Desmos classroom activities are digital experiences that help students learn algebra, geometry, and advanced mathematics by modeling and using multiple representations.
Desmos classroom activities are terrific for teachers to help students visualize their learning concepts. They have some incredibly extraordinary capabilities. Furthermore, Desmos activities are a great way to host interactive notes in the classroom and fun to make card sorting or graph-based assignments. But you should keep in my that students must be able to sign in to Desmos so that an educator can view and track their progress!
Why should teachers use Desmos Classroom Activities?
Desmos encourages students to practice their math skills and play with math to show their creativity. Kids can type in any number of math expressions and see the results right away as graphs on the page. Graphs can be turned into complex and realistic drawings by adding different colors and shapes.
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In Scatter Plot Capture, students make predictions about the location of future points on a plot based on their careful observations of existing relationships. The focus areas for analysis include determining if the association is linear or nonlinear and whether the association is classified as strong or weak. Students also identify if the plot exhibits an increasing or decreasing trend.
emed activities specifically designed to test and strengthen students’ algebraic and graphical comprehension of parabolas. The goal is to successfully navigate the course by manipulating the quadratic equations that define the parabolas’ path. Given the complexity and potential duration, it is recommended that students log in to Desmos so they can efficiently save their progress across multiple class periods.
Marcellus the Giant
This activity is designed to help your students build a solid conceptual understanding of the definition of a proportional relationship. Learners begin by creating a giant figure within the Desmos environment and are challenged to ensure that all of the giant’s physical features remain strictly proportional. A key feature is the graphical representation of these proportions, which students can observe in real-time. By manipulating the graph itself, students can dynamically watch the giant transform, reinforcing the constant nature of the proportional relationship.
What’s My Number?
In this activity, students participate in a sequential guessing game to develop their intuition concerning mean absolute deviation. The game starts simply, with the prompt “Can you guess my number?”, and students receive feedback to guide their revisions until the target is found. Following the guessing rounds, students analyze parallel dot plots that display their guesses and their classmates’ guesses over time. This visual analysis helps students establish connections between the visible “spread” of the data set on the plot and the calculated mean absolute deviation.
Polygraph: Shaded Rectangles
Polygraph: Shaded Rectangles is a custom-designed activity intended to promote rich classroom discussions centered on vocabulary related to fractions and part-to-whole relationships. Students are expected to use precise terms like “shaded,” “unshaded,” “numerator,” “denominator,” and “equivalent/equal to” during the game. If students initially use informal language, the educator is encouraged to intervene after two or three rounds to highlight effective questioning strategies and push for more precise academic language.
Mocha Modeling: Starbucks Locations
This activity requires students to construct a mathematical model that accurately describes the relationship between the growing number of Starbucks locations in the United States and the elapsed time since 1992. Using this model, students are then asked to make practical predictions regarding the number of locations for 2015 and subsequent years. Furthermore, interpreting the features of the resulting graph within the real-world context is a central requirement of the lesson. In the process of analyzing the data, students discover that not all instances of rapid growth are necessarily exponential, and a logistic function may provide a better fit.
Screens for Checking Understanding
This activity provides useful starter screens that educators can efficiently copy and paste directly into their own customized Desmos lessons. These screens are specifically intended to help teachers conduct quick checks of student understanding during instructional time. To integrate a screen, the user copies it using the command cmd+c (on Mac) or ctrl+c (on Chromebook or Windows). They then paste the desired screen into their target activity using cmd+v or ctrl+v.
Turtle Crossing
In the Turtle Crossing lesson, students focus on establishing clear connections between various turtle-crossing scenarios and the mathematical graphs that visually represent these movements. The activity presents different contextual situations involving turtles moving across a path. The core learning objective is to ensure that students can accurately interpret how time and distance are depicted on a graph for each unique scenario.
Strength in Numbers
This activity begins with students engaging in three distinct rounds of estimation challenges to build their quantitative intuition. Following these initial estimation tasks, students shift their focus to analyzing a new dot plot that is heavily skewed. The class is then challenged to determine whether the calculated mean or the median provides a more appropriate and representative measure of the center for this specific skewed data set. Educators should note that this activity is optimized for participation, working best when implemented with ten or more students.
Card Sort: Exponentials
This card sort is designed to provide students with essential practice in applying their knowledge of exponential functions. Students are tasked with matching various algebraic equations to the corresponding properties of the graphs these equations will produce. Additionally, the activity requires students to utilize their understanding of how transformations affect exponential functions. This knowledge is critical for successfully pairing the given equations with their accurate graphical representations.
Classy Cats
Classy Cats is designed to challenge the common student perception that data simply consists of disconnected, isolated points. Students are guided to understand that the relationship existing between two variables can frequently be modeled effectively using a straight line. They continue their analysis by scrutinizing the connections between the original scatter plot and the derived modeling line. This is achieved by meticulously comparing and analyzing individual points in relation to the established linear trend.
Compound Inequalities on the Number Line
This activity focuses on providing students with an opportunity to explore the characteristics and structure of compound inequalities. A primary learning goal is for students to establish clear connections among the multiple mathematical representations of these inequalities. These representations include the formal algebraic expression, the descriptive verbal statements, the visual number line graphs, and the explicit definition of the solution sets.
Two Truths and a Lie: Lines
The Two Truths and a Lie: Lines activity is a stimulating way for students to practice their command of the features and specialized vocabulary of linear equations. Each participant is required to create a unique line within the graphing environment. They then write two statements about their line that are mathematically true and a third statement that is intentionally false. The peers’ task is to critically analyze these statements and correctly identify the single fabricated lie.
