Desmos Activities for Middle School
********* Please note *********
I stopped updating this resource sometime in 2018.
Check out teacher.desmos.com for more info
Address comments / suggestions about this document to greenbloch@gmail.com or @greenbloch
These activities activities were found at Teacher.Desmos.com, at Des-Blog’s Friday Five, and sometimes @Desmos on Twitter. Descriptions are borrowed directly from Teacher.Desmos.com and Des-Blog.
You can search for activities by keyword at Teacher.Desmos.com. You might find other activities at the activities the Desmos Bank. If you are returning to this document and want to find whabattlet’s new, search for the word “added” using <COMMAND + F> or <CTRL + F> to bring up activities entered since this resource was first created. To learn more about teaching with Desmos, head over to Teacher.Desmos.com and Learn.Desmos.com!
Contents
Polygraphs (not sorted by grade level)
Visual Patterns -- linear and nonlinear (not sorted by grade level)
Counting Arrays (not sorted by grade level)
Problems / Puzzles (not sorted by grade level)
Number Line and Coordinate Plane (not sorted by grade level)
Misc. (not sorted by grade level)
Grade 6 (but could work at other grades, too!)
Grade 7 (but could work at other grades, too!)
Expressions Bundle (grade 7 etc)
Expressions/ Equations (grade 7)
Linear / Proportional (grade 7)
Grade 8 (but could work at other grades, too!)
Number System / Expressions and Equations / Exponents (gr 8)
Modeling / Scatter Plots (gr 8)
One Variable Inequalities / Linear Inequalities / Systems of Inequalities
Cool Extensions / Advanced Skills Other (gr 8)
Searchable sites for Desmos Activities
Ketchup Containers - Estimation 180 by Andrew Stadel. This series of Estimation 180 challenges focuses on the number of ketchup packets needed to fill paper containers with various sizes. Consider using one challenge per day for four days. Short tutorial videos with facilitation and dashboard tips can be found here:
Connect [puzzle] by Andrew Stadel. A fun puzzle that Fawn Nguyen gave me. (added 10/25/17)
Polygraph: Clocks by Desmos. This activity helps students understand the need for a common language to describe time and to surface early ideas about that language. We recommend you don't pre-teach that language but let students use their informal language first and then connect it to the formal language in a brief period of direct instruction. Then let students play again and experience the power of that formal language. (added 3/30/19) See also: Talking Time
Polygraph: Shaded Rectangles by Andrew Stadel. Edited with love by Desmos Teaching Faculty. Designed to spark vocabulary-rich conversations about fractions and part-to-whole relationships. Key vocabulary that may appear in student questions includes: shaded, unshaded, fraction, part, whole, numerator, denominator, simplified, and equivalent/equal to.
Polygraph: Rectangles At first glance, these are *just* rectangles, but many perimeters and areas have been strategically chosen. As students play, my hope is they will gain a deeper understanding of perimeter, area, and their independence.
Polygraph: Triangles Designed to spark vocabulary-rich conversations about triangles. Key vocabulary that may appear in student questions includes: scalene, obtuse, acute, right, isosceles, and equilateral.
Polygraph: Basic Quadrilaterals Students will be able to… Identify important features of quadrilaterals … Precisely describe these features to their peers … Increase their relevant vocabulary
Polygraph: Advanced Quadrilaterals Students will be able to… Identify important features of quadrilaterals … Precisely describe these features to their peers … Increase their relevant vocabulary
Polygraph: Hexagons Ask questions to guess which shape your classmate picked. Students will be able to… Identify important features of polygons … Precisely describe these features to their peers … Increase their vocabulary relevant to polygons
Polygraph: Hexagons, Part 2 This activity follows up on Polygraph: Hexagons, using the discussions (and students' informal language) in that activity to develop academic vocabulary related to polygons.
Polygraph: Polygons Designed to spark vocabulary-rich conversations about polygons and their physical characteristics. Key vocabulary that may appear in student questions includes: concave, convex, equilateral, equiangular, regular, parallel, quadrilateral, pentagon, and hexagon.
Polygraph: Identifying 3D Figures This Custom Polygraph is designed to spark vocabulary-rich conversations about three-dimensional objects. Key vocabulary that may appear in student questions includes: pyramid, prism, cone, cylinder, sphere, point, edge, surface, lateral, and base. (added 9/10/16)
Polygraph - Ramps What informal language might students have in their conversations about the steepness of ramps, attributes of triangles, etc.?
Polygraph: Distance-Time Graphs Designed to spark vocabulary-rich conversations about distance-time graphs. Key vocabulary that may appear in student questions includes: rate of change, increasing, decreasing, constant, velocity, and intercept. See also: Polygraph: Distance and Time
Polygraph: Rational Numbers Designed to spark vocabulary-rich conversations about rational numbers. Key vocabulary that may appear in student questions includes: numerator, denominator, positive, negative, proper, improper, simplified, equivalent, terminating, repeating, closer to 1, and closer to 0.
Polygraph: Points Designed to spark vocabulary-rich conversations about points in the coordinate plane. Key vocabulary that may appear in student questions includes: right, left, above, below, quadrant, axis, positive, negative, coordinate, x-value (or abscissa), and y-value (or ordinate).
Polygraph: Coordinate Plane Emojis by Paul Jorgens. Students use informal language about the coordinate plane as they determine the matching graph. (added 12/19/17)
O Pattern This activity consists of a patterning problem to help students understand linear relationships. (also listed below with grade 8 linear)
X Pattern In this task, students analyze the structure of a visual pattern. They describe this pattern in words and pictures, they use it to predict, and they generalize the pattern. (nonlinear)
Critter Patterns by mathycathy. "Visual Patterns" guide students through the process of generalizing patterns algebraically. This activity focuses on linear patterns. Inspired by:
*:The work of Fawn Nguyen
* This example, presented by Jo Boaler.
* "Squares to Stairs" task on YouCubed.org:
* "Match My Pattern" by Jon Orr:
Visual Patterns Workshop by Andrew Stadel. Choose your own adventure from 8 Visual Patterns!
*Inspired by patterns at http://www.visualpatterns.org/ Feel free to have students use the following handout to: 1) Describe the pattern in their own words; 2) Draw the 4th step; 3) Sketch the 43rd step; 4) Make a table; 5) Write the function for each pattern; Handout: http://bit.ly/VPhandout (added 10/9/16)
Visual Patterns Tribute by Andrew Stadel. Choose your own adventure from over 15 Visual Patterns!
*Inspired by patterns at http://www.visualpatterns.org/ Feel free to have students use the following handout to: 1) Describe the pattern in their own words; 2) Draw the 4th step; 3) Sketch the 43rd step; 4) Make a table; 5) Write the function for each pattern; Handout: http://bit.ly/VPhandout (added 10/9/16)
How Many Peaches? In this brief activity, students count the number of peaches in a photograph. Then the real fun begins. How did you see it? How did your classmates see it? And how do all of these approaches compare?
Pixel Patterns Students investigate patterns in order make predictions about the number of blue and purple squares in a grid of pixels.
More Pixel Patterns In this follow-up activity, students investigate two new patterns in order to make predictions about the number of blue and purple squares in a grid of pixels.
