## 1. Accessibility

### 1.1. Desmos is free to access online at desmos.com.

1.1.1. Teacher accounts are also free to make.

### 1.2. Desmos is generally easy to use. Tutorial videos are included online.

1.2.1. These videos may assist teachers in instructing students on how to use this learning technology.

1.2.1.1. These videos also demonstrate how to use Desmos for instruction, instead of just as a calculator.

### 1.3. Desmos is also available as an application.

1.3.1. Desmos is tailored to whatever device a student or school chooses to use.

1.3.1.1. Smart-Phone

1.3.1.2. iPad or other tablet

1.3.1.3. PC or MAC Computer

## 2. Content Area: Mathematics

### 2.1. High School and Middle School Mathematics Curriculum.

2.1.1. Algebra

2.1.1.1. Students can use Desmos to not only quickly graph an equation, but explore various transformations to that equation.

2.1.1.2. Desmos allows students to visual see how solutions appear on a system of equations. It also provides a way for students to check their work when solving matrices.

2.1.1.3. Desmos provides a way for students to check their work with basic equations, but doesn't provide the answer like some software.

2.1.2. Geometry

2.1.2.1. Desmos has an interactive Geometry mode that allows students to quickly create shapes and angles. Or for teacher to provide students with given figures.

2.1.3. Calculus

2.1.3.1. Students can see how tangent lines appear on a graph, and relate to their original function. Or when connecting the derivative to local maxes or local mins.

2.1.4. Statisitics

2.1.4.1. With the built in data plotter students can use Desmos to easily create a scatter plot. They can then use Desmos to create a regression model to approximate their given data, and see first hand if their model is accurate.

2.1.4.2. Desmos offers a variety of built in calculations for students, such as finding the mean, median or mode.

2.1.5. Pre-Algebra

2.1.5.1. Students can check work using the graphing calculator. For example, if x+3=4 is plugged in, the graph will show that the solution is x=1.

## 3. Features

### 3.1. The most well-known feature of Desmos is probably its graphing calculator, accessible either on the app or online.

3.1.1. Users have the ability to graph functions.

3.1.2. Data can be plotted.

3.1.3. Users can evaluate expressions.

3.1.4. Transformations of graphs can easily be seen.

3.1.4.1. Sliders

3.1.4.2. Color-coded Graphs

3.1.5. Geometric shapes can be plotted by graphing points.

### 3.2. The Geometry Tool is a new feature to Desmos. It is currently available in a beta version. This geometry tool is roughly comparable to math software like Geogebra.

3.2.1. Students can use the geometry tool to construct shapes, lines, angles, etc., and explore the properties that lie therein.

### 3.3. Desmos also houses a variety of classroom activities. Pre-made activities are easily accessible to teachers after creating a free account. Teachers can also create their own classroom activities to be used as labs, tasks, quizzes, and so on.

3.3.1. Some example activities include: match my Parabola, Card ort: Modeling, and Penny Circle.

3.3.2. These classroom activities are interactive, and often very intriguing lessons for students to complete.

3.3.2.1. The dashboard feature for classroom activities is very complete. It allows teachers to monitor student work in real time and even anonymize and overlay answers to present student work for discussion.

## 4. Teacher Roles

### 4.1. First, teachers should make a free account to gain access to classroom activities.

### 4.2. Teachers can search for and select relevant pre-made activities to use during lessons.

### 4.3. Teachers can also create their own classroom activities and/or quizzes.

### 4.4. While students are working, it is crucial for teachers to monitor student progress, which can easily be done in real time using the dashboard feature.

4.4.1. Teachers are then responsible for selecting and sequencing student work to share, discuss, and bring attention to.

4.4.2. Teachers should also attend to students who seem to be struggling with the activities

### 4.5. Additionally, teachers should instruct students on how to use certain features that they may not be familiar with. Such features are not limited to, but may include:

4.5.1. Sliders

4.5.2. Geometry construction tool

4.5.3. Graphs

4.5.4. Special input symbols

## 5. Learning Activities

### 5.1. Dissecting quadratic and exponential functions with the graphing tool to see how each part of the function effects the graph

5.1.1. Students will realize that different forms of a quadratic all highlight unique things about the polynomial.

5.1.1.1. Vertex form highlights the vertical and horizontal shifts of the quadratic's vertex. As well as it's compression or dilation.

5.1.1.2. Standard form emphasize the y-intercept of the quadratic.

5.1.1.2.1. Students can connect between these three modes and choose the right form for the right situation.

5.1.1.3. Factored form emphasizes the x-intercepts of the quadratic.

### 5.2. Classroom activities, whether featured on the website or hand-made by the teacher, are interactive and engaging.

5.2.1. Provide students with instantaneous feedback in a low stakes environment.

5.2.2. Allows for students to see their peers solutions instead of just their own.

5.2.2.1. Students can connect their knowledge with their peers, instead of only relying on the teacher as the source for mathematics.

5.2.3. Teachers can select particular students work to discuss with the whole class. Teachers can do this anonymously.

5.2.3.1. Teacher can address misconceptions without fear of embarrassing students who make those mistakes.

### 5.3. Students can graph several functions at once to compare and contrast their properties. Students can also use slider features to explore how functions change with different variable values.

## 6. Assessment

### 6.1. Classroom Activities

6.1.1. Some pre-made classroom activities are inherently assessment-like, such as flashcard activities.

6.1.1.1. These flash card activities may help students study for important, summative assessments.

6.1.2. Using the dashboard feature, a teacher is able to see student responses in an activity and formatively assess how to move forward in instruction.

### 6.2. Teacher-made quizzes

6.2.1. Teachers can make quizzes and/or activities specifically for the purpose of assessment. This feature may be comparable to other quizzing software like Quizlet.

6.2.1.1. Teachers can use a singular website for their mathematics courses. Instead of having students switch between a math software and a specific quizzing software.

## 7. Learning Goals

### 7.1. With so many features and possibilities, Desmos can address a variety of learning goals.

7.1.1. Almost any algebra learning goal dealing with functions, graphing, and transformations can be effectively addressed using Desmos. Desmos especially promotes independent learning by allowing students to easily explore relations and compare different functions.

7.1.1.1. For example, some practical algebra learning goals to address using Desmos might be: graphing functions, describing transformations, or solving inverses.

7.1.2. With the new geometry tool feature, Desmos can also address geometry learning goals, especially in relation to construction, and possibly to assist in theorem proofs.

7.1.2.1. For example, some practical learning goals to address using Desmos might be: make geometric constructions, understand congruence, and experiment with plane transformations.

7.1.3. With lesson plans pre-built Desmos offers free and interactive lesson plans to promote student engagement. Students can explore through a structured lesson, while teachers monitor and select specific student responses.