Polygraph: Rigid Transformations
This custom Polygraph activity is specifically designed to provoke vocabulary-rich discussions focused on the precise language used for rigid transformations. Key terms that are likely to emerge in student questions include “slide,” “shift,” “translation,” “spin,” “turn,” “rotation,” and “reflection”. After students have completed two or three rounds of the game, teachers should strategically pause the lesson to discuss effective strategies. This pause encourages students to incorporate increasingly precise academic language into their ongoing gameplay.
Match My Exponential
In Match My Exponential, students engage in a series of scaffolded graphing challenges that increase in complexity. The core objective of these guided tasks is to systematically enhance the students’ overall proficiency and mastery in graphing and manipulating exponential functions.
Will It Hit the Hoop?
Students participating in this activity first make predictions about the trajectory of various basketball shots, estimating whether the ball will successfully pass through the hoop. They then use the Desmos tools to model these shots accurately using parabolas to verify their initial predictions. Crucially, the activity employs draggable points for modeling, which means students do not need prior familiarity with the symbolic algebraic forms of quadratic functions. While the activity uses the U.S. imperial system, teachers can easily adapt the measurements to the metric system by editing the measurements after copying the activity.
Systems of Two Linear Equations
This activity guides students through the process of writing and solving a system consisting of two linear equations. Through this rigorous process, they are encouraged to explore the conceptual meaning of a “solution,” encompassing both its numerical value and its graphical representation. The activity concludes by challenging students to apply the foundational understanding they have gained to solve analogous or similar real-world situations.
Mini Golf Marbleslides
Mini Golf Marbleslides is a gamified activity that effectively combines the fun of mini golf with the practice of coordinate graphing. Students practice their proficiency in plotting points by inputting coordinates to guide the marbles.
Put the Point on the Line
The primary goal of this activity is to significantly sharpen students’ conceptual focus on the essential mathematical concept of slope. Students are challenged to place points on an imaginary line, prompting them to first estimate, then calculate, and finally observe the inherent proportionality in the relationship. Using the ideas generated by the students, the activity defines slope as the ratio of the change in y-coordinates to the change in x-coordinates. By the activity’s conclusion, students will possess various descriptive ways to talk about slope, even if they don’t yet formally write it as a fraction.
Equivalent Expressions
In Equivalent Expressions, students participate in a card sorting exercise designed to strengthen their foundational understanding of expressions that are mathematically equivalent. The activity utilizes visual representations of the algebraic expressions being sorted. This key visual component helps students conceptually understand that two expressions are equivalent because they both correctly count or represent the exact same mathematical quantity.
Avi and Benita’s Repair Shop
This classic activity presents a revised scenario where students compare two payment plans to contrast linear and exponential growth. The linear plan increases consistently by $100 each day, while the exponential plan grows by doubling the previous day’s payment. The activity is suitable for students already familiar with linear functions but who are newly encountering exponential growth concepts. For this reason, it serves as an excellent foundational activity when launching a unit on exponential functions.
Which is Steepest?
This activity serves as an initial exploration of the intuitive concept of the “steepness” observed in various line segments. By investigating steepness informally, the activity acts as a conceptual prelude. This prepares students for more formal, structured classroom conversations regarding the precise mathematical definitions of vertical change, horizontal change, and the calculation of slope.
Human Stopwatch
The Human Stopwatch lesson aims to teach students how to appropriately utilize the statistical term “variability” when describing and analyzing sets of data. Uniquely, the students are actively involved in generating the data sets that they will analyze. This is accomplished through the class collectively completing a series of interactive estimation tasks.
Solutions to Systems of Linear Equations
This activity is specifically designed to help students build a robust understanding of what it means for a point to qualify as a solution to a system of equations. Students explore the solution concept from two necessary perspectives: both graphically and algebraically. They must confirm that the point satisfies all equations numerically while also representing the precise intersection point on the graph.
Line Zapper
Line Zapper is an interactive Desmos lesson where students “zap” lines by accurately identifying their corresponding solutions. The lesson progresses from students zapping individual lines in the early stages. Subsequently, the focus shifts to systems of linear equations, where students must execute a single “zap” aimed exactly at the point of intersection. This strategic action allows the students to simultaneously capture multiple lines at once.
iPhone 6s Opening Weekend Sales
In this activity, students use historical iPhone sales data to formulate predictions about the total number of iPhone 6s units sold during its opening weekend in September 2015. Students are given the choice to utilize pre-set linear, quadratic, or exponential models for their forecasting. Alternatively, they possess the flexibility to construct their own unique predictive model based on any mathematical function they choose.
Screens for Checking In
This activity provides helpful starter screens that are easily transferable via copy and paste into any of the teacher’s custom activities. These screens are specifically tailored to enable educators to conduct a quick and effective check-in with their students. To copy a screen, users press cmd+c or ctrl+c depending on their device. The screens can then be pasted into the desired activity using cmd+v or ctrl+v.
Creating Relative Frequency Histograms
Students in this activity will gain the necessary skills to construct accurate relative frequency histograms. The learning is contextualized through the analysis of relevant social and cultural data sets. A core goal is to help students distinguish and understand the conceptual and procedural differences associated with relative frequency measurements.
Whiteboards
The Whiteboards activity offers pre-made starter screens that can be readily copied and pasted into other lessons. These screens function by providing students with a versatile, quick sketchable whiteboard area. This simple tool can be used effectively for quick tasks across a wide range of subject areas. Teachers can copy the screen and paste it into their activity using the standard keyboard commands.
Build a Bigger Field
This practical activity presents a challenge where students must apply their knowledge of quadratic models in a problem of optimization. The primary task involves determining how to maximize or optimize the total area of a field. This optimization must be performed while adhering to a given, fixed perimeter constraint.
Marbleslides: Exponentials
This activity is a delightful and challenging game that requires students to transform the equations of exponential functions. The objective is to manipulate the equations so that when the marbles are launched, their trajectory successfully carries them through all the designated stars. Students receive immediate visual feedback when they launch the marbles. This provides a valuable opportunity to revise their exponential function equations before they advance to the next challenge.
