn).

## Planning a Lesson in 3 Moments for Mathematics

NLI ELL BreakoutsfromMarie Himes## Instructional Unit: Rates of Change

Focus: Covariational Reasoning Using Bottles of Different Shapes

Have students first explore rates of change with dynamic software such as GeoGebra. Some pre-made files already exist (https://www.geogebra.org/o/LevmWZj1, https://www.geogebra.org/o/RctGlhsY). Then have students do some reading on rates of change and also explore adding water to different shaped bottles. Eventually, provide students with different shaped bottles and ask them to imagine that you are adding water at a constant rate and to draw a graph of theDirectionsvolume of waterwith respect toheight of water. This can lead to discussions on rates of change and ultimately derivative (see https://www.geogebra.org/o/pBiYaUxR and https://www.geogebra.org/o/QSUFdCGn).Text Options:Mathematics Standards:PREPARE, INTERACT, & EXTEND (PIE) Instructional Strategies(across content)