Elementary Mulitiplication & Division

Graphing Technologies in the Common Core ClassroomPCMI/IM : Park City Mathematics Institute / Illustrative MathematicsApologiesSetupCal ArmstrongMathematics TeacherDirector of Teaching & Technology InnovationFacilitator at Park City Mathematics Institute mathforum.org/pcmi Auxiliary Police Constable

Everything on the OneNote : bit.ly/nctmindy http://dwhconsultingukgroup.blogspot.com/2012/09/when-will-politicians-approach-teachers.html

Goals:You will have a better understanding of how to implement the following mathematical practices in your classroom: From CCSS MP5[Students] are able to use technological tools to explore and deepen their understanding of concepts.From CCSS MP1: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.

Other goalsBecome accustomed to a new graphing toolLearn a few new tips to make life easierDo some mathThink like a studentConsider misconceptions

ToolsDesmos www.desmos.comFree No offline mode (i.e. need internet)GeoGebra www.geogebra.org FreeCan work offlineLots of other options!

Lets explore with some technology!Please go to the webpage tinyurl.com/cTAPgame1

Play with the sliders to see what happens to the graphs. Notice that the equation has the form y=a*xb, and you control a and b.

Take notes on your observations sheet. When we play the game, you will not be able to use the computers to test out your ideas! Target Practice, Round 1RulesYour goal is to create a curve that passes through each of the two targetsYou can change the values of the parameters given. You cant change the form of the equation (y=a*xb)Each team gets one guess. The next team must come up with parameter values that have not been used before.

Link to gamehttps://www.desmos.com/calculator

Lets explore again, making it harder!Please go to the webpage tinyurl.com/cTAPgame2

Play with these sliders to see what happens to the graphs. Notice that the form of the equation has changed to y=a(x-b)(x-c)(x-d)

As you explore, record observations on the sheet given. In a few minutes, we will start Round 2, where you use this equation to aim for three targets. Target Practice, Round 2RulesYour goal is to create a curve that passes through each of the three targetsYou can change the values of the parameters given. You cant change the form of the equation y=a(x-b)(x-c)(x-d)Each team gets one guess. The next team must come up with parameter values that have not been used before.

Links to gamehttps://www.desmos.com/calculator

At your table, share through a round robin. How did you engage with math while playing this game?What comments or observations in your group discussions ended up being the most helpful and insightful?How does this activity relate to the mathematical practices mentioned earlier? From CCSS MP5[Students] are able to use technological tools to explore and deepen their understanding of concepts.

From CCSS MP1: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.

Building a solid foundation

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Sample student work

What was the student thinking when they created this graph?

What misconceptions did they have?

Dweck: the moment a misconception is recognized, it should be explored!

Wouldnt it be nice to have a virtual Ferris wheel, one where you could easily measure the heights at different times? For questions 1 4tinyurl.com/cTapFerrisWheel1

For questions 5 and 6tinyurl.com/cTapFerrisWheel2

Discuss your answers with your group mates. Use the Ferris wheel to explain your reasoning.

Discussion QuestionsHow did technology aid your ability to understand and explain the shape of the graph?

How is the experience of using a computer program to measure heights different from using a ruler and protractor to do the same thing? Which do you prefer and why?

How does this activity reinforce the Mathematical Practices we brought up at the start of the session? How did the technology influence the discourse at your table?Tech Tools - Explorations

NCTM Illuminations

Shodor Interactive

National Library of Virtual ManipulativeAnd many, many more

MARS TasksMore Tech ToolsExcel Online, Google SpreadsheetsGeogebraGeometers Sketchpad

Park City Mathematics Institutehttp://mathforum.org/pcmi Additional Resourceswww.illustrativemathematics.orgwww.corestandards.orgwww.mathalicious.orgwww.cpalms.org

Thank you for your participation!