### Investigating the Ambiguous Case

In this investigation, students can get practice using sine law while investigating the nature of the ambiguous case. Once they are done, then students can create their own problems for each other to solve using the Challenge Creator at the end. Because we ask to write down their solutions, this would be best done with iPads or touchscreen laptops.

Curriculum Tags: MCR3U, MCT4C

### Graphing Random Points

This is a simple three slide sketch to help students graph points. On it there is a target and students have to graph the point in the centre. The closer they get to the centre the more points they get. Then they can randomly generate a new target. There are three pages, the first page is is first quadrant only, the second page is all four quadrants and the last page is all four quadrants with points that include decimal values (to tenths).Curriculum Tags: Gr7G, Gr8G

https://teacher.desmos.com/activitybuilder/custom/5b967ef4edb93c0cae8d1dac

### Geometry from Gr 7-9

Below are a list of over 20 Desmos Activities that investigate basic geometric theorems that span grade 7-9 here in Ontario (some of which can be seen below). Though these are very basic activities (with some dynamic features) and could be done via paper and pencil, ultimately the power in using them is in exploiting the features of the teacher dashboard to show student work and pace the class.

Curriculum Tags: Gr7G, Gr8G, MPM1D, MFM1P

### Playing with Tessellation

This is a Desmos version of a Websketch I made years ago. In this sketch students explore creating Escher like tessellations by dragging any of the red points to change all of the shapes

Curriculum Tags: Gr7G

### Investigating Congruent Triangles

Curriculum Tags: Gr7G

### How Steep is this Hill

This is meant to be an short introductory activity to Calculus concepts. Specifically the connection between the slope of the secant and the instantaneous rate of change. The other thing that touches on is the idea that if you zoom in to any curve enough, it can be approximated by a straight line. This was based on an idea originally shown to me by @MathGeek76Curriculum Tags: MCV4U

https://teacher.desmos.com/activitybuilder/custom/597a42cafd8c521bda2e6f27

### EQAO Grade 9 Geometry Practice

So this is bit of an experiment. What I have done is taken all of the Grade 9 EQAO (Applied and Academic) geometry questions and put them into a Desmos Activity (one for each stream). The idea here is that students would practice by working out the answers to the angles using the Desmos Sketch feature (ideally this works best on a touch screen device) and then they can check their answer immediately by measuring the angles on the next slide using Desmos geometry. It doesn't really exploit a lot of Desmos features but still could give you some insight into where students are having difficulties.

Curriculum Tags: MPM1D, MFM1P

### Constructing Lines and Angles

In grade 7 in Ontario, students are required to physically construct parallel lines, perpendicular lines, perpendicular bisectors and angle bisectors. To do this, they would ideally only have a ruler and compass. In these four activities, students are walked through the steps to create these using Desmos and then given the same instructions to use via physical constructing. Note that, even though Desmos geometry has tools to create perpendicular and parallel lines we won't be using them in order to mimic what would be done in the real construction.Curriculum Tags: Gr7G

Create Parallel Lines Create Perpendicular Lines

Create a Perpendicular Bisector Create an Angle Bisector

### Introduction to Vector Equations

Curriculum Tags: MCV4U

### Varignon’s Theorem

A short quick construction of Varignon’s theorem where students use the geometry tools to build and discover the theorem then use the graphing tools to prove it's true. For an added bonus you can listen to this episode of My Favourite Theorem where @MrHonnor talks about it. As an added bonus you might like this simple @Desmos 2D sketch or this @Geogebra 3D sketch.Curriculum Tags: MFM1P, MPM1D, MPM2D

### Parabola Transformation Investigations (Pt1 & Pt2)

Curriculum Tags: MPM2D, MBF3C

Part 1: https://teacher.desmos.com/activitybuilder/custom/59f62b7e58d2772c9dd86ee1

Part 2: https://teacher.desmos.com/activitybuilder/custom/5a146f72c58c00060d268a38

