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I concur with Tanesha’s and Marianne’s comments regarding the richness of the coffee mug task as it addresses an array of objectives from multiplicative comparisons, fractional reasoning, fair sharing also known as partitive division as well as ratios, rates and graphing on the x and y axis. It is in the quality of the problem solving tasks teacher’s select that determines the depth of the mathematics learned. As a learner, I found myself thinking about my thinking as I processed the varied models of problem solving the relationship between cups of water to mugs of coffee progressing from the concrete use of linking cubes, to the area models of cups of water to mugs, to the vertical number line representing the composed units of measure and then transferring to the ratio table which visually lends itself to the vertical scaling up and down as well as the horizontal relationships which lead to revealing the rates, resulting in the linear proportional relationship leading to the algebraic expression where y = kx or x = ky which lends itself to graphing the points on a two variable graph like a scatter plot.
I have benefitted greatly from these mindstretching scenarios.