Online Tools: Math Manipulatives

Having math manipulatives in class is always helpful to show our thinking in different ways and we usually encourage students to use them, but they are more important for use in my role as "teacher". I like to think that I can communicate ideas clearly with my voice, but I know that I am only saying the words that make sense to me. If I show a picture I can allow my students to use their words to share what they see.

The following are free online math manipulatives that you can use with your students. I have seen them be used when doing a PD session by Dr. Theresa Wills. During her classes, she provides the links to the sites that best match the problem she is presenting, encouraging students to go and use them to communicate their thinking. She usually presents 4 tools and encourages students to show their thinking using more than one. Students can screen capture or copy what they have created into a group slide/document, showing their thinking and helping them communicate with their peers.

Math Manipulatives:

Unifix Blocks: A simple drag and drop tool that allows students to create stretches of blocks. They can represent anything from patterns to measurement to ratios.

Cuisenaire Rods: Quickly drag the control to create bars of different sizes. Click and drag them onto the mat. They can be used to represent anything you need.

Ten Frame: The Ten Frame was a new manipulative for me as a MS/HS teachers, but I feel it is important to be aware of all the tools students may have used in the past that they connect with. I can see how this can also be used to help with integers. All students need to do is drag and drop.

Number Line: I use a number line in my class all the time when exploring ratios, rates, integers or just general problem-solving. The tool requires just a few students to start playing with it to see what it can create. Also, the information button provides a clear explanation of all the tools. Have students create their number lines, take a screenshot, and share them with the class.

Algebra Tiles, Base 10 Blocks, Number Lines and More: This site provides lots of visuals tools. By having the blocks and number lines in one location, students can easily combine the tools together to represent what they are wanting to create. There are also backgrounds that can be used that can support algebraic reasoning.

GeoBoard: Just like in person, but now without the hassle of trying to find elastic bands or having the plastic nobs break off. Students can use this to explore various geometric representations.

Fraction Bars: Create your own fractions in either a rectangle or a circle. You decide how many parts it is out of and then add the colours as you need. This is a great tool for students to quickly create the fraction bars they are wanting to represent, make them the same size and compare values.

Pattern Blocks: Never lose the blocks again. Students can pull as many as they need to their board, manipulate the direction and copy/paste to create patterns. There is a protractor that snaps into place to measure any angles. This can use used for patterns, geometry and number sense. There are also backgrounds that have shadows of shapes, allowing students to cover them with the tiles.

Additional Resources:

• Math Learning Centre: Many of the tools listed above are on the site. There are others as well as additional resources to explore
• DiDax Virtual Manipulatives: Some cross over with those in the Math Learning Centre, but there are a few new ones: 120 board, balance boards, spinners and more.
• Math Playground: Many of these require Flash to work which may cause problems with access by students. However, there are lots of options here as well.
• Geogebra Graphing and Calculator: This site provides a geoboard, calculator and graphing software. Students can save their work for later review.
• Desmos Graphing: Students can quickly create a graph, build a table of values or write a function. When finished, they can screenshot the image and add it to their work.
• Desmos Scientific Calculator: Use this as the class scientific calculator, making it easy for everyone to have access and talk about how to use the same device.

Digital Tools: Opening my eyes to online learning

I am now entering week 10 of online learning, and it has been a pivot. I decided to lean into the pivot and use these weeks as an opportunity to explore. In my explorations, I came across Dr. Theresa Wills. She is a professor from George Mason University and has been teaching math online for years. I forget how I found her, but she has opened my eyes to what is possible. Since she has been teaching online for years, her strategies are very well developed and the free daily PD she offers allows anyone to learn from her. I sat and watched many of her recordings and learned the following:

• Teaching is a skill you develop over time and with practice. Teaching online means applying the skills I have developed but in a new medium. I have to now practice these tools, giving myself the time and play to learn them. I can't expect to be good at this unless I practice. 
• There are so many other people who have been doing this for a while and doing it well. There are benefits to this method of learning that I can learn and help my students, now and in the future, if we go back to class. 
• The online teaching community is supportive and caring. I have taken two of Dr. Wills PD sessions and all the teachers I have been grouped with make me feel supported and help me where I am at. 

I recommend that anyone who is teaching online to explore what Dr. Theresa Wills is doing to develop community and collaborative learning in her classes by using Google Slides.

This is the video that hooked me. I hope that it hooks you. 

Combining Expectations: Integers, One Step Equations and Translation Vectors

When looking at my curriculum, as I think many other teachers do, thought "How am I going to cover all of this". However, when I started looking through the parts I thought of how each expectation didn't have to be taught separately, but that perhaps if they are taught and explored together they would provide great context and then also the time to think through each of them.