#HWYC: How Would You Count - CORNER How would you count the filled in purple dots?
#HWYC: How Would You Count - 2AND4 How would you count the filled in purple dots?
#HWYC: How Would You Count - BOAT How would you count the filled in purple dots?
Array This is a graph, not an activity. But it’s a graph that we have seen multiple requests for over time. If you have ever wondered, How do I build adjustable rows and columns? then this graph has your technique.
Dot-to-Dot Puzzles This activity is an interaction version of puzzles that can be found in an article written by Alex Bellos.
Calendar Arithmetic Students use numbers from the calendar to write expressions with a given value. Note: Since the numbers used are based on today's date, this activity can be used multiple times with the same students.
Twin Puzzles A novel way to assess and/or review Order of Operations with students! Using Desmos "Sketch" and projecting the "Overlay" of student work could create powerful classroom experiences for dialogue and error-analysis! Puzzles created by: Naoki Inaba. Answer key here.
Number Line, Number Sense This activity is designed to probe students' sense of numbers and their magnitudes. The overlay screens on the teacher dashboard can be used to facilitate class discussions related to scale and relative magnitude of increasingly large numbers.
Putting Points on the Line Students place points to show values along straight or curved paths.
Where’s ⅔? This brief activity has students place 2/3 on the number line and describe their thinking.
Fractions on a Number Line Students build number sense by partitioning rectangles, placing fractions on a number line, and making connections between these two representations.
Solving One-Step Equations by Seth Leavitt. Edited w/love by Desmos. Students connect solutions to one-step addition and subtraction equations to distances and locations on the number line. (added 8/25/16)
Solving One-Step Equations by mathycathy. Here's an intro activity on solving one-step equations that includes opportunities for organizing work using "Sketch" and "Card Sort" and error analysis using "Sketch". A silent video helps students visualize how a balanced scale can model solving an equation. (added 11/20/16)
Sum and Differences on the Number Line In this short activity, students explore the relationships among a + b, a – b and b – a on a number line when the precise values of "a" and "b" are unknown, but their signs are known.
Ordered Pairs and the Coordinate Plane | Target Practice by Nathan Kraft This activity will introduce students to all four quadrants of the coordinate plane through a variety of activities – graphing points, bulls-eyes, connect the dots, and mazes. (added 9/17/16)
Sums to Sixty by Cindy Whitehead (added 12/3/16)
Chance Experiments by Desmos. 30-45 minutes. Introduction. This activity introduces students to probability through a spinner game. Which result is more likely—red or blue? Students answer this question by gathering and analyzing class data and then apply what they've learned to consider the likelihood of other chance experiments. (added 12/19/17)
Talking Time This activity helps students understand different ways that people talk about time. They will read different descriptions of time – for example 5:15 or 15 after 5 or quarter after 5 – and try to set a clock to that time. Teachers will see which time formats are easier and harder for students. Teachers will have the opportunity to discuss with students how different ways of talking aren't right or wrong or smart or dumb. Rather, they're useful or less useful, and that's evaluated not by an answer key but by the people who are talking with each other. (added 3/30/19)
Exploring Triangle Area with Geoboards In this activity, students use Desmos-powered geoboards to explore triangles and their areas. (6th or 7th Grade?)
Mean, Median, and Variability Students adjust movable points to explore mean, median, and variability.
Population Stories Students analyze features of a graph to match five population-vs-time graphs with five US cities. As an extension, students use the graphs for two of these cities to make predictions about future populations.
Number Properties (Card) Sort Basic number properties card sort. Beware of false "BOGUS" properties! A quick pre- or post-assessment.
Tile Pile Students will be able to… Use a ratio table to scale values in a proportional relationship... Find missing and incorrect values in a ratio table... Use the population of a sample to calculate the total population. “Recommended based on classroom use.” (Soltani)
Sketchy Fractions Students demonstrate (and deepen) their understanding of fractions by shading part of a square, and later, part of an equilateral triangle. At the end, students create their own sketches for a fraction of their choosing. Along the way students explain their thinking and look for multiple shadings for a given fraction.
Pizza Slices Have students guess how many slices of a pizza make a whole.
Exploring, Comparing and Finding Equivalent Fractions by Jennifer Vadnais. This activity builders is different. It does not walk a student through a series of guided questions. Teachers and students have the flexibility to create their own problems. It’s more of a general or open tool to be use as desired. Learn more in this post: Comparing Fractions w/ Desmos (added 9/10/16)
Six Sliding Shapes: Parts Placements by Cindy Whitehead. Locating fractions on a number line.
Some sets include 1/10 scale as transition to fraction and decimal equivalents. Teachers can use overlay feature to discuss placement as a whole class. (added 12/3/16)
Number Sense – Multiplying Fractions In this activity, students drag movable points along the number line to show the value (and meaning) of multiplication of fractions.
Visual Ratios by Andrew Stadel. Visual Ratios. (added 12/3/16)
All About Area by Cindy Whitehead. This activity is NOT really "All About Area!". Students are forced to find common factors and greatest common factors to create adjacent rectangles with a common side. Activity includes opportunities to analyze and advise student work. 6.NS.B.4, SMP1, SMP3, SMP6, SMP7 (added 12/3/16)
Polygons on the Coordinate Plane Students find areas of a rectangle, a triangle, and a parallelogram on a coordinate plane. They consider the relationships between the coordinates of the vertices and the polygons' dimensions, and between the areas of the various figures. A useful tool for assessing students’ ability to see these important attributes of triangles. Adapted from CPM CCC1 Problem 5-89.
Polygraph Points by Robert Kaplinsky. Edited with love by Desmos Teaching Faculty. This Custom Polygraph is designed to spark vocabulary-rich conversations about points in the coordinate plane. Key vocabulary that may appear in student questions includes: right, left, above, below, quadrant, axis, positive, negative, coordinate, x-value (or abscissa), and y-value (or ordinate). (added 9/10/16)
The (Awesome) Coordinate Plane Activity This activity will introduce students to coordinate plotting in all four quadrants through a variety of activities – bullseyes, connect the dots, and mazes.
Battle Boats by Desmos. 30-45 minutes. Practice. In this activity, students build coordinate plane proficiency through a guess-the-location-style game. (added 4/16/17)
Battle Boats [Primary Grades] by Desmos. 30-45 minutes. Practice. In this activity, students build coordinate plane proficiency through a guess-the-location-style game. This version addresses quadrant 1 only. (added 12/20/17)
Coordinate Plane by Jeff Jelus. Coordinate Plane - Card sort, plotting points, similarities & differences between different sets of points. (added 10/9/16)
Zombie Apocalypse by Andrew Stadel. Edited with love by Nathan Kraft. Avoid the zombies by traveling vertically and horizontally on a coordinate plane. Learning objective: • find the distance between two points on a coordinate plane. (10/9/16) [also listed with grade 8]
Marbleslides Junior: Geometric Figures Very simple 6th grade activity. The standard is plotting points, finding side lengths, and then their areas: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. This is to be a follow-up to the Awesome Coordinate Plane activity (see above).
