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Desmos Graphing Calculator in NC

Nolan Doyle

Desmos Support Team support@desmos.com

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Learning Goals

Introductions

and a little about Desmos Studio PBC

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Comfort, Confidence, Inspiration

Teaching

vs

Testing

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Questions & Survey

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Nolan Doyle

Midlothian, Va

About Me

Classroom Teacher

Chesterfield County, Va

Desmos Teaching Fellow 2015

Desmos Certified Presenter 2017

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We're on a mission to help everyone learn math, love math, and grow with math.

We Believe

We believe that everyone has an inner mathematician and that some people haven’t been given the opportunity, encouragement, or tools to discover theirs.

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About Desmos

Desmos Studio vs Desmos Classroom

(calculators) (activities)

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Why Desmos?

Technology that thinks with you, not for you.

Helps all of us focus on the math and not the tool
Helps all of us ask questions and find answers
Creative approach to learning mathematics

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Is Desmos on your test?

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Create a free account�desmos.com

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Desmos Graphing

Calculator Basics

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Explore the calculator

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Explore the calculator

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Graphing Calculator

Basic Tools

Graph & Window Settings
Calculations
Points & Tables
Equations & Functions

Next Level Advantages

Simple
Dynamic
Mathematical Sandbox
Connect Representations
Classroom Discourse
Feedback

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Things to think about when using a graphing calculator…and advantages within the desmos graphing calculator

Simple

Not teaching button pushing
Used it before my students needed it to take a test - was not something additional to teach

Dynamic

Animate - sliders - visuals that students can play with and make connections on their own

Mathematical Sandbox

Connect Multiple Representations

Classroom Discourse

Get students talking about math
We will focus on what students are doing when we use it instructionally

Predicting, connecting, playing or experimenting

Feedback

For students (not always coming from teacher, not a simple right or wrong - shows students their thinking), for teachers

Give feedback that attaches meaning to student thinking.

Whenever possible, we use computers to interpret rather than evaluate student thinking. Where evaluative feedback says, “You’re right” or “You’re wrong,” interpretive feedback says, “Here’s how we’re understanding your answer. What do you think now?” ^{2, 3} For example:

Let’s see some of these features through a task you might use in class
Don’t want to start with “here is how you add numbers. Here is how you graph equations” in a vacuum
Want to give context and show how to use instructionally
Reminder of benefits

Simple
Dynamic
Mathematical Sandbox

Connect Multiple Representations

Classroom Discourse

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Apple Juice (table, calculations, regression)

Take a look at this picture

Students notice, wonder and we raise the question

How much would 5 apple juices cost? (if allowed)

Desmos will be our tool to find out

Table - before tracking back to 5, look forward to 12 and 18

Calculate right in the same window (not navigating back and forth through screens/menus)

We might now want to represent this proportional relationship algebraically

y=2/3/x

Slider instead

Between 0.5 and 0.6

Type in 0.55

1 step further, moveable point (plotting points, use sliders though)

Another sandbox for kids to explore in

Drag to find other points

Find a point on the line - what does it mean in context?

Rewind to 1 can - unit rate (1, 0.55) 55 cents for 1 can

Push forward to 5 cans (5, 2.75) 2.75 for 5 cans

*show regression

Wrap Up Overview of Features

Calculations

Points, Tables

Equations, functions, INEQUALITIES

Convert to table *needs to be y= or f(x) =

Edit screen for points, tables, equations, ….

Function notation - evaluate

Help menu

Regression

Reminder of benefits

Simple
Dynamic
Mathematical Sandbox

Connect Multiple Representations

Classroom Discourse

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Explore the calculator

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Explore the calculator

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Graphing Calculator Resources

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Desmos for Instruction

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Using Desmos Instructionally

Enhance Student Engagement and Learning

Predicting
Inviting informal before formal
Noticing patterns
Identifying & building structure
Connecting Representations

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Shift from testing to instruction

States not adopting desmos on end of course testing because it’s the best tool to take a test with

It’s the best tool to use for learning and understanding math

So we want to find ways to use it in our instruction

We want to find ways that the calculator doesn’t replace student thinking and understanding

But instead pushes student thinking and understanding forward

I find it best to think in terms of verbs….what do we want students DOING? How can this tool support those things?

In many cases this technology can help teachers get students….

Predicting
Inviting informal before formal
Noticing patterns
Identifying and building structure
Connecting representations

I want to emphasize that this functionality should not be used to avoid algebraic methods. This functionality can be used as an exploration tool.

A progression I like to use with some topics:

Use technology to introduce, explore, figure out what’s going on

What is the technology doing?
Make sense of what the results are

Then work without the calculator

Now you do what the calculator is doing

Bring back the technology to allow students to check and become comfortable using it

Now use this calculator to check/confirm your work

Do this with function notation. NOT AVAILABLE on TESTING VERSION but CAN USE INSTRUCTIONALLY TO EXPLORE

What’s the calculator doing? Now let’s do it by hand and then verify with the calculator.

…move over to graphing calculator and connect representations - students make those connections

Verify Algebraic Procedures

Deeper Understanding of Algebraic Procedures

develop a deeper understanding of variables and EQUIVALENCE

Exponents

a^2*a^3

a^5

a^6

a*a*a*a*a

Combining like terms

a*a

a+a

a^2

2a

Can do on graphing calculator for even more examples quickly….

Trig Identities

Sin2b

2sin(b)cosb *error message without parentheses

1 variable inequality feedback for students - equivalence - GRAPHICALLY!

6x-11-13x<7-5x

SLIDERS for DYNAMIC GRAPHS

Basic Intro to…

y = mx+b

y = a(x-h)^2 + k

(x-h)^2 + (y-k)^2 = r^2

y = sin(x) + c

(2.43, 2.43)

(2.43, a) SLIDERS

a=[-5,5] LIST what will happen? (don’t wait for their answer)

a=[-5,-4,-3,-2 this is taking too long a=[-5,-4,5]

a=[-5,-4.5,...5] change pattern/scale

Now play…

What if `(a,a) (a,a^2) y=ax+1 y=x+a x^2+y^2=a =a^2

------------------------------------------------------------

(-a,-a)

(2a,a)

(a,sqrt(a^2))

(a+1,a-1)

Table x1,y1

Polygon (x1,y1) → change it up….adding/subtracting, multiplying -1, switching x1 and y1, multiplying by other values

Create your own

Get students thinking mathematically - making conjectures

Make it social

In Person - think pair share

Remote - chat/activity builder

ask them for suggestions

POLYGON TOOL

IMAGE and TRACE and ART

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Q & A

What questions do you have?

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Let us know how we did!

Your feedback is really, really important to us.

Desmos Studio PBC Sharing

Please open link in shared doc

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Thank You!

Nolan Doyle

support@desmos.com

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