### Explore Projectile Motion

In this investigation students explore the variables that affect projectile motion. They start by first exploring the speed, then the angle then combinations of speed and angle and finally speed, angle and launch height. They are given challenges along the way and finally end with a "sandbox" where they can explore and perhaps create their own equation.Curriculum Tags: MCR3U, MCF3M, MBF3C, SPH3U

https://teacher.desmos.com/activitybuilder/custom/5a5e19b0c100d30a8af7804f

### Investigate Quadrilateral Diagonals

In this investigation students explore the properties of the diagonals of a quadrilateral to help classify what type it is. There is some minor geometry construction they have to do but there are instructions on how to do it. On the last slide students are challenged to use their knowledge to guess the type of quadrilateral based on the characteristics. NOTE: Geometry in Activity Builder is still in beta form. So there may be times when this is not working correctly (or at all). For a brief walk through video, click here.Curriculum Tags: Quadrilaterals, Gr8

https://teacher.desmos.com/activitybuilder/custom/59f0be8c02bd2107db0aeca7

### Subtracting Integers

In this activity students subtract integers by, first, rewriting the questions as addition problems. Then getting a visual solution via a numberline. Finally, they get to practice with randomly generated problems that will self check for the students.Curriculum Tags: Subtracting Integers, Gr7, Gr8

https://teacher.desmos.com/activitybuilder/custom/59e8b1797188fa18debdca96

### Cardsort: Solutions of Quadratics

In this card sort students focus on the solutions of quadratic relations. They are to match up the table, factored and graphical forms for each quadratic. You may wish to switch the factored form to the standard form to make this more difficult. The original version of this was a physical card sort that is used to put students into groups of three http://engaging-math.blogspot.ca/2015/03/sort-students-into-groups-using.htmlCurriculum Tags: Solving Quadratics, Quadratics, Parabolas, Graphs, MPM2D, MBF3C, MCF3M, MCR3U

https://teacher.desmos.com/activitybuilder/custom/58e791d2a3cb2342b3ec93a8

### Position, Velocity, Acceleration

Investigating the relationship between position, speed, and acceleration. This is meant to to help students connect the three conceptually to help solidify ideas of what the derivative (and second derivative) means. Students should have had some introduction of the concept of the derivative before they start. Note that this uses the Sketch feature and so is ideally suited to a tablet, though it can be used on a laptop as well. This is a bit long so you may want to give this to students as a take home assignment to be consolidated on the following day. And thanks to @bmorris76865383 there is now a French version.

Curriculum Tags: rates of change, position, speed, acceleration, 2nd derivative, Calculus, MCV4U

### Marbleslides: Rational Functions MHF4U

This marbleslides activity is meant to be a consolidation activity after students have studied the properties of rational functions based on linear & quadratic relations as well as functions in the form f(x) = (ax + b)/(cx + d). Note that on each slide, if you create your own copy and edit the activity, there are hidden answers that are suggested. Note: The intent is that students DO NOT use transformations here but, instead, the properties of these rational functions This is part of a bigger investigation with multiple Desmos activities http://engaging-math.blogspot.ca/2017/02/investigating-graphs-of-rational.html

Curriculum Tags: Rational Functions, MHF4U

### Cardsort: Reciprocal Functions

This activity is intended to be a consolidation of ideas when looking at graphs of linear & quadratic functions and their corresponding reciprocal functions. Before students do this activity, the idea is that they would have already been introduced to the graphs and started to identify characteristics of reciprocals of linear and quadratic functions. Students, however, at this point shouldn't need much algebraic knowledge of these functions. There are two parts to this activity, first there are two cardsorts. Those are the main thing for students to do. Afterwards there are a few more slides to investigate properties of reciprocal functions based on linear and quadratic functions. They are intended for students who have gone through the cardsort quickly and need extensions. This is part of a bigger investigation with multiple Desmos activities http://engaging-math.blogspot.ca/2017/02/investigating-graphs-of-rational.html

Curriculum Tags: Rational Functions, MHF4U

https://teacher.desmos.com/activitybuilder/custom/581166df0436f1e60592aa04

https://teacher.desmos.com/activitybuilder/custom/581166df0436f1e60592aa04

### Investigate Reciprocal Functions

This is meant to be an introductory activity when looking at reciprocal functions of linear and quadratic functions. This is part of a bigger investigation with multiple Desmos activities http://engaging-math.blogspot.ca/2017/02/investigating-graphs-of-rational.html