Mini Golf Marbleslides by Jennifer Vadnais. 30-45 minutes. Practice. Edited with love by Desmos. Students practice graphing coordinates in a game of a mini golf. (added 3/12/17)
Volume of Rectangular Prisms by Nathan Kraft. This activity tries to build on student intuition to develop an understanding of the volume of rectangular prisms. (added 9/18/16)
Polygraph: Shady Lines [inequalities] by Andrew Stadel. What will students discuss with inequalities, shading, open circles, closed circles? (added 10/9/16)
Polygraph: Shady Lines II [inequalities] by mathycathy. Inspired by Andrew Stadel's "Shady Lines", this Polygraph also includes graphs of compound inequalities. (added 11/20/16)
Inequalities [math 6] by Andrew Stadel. Use a number line to: • better understand inequality notation;
• write, graph, and shade inequalities; • apply inequalities to real-world contexts (added 10/9/16)
Lawnmower Math by Desmos. 30-45 minutes. Application. Students will learn how math can give them the power to quickly mow dozens of lawns without breaking a sweat. They'll first estimate the correct radius for a pole that'll guide a lawnmower in a spiral around a lawn. Eventually they'll create an algebraic expression and see how it helps them mow lots of lawns very quickly. Math is power, not punishment. (added 2/9/17)
Sector Area by Desmos. 30-45 minutes. Development. In this proportional reasoning activity, students explore the relationship between circle area, sector area, and sector angle. The final screens provide an opportunity for students to experience the power of algebraic expressions.
Pool Border Problem by Desmos. 30-45 minutes. Application. In this Desmos-ified treatment of a classic math problem, students will first construct expressions with numbers to determine the number of tiles that border a pool. Then they'll use those numerical expressions to help them write an expression with VARIABLES. Then they'll put the algebraic expression to the test, and see if it helps them find the tiles for lots of pools very quickly. (added 2/9/17)
Central Park How far apart do parking space dividers need to be? Students will be able to… Use arithmetic computations to inform their use of algebraic symbols … State the meanings of variables in context. (Also works well with Grade 8)
Picture Perfect by Desmos. 45-60 min. Application. In this activity, students will use algebraic thinking to precisely (and efficiently) hang picture frames on the wall. This activity will provide opportunities for students to deepen their previous understanding with linear equations. (added 3/21/17)
Pentomino Puzzles In this activity, students work through a series of "pentomino sum" puzzles. They begin informally (and rather inefficiently). But later, they'll develop and apply an algebraic approach, demonstrating the power and efficiency of mathematics along the way. See also this blog post http://mrorr-isageek.com/pentomino-puzzles/ (added 9/10/16)
Expressions Mash-Up (card sort) by mathycathy. Edited with love by Desmos Teaching Faculty
In this activity, students sort cards to strengthen their understanding of multiple representations, including: algebraic expression, verbal description, table of values, and algebra-tile model. After the card sort, students discuss whether a given student has sorted two pairs of cards correctly, and in the process consider equivalence and commutativity.
Integer Game Students play three rounds of an integer game where they (1) find the sum of a set of five integers, and (2) decide whether their sum is greater than their partner's.
Card Sort: Integer Chips by Michael Fenton (added 9/18/16)
Adding Integers by Glen Lewis. Students will learn how to add integers using the number line. They progress through adding two positives, two negatives, opposites, and one of each. (added 10/9/16)
Sum and Differences on the Number Line In this short activity, students explore the relationships among a + b, a – b and b – a on a number line when the precise values of "a" and "b" are unknown, but their signs are known.
Addition of Integers - Hot Air Balloon by Elizabeth Raskin. Edited with love by Adrianne Burns. This activity is intended to be used to help students understand addition of positive and negative numbers on a vertical number line (CCSS.MATH.CONTENT.7.NS.A.1) (added 10/9/16)
Polygraph: Angles and Triangles Created by: Lisa Soltani. Students build vocabulary around angle relationships and classification of triangles. It includes corresponding angles, but does not require that student know alternate interior, etc. Vocab: angles, complementary, supplementary, isosceles triangle theorem, corresponding, vertical, adjacent
Random Penguins Created by: Norma Gordon. Students use random samples to estimate the size of a population. If students want more data, send them to this link (on which this activity is based).
Collecting like terms by Alyssa Gilbert. Card Sort. (added 10/9/16)
Distributive Property by Andrew Stadel. Explore the distributive property both conceptually and algebraically. (added 10/9/16)
Pondering Percent This activity builds on students current knowledge of percent before it creates a driving need to use an algebraic solution to determine percent of a number. [Editor’s note: This activity by Jonorr may be a work in progress as of 9/10/16, but it’s pretty nifty already.] (Add 9/10/16)
Click Battle by Desmos. 30-45 minutes. In this proportional reasoning activity, students will explore unit rate in the Click Battle arena. (added 12/19/17)
Marcellus the Giant by Eli. Edited with love by Desmos and Dan Meyer. This activity will help your students understand the definition of a proportional relationship. They'll create a giant and then make sure all of his features are proportional. They'll see the representation of his proportions on a graph and manipulate the graph to see the giant change dynamically. (added 10/22/16) For more info, see this post from Dan Meyer
The Running Game Students use proportional reasoning to predict how long it will take someone to run seven miles. Students will also interpret the meaning of the graph and equation in context. Note: There is a bonus question at the end. The answer is "current pace."
“Haven’t run it but looks good, would do this before doing Sugar Sugar.” (Soltani)
Sugar Sugar Students will use unit rates in various ways to compare the sugary-ness of five cereals.
Music and Money Students use a table, graph, and equation to calculate how much a musical artist earned on Spotify in 2015. Proportional / Linear
Walking and Wondering Students gather and analyze walking data (distance in feet compared to time in seconds), write equations to represent this distance-time relationship, and compare their own walking rates to others through multiple representations (numerical, graphical, and algebraic). Note: This activity requires that students collect walking data prior to completing the activity. This can be done at the start of the activity, or during the previous day. A stopwatch (or smartphone) and some measuring tapes are sufficient. (Grade 7/8?)
Measuring Circles Students measure circles, plot (diameter, circumference), and discuss how they know this is a proportional relationship. Image credit to kidsmathgamesonline.com. Teacher notes here.
Traveling to School Students consider 4 students and their trips to school comparing their distance traveled over time.
Des-Patterns by Desmos. 45-60 minutes.In this activity students will practice writing coordinate rules to transform figures to complete patterns. They'll end by designing their own pattern and using the math they've learned to extend a pattern designed by a classmate. (added 10/29/17)
Transformation Golf: Rigid Motion by Desmos. 30-45 minutes. In this activity, students use their existing understanding of translations, reflections, and rotations to complete a round of transformation golf. For each challenge, their task is the same: Use one or more transformations to transform the pre-image onto the image. We recommend you solve the challenges yourself before assigning this activity. (added 9/21/17)
Polygraph: Translations Designed to spark vocabulary-rich conversations about translations. Key vocabulary that may appear in student questions includes: horizontal, vertical, translation, shift, and slide.
Polygraph: Transformations Designed to spark vocabulary-rich conversations about transformation. Key vocabulary that may appear in student questions includes: translation, rotation, reflection, dilation, scale factor, pre-image, and image.
