Grow Beasts: Growing students’ understanding

of ratio, proportions and slope

Grow Beasts: Growing students’ understanding

of ratio, proportions and slope

2010 National Council of Teachers of Mathematics

Annual Conference

April, San Diego, CaliforniaMark 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?

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.

WSMC WSMC

How does your Grow Beast grow?

Simulated Grow Beasts

Grow Beasts A, B and C

Grow Beasts A, B and C

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 (~30oC)

• “C” was grown in room temperature water (~20oC)

HOURS elapsed  Med Salt Warm Water Just Water

begin 10AM 10/8/08  10cc/200ml 30 degrees C 20 degrees C

0   4.3 4.2 4.1

1   4.3 4.4 4.3

2   4.3 4.7 4.5

4   4.5 5.2 4.8

6   4.6 6.0 5.4

8   4.7 6.8 6.0

1012 4.9 7.4 6.4

12   5.0 8.4 6.9

14   5.0 8.9 7.2

22   5.3 11.0 8.1

24   5.3 11.5 8.3

28   5.4 12.1 8.7

32   5.4 12.5 9.1

37   5.6 12.9 9.4

48   5.7 13.6 10.1

50   5.8 13.9 10.3

56   5.8 14.2 10.6

62   5.8 14.6 10.9

72   5.8 14.8 11.0

A B C

Grow Beasts: salt water, warm water, and just waterCA B

Tabular

Grow Beasts: warm water, water, and salt waterAB C

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

• 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

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

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 21 - 24San Diego, California

Mark Roddy, Ph.D.Seattle University

Three Grow Beasts: salt, lemon, water