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

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

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

4. How does a Grow Beast grow? Let’s take a look, shall we?look 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.

6. How does your Grow Beast grow?

7. Simulated Grow Beasts

8. Grow Beasts A, B and C

11. Here are your three GBs: “A” was grown in a medium salt solution (10cc/200ml) “B” was grown in warm water (~30 o C) “C” was grown in room temperature water (~20 o C) HOURS elapsed Med SaltWarm WaterJust Water begin 10AM 10/8/08 10cc/200ml30 degrees C20 degrees C 0 4.34.24.1 1 4.34.44.3 2 4.74.5 4 5.24.8 6 4.66.05.4 8 4.76.86.0 10 12124.97.46.4 12 5.08.46.9 14 5.08.97.2 22 5.311.08.1 24 5.311.58.3 28 5.412.18.7 32 5.412.59.1 37 5.612.99.4 48 5.713.610.1 50 5.813.910.3 56 5.814.210.6 62 5.814.610.9 72 5.814.811.0 ABC Grow Beasts: salt water, warm water, and just water CAB Tabular

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

13. 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. How does a Grow Beast grow? Kinesthetic -> Tabular -> Graphical -> Abstract

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

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 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