My first attempt at this is exploring translation vectors, integer addition/subtraction and one step equations all in one hit. By doing this, I feel that my students will have longer to look at each concept and also use their strengths in one area to help them in another. I have already seen that my visual students have grasped the addition and subtraction of integers through their translation vectors, better than they would have done if it was taught separately.

I have put below each days goal and the related handout that the students completed (if applicable). My classes next steps are to explore the rest of the transformations on a Cartesian Plane. Through this we will also be looking at composite areas, similar and congruent shapes and two step equations. If you have any ideas of how these can lead into each other please let me know. I have a plan but open to change.

Outline and Resources:

Previously to this we had already explored the transformation terms through dance. Please see the previous post about this exciting activity.

Day 1:

• Explore the Cartesian Plane and how coordinate points are communicated. Translation Vector Intro.
• Resources: Click Here. 

Day 2:

• Translation Vectors Review and Thinking -> Inquiry into integer addition and subtraction.
• Resources: Click Here and Click Here. 

Day 3:

• Determining Translation Vectors through One Step Equations
• All class handout: Click Here. 
• Challenge by Choice
• Green level: Click Here
• Blue Level: Click Here
• Black Level: Click Here

If you are interested in my challenge levels please read my blog post about it. Click Here. 

UPDATE: Dancing Through Transformations

So the transformation dancing is almost done (Click Here for the post). Things that I have learned from the experience are listed below as well as the documents that were given to the students:

Things that went well:

• Students were more open to risk taking since it was not done on paper. 
• It was a great activity to use for students to get to know a different member of the class. 
• Students helped each other.
• It illustrated that even though these terms have been learned before, they are not concrete in their heads. 
• Having them communicate the dance with the boxes on the ground was a good introduction to coordinate points and communicating a transformation. 
• Having the three different challenge levels allowed each groups to work on the dance for the same amount of time and with the same amount of attention to detail. 

Things that were a challenge:

• Time. It took longer than I previously thought.
• Music. Giving them music to dance to caused stress. 
• Assessment. Finding the right time/place to give formative feedback.

Things to do next time:

• No music, but indicate that they will use only 10 moves. 
• Have mini due dates for each day. Make sure that the students film their translation dance in class since the communication of it can be done at home. 
• Now that I have done this once, create a rubric that the students can refer to, and can be attached to their completed Google Doc by Goobric. 
• Determine a time when formative feedback will be given. This feedback will be on their ability to apply the terminology as well as if they are able to communicate specific steps. 

Documents:

This link is to the Google Drive folder for the class. In it are the handouts, as well as example videos for them to complete. This folder was used on the first day. Click Here. 

Toronto Resources: My favourite sites to use in my classroom

With the upcoming Toronto election, I wanted to share the online resources that I have used with students to learn about the election, but also about Toronto as a city. So far this is my list. Please let me know if you have any others that can be added.

Great Election Sites:

• www.pollenize.org/toronto - Get to know your mayoral candidates with this clearly laid out website. The site takes information directly from each candidates platform and presents it in a visual and simplified manner. 
• FOR MATH: We have been discussing bias in data collection. We have also extended this into the election and how it can be challenging to gain an unbiased opinion of a candidate when reading an article in the paper as the author could have an opinion. This website has a disclaimer at the bottom of each page explaining how they attempt to provide unbiased and correct information. 

Great Toronto Data Sites:

• www.http://map.toronto.ca/wellbeing/ - Using Toronto Open Data, this website organizes many different indicators into various neighbourhoods of the city. Click on a neighbourhood and you get the 2011 census data.
• FOR MATH: Students are able to calculate percentages from the data. They can then compare various neighbourhoods and their populations or different indicators given. With the election in play, they can also consider what platform topics the neighbourhood could be most concerned with based on the indicators. 
• Open Data Toronto: This is a great site providing direct access to all the data that has been collected in the city. 
• FOR MATH: I have used this in my class many times from analyzing tables to creating infographics to display the data clearly. I have used the Food Bank attendance as well as Bike data. This raw data is easily accessible and related directly to Toronto students. 
• Toronto Demographics: This site is where the analyzed data from Open Data Toronto is placed. I have used this site for the Ward reports. 
• FOR MATH: I have used the reports here with students to complete a "If Ward 11 went to my school" or "If Toronto went to my school" project, which runs just like the "If the world was 100 people". The difference with this project is that students can think about the data and consider if they feel our classroom reflects Toronto. This can start great conversations about diversity, civic responsibility and who are we in our community.

Great Toronto Article Sites:

• Spacing Toronto: I am a big fan of this magazine, especially for articles for Middle School students to read. The focus of this magazine is how design is important in the creation and sustainability of a city. Articles are short and can be a good way to start a conversation about a topic or Toronto issue. 
• BlogTO: I use this site to become aware of great activities and events that are occurring in Toronto. I believe that if I want my students to be active citizens, than I must explore the city as well. The events section outlines great events each day and weekend.