Curriculum Tags: Rational Functions, MHF4U

### Rational Functions in the form (ax+b)/(cx+d)

In this investigation, students look at the connections between the the coefficients and the intercepts & asymptotes of the function in the form f(x) = (ax+b)/(cx+d). There are three parts, first there is an investigation of the intercepts, then the asymptotes, and finally, students test their knowledge with several Match my Function slides. There are a lot of slides here and this could easily be done as a homework assignment that is consolidated the next day in class. This should take 30-50min This is part of a bigger investigation with multiple Desmos activities http://engaging-math.blogspot.ca/2017/02/investigating-graphs-of-rational.html

Curriculum Tags: Rational Functions, MHF4U

### Polygraph - Distance - Time

This Polygraph focuses on describing the characteristics of distance-time graphs with linear sections (or more generally piecewise continuous linear functions)

Curriculum Tags: Polygraph, Distance Time Graphs, Gr8, MPM1D, MFM1P

### Histograms

This is meant to be a consolidation task to be done after the class has been introduced to histograms and the distinction between continuous and discrete data. It starts with two card sorts then there are a few slides to get some idea of the connection of average.

This is part of a bigger activity http://engaging-math.blogspot.ca/2016/12/introducing-histograms.html

Curriculum Tags: Histograms, Gr8, MBF3C, MDM4U

### Graph Sort

This activity is an introductory activity meant to introduce histograms. By showing students bar graphs and histograms and asking them first to sort them in any way, then to sort them into two groups and then finally two groups where one are bar graphs and the other are histograms (don't tell them that, just show them an example of each). This is part of a bigger activity http://engaging-math.blogspot.ca/2016/12/introducing-histograms.html

Curriculum Tags: Histograms, Gr8, MBF3C, MDM4U

### Catch em All

In Pokemon Go players try to "Catch em All" but sometimes they just can't. In this activity students will explore some data collected about the number of times particular Pokemon were seen and caught.

This is intended for students just starting to explore the idea of interpolation/extrapolation and the line of best fit

This is part of this larger blog post where all the data is collected and there is opportunity to collect more http://found-data.blogspot.ca/2016/09/collecting-data-from-pokemon-go.html

Curriculum Tags: Linear Regression, Interpolation, Extrapolation, MPM1D, MFM1D, MAP4C, MDM4U

### Derivatives of Polynomials

Investigate the nature of the derivative with simple polynomial functions (in this case mostly quadratics). This meant to be a graphical introduction to the power rule so if students have not done the algebraic work of using the limit to determine the derivative, they should be fine. If that is the case then the word "derivative" may be new to them. If they have experienced taking the limit to determine the derivative of a polynomial then this could be a way to consolidate it graphically. This was based on a sketch originally done by @Eluberoff and a full activity including a physical construction can be found here.Curriculum Tags: Derivatives, Calculus, MCV4U

https://teacher.desmos.com/activitybuilder/custom/571ed42ef68cf5f10ee49d22

### Match My Line (Direct Variation)

In Ontario our grade 9 students describe linear relationships as direct or partial variations. Our grade 9 applied students are supposed to look at linear relationships only if they are in context. This activity investigates direct variations in the context of a distance time graph.Note that you may want to change the title so that the phrase direct variations does not appear so it does not give away the topic. This was inspired by Michael Fenton's Match My Line which is awesome. Check it out here

Curriculum Tags: Linear Functions, MPM1D, MFM1P

https://teacher.desmos.com/activitybuilder/custom/55dc5f63265fda125f26f67f

### Match My Line (Partial Variations)

In Ontario our grade 9 students describe linear relationships as direct or partial variations. Our grade 9 applied students are supposed to look at linear relationships only if they are in context. This activity investigates partial variations in the context of a distance time graph.Note that you may want to change the title so that the phrase direct variations does not appear so it does not give away the topic. This was inspired by Michael Fenton's Match My Line which is awesome. Check it out here

