Math APPs A key to CCSS and Problem Solving Presented by Diana Herrington

Before we begin Always Remember: An APP is only a tool You are always the teacher - and a teacher’s job is to engage students in learning

Why Problem Solving? Creates thinkers Gives self-worth Ownership Helps develop curiosity - the “what if” factor Strategies for life-long learning Allows for bumps in the learning

Problem Solving competency areas Initiative - you set up and take action without being asked. You look for opportunities to make a difference Look for and make use of structure (CCSS) Creativity - you are an original thinker and have the ability to go beyond traditional approaches Look for and express regularity in repeated reasoning (CCSS)

Problem Solving competency areas Resourcefulness - you adapt to new/difficult situations and devise ways to overcome obstacles Reason abstractly and quantitatively (CCSS) Analytical Thinking - you can use logic and critical thinking to analyze a situation Attend to precision and Construct viable arguments and critique the reasoning of others (CCSS)

Problem Solving competency areas Determination - you are persistant and do not give up easily Make sense of problems and persevere in solving them (CCSS) Results oriented - your focus is on getting to the desired outcome - solving the problem Model with mathematics and use appropriate tools strategically (CCSS)

Problem Solving and APPs Students embrase technology APPs will engage students in learning and used with questioning techniques will create a rich CCSS learning environment to develop problem solving thought processes and opportunities We will focus on Pattern Recognition and Mathematical Modeling as our process for today

Purposes for APPs Review Practice Organization Communication Collaboration Thinking Differently

APPs that I use Notability Doceri iBooks Author Geoboard Myscript Calculator Desmos All things Wolfram

APPs that will change your teaching Desmos - for the math classroom Wolfram - for math, physics, and chemistry

Examples we will explore Wolfram Fractions - a fraction resource Desmos - a non-function based graphing utility Wolfram Chemistry - look at the liquids and solids boiling points - what patterns are noticed

Wolfram Fractions For this activity we are going to have students notice patterns and describe what is happening Useful for engaging the mind of a student who “cannot remember” how to work with fractions A beginning step into problem solving by comparing and analyzing patterns in written work

Fractions screen shot of answer and step-by-step solution

Fractions what process is the same in each exact result? write down what you notice share time - group and then room

Fraction Check Check to see if your process works with this addition result

Elevation vs Boiling Point Sometimes we get golden opportunities by looking outside the math APPs. This is from General Chemistry.

Elevation vs Boiling Point Your task is to determine if there is a mathematical model between the elevation and the boiling point of water with the given data. Elevation (ft)Boiling pt ( C) o o o o

Elevation vs Boiling Point Test your mathematical model idea with the following information: Tioga ft, water o C Mount ft, water o C How accurate was your model?

Desmos for understanding Desmos is a non-function based graphing utility This is an investigation for strong pattern pattern recognition and a different understanding of trig.

Desmos for understanding Graph the circle x 2 +y 2 =25 Now what happens if we add a trig function?

Desmos Notice what happens. Identify what is the same and what is not

more desmos does your pattern continue?

Desmos At what amplitude do you go from a simple closed area to more than one area?

Desmos Investigation Generalize the relationship between the amplitude and the radius of the circle to create more than one simple closed region.

Desmos Investigation Now the period has been changed, notice what the amplitude does - how does your generalization work?

Desmos Investigation 2 Now we are going to look at period changes

Desmos Investigation 2 At what period will there be more than one region?

More APPs remember new APPs are emerging daily TI-Nspire CAS fxIntegrator mathstudio mathsnacks Amazingscienc e geometrypad+ isosceles ratio rumble SketchExplorer GeoGebra

thank you for your time