Transformation Golf: Rigid Motion
Transformation Golf: Rigid Motion is a gamified activity where students utilize their established understanding of rigid motions to complete a course. Students leverage their knowledge of translations, reflections, and rotations to solve the challenges. The core task requires them to apply one or more transformations to precisely map a pre-image shape onto the final image. It is recommended that educators attempt to solve the challenges themselves before assigning the activity to their class.
Graphing Stories
Graphing Stories is a transitional activity designed to help students move from simple one-variable representations, such as basic number lines, to the more complex two-variable coordinate plane. Students observe short, 15-second video clips that depict motion or change. Their task is to translate the visual narrative of the video directly into an accurate mathematical graph, often with teacher guidance.
Robots: What a Point in a Scatter Plot Means
This activity intensely focuses on helping students determine the meaning of individual data points plotted within a scatter plot. Students are required to precisely identify the quantities represented by the plot’s axes and compare the individuals represented by different points. The successful interpretation of the data necessitates two distinct levels of rigorous analysis. The activity strongly emphasizes the mathematical practice of precision (MP6).
Editable Fraction Tasks
Editable Fraction Tasks offers a collection of pre-made starter screens specifically created to assist teachers in generating tasks related to fractions. Educators can easily copy these screens and integrate them into their custom Desmos activities. The process involves copying the screen using cmd+c or ctrl+c. The screen is then pasted into the intended activity using cmd+v or ctrl+v.
Marbleslides: Rationals
This is a delightfully challenging Marbleslides activity that focuses on the graphical transformation of rational functions. Students must manipulate the equations of rational functions so that the resulting graph directs the launched marbles through the designated stars. The interactive nature allows students to test their functions immediately by launching the marbles. This process provides an opportunity to revise their equations before they attempt the subsequent challenge.
Marbleslides: Parabolas
Marbleslides: Parabolas offers a challenging and engaging environment for students to practice manipulating quadratic functions. The objective requires students to successfully transform the parabola equations so that the trajectory of the launched marbles passes through all the star targets. Students are provided with immediate feedback by launching the marbles to test their transformations. They are encouraged to revise their parabolic equations based on the results before proceeding to the next level.
Domain and Range Introduction
This activity provides focused practice for students learning how to determine the domain and range of piecewise functions. The lesson begins with an informal conceptual exploration of domain and range conducted through analyzing a function’s graph. Students then gradually build upon this visual understanding, culminating in the formal representation of the domain and range of piecewise functions using proper inequality notation.
LEGO Prices
In this activity, students utilize interactive sliders to explore the numerical relationship between the retail price and the piece count of various Star Wars LEGO sets. After constructing a model, they use it to make several predictions based on the observed data. A key learning requirement is that students must successfully interpret the parameters of their final equation. This ensures they can explain the meaning of those parameters within the context of LEGO pricing.
Playing Catch-Up
Playing Catch-Up is designed to deepen students’ conceptual understanding of systems of equations. The activity emphasizes analyzing how these systems are represented across multiple forms, including structured tables, algebraic equations, and visual graphs. This integrated knowledge is then applied to solve a contextual problem: determining if one moving racer will successfully overtake, or “catch up” to, another.
Des-pet
The Des-pet activity encourages and rewards student creativity within the mathematical environment. While engaged in creative construction, students simultaneously reinforce crucial concepts. Specifically, they must review and apply their knowledge of function inequalities to shape their creations. They also utilize their understanding of domain and range restrictions to precisely control the boundaries of the digital pet they design.
Expressions Mash-Up
Expressions Mash-Up is a card sorting task intended to strengthen students’ comprehensive understanding of multiple mathematical representations. The cards require students to match algebraic expressions, verbal descriptions, tables of values, and visual algebra-tile models. After completing the sort, students engage in a discussion about whether a specific student correctly paired cards. This discussion naturally prompts consideration of equivalence and the commutative property.
Laser Challenge
The Laser Challenge presents a series of puzzles where students must use their knowledge of angles to strategically adjust lasers and mirrors. The objective in each task is to successfully hit all three designated targets with the redirected laser beam. For younger students, this is an excellent introduction to angle measure, while older students can engage in critical thinking about the properties of lines and reflections. Because the activity may extend beyond a single class period, students are recommended to log in to save their progress.
Transforming Functions
In this activity, students receive direct practice in representing graphical transformations using appropriate algebraic notation. A vital feature is the timely feedback provided by the activity. This immediate response allows students to visually verify the precise effect that their algebraic transformations have on the graph itself.
Card Sort: Parabolas
Card Sort: Parabolas focuses on helping students determine the shape and characteristics of a parabola based solely on its algebraic form. The activity starts with a necessary review of both the key characteristics of parabolas and their various standard equation forms. Students then apply these principles to the card sort, identifying the graphical shape by revealing its characteristics from the equation’s structure.
Card Sort: Linear Systems
This activity provides students with practice in the process of solving systems of linear equations. It starts by reviewing the graphical meaning of a solution, which is the intersection point of the lines. Students are then challenged to evaluate and choose the most efficient algebraic method, substitution or elimination, for solving a given system. The activity concludes with guided practice in solving the equations using both the substitution and elimination methods.
Balloon Float
Balloon Float is a hands-on activity that requires students to apply the concept of ratios to a contextual problem. Students must determine the precise number of balloons necessary to provide enough lift to float various objects.
Scatter Plot Capture
In Scatter Plot Capture, students make predictions about the location of future points on a plot based on their careful observations of existing relationships. The focus areas for analysis include determining if the association is linear or nonlinear and whether the association is classified as strong or weak. Students also identify if the plot exhibits an increasing or decreasing trend.