Blue Point Rule by Desmos. 45-60 minutes. Students will observe a red point transform into a blue point by way of a mystery transformation. Students will first write about that transformation verbally, developing their intuition about the transformation, before then writing it algebraically. (added 4/2/17)
(This activity takes students into the realm of alternate possibilities, and it introduces new notation. Leading up to this point in the bundle, students have worked with transformations of functions. Here, they work with transformations of an individual point, but one that they can move in order to investigate the relationship between the original point and its image.)
Translations by Andrew Stadel. Edited with love by Desmos Teaching Faculty. In this lesson, students: 1) describe and execute translations in words and coordinate notation, and 2) perform error analysis by critiquing a classmate's mistake and then fixing it.
Translations Quick Check by mathycathy. A quick warm-up assessing TRANSLATIONS in the coordinate plane, designed for Math 8 students. (added 4/18/17)
Reflections by mathycathy. 30-45 min. Introduction. Edited with love by Desmos. Students explore reflections over the x-axis and y-axis, with an emphasis on how the coordinates of the pre-image and image are related. There is also an extension where students try to reflect a pre-image across the line y = x.
Translations and Reflections by Paul Jorgens. Students practice performing translations and reflections of triangles. (added 12/8/16)
Rotations by Andrew Stadel. Rotate images in a coordinate plane using academic language and coordinate notation. *HINTS are included for students challenged with the abstract idea of rotations. (added 10/9/16)
Working with Dilations This is a beginners activity for introduction to dilations (8.G.A.3 & 8.G.A.4). Students explore a little bit of coordinate geometry by using Desmos sliders to dilate triangles and consider the consequences.
Dilations by Andrew Stadel. Students (1) describe and execute dilations using reductions, enlargements, and scale factor; (2) perform error analysis, critiquing a classmate's mistake, and then fixing it. (added 10/9/16)
Transformations Revisit and Review by mathycathy. A transformations review designed for Math 8 students. (added 4/18/17)
Geometry Basic Vocabulary Matching Card sort. Match each geometric term with the correct definition.
Laser Challenge by Desmos. 45-60 minutes Introduction. In this activity, students use angles to adjust lasers and mirrors as they seek to hit all three targets in a series of challenges. For younger students, this may serve as an excellent introduction to thinking about angle measure. For older students, this offers a chance to think critically about the properties of angles, lines, and reflections. (added 2/9/17)
Polygraph: Angle Relationships by mathycathy. Students practice asking questions using vocabulary such as: acute angle, obtuse angle, right angle, complementary angles, supplementary angles, corresponding angles, vertical angles, alternate interior angles, alternate exterior angles, congruent angles, transversal, parallel lines, perpendicular lines. (added 1/2/17)
Card Sort: Angle Pairs Created by Transversals by Jarrod Huntimer
Lines, Transversals, and Angles Students explore the relationship among angles formed by a transversal and a system of two lines. In particular, they consider what happens when the two lines are parallel vs when they are not.
Kung Fu Transversals by Andrew Stadel. Challenge students to a few puzzles with transversals. (added 9/17/16)
Similar Polygons Quick Check! by mathycathy. It's a new day with new Desmos features. I want to test them out, using an old faithful Socrative SOC-18310521 quick-check I made previously. Let's see how these new "choice" features work with students today! Woot! (added 12/3/16)
Exploring Lengths of Line Segments by Danielle Braun. (added 12/3/16)
Square Builder In this activity, students build squares with integer area in order to reason about their side lengths. Use this as an introduction to irrational numbers, or as a prelude to the Pythagorean theorem.
Zombie Apocalypse by Andrew Stadel. Edited with love by Nathan Kraft. Avoid the zombies by traveling vertically and horizontally on a coordinate plane. Learning objective: • find the distance between two points on a coordinate plane. (10/9/16) [also listed with grade 6]
Exploring Length with Geoboards by Michael Fenton. Edited with love by Desmos Teaching Faculty.
In this activity, students use Desmos-powered geoboards to explore length and to further develop their proficiency with the Pythagorean relationship. (10/9/16) [Returns message for: “This activity is only for CPM users.”]
Complete the Quadrilateral by Lisa Bejarano. This activity is from Don Steward’s post “Complete the Quadrilateral”, with images created by Fawn Nguyen. Given one side, students must construct the specified quadrilateral with the largest possible area. This task requires students to have an precise understanding of the definitions of specific quadrilaterals and is also a great introduction to slope of parallel and perpendicular lines. (added 10/25)
Quadrilateral Sort: ALWAYS, SOMETIMES, NEVER by mathycathy. Edited with love by Lisa Bejarano
Once students have learned about the properties of quadrilaterals, this task encourages deeper thinking about the relationships between these quadrilaterals. Individuals, pairs, or small groups sort the statements in the appropriate categories of ALWAYS being true, SOMETIMES being true, or NEVER being true. (added 10/25/16)
Similar Rectangles by mathycathy. Let's explore similar rectangles, their perimeters, and their areas! (added 11/20/16)
Complete the Arch by Desmos. 30-45 minutes. Students will apply their understanding of the angles of an isosceles trapezoid to create a complete archway. We recommend students work on this task using computers AND paper. (added 10/11/17)
Longfellow Linears. by Desmos. 15-30 minutes. Practice. I found a link to this activity in this post by Dan Meyer. This activity includes the Least Solution challenge (see next activity below).
Smallest Solution by Desmos. 15-30 minutes. Practice. In this activity, students will practice solving equations with multiple steps and with variables on both sides of the equality. They will CREATE an equation so that it has the smallest possible solution for x. Students will reason abstractly and structurally, arguing that their expressions are the greatest or least possible. We have used "smallest" in the title of this activity even though it is not a well-defined mathematical term. By "smallest solution" we mean "the solution—not necessarily unique—with least absolute value, whether positive or negative." We believe that "smallest solution" is a more intuitive, early title, which you can then specify and formalize later in the activity. (added 11/19/16)
Number Sentences - Expressions by David Petro. A very simple sorting activity where students are given expressions and the sentence to describe them and have to match them up. Meant to be a relatively quick activity. There are four sorts that are all very similar to each other; you may wish to assign different sorts to different groups. For a the more traditional "hands on" version click here. (added 9/10/16)
Number Sentences - Equations by David Petro. A very simple sorting activity where students are given expressions & equations and the sentence to describe them and have to match them up. Meant to be a relatively quick activity. There are three sorts that are all very similar to each other; you may wish to assign different sorts to different groups. In each sort there are some equations that have no match. Students will have to create their own sentences following the sort. For a the more traditional "hands on" version click here. (added 9/10/16)
When Are Equations True? This Card Sort was adapted from the MAP Formative Assessment Lesson for Gr 8 "Solving Linear Equations in One Variable". (added 9/10/16)
#WODB Equations Warm-Up by mathycathy. Which One Doesn't Belong? Let's start a "math fight"! In this brief activity, students are given four equations with variables on both sides of the equals sign. Using Desmos Card Sort, students must take a stand on which equation they believe doesn't belong, and justify this choice. Students will see what other students choose, and consider different opinions and justifications. Additionally, students have the opportunity to create their own #WODB task to share. (added 10/9/16)
Equations on a Double Clothesline - Fractions by Nathan Kraft. Edited with love by Matt Vaudrey and Desmos Teaching Faculty. Fraction coefficients are weird, this might make them less so. (added 9/18/16)
Squares and Square Roots Card Sort Students often confuse the concepts of "square" and "square root". This Card Sort provides numerical expressions, word phrases, and red images that will help students make connections between concrete visuals and abstract notation. (added 9/10/16)
Square Dance (Tango) Explore the relationship between the area and side length of squares as a segue to rational and irrational numbers. Learn more about: perfect squares and square roots, rational and irrational numbers, approximately place rational and irrational terms on a number line. Link to clothesline cards used with the lesson. Link to blog post about this activity.
