Picture That: Big Ideas in Math

Early in the year, students took a deep look at numbers one-ten as we reviewed past and new math concepts and vocabulary. It was difficult to hold on to all that language and concept until one educator, Mr. Rockwell, placed all the main concepts in one sight-bite, picture, or model:

We've been revisiting that model all year as we moved from concepts of the base-ten number system to greater decimal discussions to positive and negative numbers to fractions.

Base ten model made to scale
on 3D Printer

Now as students get ready for a systemwide test, we'll revisit the idea of using sight bites (models, diagrams, tables, pictures. . .) to represent the big ideas in math. With that in mind, we'll color code a host of staircase models  (note I like the idea of these models, but the ones I made are too inaccurate--I'll recreate in time or better yet, I'll have students recreate the models.) that demonstrate the relationships between and amongst metric and U.S. Customary measurement values for distance/length, capacity/liquid measure, mass/weight, time, and money. As we study I'll pose the questions:

• What is the best way to grasp, learn, and remember the big ideas in math?
• Is it better to memorize a list of facts or study and memorize a model that includes both concept and fact? 
• Is it even better to utilize a hand-held model, like the base-ten model I made on the 3D printer, to represent the base ten system?
• Do our brains hold on to "sight bite" information better than word/number information alone? (I'm not sure of this answer--if you know it, let me know.)

While we study the models like the one below, we'll also make number lines that relate to the model. Always, we'll focus on the concept of standard measurements, the movement from less to more or more to less, and the proportional relationship between one measurement to another. A relationship actually best represented with animations like the ones we've created on SCRATCH. 

While this model is not to scale perfectly, I may ask students how they might change this
model to make it to scale. 

In summary, what are the best ways to embed the building block concepts, skills, and structures into children's working memory in ways that create a strong foundation for future math learning and application? How do you respond to this approach? In what ways have you used a similar approach and in what ways would you enrich or modify this work.

As I write and, in part, due to my reading of Boaler's book, Mathematical Mindset, I want students to spend more of their time building these models online and off, 2D and 3D. to solve mathematical problems and engage in mathematical explorations. I want to build the math units out with greater collaboration, problem solving, and multi-modal online and offline exploration with multimedia share and explanation. I'm excited about this movement towards making math more relevant, exciting, and deep. I look forward to your share in this regard. 

Note: Please feel free to report inaccuracies. 

Note Two: It's imperative that schools today host 2D and 3D models to scale all over the school and playground so that students can regularly interact with and use as reference points during play and as they work on mathematical exploration and understanding. I can "see" this, but have not had the time or resources yet to make it come true. If you want to work with me on this--I'm game. Let me know.