Polygraph: Transformations
This Custom Polygraph is designed to spark conversations focused on the development and use of precise vocabulary related to geometric transformations. Key terms include “translation,” “rotation,” “reflection,” “dilation,” “scale factor,” and “pre-image”. Teachers should utilize breaks after two or three games to discuss questioning strategy. This encourages students to use precise academic language when differentiating between the transformation options.
Point Collector: Lines
Point Collector: Lines is a challenge activity where students apply and deepen their knowledge of linear inequalities in two variables. The objective is to define inequalities that allow them to “collect” the maximum possible number of points within the coordinate plane. This activity reinforces how linear inequalities define specific regions on a two-dimensional graph. Because the challenge may require more than one class period, it is recommended that students log in to Desmos to save their progress.
Two Truths and a Lie: Parabolas
Students use this activity to practice and reinforce their understanding of the features and specialized vocabulary related to parabolas. The process begins with the creation of a parabola, followed by the composition of three descriptive statements about it. These statements must include two mathematical truths and one intentional, verifiable lie. The remaining class members are then tasked with correctly identifying which of the three statements constitutes the fabrication.
Pool Border Problem
This is a Desmos adaptation of a classic mathematical task that bridges arithmetic and algebra. Students first construct numerical expressions to accurately determine the count of border tiles surrounding a pool. They then use the structure found in those numerical expressions to help them write a single algebraic expression containing variables. The lesson concludes by testing the algebraic expression, demonstrating its efficiency in quickly calculating the tile count for many different pool sizes.
The Fraction Challenge
The Fraction Challenge provides students with focused practice in the operations of adding and subtracting fractions. The activity requires them to construct original mathematical expressions that strictly adhere to specific given criteria, such as achieving the greatest possible value. This process demands that students engage in abstract and structural reasoning. They must persuasively argue and prove that their constructed expression is the greatest or least possible value based on the parameters.
Puzzling It Out
In this lesson, students engage with and solve a variety of angle puzzles by applying their existing knowledge of angle relationships. The successful completion of these puzzles reinforces their conceptual understanding of how angles interact geometrically. Critically, this activity also functions as an informal introduction to the Triangle Sum theorem. The goal is for students to discover that the sum of all angle measures within any triangle is consistently 180 degrees.
Absolute Value Inequalities on the Number Line
This activity guides students through the complexities of exploring inequalities that incorporate absolute value. The key objective is to facilitate the students’ ability to make robust connections among the multiple mathematical representations of these concepts. These representations include the formal algebraic expressions, the corresponding verbal statements, the visual number line graphs, and the precise definition of the solution sets.
American Time Use Survey
The American Time Use Survey activity prompts students to analyze how they, and Americans in general, allocate their time and how those patterns shift over a lifetime. Students are first asked to sketch graphs representing their predictions of these long-term time-use trends. They then compare their initial hypotheses directly against actual, authoritative data released by the U.S. Bureau of Labor Statistics.
Scaling Machines
The core purpose of Scaling Machines is to help students form a clear conceptual understanding of what constitutes a scaled copy. Students articulate the characteristics of scaled copies using intuitive, informal language. After creating an original shape, they attempt to replicate it using several different virtual “printers,” some of which are intentionally flawed. By analyzing the failures of the broken printers, students systematically develop criteria for shapes that are, and are not, true scaled copies.
Land the Plane
This activity is a practical skill-building exercise where students practice determining the equations of lines. The goal is to accurately guide a virtual plane to land safely on a runway. Although most challenges are well-suited for the slope-intercept form, the activity offers flexibility. Teachers can easily adapt the challenges to integrate other forms of linear equations based on their specific instructional goals.
Creating Histograms
In this lesson, students analyze a large volume of movie data, which leads them to confront the intrinsic limitations of organizing data solely in tables. This exposure helps students recognize and appreciate the superior value and utility of histograms for data visualization. A main educational outcome is to empower students with the skills required to successfully build histograms from the ground up.
Inequalities on the Number Line
This activity focuses on providing students with an opportunity to explore linear inequalities and their expression across different forms. Students are tasked with establishing connections between the algebraic expressions of the inequalities and their descriptive verbal statements. They also must relate these forms to the visual number line graphs and the defined solution sets.
Make It Balance
Make It Balance is designed to help students conceptually understand the mean by visualizing it as the critical balance point on a beam. Students start the activity by using a simple guess-and-check method for placing the weighted bears. They then progress toward developing precise strategies for locating the balance point. This strategy relies on observing the principle that the sum of all distances to the left of the mean must be exactly equal to the sum of all distances to the right of the mean.
Limits and Continuity
This activity is intended to provide students with an initial, informal exposure to the sophisticated mathematical ideas of limits and continuity. Students explore the behavior of functions by analyzing the values approached from both the left and the right side of a specific point. By evaluating these directional limits and the function’s value, students gradually formulate an introductory conceptual understanding of continuity.
Match My Line
Match My Line engages students in a structured sequence of linear graphing challenges that are carefully scaffolded in difficulty. The explicit goal is to enhance their proficiency across several standard linear function forms. These key forms include direct variation, slope-intercept form, point-slope form, and other essential linear equation structures.
Marbleslides: Periodics
This delightful and challenging activity requires students to transform the equations of periodic functions. The objective is to manipulate the waves and curves so that the marbles, when launched, successfully pass through all the designated star targets. Students test their function modifications by launching the marbles. They have a chance to immediately revise their equations before advancing to the next level challenge.
Click Battle
Click Battle is an interactive activity specifically designed to reinforce students’ skills in proportional reasoning. The activity is set within a themed “Click Battle arena” environment. The primary mathematical focus of the challenges is on the exploration and application of the unit rate concept.