Card Sort: Real Number Statements (Always, Sometimes, Never) by mathycathy. Edited with love by Desmos. Once students have learned about various classifications in the real number system, this task encourages deeper thinking about the relationships between those classifications. Individuals, pairs, or small groups sort the statements according to whether they are ALWAYS, SOMETIMES, or NEVER true. (updated version added 10/17/16)
Card Sort: Real Numbers by Shena Wald. Students sort cards into four categories: whole numbers, integers, rational numbers, irrational numbers. (added 9/18/16)
Rational Irrational Card Sort by Greta (added 4/10/18)
Irrational vs. Rational Card Sort by Joel Bezaire. A simple card sort for Rational vs. Irrational numbers, and then a couple of follow-up questions after that. Used in my Pre-Algebra class after introducing the concept of Irrational Numbers. (added 4/10/18)
Open Middle Warm-Up: Exponents & Order of Operations by mathycathy. Inspired by OpenMiddle.com, this brief warm-up experience is designed to help students apply the correct order of operations to numerical expressions that contain exponents. (added 9/2/17)
Zero and Negative Exponents by mathycathy. Using Desmos "Sketch", students generate patterns to explore zero as an exponent and negative exponents. (added 9/18/16)
Exponent Mistakes A riff off an Andrew Stadel "Exponent Mistakes" classic. Even a great worksheet can be an even more awesome Desmos experience.
Exponent Match Card sort. Match the equivalent expressions. (added 9/10/16)
Evaluate Expressions With Exponents by Mr. Adam Santos. Edited with love by mathycathy. Students will evaluate numerical and variable expressions containing exponents with positive or negative bases. (added 4/18/17)
Standard Form and Scientific Notation Sort Students sort numbers written in standard form and scientific notation to make sure they understand the difference between "really large numbers" and "really small numbers" before they begin learning how to convert between the two forms.
Scientific Notation by Lars King. This is from the MAP lesson Estimating Length Using Scientific Notation (added 9/18/16)
(8 activities) Starting with Polygraph and building towards Marbleslides, the linear bundle is for classrooms where students have plotted points in the coordinate plane, but have not yet mastered any of the various forms for linear equations. Key Understandings: Rates of change express themselves as slope of a line, and as a coefficient of x in a linear equation. Y-intercepts express themselves as constants in linear equations.
Polygraph Lines Students will be able to… Identify important features of lines … Precisely describe these features to their peers … Increase their vocabulary relevant to lines
Polygraph: Lines, Part 2 This activity follows up on Polygraph: Lines, using the discussions (and students' informal language) in that activity to develop academic vocabulary related to the graphs of linear functions.
Put the Point on the Line The goal is to sharpen students’ focus on slope. In particular, the activity asks students to estimate first, then to calculate, then to notice proportionality as they place points on an imaginary line. Use student ideas here to define slope as a ratio of change in y-coordinates to change in x-coordinates. By the time students get to the end of the activity, they should have a number of ways of talking about this, but it’s unlikely they’ll write a fraction with ∆y in the numerator and ∆x in the denominator. They’ll be ready for you to introduce this idea.
Match My Line A series of graphing challenges designed to build student understanding of linear functions in various forms.
[see also: Match My Line (Lite Version) by Michael Fenton. Edited with love by mathycathy. A series of graphing challenges designed to build student understanding of linear functions. (added 9/2/17)
Land the Plane by Desmos. 30-45 minutes. Practice. In this activity, students practice finding equations of lines in order to land a plane on a runway. Most of the challenges are well-suited to slope-intercept form, but depending on the goals of an individual class or student they are easily adapted to other forms of linear equations. (added 2/9/17)
Card Sort: Linear Functions This activity asks students to notice and use properties of linear functions to make groups of three. Different properties will lead to different groupings by different students. Later we ask students to make conjectures about different groupings – why might another student have grouped the cards in a particular way?
Marbleslides: Lines Transform lines to send the marbles through the stars. Students will be able to: Restrict, reposition, and rotate lines at will using slope-intercept form … Use precision in describing these transformations using words and/or symbols.
See also:
Marbleslide Challenge Set by Sean Sweeney. A set of 36 Marbleslide Challenges to run throughout the year. You can use teacher pacing to unlock a new challenge each week. These challenges can be used with any level from Algebra 1 through and beyond Calculus. Some of the challenges are very difficult to complete using a single equation, but all should be possible to complete using a number of linear equations. (added 8/17/17) See this post for more information and suggestions.
Marbleslides Challenge Set 2 by Sean Sweeney. A set of 30 Marbleslides Challenges to run throughout the year. These challenges can be used with any level from Algebra 1 through and beyond Calculus. Encourage higher level students to use fewer equations to increase the difficulty level. Some of the challenges are very difficult to complete using a single equation, but many can be completed using a number of linear equations.
LEGO Prices by Desmos. In this activity, students use sliders to explore the relationship between price and number of pieces for various Star Wars LEGO sets and to make several predictions based on that model. Students will also interpret the parameters of their equation in context. (this updated version added 11/4/16)
Rogue Planes by John Rowe. The aim of this activity is to challenge students' understanding about graphing linear functions and hopefully consolidate their learning of graphing slope-intercept form. This activity reverses the question of sketching linear functions. Instead of students changing the orientation of the line, they must change the orientation of the Cartesian Plane or draw the $$x and $$y axes to fix the graphs and correctly show the equation of the straight line given. (added 3/26/19)
Match My Lines by Jeremy Bloch. Practice with slope-intercept form. Graph four sets of 3 lines. For each set, identify what the s lines have in common.
Match My Picture by Desmos. 30-45 minutes. This activity is designed to strengthen students' linear graphing skills through a series of "match my picture" challenges. As students work, they use Lists in the graphing calculator to look for and make use of structure. Inspired by Jon Orr.
Which is Steepest? by Desmos. 30-45 minutes. Introduction. In this activity, students explore the idea of "steepness" of line segments. This activity serves as a prelude to formal conversations about vertical change, horizontal change, and slope.
Slope-Intercept practice [math 8] by Andrew Stadel (added 10/27/17)
Linear Slalom by Desmos. 45-60 minutes. Practice. In this activity, students work through a series of slalom-themed challenges to strengthen and stretch their algebraic and graphical understanding of lines. (added 7/1/18)
Talkers & Drawers - Linear Relations by Jonorr. Students will generate a need to use less informal language and more formal language when describing linear relations. One student will attempt to "describe" (without using their hands) a graph for their partner to sketch (who can't talk). Then the two will swap roles. After a few challenges your class will have used a number of words to describe linear relations. Now you can swap out those informal words for more formal ones. (added 10/22/17)
Sketchy Lines Students respond to a variety of graph-sketching prompts to demonstrate (and deepen) their understanding graphs of linear functions.
