Engagement: Many teachers start their mathematics classes with a pre-determined question written on the whiteboard or projected on a screen for students to contemplate at the beginning of the class. How can you open up these warm-up mathematics questions so that they become flexible with multiple entry levels as well as multiple pathways to solution(s)? Bryan Meyer has blogged two examples of this on his “Asking Different Questions” blog post. Particularly engaging for those of you exploring place value and decimals is the second example. Though it includes scientific notation (exponents too, woot!), it could easily be adjusted to eliminate the exponent component (ooh, I like that phrase!) for younger grades or more flexibility with the question. This is a great example of a question rich with opportunity for discussion and follow-up.
Critical Thinking: How can you teach students to move beyond counting individual objects towards thinking in groups or multiples? How do we encourage students to begin to see a collection of objects as “arrays”, organized groups that help us mentally (and more efficiently) determine the total number of objects? Twitter has a lovely ongoing collection of photos under the hashtag #arraychat. As well, Christopher Danielson has a blog post that has some good photos of arrays in real life, along with a very thoughtful explanation of this progression from counting to grouping. He also includes the “why” – why should we move towards array thinking? Check out the photo collection on Twitter, or the blog post, or both – and maybe start adding to the online photo collection yourself!
Connections: I have highlighted the Mathalicious website before – wonderful collection of lessons that encourage deeper thinking by students. They’ve published a new (free) lesson recently titled “Licensed to Ill”, a lesson exploring how life insurance works. Since this is U.S.-based, please keep in mind that grade levels aren’t a direct match to Manitoba’s. This “Licensed to Ill” lesson can work for the exploration of percentages in MB grades 6-9, and can also support Essential Mathematics students when exploring the concept of insurance and probabilities.
Professional Learning: This week’s PD opportunity is also a resource to use with students. Buzz Math and Dan Meyer have teamed up to create the website called “Graphing Stories”, a collection of 15-second videos that encourage students to look at the real life situation, glean data from it, and come up with a graphical representation. It’s a wonderful collection that will continue to grow – how about contemplating adding a video to the collection yourself and sharing in the global PD discussion occurring amongst mathematics teachers online?
Ressources en Français: J’aime les vidéos « Problème DUDU » par Arnaud Durand. Il a pris un vidéo par maths-et-tiques avec la notion mathématique du pourcentage. Excellent pour la discussion! (Touts ces ressources sont de France.) (Note – I’m trying to practice my French, forgive me if I have made errors, and please let me know! I’m trying not to use Google Translate for this!)