The Running Game
In The Running Game, students are required to use proportional reasoning to estimate the time it would take an individual to complete a run of seven miles. In addition to making the prediction, students are prompted to analyze the graph. They must thoughtfully consider the real-world meaning of various visual features presented on the graph within the context of the running scenario.
Turtle Time Trials
Turtle Time Trials is a lesson structured around a race between several turtles moving at constant speeds, which allows students to explore proportional relationships. After viewing an introductory animation, students analyze and create various mathematical representations of the scenario. These representations include number lines, graphs, structured tables, and corresponding equations that model the turtles’ race.
The (Awesome) Coordinate Plane Activity
This activity presents students with a series of engaging challenges designed to bolster their mastery of the coordinate plane. Each task requires students to accurately plot a specific point onto the bullseye target. Students gain repeated practice plotting points across all four quadrants. They transition from plotting points using a structured table to plotting points using standard ordered pairs.
Picture Perfect
Picture Perfect is a contextual activity that utilizes algebraic thinking to solve a practical problem: achieving the precise and efficient hanging of picture frames on a wall. Students must determine the optimal positioning and spacing using mathematical reasoning. This application of linear equations is designed to provide opportunities for students to deepen their existing understanding of these concepts.
Racing Cars
In Racing Cars, students must predict the exact location where a pair of moving cars will intersect or meet. Students are given the flexibility to use different tools for their prediction, including analyzing tables, drawing graphs, or manipulating equations. While multiple methods are permitted, the activity is intentionally structured to promote the use of the substitution method for solving systems of linear equations.
Polynomial Equation Challenges
This activity challenges students to construct polynomial equations of degrees 2, 3, and 4, ensuring they match a given set of zeros and specific points on the graph. Through this construction, students actively investigate the relationship between the factored form of the equations and the resulting zeros. They also explore how the order, or multiplicity, of those zeros affects the graph’s behavior.
Talking Time
Talking Time is designed to make students aware of the variety of ways people linguistically describe time, such as “5:15” or “15 after 5”. Students read these different descriptions and are tasked with setting a clock to the correct time. The activity allows the teacher to observe which time formats are easier or harder for students. This sets up a crucial discussion where the teacher can emphasize that different expressions are not right or wrong, but simply more or less useful.
Adding Whole Numbers
This activity is structured as a card game that provides a fun context for students to practice the fundamental operation of adding whole numbers. The central objective is for students to successfully create exactly two separate groups of cards. The winning condition dictates that both of these resulting groups must possess the exact same calculated sum.
Polygraph: Circles and Ellipses
This Custom Polygraph is intended to stimulate classroom discussions that are rich in vocabulary specific to circles and ellipses. Key vocabulary students will use includes “center,” “radius,” “horizontal,” “vertical,” “translation,” “dilation,” and “origin”. Following a few rounds of play, teachers are encouraged to pause the activity to discuss effective questioning strategies and highlight the use of precise mathematical terms.
The Decimal Challenge
The Decimal Challenge provides students with necessary practice in the operations of adding and subtracting decimals. Students are tasked with creating original mathematical expressions that satisfy specific criteria, such as achieving the value closest to zero. This requires students to engage in abstract and structural reasoning. They must construct arguments proving that their generated expressions meet the criteria of being the greatest or closest to zero possible.
Balance the Scale
In the Balance the Scale lesson, students learn crucial operations involving numbers expressed in scientific notation. The lesson is contextualized as a physical challenge where students must successfully balance various objects on a scale. Through this task, students gain practical experience in accurately estimating, multiplying, and dividing with numbers in scientific notation.
Card Sort: Functions
Card Sort: Functions is an activity specifically designed to solidify students’ foundational understanding of what constitutes a mathematical function. The core task requires students to sort a collection of cards into categories based on whether the item successfully represents a function. The cards contain various forms of representation, including visual graphs, algebraic equations, and descriptive real-world contexts.
Circle Patterns
In Circle Patterns, students begin by closely observing a given set of circles to identify the similarities and differences that define the pattern. They then apply this information to practice writing the precise equations for circles. The challenge involves either extending the established pattern or creating an equation that perfectly matches a specific set of geometric conditions.
Parallel Lines
This activity guides students through an exploration of the mathematical connections that inherently link the equations of parallel lines. The focus of the investigation is specifically constrained to lines that are represented in the slope-intercept form. Through comparison, students should discover the relationship between the slopes of two lines that are parallel and therefore never intersect.
Transformation Golf: Non-Rigid Motion
Transformation Golf: Non-Rigid Motion extends the transformation challenges to incorporate non-rigid motions, specifically dilations, alongside translations, reflections, and rotations. Students must apply one or more of these transformation types to accurately map a pre-image onto its designated final image. This comprehensive task requires students to demonstrate a full understanding of all geometric transformations, including scaling.
Polygraph: Basic Quadrilaterals
Polygraph: Basic Quadrilaterals is part of a series engineered to promote vocabulary mastery in an engaging way, without requiring rote memorization. The Desmos Polygraph format is used as a tool to successfully transition students’ informal, descriptive language into precise, formal academic vocabulary. This approach is based on the pedagogical belief that words gain their maximum power when students feel a genuine need to describe their mathematical world accurately.
Coin Capture: Lines
Coin Capture: Lines is an interactive activity designed for students to practice and demonstrate their understanding of how to correctly write linear equations. The core task challenges students to strategically place digital coins onto a coordinate grid. This challenge demands that students apply their knowledge of linear equations to control the placement accurately.
Exploring Length With Geoboards
This activity utilizes digital, Desmos-powered geoboards to provide students with a dynamic, visual environment for exploring concepts related to geometric length. The primary mathematical goal is to further deepen students’ existing proficiency in applying the fundamental Pythagorean theorem. It is noted that students should ideally have some foundational experience with the Pythagorean theorem before beginning this activity.