Finding the Slope of a Line Using Rise/Run Finding the slope of a line using rise/run. See this tweet for a good pic of the template.
Point, Point, Slope by Christopher Kunkel. Edited with love by Desmos Teaching Faculty
In this activity, students tackle several slope-themed open middle problems.
Investigating Rate of Change by Desmos. 30-45 minutes. Development. In this activity students will compare slopes of lines with a y-intercept of zero. They'll use their comparisons to learn how to write the equations of lines of the form y=ax. Inspired by Investigating Rate of Change from an Equation by Mr Rothe (see below).
Where Will They Meet? Students make predictions about where lines will intersect. The emphasis is on a graphical understanding of linear equations, and visual/numerical rate of change in particular. (Does not require writing equation for the line.)
Investigating Rate of Change from an Equation This activity walks students through the discovery of the meaning of slope in a graph and equation. Students to think about the effect of a coefficient on the steepness of a line in the coordinate plane, and vice versa. The activity starts gently, and over the course of some 30 screens builds in complexity and surprise, culminating in a coefficient-less Bonus Round.
Slope: Formative Assessment This activity is designed to serve as a formative assessment on student understanding of slope (graphically, algebraically, and numerically). It is not recommended as an introduction to the topic, but rather assumes some prior knowledge.
Introduction to Parallel Lines Students take their existing geometric understanding of parallel lines and build an algebraic understanding of parallel lines on top of that. The key understanding is that parallel lines have the same slope and their y-intercepts may differ.
Slope-Intercept Stars by mathycathy. This Marbleslides activity encourages students who are new to slope-intercept form to explore how adjusting the slope and y-intercept in a linear equation impacts the graph. (added 11/20/16)
Graphing Linear Equations in Slope-Intercept Form by roxygirlteacher. Graphing linear equations in slope-intercept form. (added 10/9/16)
Coin Capture by Desmos 15-30 minutes. Students will practice their understanding writing linear equations by placing coins on a coordinate plane and writing as few equations as possible to "capture" all of the coins. (added 11/12/18)
Nine Points, Three Lines Students practice constructing linear equations and also learn properties of collinearity. This activity is based on the work of Don Steward.
Hit 'Em Have your students construct lines that go through the points while thinking about their strategy as they do!
Writing the Equation of a Line Students begin by exploring rate of change in a graphical setting by plotting lines through various points. The activity concludes with several parallel and perpendicular graphing challenges, and two reflection questions on the connections between the graphs and equations of parallel and perpendicular lines.
Is It...? by mathycathy. A triple card sort to help students practice classifying functions: * that are and are not linear; * that are and are not parallel to a given line; * that are and are not perpendicular to a given line. Grab some scrap paper, folks. You're gonna need it. (added 11/20/16)
Constructing Rectangles This activity helps students discover that perpendicular lines need opposite AND reciprocal slopes. It uses the context of quadrilaterals in the coordinate plane. (added 9/10/16)
Constructing Squares This activity will reinforce the basics of coordinate geometry and linear graphs with restrictions. In your summary conversation with your students, draw their attention to the relationship between slopes in parallel & perpendicular lines.
Introduction To Desmos: Letter Graphs Students learn the basic of graphing lines, using sliders, and restricting domains. Then they apply that knowledge to make a graph of one letter of the alphabet.
Parallelograms in the Coordinate Plane In this activity, students use (or develop) their understanding of rate of change to determine whether a set of four points in the coordinate plane will form a parallelogram.
Writing Linear Equations with restricted domain and range by Nora Oswald (added 10/25/17)
Des-face Using Domain and Range by Elizabeth Kerns. Edited with love by Desmos. Students will learn how to use restrictions on equations of horizontal and vertical lines in order to draw a face on Desmos. (added 10/26/16)
Des-Draw (linear) While the original Des-Man is receiving a makeover, give Des-Draw a try! My hope is to leave it open to encourage students' creativity while helping them brush up on restricting the domain and range of various functions, gently reminding them that using inequalities can create some rad shading. (Also see Des-Draw which includes nonlinear.)
Winking Boy by Andrew Stadel. Edited with love by Desmos Teaching Faculty. Students create "Winking Boy" (a simplified Desman) by using linear equations with domain and range restrictions. Shading the hat can be optional. Any student who can graph a line can make satisfying progress on Winking Boy.
Segmented Functions by Katina Vlastos. Piecewise Functions--Segmented Functions. Match graphs with their equations and evaluate. (added 10/9/16)
See also: Desmos Puppy House mini-project (also in our projects folder)
String Art 2.0 Students will be able to use slope intercept form and limit on the domain to create string art designs. How to get kids exactly one ton of practice writing equations for line segments, while engaging in purposeful image making.
Who's Faster? Students analyze time vs distance relationships in graphs, tables, and equations, and interpret the results (and parameters) in context. This one’s short but it will make your brain ache. How can I tell who’s faster when time is on the vertical axis? What does this even mean? Good times!
Abe and Ben's Repair Shop In this twist on a classic activity, students compare linear and exponential growth in the context of daily payments. One plan increases by $100 each day, while another grows by doubling the previous day's payment. This activity is appropriate for students who have studied linear functions but may not have an experience with exponential growth. With that in mind, it makes a great first activity in an exponential functions unit.
Application of Linear Equations This activity is adapted from Eureka Math Algebra 1, Module 1, Lesson 20. It presents a linear modeling situation and asks students to interpret the equation, coordinate pairs that are solutions, and coordinate pairs that aren't solutions. (Note: Equation in standard form.)
O Pattern This activity consists of a patterning problem to help students understand linear relationships.
X Pattern In this task, students analyze the structure of a visual pattern. They describe this pattern in words and pictures, they use it to predict, and they generalize the pattern. (nonlinear)
Linear Relationships - Tables Activity by Joel Bezaire. Students (Pre-Algebra or beginning Algebra 1) look at tables of linear solutions to predict other solutions that are part of the linear relationship. (added 8/2/17)
Linear Pattern Match In this activity students are able to interact and explore different representations of a linear growing pattern.
(7 activities) From Polygraph to Oreos, the linear systems bundle introduces students to the meaning of a solution to a system of linear equations, and gives them some instruction and practice in introductory solution techniques. Key Understandings: A solution to a linear equation can be interpreted in two ways: (a) graphically, as a point on the line, and (b) algebraically, as an ordered pair that yields a true statement when substituted into the equation. Likewise, a solution to a system of linear equations can be interpreted in two ways: (a) graphically, as a point that lies on each line in the system, and (b) algebraically, as an ordered pair that satisfies each equation in the system. There are multiple ways to solve a system, including: graphing, substitution, and elimination. The best method often depends on the structure of the equations involved.
Polygraph: Linear Systems Designed to spark vocabulary-rich conversations about systems of linear equations. Key vocabulary that may appear in student questions includes: parallel, intersect, solution, quadrant, axis, vertical, horizontal, slanted, increasing, and decreasing.
System of Two Linear Equations Students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution." The activity closes by asking students to apply what they've learned to a similar situation.
Solutions to Systems of Linear Equations by Desmos. In this activity, students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution." The activity closes by asking students to apply what they've learned to similar situations.
