Month: November 2014

Daily Desmos Day 4

Ok so it’s been more than a day but I am excited to share my other Desmos ideas with you!

Desmos offers class activities too! It’s Teacher website allows students to inquire and explore mathematics through interactive activities. One of my favourites is the function carnival.

Function_Carnival_by_Desmos

You are given a class code so that your students work is saved to your account. You see all entries as pictures in the table and can select any for closer inspection.

Water_Line_by_Desmos

Student work for each exercise is stored under the activity title visually so you can compare student work at a glance. Function carnivals focus on position-time graphs is great at confronting common student misconceptions by illustrating how time always moves forwards. This is harder to communicate through a static graph or worded example. Here the students experiment and create, and by doing so develop a deeper understanding of the nature of travel graphs.

Water_Line_by_Desmos2

In addition to function carnival which is beautiful at illustrating travel graphs, the Desmos Teacher activity centre offers activities on functions, volumes and algebra as problem solving with patterns. I hope that they are developing more because there resources are very effective!

In a nutshell, the Desmos Teacher Activities are dynamic, illustrative and student-centered. They are a great addition to your teaching toolkit. Let me know how you find these activities or how you use them in your classroom.

Daily Desmos Day 3

This next one is one of my Desmos activities that I use with my senior students. If you have a Desmos account (which is free and makes activities easy to set up before time and just link to) you can save it to your templates. This helps you explore the standard form of a parabola by clicking and dragging the focus or by moving the sliders to show the infinite possibilities from the standard form.

Standard_form_of_a_Parabola

Or you could use the other Standard form

Other_Standard_Form_Parabola

I think these work well for demonstrating how all parabolas fit into the standard forms. Let me know how these resources work for you or if you have a similar resources.

Daily Desmos Day 2

It’s often better to have students explore concepts and identify patterns themselves through investigation. Thats why I prefer to introduce the gradient-intercept form of a line with the following Desmos activity.

I start the lesson by showing students a collection of different lines with their equations on them and ask pairs to establish patterns in the shape and equations of lines. I then ask my pairs to pair up to discuss competing theories before the groups of four share the findings with the class. This is called “Think-Pair-Share” and it helps students communicate their ideas in a non-threatening way. It often helps the discussion as students don’t feel like their ideas are “too silly to share” because they have been bounced off three peers before being shared with the class. It also opens up some interesting vocabulary debates which consolidate understanding of terminology and general mathematical ideas.

Once the theories are “chalked” up on the whiteboard, I get the students to open Desmos and type “y=mx+b” into the input bar on the left hand side. Desmos will then ask you “Add sliders”? Choose the blue “all” button.

Add Sliders

Desmos will draw the line with the sliders for the gradient and intercept set at one.

Gradient-Intercept_form

Now you can choose the animate icon to the left of m and b to see the sliders move smoothly to illustrate the affect of changing the gradient and the y-intercept.

I end the lesson by a matching activity between the equations and their graphs to consolidate student understanding.

How do you teach the Gradient-Intercept formula? Share your tips and techniques in the comments below.

Daily Desmos Day 1

When teaching transformations of functions one traditionally spends a significant amount of time sketching various transformations of each function. This has always been a great way to illustrate the “shift” yet a lot can be lost in the amount of time and effort each function takes to sketch. Then I found Desmos.

Transformations_of_a_Parabolic_Function

Desmos can sketch large numbers of functions on the same graph almost instantly. This shortens the time it takes to illustrate the idea of shifting parent functions. Also you could break students into teams to explore different transformations if you are short on time (which most of us are). You can share your graphs by linking to your google account and choosing save.

Desmos Save graph

So here is one resource I’ve used multiple times to explore transformations to functions. Investigating Absolute Value Transformations. I hope that it proves useful to you.

Designing Student-Centered Activities with Desmos

Teaching at a BYOD school brings its own unique set of challenges. The steepest learning curve for me has been finding resources I can use which will work perfectly on any brand of computer. These resources are called “platform independent” because they do not rely on a particular operating system to function effectively. One of my favourite finds is Desmos.

Desmos_Graphing_Calculator

Desmos is a visual, free graphing calculator which requires a newer web browser like Chrome (which can be downloaded here). Desmos elegantly explores all things Coordinate Geometry with such idiot-proof design that it is particularly suited to student-centered activities or for the technologically challenged teacher. Students can explore concepts in an easy yet engaging manner. I have also found it particularly helpful in demonstrating concepts when teaching Functions and elementary Calculus.

You don’t have to take my word for it but it is worth checking out. Head to Desmos and start playing.

Desmos_Graphing_Calculator2

There is a growing user and resource base to help you out, including a thorough user guide. To further persuade you to try this resource, I’m going to post a Desmos activity I have designed each Day for the next week. Remember that feedback is appreciated and I would love to hear your own Desmos Activity ideas.

As always, I look forward to learning with you.

Google Form Warm Ups

I have recently been using Google Forms to give me real-time feedback on student learning. I use this for diagnostic assessment purposes to inform my approach to lessons either at the beginning of a lesson to gauge foundational understanding or at the conclusion of the lesson to determine whether students are ready to build on the concepts previously taught.

To try out this technique you can follow these simple steps:

1. Create the Google Form. Choose the create icon in your Google Drive and select “Form”.

Create_-_Google_Drive

 

2. Type your questions to assess student understanding. Be sure to include a “Name” or “Email” section if you want to identify individual students.

 Warm_up_19_6_-_Google_Forms

3. Complete your Form. This is so that you have an answers key when you go to grade it.

4. Share or link to the Form. Choose the blue “Send form” button in the top right hand corner. Share the Form with the students in the class or obtain the link to the form from the Share menu.

SendForm_-_Google_Forms

5. Grade assessment. Go back into your Google Drive and enter the Responses sheet for your Form which automatically appears underneath your form. Choose “Add ons” and “Flubaroo” (which can be added through “Get add- ons” if not already present). Flubaroo will ask you to “Grade assessment” where you will select the response to grade all subsequent responses against. Naturally choose your answer response which should have the earliest timestamp or your name.

Flubaroo-_Google_Sheets

6. Analyse your data. You can now see at a glance where some common misconceptions and misunderstandings lie and can address them before attempting to build on a shaky foundation.

Graded-_Google_Sheets

So my post-holiday diagnostic revealed that 12% of my students couldn’t remember opposite operations and 40% struggled with the two step equation (though a few ran out of time for the last two questions). In addition I get to keep this information electronically to help me talk about the improvement of individual students understandings etc.

 

I hope that this info-torial helps you give Google Forms a try in your diagnostic assessment procedures.