Wafers and Crème
Wafers and Crème begins by presenting a real-world prediction challenge, asking students to guess which of two cookie packages contains a higher total calorie count. Students are then provided with the specific calorie information for each package. They must use this data to calculate the total number of calories that would be contained in a third, newly described cookie pack. This contextualized problem serves as an excellent introduction to the algebraic method of solving systems of equations.
Polygraph: Exponentials
Polygraph: Exponentials is a specialized activity intended to provoke detailed conversations focused on exponential functions. A key emphasis is placed on ensuring students can differentiate the features of exponential graphs from those of linear functions. Core vocabulary includes terms such as “increasing,” “decreasing,” “intercept,” “rate,” “asymptote,” and “curve”. Teachers should utilize breaks between games to encourage the strategic use of precise terminology.
Blue Point Rule
The Blue Point Rule activity is designed to help students first develop their spatial intuition about a geometric transformation. Students analyze the transformation and are required to describe it using their own verbal language. Only after successfully establishing this verbal description are they then prompted to translate their understanding into the precise, formal language of algebraic notation.
Building Conic Sections
Building Conic Sections is an advanced activity that guides students through a demanding series of graphing challenges. The essential objective is to facilitate the students’ exploration of the fundamental connections that exist between algebraic equations and their corresponding graphical representations. Students investigate how parameter changes in the equations directly influence the resulting shapes of various conic sections.
Match My Parabola
Match My Parabola consists of a structured series of quadratic graphing challenges that are carefully scaffolded in complexity. The core purpose of these guided tasks is to systematically enhance the students’ overall proficiency and mastery of working with quadratic functions.
Card Sort: Modeling
Card Sort: Modeling challenges students to improve their ability to identify the most appropriate function family for modeling a specific scenario. Students must successfully match descriptive scenarios with their corresponding scatter plots, algebraic equations, and the correct function types. A significant element involves analyzing the negative consequences that arise when an incorrect mathematical model is erroneously paired with a real-world scenario.
Exploring Triangle Area With Geoboards
This activity utilizes dynamic, Desmos-powered geoboards to provide students with an interactive environment for geometric exploration. Students actively manipulate the geoboards to construct various triangles. The primary focus of this exploration is on calculating and understanding the concept of the area occupied by these triangles.
Lines, Transversals, and Angles
Lines, Transversals, and Angles directs students to investigate the angular relationships that are formed when a transversal line intersects a system of two other lines. The activity encourages critical comparison of the angle formations. Students look closely at the angle relationships that occur when the two intersected lines are parallel versus the relationships that occur when the lines are not parallel.
Parabola Slalom
Parabola Slalom presents a challenging series of slalom-themed activities specifically designed to test and strengthen students’ algebraic and graphical comprehension of parabolas. The goal is to successfully navigate the course by manipulating the quadratic equations that define the parabolas’ path. Given the complexity and potential duration, it is recommended that students log in to Desmos so they can efficiently save their progress across multiple class periods.
Marbleslides: Lines
Marbleslides: Lines is a challenging and engaging game where students must transform linear functions to achieve a specific goal. The objective requires students to manipulate the line equations so that the launched marbles successfully pass through all the targeted stars. Students test their theories immediately by launching the marbles. This interactive testing allows for revision and refinement of their linear equations before advancing.
Getting to Know Each Other
This activity is explicitly designed to foster a stronger sense of community within the classroom. The main goal is to help the teacher become more familiar with the students and to allow the students to learn about their peers. Teachers have the pedagogical flexibility to spread the various introductory screens out over several days or to use the entire activity in one dedicated session.
Battle Boats
Battle Boats is an interactive, gamified activity modeled after a traditional guess-the-location style game. The primary educational goal is to significantly build and reinforce students’ overall proficiency with the coordinate plane. By engaging in the game, students gain repeated, competitive practice in accurately locating and identifying ordered pairs.
Penny Circle
Penny Circle is a comprehensive modeling activity that integrates data collection with real-world problem solving. Students begin by actively gathering the necessary data points through observation. Based on the collected data, they are then tasked with constructing a robust mathematical model. Finally, this model is used to answer the driving question of the lesson: determining exactly how many pennies can fit within the boundaries of a large circle.
Transformers
In this lesson, students explore the effects of various transformations applied to plane figures. Students initially describe these complex movements using intuitive, everyday language such as “slide,” “shift,” “turn,” or “flip”. The activity is intentionally structured to avoid requiring formal math vocabulary early on. By experimenting with different descriptions, the activity creates the intellectual need for the class to ultimately agree upon precise, common mathematical language.
Game, Set, Flat
Game, Set, Flat focuses on helping students understand the exponential relationship that governs the decay of a bouncing tennis ball. Students learn to analyze successive terms in a sequence to determine if the pattern truly represents an exponential relationship. If the pattern is confirmed as exponential, the activity then guides students through the necessary steps to correctly construct the algebraic exponential equation itself.
Functions and Their Derivatives
This activity is designed for students to practice the high-level skill of matching a given function to both its first and second derivatives. After mastering the matching tasks, students are prompted to create their own original function. Upon successfully matching their creation to its derivatives, they submit the function to a shared gallery as a new challenge for their classmates to solve.
Guess My Rule
Guess My Rule introduces students to the foundational concept of a function by analyzing input-output pairs organized within a table format. Students are guided to explore a variety of different rules that might govern these pairs. Critically, some rules meet the definition of a function while others do not. The rules vary in style, utilizing both traditional numeric relationships and those involving letters and words.
Polygraph: Parabolas
Polygraph: Parabolas is an effective tool for developing students’ command of mathematical vocabulary organically, without resorting to tedious lists. The Desmos Polygraph framework is used to transition students’ initial, informal descriptions of parabolic features into precise, formal academic vocabulary. This approach emphasizes that mathematical terms gain their greatest power when they are adopted out of a genuine necessity to accurately describe the visual world.