Playing Catch-Up by Desmos. Students will develop their understanding of systems of equations, particularly as they're represented as tables, equations, and graphs. They'll apply that understanding to the question, "Will one racer catch another?" (added 11/4/16)
Racing Dots Students make predictions about where a pair of moving dots will meet. They gather more information to increase the accuracy of their predictions. Later, they write a system of two linear equations to model the path of the dots in order to make an even more precise calculation. While students can solve the systems of equations that arise here by graphing, the activity lends itself quite well to solving systems by substitution. Based on this Desmos activity: The Great Collide.
Wafers and Crème Students use informal math reasoning skills to answer the question of which has more calories: a single chocolate Oreo wafer, or a single layer of crème. The activity then leads students through the process of writing a system of linear equations to represent the scenario, followed by an introduction of solving systems by elimination. The activity should be followed (immediately, if possible) by a teacher-led review of the method used at the end, which may lead well into additional examples and practice. Note: Students may get stuck on Screen 7. After appropriate wait time, you may want to encourage them to consider the "difference" between the stacks. If you prefer to facilitate the introduction/exploration of elimination in a whole class discussion, ask students to stop after Screen 7 (or, duplicate the activity and delete Screens 8-15). In that case, you may find the following images useful.
Card Sort: Linear Systems Students practice what they've learned about solving systems of linear equations. The activity begins with a review of the graphical meaning of a solution to a system. Later, students consider which algebraic method is most efficient for solving a given system. Finally, students practice solving equations using substitution and elimination. Prior to beginning this activity, students should have experience solving systems of linear equations graphically and algebraically.
Pet House: A Linear Project! by mathycathy. Edited with love by David Petro. A graphing project inspired by David Petro, Kathy Henderson, Heather Bolur and her students' work, and Fawn Nguyen!
The Intersection by Desmos. 30-45 minutes. In this activity, students predict the point of intersection for a system of two linear equations, at first without a grid, and then later with one. With the grid in play, students are able to use the slope of the lines (whether formally, or informally) to improve the accuracy of their predictions. This activity serves as an example of the usefulness of mathematical structure in general (in this case, the coordinate grid) and a potential launching point into discussions about rate of change for linear functions. (added 4/18/17)
Target Practice [linear systems] by Andrew Stadel. A short review on linear systems that taps into student intuition and their understanding of: • slope-intercept form • attributes of a system with one solution • attributes of a system with no solution (10/9/16)
Linear Systems: Gym Membership Students analyze several gym membership plans in order to make "best plan" recommendations for a friend. The activity begins with a quick review of graphing linear equations, and ends with several "create your own story" challenges.
Systems of Linear Equations: Discoveries This activity will guide students to think about what it means to be a solution to an equation and to a system of equations. [editor’s note: Seems redundant to activities in “Systems Bundle”]
Solving Linear Systems by Elimination Use this lesson to introduce students to the elimination method for solving systems of equations. Students will learn that adding multiples of the original equations produces a new equation of a line that has the same intersection point as the original equations. This visual introduction helps students self-check their algebraic steps along the way. (Note: Abstract, but interesting.)
Polygraph: Distance-Time by David Petro.This Polygraph focuses on describing the characteristics of distance-time graphs with linear sections (or more generally piecewise continuous linear functions). (added 11/19/17)
Graphing Stories by Desmos. 60+ minutes. Introduction. This activity will help students make the transition from one-variable representations (eg. number lines) to the TWO-variable representation of the coordinate plane. Students will watch 15-second videos and translate them into graphs with your help.
Card Sort: Linear or Nonlinear Students begin this activity by sorting equations and tables of values into two categories - linear and nonlinear. They reflect on these choices, and apply their learning by creating their own equations and tables of values that fall into each category. Inspired by by Beth Ferguson’s blog posts. (Added 9/10/16)
Polygraph: Piecewise Functions Designed to spark vocabulary-rich conversations about piecewise functions. Key vocabulary that may appear in student questions includes: piecewise, continuous, and interval.
Polygraph: Functions & Relations Designed to spark vocabulary-rich conversations about functions and relations. Key vocabulary that may appear in student questions includes: domain, range, hole, and points.
Intro to Functions by Mark Wigand. This is a basic introduction to Functions activity for an Algebra 1 class with some knowledge of Functions. It explores telling whether a relation is a function from a table or graph, writing a rule for a function from a table or graph, the idea of domain and range, and the vertical line test. (added 10/9/16)
Function, or Not? In this activity, students determine whether a series of relationships represent functions. Three of the relationships are expressed algebraically, while two are expressed verbally in the context of a classroom: (person, grade level) and (person, shirt color).
Function or Not? (card sort) Students decide whether various representations are functions or not, and sort them accordingly.
There are a number of domain and range activities in the Desmos database. Here’s a nice one for practice. It assumes your students have encountered these terms, and gives them interesting cases to consider. In this activity, describe in words the domain and range of six relationships represented graphically. Afterwards, students use movable points to create three functions whose domain and range match specific criteria.
TRUTH or LIE? Domain and Range From a Graph by mathycathy. Inspired by the "Two Truths and a Lie" math strategy, this quick check provides students with opportunities to analyze graphs. Follow-up questions prompt discussion and debate! (10/9/16)
Domain and Range Practice by Suzanne von Oy. Edited with love by mathycathy. Practice with domain and range, edited for Algebra 1 students. (10/9/16)
Commuting Times This activity illustrates the relationship between a dataset (which is usually not a function) and a model of the data (which—in algebra—is a function).
Three Graphing Stories Students make connections between graphical, numerical, and verbal representations of three "something vs time" scenarios. (Note: Several of these problems are from Engage NY Algebra, Module 1, Lessons 1-3.)
Water Line Students watch glasses filling with water and graph what they see to uncover (mis)conceptions about graphs.
Charge! and Charge! V2 by Desmos. In this activity, students use linear modeling to predict how long it will take for a smartphone to reach full charge. Students will also interpret the parameters of their equation in context. (added 12/11/16) [For background, see Charge! v2 – Activity Makeover by Michael Fenton.]
Are People Waiting to Get Married? by Michael Fenton. 30-45 minutes. Application. Edited with love by Desmos. In this activity, students explore the relation between median age at first marriage and time (number of years since 1960) for men and women. They make predictions, write equations, and reflect on the behavior—and contextual meaning—of graphs and parameters. As the activity closes, students consider whether two lines of fit will help in making long-term predictions.
LEGO Comparison Students explore the relationship between price and number of pieces for to different LEGO series ("Marvel Superheroes" and "Creator"). In particular, students use sliders to informally find lines of fit, use those lines to estimate the price of 1000-piece sets, and interpret the parameters (slope, y-intercept) in context. See also this modified version: LEGO Comparison v2 These activities are similar to LEGO Prices which is listed above in the “Linear Bundle”.
Home Run Kings Students interpret quantitative data in order to predict whether Bryce Harper—a promising young professional baseball player—will break the all time record for most career home runs. This one is good for statistics or early algebra; it requires no equation expertise.
Pomegraphit by Desmos. 30-45 minutes. Introduction. In this activity, students sort 10 types of fruit by tastiness and ease of eating in order to learn how those attributes can be represented on a coordinate plane, and to determine which fruit truly is "best". Featured in this post by Dan Meyer. (added 8/2/17)
Interpreting Points by Paul Jorgens. Adapted from Malcolm Swan's Language of Functions and Graphs.
