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

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

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

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

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.

How does your Grow Beast grow?

Simulated Grow Beasts

Grow Beasts A, B and C

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 ABC Grow Beasts: salt water, warm water, and just water CAB Tabular

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

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

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

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….

Grow Beasts: Growing students’ understanding of ratio, proportions and slope Mark Roddy, Ph.D. Seattle University

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

Three Grow Beasts: salt, lemon, water