Point Collector
Point Collector is a challenge activity where students apply and deepen their foundational knowledge of one-variable inequalities. The objective is to define inequalities that allow them to successfully “collect” the maximum number of target points along the number line. The activity specifically focuses on ensuring mastery of both simple and compound inequalities.
Polygraph: Conics
Polygraph: Conics is a custom activity created to stimulate vocabulary-rich discussions centered on the four primary conic sections. Students are prompted to use key mathematical terms, including “ellipses,” “hyperbolas,” “circles,” and “parabolas”. Teachers are encouraged to pause the game after a few rounds to discuss strategy. This intervention is designed to promote the consistent use of increasingly precise academic language when differentiating between the graphs.
Circles
This activity serves as a dedicated review of whole number exponents, preparing students for subsequent, more extended study of exponent rules and scientific notation. Exponents are introduced with an engaging animation that visually depicts the concept of repeated doubling, similar to cell mitosis. This visualization helps students solidify their understanding of expressions like 2^5 as the result of doubling five times. The visual aid is later removed to encourage students to think abstractly about large numerical stages.
The Intermediate Value Theorem
The Intermediate Value Theorem activity is designed as a focused, initial exposure to the core ideas underpinning the theorem. It provides rich material for classroom discussions about the theorem’s essential conditions and implications. Key conversation points include emphasizing that the “continuous” condition is necessary, though often overlooked. The activity also clarifies that the theorem addresses where roots are present under certain conditions, but remains silent on where they are not.
Des-Patterns
In Des-Patterns, students are given geometric figures and are required to practice writing coordinate rules to execute necessary transformations. The successful application of these rules allows them to accurately complete the presented patterns. The activity culminates in a creative stage where students design their own unique pattern. They then use the transformational math they mastered to successfully extend a pattern that was originally designed by one of their classmates.
Polygraph: Parabolas, Part 2
This activity functions as a direct follow-up to the initial Polygraph: Parabolas lesson. The primary goal is to formally develop the precise academic vocabulary related to the features and graphs of quadratic functions. It builds directly upon the informal language and concepts that emerged from student discussions during the first activity. It is advised that students who rely on a screen reader should be paired with a sighted partner for optimal participation.
What’s in a Name?
What’s in a Name? is a foundational activity designed to introduce students to essential methods of statistical representation. The primary focus is on familiarizing students with dot plots. This visual tool is presented as an effective method specifically for representing and analyzing data sets that contain only one variable.
Two Truths and a Lie: Conics
This version of the “Two Truths and a Lie” framework focuses on building students’ mastery of the features and specialized vocabulary associated with conic sections. Students begin by creating a specific conic section, such as an ellipse or hyperbola. They then compose two accurate descriptive statements and one statement that is a deliberate mathematical lie. Peers are then challenged to analyze the claims and correctly identify the single fabricated statement.
Creative Conics
Creative Conics is an open-ended activity that provides students with the freedom to actively explore the diverse geometric forms of conic sections. Students begin by manipulating the equations to create their own unique conic sections. A key benefit of this activity is the ability for students to view and share the graphical explorations and creations generated by their classmates.
Sketchy Dilations
Sketchy Dilations offers a visual and informal introduction to the concept of geometric dilations. Students experiment with virtual “sketching machines,” which allow them to adjust components of a drawing to immediately observe the proportional effects on the pre-image. This experimentation helps build an intuitive understanding of scaling. The lesson then formally introduces the concept of similarity, defining it as the direct result of applying a dilation transformation.
Polygraph: Clocks
Polygraph: Clocks is designed to help students recognize the critical need for a consistent, common language when communicating concepts of time. The activity is structured to organically surface students’ initial, informal ideas about this language. Teachers are strongly encouraged not to pre-teach the formal language of time, allowing the necessity for precision to arise naturally during the game.
Collect the Coconuts
Collect the Coconuts serves as a contextual introduction to calculating distance within the coordinate plane. The activity involves students sailing virtually from island to island, simulating a search for fruit. Initially, students calculate the distance by counting units along either the x-axis or the y-axis. The challenge progresses, requiring them to use coordinate pairs to find distances for islands located both on and off the primary axes.
Popular Screen Remixes
This resource is a curated collection compiled by the Desmos team featuring some of their most highly rated and favorite screens. This compilation provides educators with immediate access to proven, engaging, and effective lesson components. These screens are selected from the larger pool of activities available on the Desmos teacher platform.
Predicting Movie Ticket Prices
In this activity, students undertake the task of building a mathematical model that describes the historical relationship between the passage of time and the average price of a U.S. movie ticket. Once the model is constructed, students utilize it to generate predictions regarding both past and future ticket prices. Students are also required to interpret the precise parameters within their equation. This ensures they can explain the significance of these parameters within the economic context of movie ticket costs.
Polygraph: Advanced Quadrilaterals
Polygraph: Advanced Quadrilaterals is part of the Polygraph series designed to cultivate advanced mathematical vocabulary in an engaging manner. The activity works by transitioning students’ initial informal descriptions of complex quadrilaterals into precise, formal academic terminology. This method is rooted in the idea that words gain their utility and power when they are adopted out of a genuine need to accurately describe the mathematical world.
Make Them Balance
Make Them Balance uses the visual analogy of balancing hangers to explore solutions for both single equations and systems of equations. Students first analyze a single hanger, recognizing that the values required for balance are solutions to an equation that plots as a line. When two hangers are introduced, they discover that only the values balancing both hangers simultaneously are solutions to the system. This context effectively illustrates systems resulting in one solution, no solutions, and infinitely many solutions.