I would recommend working in pairs. (added 12/19/17)
Scatter Plots Students will explore various types of scatter plots and will build their understanding of positive and negative associations, linear and nonlinear associations, and outliers. (8.SP.1) This activity serves as a great precursor to an investigation of lines of best fit.
Scatterplot Capture by Desmos. 30-45 minutes. In this activity, students use observations about scatterplot relationships to make predictions about future points in the plot. In particular, students focus on linear vs nonlinear association, strong vs weak association, and increasing vs decreasing plots. (added 4/25/17)
Correlation Card Sort by mathycathy. A card sort with follow-up questions for students beginning their studies of bivariate data. Sort graphs that represent positive, negative, and no association. Describe scenarios representing bivariate data with positive, negative, and no association. (added 4/18/17)
Polygraph: Scatter Plots Designed to spark vocabulary-rich conversations about scatter plots. Key vocabulary that may appear in student questions includes: strong association, weak association, no association, positive association, negative association, linear, non-linear, increasing, and decreasing. In the early rounds of the game, students may notice graph features like strong and weak associations, even though they may not use those words to describe them. That’s where you can step in. After most students have played 2-3 games, consider taking a short break to discuss strategy, highlight effective questions, and encourage students in their use of increasingly precise academic language. Then ask them to play several more games, putting that precise language to work.
Line of Best Fit In this activity, students make predictions about—and with—a line of best fit.
College Tuition Students explore the relationship between college costs and time. They begin by identifying which graph is which (private, public, two-year), and continue by making a prediction, building and using a model, and testing their prediction against actual data. They conclude by reflecting on the rates of change, and interpreting those values in context.
Star Wars Earnings Students use U.S. opening weekend movie data to predict total U.S. gross for Star Wars: The Force Awakens. Students work with bivariate data and construct scatter plots. Could be used for and tinkered with to address 8.SP and high school stats and probability standards.
Celebrity Age Guessing (Bloch). The slides for this are at Age Guessing Updated 10-21-15 ; and the handout for guessing is at http://bit.ly/1234-guess Before the lesson I had students work on “How good is your line of best fit? . After they checked out Guess the Correlation (these are interactive activities that would be good at other times, too)
Womens 4x100 Olympic Relay Students examine a scatter plot showing winning times for the 4x100 m Olympic relay from 1928-1980. They identify and explain missing Olympic games and an outlier in the data set. They find a trend line and interpret the slope of the line. They use a line of best fit to make predictions (interpolation and extrapolation) and reflect on whether it is reasonable for the trend to continue. They examine actual data from 1984-2012 and notice changes in the trend, reflecting on the strength and weakness of the linear model.
400 Meter Modeling Students will make predictions about the world record times for the women's 400 meter dash. They'll use data and linear models to make predictions. The data has appears linear for a 15-year interval. As students extend that linear model, the teacher can facilitate a discussion about the difference between what math predicts and what the world reveals. (For example, runners can't keep getting faster linearly. The linear model predicts they'll eventually have an instantaneous running time.) Students will also interpret the parameters of their equation in context.
Cricket Chirps Students explore the relationship between the number of cricket chirps and the temperature. They consider a suggested (and rather inaccurate) conversation formula in multiple representations, and then build a more accurate model. The activity closes by asking students to interpret the parameters in context.
WNBA Scoring Averages Students make predictions about the number of points per game the top pick in the 2016 WNBA Draft will score in her rookie season, based on the number of points per game she scored in her NCAA senior season. After making an initial prediction, students use a graph to make a more accurate prediction. Later, students use an algebraic model to make what we hope will be an even more accurate calculation. Along the way, they'll consider the "story" told by the graph, regression equation, and (in a bonus challenge at the end) its residuals.
The 2-Hour Marathon Students build a model for world-record marathon times, then use this knowledge to critique a sports medicine news story, and to consider the process of mathematical modeling itself. Inspired by a New York Times article May 15, 2016 (Includes an exponential model, but okay for gr 8.)
Linear Regression and Correlation Coefficients Students describe relationships between quantities, make predictions about the correlation coefficient (r), use sliders to approximate lines of best fit, and use these lines to make predictions.
IM1.1.3 One Variable Inequalities “Ok, I might have overdone it on this one (is 5 card sorts too many? I just can't get enough of them. Meant for a 90-minute class period.” (Added 9/10/16)
Graphing Linear Inequalities Students work through a series of graphing challenges to strengthen their understanding of linear inequalities.
Point Collector by Desmos Teaching Faculty. Edited with love by Eli. In this activity, students apply (and deepen) their knowledge of one-variable inequalities to "collect" as many points on the number line as they can. The activity focuses on simple and compound inequalities. More advanced inequalities are welcome, but not required. (added 10/9/16)
Polygon Challenges This activity is designed for an Algebra 1 class working on systems of linear inequalities. Students will use linear inequalities with domain and range restrictions to draw (and shade) several polygons. Encourage students to select one or more of the challenges during class, and possibly one additional challenge at home. It is not expected that students will complete all of the challenges.
Three's A Crowd by Andrew Stadel Edited with love by Desmos Teaching Faculty. In this activity, students explore linear inequalities (and systems of linear inequalities), with an emphasis on the graphical and algebraic meaning of solutions. (added 10/9/16)
Card Sort: Number Properties by mathycathy. Edited with love by Desmos Teaching Faculty. In this brief card sort activity, students sort equations according to the property they illustrate (commutative, associative, identity, and distributive). Beware of false "Bogus" properties! (added 10/9/16)
First Properties Card Sort Sort equations into the following properties: Commutative, Associative, Multiplicative property of zero, Identity, Inverse, and Distributive (added 9/10/16)
Penny Circle How many pennies fit in the circle? Students will be able to… Use smaller things to make predictions about bigger things … Understand the difference between linear, quadratic, and exponential models
Function Carnival - Students watch a video and graph what they see to uncover (mis)conceptions about graphs.
Function Carnival, Part Deux This activity follows up on Function Carnival, using the contexts (and students' intuitions) in that activity to build some more formal ideas about functions and function notation.
Modeling the Fastest Mile Students explore the relationship between world record time and distance for various track and field events. Students will also interpret the features of the graph in context. (Includes a nonlinear model.)
Piecewise Linear Functions Students use piecewise functions to match graphs of rays and segments, interpret function values in a graphical context, and apply what they learn to a postage rates problem.
Circle Patterns by Desmos. 45-60 minutes. Practice. In this activity, students notice similarities and differences in a set of circles. They use this information to practice writing equations of circles that extend a given pattern or match a given set of conditions.
Just Google: desmos + topic
Teacher.Desmos.com search for activities by keyword; bundles are well curated
Custom Desmos Activities - Jon Orr
Mr. Chow Math -- Desmos Activities
Mr. Chow Math -- Breakout Activities (Desmos)
Desmos Activities by Andrew Stadel
A list of MathyCathy's Desmos Activities and Card Sorts
Custom Desmos Activities - Paul Jorgens (@pejorgens)
Custom Desmos Activities - Richard Hung (Twitter: @rnhung)
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