MATHEMATICAL MODELLING 1 (INTRODUCTION)

SETTING THE CONTEXT

The following photos were taken along pavements and roads. 
They show 'cracks' or 'gaps'. 

• Are these cracks common phenomena?  
• Do they serve specific functions?

PICTURE 2

PICTURE 1

PICTURE 3

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REVISIT THE CONTEXT

joints in concrete pavements

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MATHEMATICAL MODELLING 2 (OBJECTIVES)

OBJECTIVES

Understand the facets of Applied Learning through a Mathematics Lesson

Authentic (Real World Application) 
The focus on a science experiment as a basis to gather data and information

Active & Relevant
Students will be engaged throughout the process as they are the co-constructors of knowledge (making Prediction, Observing patterns and Explaining the final outcome(s))

Integration (through inter-disciplinary approach)
Learning of cooling curve and using the Mathematical modeling to draw conclusion.

MATHEMATICAL MODELLING 3 (POE)

RECALL - REVIEW - REFLECT

ACTIVITY 

Measuring of body temperature against time

PREDICT
(before the experiment)
What do you think will be the characteristics of the temperature against time graph of this experiment?

OBSERVE
(during and after the experiment)
What do you notice about the graphical function(s) obtained?
Describe the characteristics?
Any unusual / distinct patterns observed?

EXPLAIN
(after experiment)
Are the experimental observations similar to the prediction? Why?
Can the outcome(s) be generalised for all cases?

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RECALL - REVIEW - REFLECT

TYPES OF GRAPHS 

Graphs

MATHEMATICAL MODELLING 4 (ROUTINE)

CLASS LEARNING ROUTINE

Task in a Collaborative learning environment
You will be working in groups of 4 with the following roles:

• Student 1: Leader (lead the task and present findings)
• Student 2: Scribe (capture learning and post in Mathematics Blog)
• Students 3 & 4: Researchers (set-up apparatus for activities)
• All members will be involved in the activities through
• Group discussion
• Prediction Making
• Conduct of Experiment
• Data Gathering (recording observations)
• Presentation of Findings (explain the Mathematics model - graphical functions)

Use of Apparatus / Equipment

Each group will have

• Learning Devices (for recording, researching, presenting)
• One beaker
• One TI-Nspire Calculator 
• One temperature probe

Set-up

• Go to your Class Math Blog.
• Set up and connect the TI-Nspire Calculator to the Local network. Refer to the instructions given.  (ensure that your group appears on the teacher's screen)

Class Math Blog

MATHEMATICAL MODELLING 5 (STUDENT CENTRED EXPERIMENT)

STUDENT-CENTRED ACTIVITY 

STUDENT-CENTRED ACTIVITY 

In this experiment, You have to use the POE thinking routine approach to learn about the temperature change in 2 scenarios.

TASK STRUCTURE

in brief

• Predict by sketching the possible relationships between Temperature against time for BOTH scenarios. Indicate any intersections, turning points and any other possible characteristics based on your prediction.

• You are given 40 minutes to do prediction, experiments, discussions and uploading of presentation on the S3-05 class Math blog (create a new page). You have to decide on the time and task management. 

• Follow the format of your Presentation for BOTH scenarios as shown below.

in detail

1. Post your PREDICTION in the Class mathematics blog. 
1. Include a Sketch (you may use any sketching tools) and 
2. a brief writeup of the Predicted mathematical model Example. Quadratic with a maximum turning point at ...(BEFORE THE EXPERIMENT)
2. Conduct the scenario and OBSERVE patterns, unusual phenomena /patterns /observations (if any). You may repeat it a few times. 
1. Do a screen capture and post your experimental findings and 
2. identify the Mathematical model(s) that best suit the graphical function(s). example Linear from 0-4 s and then Quadratic etc.  
3. EXPLAIN your Prediction and Observations by posting the following in your blog.
1. Compare and contrast the predictions with the actual results, are there any significant differences? Why?
2.  What are the characteristics of the graphs?
• a.    the slope from start to finish (steeper, gentler)
• b.    intersections with axes (if any)
• c.     possible turning point (if any)
• d.    any asymptote?
• e.    And any other evidence
4. What are the assumptions you have to make for this experiment? What are the sources for discrepancies?

Sample format:

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SCENARIO 1 

Start with your prediction: Predict the relationship between temperature against time when you place the probe in hot water ONLY. 

SCENARIO 2 

Predict the relationship between temperature against time when you add few ice cubes into the hot water. 

MATHEMATICAL MODELLING 6 (POST ACTIVITY REFLECTION)