Two Truths and a Lie: Exponentials
This activity challenges students to practice their understanding of the characteristics and vocabulary associated with exponential graphs. The task begins with each student creating their own exponential curve using the graphing calculator. They then write three statements about their graph, consisting of two truths and one intentional lie. The peers’ task is to critically analyze these mathematical claims and successfully identify the single fabricated statement.
Tessellations
Tessellations is a project-based activity where students apply their knowledge of rigid motions to create and analyze geometric patterns. The focus includes generating true tessellations, which fully tile a plane, and complex designs that demonstrate rotational symmetry. Students use the precise language of transformations to describe these patterns, often studying examples from Islamic art and architecture. The culmination of the project is the design and successful construction of their own unique pattern and corresponding tessellation.
Symmetry
This activity guides students toward developing an intuitive, informal understanding of function symmetry. The exploration centers on the visual analysis of the function’s graph within the coordinate plane. By the end of the activity, students should be capable of confidently identifying the type of symmetry present in a function. They specifically learn to distinguish between reflectional symmetry and rotational symmetry based on the graphical evidence.
Polygraph: Angle Relationships
Polygraph: Angle Relationships is a custom activity designed to spark robust, vocabulary-rich conversations focused on various angular relationships. Key terminology includes “parallel,” “transversal,” “adjacent,” “opposite,” “alternate interior,” “corresponding,” and “vertical” angles. After the initial rounds of gameplay, teachers are advised to pause the activity to discuss effective questioning strategies. This ensures students are encouraged to utilize precise vocabulary when differentiating between the angle configurations.
Polygraph: Lines
Polygraph: Lines is implemented using the successful Polygraph model to foster students’ mastery of the vocabulary associated with lines. The activity’s structure helps develop students’ initial, informal language into precise, formal academic vocabulary. This method is favored because mathematical terms gain their greatest utility when adopted out of a genuine need to describe the features of lines accurately.
Adding Integers
Adding Integers is structured as a card game that provides an engaging, competitive context for students to practice the arithmetic operation of adding integers. The central objective of the game requires students to successfully divide their set of cards into two distinct groups. The critical rule is that both of these resulting groups must possess an identical calculated sum.
Cylinders
In the Cylinders lesson, students are guided to explore and adopt a structured strategy for accurately calculating the volume of a cylinder. This strategy relies on a foundational concept that students may have encountered in earlier grades. Specifically, they find the volume by multiplying the calculated area of the cylinder’s base shape by the total height of the three-dimensional prism.
Dilation Mini Golf
Dilation Mini Golf is a game-based activity that allows students to investigate the geometric effects of dilating a single point from a defined center. Students achieve this exploration by playing multiple rounds of the mini golf simulation. Through this repeated, interactive experience, they are guided from using informal, intuitive methods of spatial analysis. The activity ultimately transitions them toward using more formal methods for precisely determining the resulting relationships.
Commuting Times
This activity is designed to clearly illustrate the fundamental relationship that exists between a raw data set and the refined mathematical model used to interpret that data. A key distinction highlighted is that the initial raw data set itself is typically not structured as a function. However, the derived algebraic model used for analysis, particularly in algebra courses, must adhere to the definition of a function.
Polygraph: Triangles
Polygraph: Triangles is a custom activity aimed at sparking detailed, vocabulary-rich conversations specifically about the various classifications of triangles. Essential terms used by students include “scalene,” “obtuse,” “acute,” “right,” “isosceles,” and “equilateral”. After students have engaged in a few rounds of play, the teacher is encouraged to interrupt the game. This brief pause is intended to highlight effective questions and encourage the consistent use of precise, academic language.
Connecting the Dots
In Connecting the Dots, the central focus is on teaching students how to communicate about geometric transformations with maximum precision. Students work with transformations applied to polygons displayed specifically on the coordinate grid. They are challenged to critically assess and define exactly what information is necessary to formulate a clear and mathematically unambiguous description of a transformation. The coordinate grid is vital, providing the standardized framework needed to effectively communicate the locations of polygons.
Free-Range Functions
Free-Range Functions is designed to specifically address and correct persistent misconceptions that students may hold regarding the range of functions. Even students capable of using formal notation may adhere to mistaken ideas. For instance, students commonly assert that the value π is not included in the range of the function y = x^2. This misconception arises because they cannot immediately conceive of a number that, when squared, would result in π.
Taco Truck
The Taco Truck activity centers on applying the Pythagorean theorem as a versatile tool for solving problems involving diagonal distances. The lesson includes a prelude where students reason with the Pythagorean theorem to analyze the efficiency of taking a shortcut. The core challenge requires students to determine the optimal, shortest path from a location on the beach to a parked taco truck. The activity culminates in a class-wide race that tests their calculated optimal paths.
Fit Fights
Fit Fights is an interactive activity designed to enhance students’ conceptual understanding of the crucial process of fitting lines to observed data. Students actively participate by manually placing a line onto a scatter plot of data points. Their primary objective is to maximize a digital meter that provides a quantitative measure of the line’s overall goodness of fit to the data.
What’s My Transformation?
What’s My Transformation? guides students through exploring the concept that entire families of functions, such as all lines or all parabolas, are intrinsically related to one another. Students are then tasked with extending this generalized idea to analyze and manipulate a completely new function type. By engaging with the new function, they concurrently develop strong skills in utilizing the precise symbolic representations required for function transformations.
Burning Daylight
Burning Daylight is a robust modeling activity where students use sinusoid functions to accurately represent the daylight duration data for two distinct U.S. cities. Students begin by predicting which city, Fairbanks, AK or Miami, FL, receives a greater total amount of daylight over a specific calendar year. They then leverage their trigonometric model to mathematically calculate the definitive answer to this question. For Calculus students, this activity offers a valuable opportunity to practice defining and accurately calculating definite integrals.