Curriculum Tags: Linear Functions, MPM1D, MFM1P

https://teacher.desmos.com/activitybuilder/custom/55dc9768265fda125f2847d5

### Number Sentences - Equations

This is a very simple sorting activity where students are given expressions & equations and the sentence to describe them and have to match them up. This is meant to be an activity that is relatively quick. There are three sorts that are all very similar to each other so you may wish to break students up into groups and assigning different sorts to each group. 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 http://engaging-math.blogspot.ca/2016/02/number-sentences.htmlCurriculum Tags: Algebra, Equations, Gr7, Gr8, MPM1D, MFM1P

https://teacher.desmos.com/activitybuilder/custom/578a839d2458b548194bdb75

### Number Sentences - Expressions

This is a very simple sorting activity where students are given expressions and the sentence to describe them and have to match them up. This is meant to be an activity that is relatively quick. There are four sorts that are all very similar to each other so you may wish to break students up into groups and assigning different sorts to each group. For a the more traditional "hands on" version click here http://engaging-math.blogspot.ca/2016/02/number-sentences.htmlCurriculum Tags: Algebra, Expressions, Gr7, Gr8, MPM1D, MFM1P

https://teacher.desmos.com/activitybuilder/custom/578a780c861c7b82316ed2d9

### Investigating Rates of Changes of Functions

This is a short investigation to introduce the idea of regions of increase and decrease as they relate to rate of change and maxima and minima of functions. It is based on an interactive Flash object I designed for the Ministry of Ontario over 10 years ago for their eLearning project.Curriculum Tags: Rates of Change, Calculus, MCV4U

https://teacher.desmos.com/activitybuilder/custom/56c35b1c5da35e0b4c1efec5

### Can You Survive a Jump off of a Cliff?

The purpose of this activity is to conceptually investigate projectile motion by first looking at D-t graphs as well as graphs that represent the path of motion. There is very little calculation involved in this series of slides (though a clever kid might still do some) and it makes use of the Sketch feature of Activity Builder so students can draw right on some of the graphs.Curriculum Tags: Parabolic Motion, MPM2D, MFM2P, MCR3U, MBF3C

https://teacher.desmos.com/activitybuilder/custom/574d8cf4436eb9c449fc0906

### Show Me a Triangle

This is meant to be a very simple activity that lets teachers quickly see if students have the general idea of the difference between acute, right, obtuse, isosceles and equilateral triangles. When you look at the OVERLAY view of your student work, any students who have issues should stand out from the others.Curriculum Tags: Triangle Properties, Gr 7

https://teacher.desmos.com/activitybuilder/custom/57178f667e5eb51b06de9287

### Shown Me an Angle

This is meant to be a very simple activity that lets teachers quickly see if students have the general idea of the difference between acute, right, obtuse, and straight angles. When you look at the OVERLAY view of your student work, any students who have issues should stand out from the others.Curriculum Tags: Angle Properties, Gr6

https://teacher.desmos.com/activitybuilder/custom/570d413d22c6711a062efc28

### Des-Draw Linear

This activity was modified from @mathycathy's activity so that students would only use linear relationships. Below is her description: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

Curriculum Tags: Linear Functions, MPM1D, MFM2P

https://teacher.desmos.com/activitybuilder/custom/57071a80e51ffd0909962916

### Intercepts

A simple activity to introduce the idea of x intercepts to students. Students should be familiar with the y intercept before they start this. It might also help if they know that if they click on a particular point, then its label will stay visible.Curriculum Tags: Intercepts, Linear Functions, MPM1D, MFM2P

https://teacher.desmos.com/activitybuilder/custom/5661d9faa75709a709db400a

### Anscombe's Quartet

Anscombe's Quartet is a set of data that is curious in that each set of values is different yet they all have similar numerical analysis but very different graphical representations. It is great for showing the importance of both graphical and numerical analysis of data.Curriculum Tags: Regression, lines of best fit, MDM4U, MAP4C

Desmos skills needed: making a graph or points visible, creating a regression model

https://teacher.desmos.com/activitybuilder/custom/56364b6f58d09115172b6a3c

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