Grow Beasts: Growing students’ understanding of ratio, proportions and slope

1. Grow Beasts: Growing students’ understanding of ratio, proportions and slope • National Council of Teachers of Mathematics Annual Conference April, San Diego, California Mark Roddy, Ph.D. Seattle University

2. Grow Beasts: Growing students’ understanding of ratio, proportions and slope Objectives:Session participants will build understanding of: • an application of data gathering, prediction, slope, linear (and non-linear) rates of change; • the use of inquiry to engage students in the construction of understanding and skill; • Grounds for decision making as to the use of technology (spreadsheets); • the role of positive disposition in the development of understanding and skill. Participants will be invited to join a Web-based network of teachers using this investigation.

3. Grow Beasts: Growing students’ understanding of ratio, proportions and slope Objectives:Session participants will build understanding of: • an application of data gathering, prediction, slope, linear (and non-linear) rates of change; • the use of inquiry to engage students in the construction of understanding and skill; • Grounds for decision making as to the use of technology (spreadsheets) • the role of positive disposition in the development of understanding and skill. Participants will be invited to join a Web-based network of teachers using this investigation.

4. How does a Grow Beast grow? Let’s take a look, shall we? Kinesthetic -> Tabular -> Graphical -> Abstract (After AIMS)

5. Using Grow Beasts to teach math • In a second grade class • measurement, data recording, prediction and estimation. • In middle school • ratio, proportion, rate and slope • In high school • Inquiry, modeling, research, presentation, etc. WSMC

6. How does your Grow Beast grow? Let’s (pretend to) grow some!

7. Simulated Grow Beasts A B C

8. Grow Beasts A, B and C

9. Grow Beasts A, B and C

10. Grow Beasts A, B and C

11. Grow Beasts: salt water, warm water, and just water A B C Here are your three GBs: • “A” was grown in a medium salt solution (10cc/200ml) • “B” was grown in warm water(~30oC) • “C” was grown in room temperature water (~20oC) Tabular

12. Grow Beasts: warm water, water, and salt water B C A B C A Graphical

13. How does a Grow Beast grow? To 500 ml of room temperature water I will add: • somewhere between 5 and 50 cc of salt,or • somewhere between 5 and 50 ml of lemon juice. Your team’s mission is to develop a mathematical model that will enable you to accurately predict the length of the GB at 6-hour intervals for four days. Kinesthetic -> Tabular -> Graphical -> Abstract

14. Using Grow Beasts to Teach Math • 5th grade: measurement • 6th grade: ratio and rate • 7th grade: rates of change, slope and linear equations • 8th grade: more linear functions and the analysis and summary of data sets Try It!

15. Height vs stride This is an example of middle-level students exploring, exercising choice and making use of the spreadsheet, having had the kinesthetic, the tabular and so forth….

16. Grow Beasts: Growing students’ understanding of ratio, proportions and slope http://growbeast.wikispaces.com Mark Roddy, Ph.D. Seattle University

17. Grow Beasts: Growing students’ understanding of ratio, proportions and slope 2010 National Council of Teachers of Mathematics Annual Conference April 21 - 24 San Diego, California Mark Roddy, Ph.D. Seattle University

18. Three Grow Beasts: salt, lemon, water