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I really appreciated the developmental road map as a unifying framework to all the modules. I really hadn’t connected spatial measurement to multiplicative thinking to ratios/rates before and now I’m seeing so many connections. I was already using number lines lots, but I wasn’t working my way up to the abstraction of a number line and some of my students are uncomfortable with them. Now I see that for some kids (and the rest will benefit) we need to look back at a train of snap cubes and see again what the number line is representing. We were using a double number line today to divide by 6 (from Fosnot’s Contexts for Learning – how many six packs will fill the water bottle machine that holds 156 bottles?) and there was some confusion. So I made a line of lego bricks, each with 6 dots, which I will project on the screen tomorrow and we can draw 2 number lines over it, one counting the number of bricks and one counting the number of dots. I think the concrete model will help the abstract number line make sense. My insight to put together a concrete model comes from this course.