Math APPs A key to CCSS and Problem Solving Presented by Diana Herrington [email protected] .

Math APPsA key to CCSS and Problem Solving

Presented by Diana [email protected]

www.dianaherrington.com

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

teachingDesmos - 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)

300 99.96

1000 99.25

2000 98.23

3000 97.22

4000 96.20

5000 95.18

o

oo

o

Elevation vs Boiling Point

Test your mathematical model idea with the following information:

Tioga Pass @ 10000 ft, water boils @ 90.08 oC

Mount Whitney @ 12500 ft, water boils @ 85.47 oC

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 x2+y2=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 APPsremember new APPs are emerging

daily

TI-Nspire CAS

fxIntegrator

mathstudio

mathsnacks

Amazingscience

geometrypad+

isosceles

ratio rumble

SketchExplorer

GeoGebra

thank you for your time