Mathematical Modeling with Strawberries and Videos Sean Nank, PhD October 24, 2014 Session 466

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Mathematics English General Formative Assessment Strategies SBAC Guides

Four attributes of formative assessments 1)Clarify intended learning - Help students and/or teachers understand their goal 2)Elicit evidence - No single way, can be strategic or on-the-fly 3) Interpret evidence - In relation to the learning target (misunderstandings) 4) Act on evidence

Let’s try a problem! But first – why introduce modeling in this manner? “real math” vs. real math Do we believe all students can learn? Do we REALLY believe all students can learn? So why aren’t they all learning?

MP 4 – Modeling with Mathematics Modeling is one of the most misunderstood MPs This can be modeling, but often they are manipulatives: They can be great resources! They can also be used while modeling

1)Identify essential variables 2)Formulate a model that describes relationships between variables 3)Analyze and perform operations on the relationships to draw conclusions 4)Interpret the results in terms of the original situation 5)Validate conclusions by comparing them with the situation and then improve or accept the model. 6)Report the conclusions and reasoning Common Core State Standards for Mathematics, pp MP 4 – Modeling with Mathematics

“old school” modeling You go online to buy your favorite shampoo. Company A charges $5 per bottle plus $8 for shipping and handling. Company B charges $3 per bottle plus $24 for shipping and handling. How many bottles must you buy to justify using company B? y = 5x + 8 y = 3x x + 8 = 3x + 24 x = 8 (8, 48)

CCSS modeling The shampoo problem isn’t “bad.” But it begs a question: When have you had a problem as an adult (personal or professional) where someone came to you and identified the problem, provided the data, isolated the variables, and asked you to solve it?

Have you ever been stuck at an airport?

San Francisco Airport Why have I been stuck at this airport more than any other and what can be done about it?! 1)Identify essential variables a)How many flights per day b) How many airlines c)International – does that matter? d)Pilots take off sight seeing? e)Air traffic control – does that matter? f)What about the topography g)There is a lot of fog in San Francisco – does that matter? This is the richness of modeling problems and we have only started step 1!

Let’s try a problem! Mathematical Modeling with Strawberries and Videos This is an example of how to use videos Ideally, students will create their own inquiries and videos!

I notice… I wonder… The video shown during this presentation can be found on youtube or the digital library.

Mathematical Modeling with Strawberries What do you notice? What do you wonder? These questions are important as students are (1) identifying variables so they can (2) formulate a model.

Build your model. Then we will validate it! The video shown during this presentation can be found on youtube or the digital library.

1) Identify all the variables in this situation. Be sure to label all variables. 2) Formulate a model by creating equation(s) relating the variables. 3) Analyze the model and state conclusions about the variables. 4) Interpret the results in the original situation. How long does it take for him to chop all the strawberries? 5) Validate your results In this step, show the video in its entirety while timing how long it takes the person to chop all the strawberries. 6) Report on your conclusions and reasoning behind them Were you correct? Was your predicted time close to the actual time? What varied between your model and what actually occurred? Should you have been able to foresee the difference between your model and what actually occurred?

Sean Nank, PhD

Send your text message to this Phone Number: Strongly Disagree Strongly Agree Disagree Agree Speaker was well- prepared and knowledgeable (0-3) Speaker was engaging and an effective presenter (0-3) Session matched title and description in program book (0-3) Other comments, suggestions, or feedback (words) ___ ___ ___ ___________ Example: XXXXX 323 Great session! 5 digit poll code for this session (no spaces) Non-Example: XXXXX Great session! (1 space) Non-Example: XXXXX3-2-3Great session!