Since sites like @estimation180 have began popping up and adding all these amazing resources to our bank of routine math activities I have found myself looking for math opportunities more often in the world around me. Two amazing math coaches (Joe Swhartz and Graham Fletcher) whose math blogs and twitter I follow have wrote about this and also shared some of their ideas. Graham Fletcher calls it mathematizing your world. Now, I must admit, I am already a math geek but since I have started showing the teachers I work with these resources I find myself looking for these situations constantly. What are these situations you ask? Well they can be anything from pictures I take of cool situations, pictures/videos I find on the web or videos I make myself. The potential is limitless once you start seeing them and realizing how cool these opportunities can be for student learning.
Most of these math situations are being used to create math discourse in class, which we all know is absolutely critical in creating a quality math program. Sites like @estimation180 allow students to work on estimating but also create quality math discussions in class while building students ability to reason and prove. They also hit many other math processes but I feel reasoning and proving is front and centre. Looking at @estimation180 as an example, I feel Andrew Stadel only started the conversation. I believe he wants us as teachers to start seeing these opportunities and create our own situations to use in classes. These math situations that we capture in our world also can have a specific math focus such as: a concept, a key understanding or a math process.
I used @estimation180 as an example but there are many more like it for example, wodb.ca, fractiontalks.com and visualpatterns.org! All of them are to get kids talking, agreeing/disagreeing, explaining and building on each others ideas. Ideas to use for these situations appear around us all the time, once you start seeing them and capturing them you may not stop!
Here are two I have captured in the last week or two. I have many more on my phone but thought these two are good examples to share.
I found the above picture as I was reading an article on yahoo about ice coverage on the great lakes. I used a photo editor to cut out the information on the bottom with the answer creating one picture that just shows the lakes and ice coverage and then the orginal picture for the answer. If I was using this for a number talk I would show the picture on the left first and ask this question. How much more ice is covering the great lakes in February than in January? The photo on the left has the answer to show afterwards. The answer is listed as a percentage but I didn’t ask the question as a percentage question. This would leave it open for students to use fractions, decimals or percents. They might also use add in units, for example square kilometres could be an option. There is just so much math here to get students talking. This is an excellent number talk for fraction reasoning or making the connection between fractions, decimals and percents. It also could be used to look at fractions as an operator. Students could be given the total area of the great lakes and then using February’s percentage ask: What is 40 hundredths (which is close to 40.4 percent) of the total area?
Here is the second image I want to share. (The treadmill odometer is in miles)
This came to me as I was doing my run last week. My goal was to reach 5 km (3.15 miles) in 26 min. Showing the students the image you could ask: Using the info provided do you think Mr. Stamp will achieve his goal of reaching 5km (3.15 miles) in 26 min? Students can use their fraction sense to help solve this, but it also involves number sense (operations, decimals, fraction sense) and measurement (time, distance). Depending on what grade level, this could be a number talk or an actual task.
These opportunities pop up all over the place when you are out in the world. I bought a pound of finishing nails at the hardware store on Saturday, as the lady was scooping them into the scale that hangs from the roof I was trying to get my camera out in time to snap a picture. It would have made a great number talk or estimation talk. I think back to last summer when my father-in-law and myself were squaring up the playhouse we built (he built mostly! LOL) for my kids. We used the pythagorean theorem to do it, it would have made a great picture prompt to help students discuss its use in real life. Once you start seeing these situations you may never stop! Teachers ask me all the time where do you find tasks, or prompts etc. They are everywhere, just have your camera ready at all times!