Math APPs A key to CCSS and Problem Solving

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Math APPsA key to CCSS and Problem Solving

• Presented by Diana Herrington
• dianaherringtonmath_at_gmail.com
• www.dianaherrington.com

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Before we beginAlways Remember

• An APP is only a tool
• You are always the teacher - and a teachers job
  is to engage students in learning

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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

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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)

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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)

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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)

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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

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Purposes for APPs

• Review
• Practice
• Organization
• Communication
• Collaboration
• Thinking Differently

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APPs that I use

• Notability
• Doceri
• iBooks Author
• Geoboard
• Myscript Calculator
• Desmos
• All things Wolfram

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APPs that will change your teaching

• Desmos - for the math classroom
• Wolfram - for math, physics, and chemistry

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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

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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

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Fractions

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

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Fractions

• what process is the same in each exact result?
• write down what you notice

• share time - group and then room

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Fraction Check

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

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Elevation vs Boiling Point

• Sometimes we get golden opportunities by looking
  outside the math APPs. This is from General
  Chemistry.

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Elevation vs Boiling Point
Elevation (ft) Boiling pt ( C)
300 99.96
1000 99.25
2000 98.23
3000 97.22
4000 96.20
5000 95.18

• Your task is to determine if there is a
  mathematical model between the elevation and the
  boiling point of water with the given data.

o
o
o
o
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Elevation vs Boiling Point

• Test your mathematical model idea with the
  following information
• Tioga Pass _at_ 10000 ft, water boils _at_ 90.08 oC
• Mount Whitney _at_ 12500 ft, water boils _at_ 85.47 oC
• How accurate was your model?

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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.

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Desmos for understanding

• Graph the circle x2y225
• Now what happens if we add a trig function?

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Desmos

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

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more desmos

• does your pattern continue?

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Desmos

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

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Desmos Investigation

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

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Desmos Investigation

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

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Desmos Investigation 2

• Now we are going to look at period changes

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Desmos Investigation 2

• At what period will there be more than one region?

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More APPsremember new APPs are emerging daily

• geometrypad
• isosceles
• ratio rumble
• SketchExplorer
• GeoGebra

• TI-Nspire CAS
• fxIntegrator
• mathstudio
• mathsnacks
• Amazingscience

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thank you for your time