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I am at the beginning of our linear equation unit. I started with a couple of “Notice and Wonder” activities involving pizza from two different pizza places in our town. My goal is for students to conceptually understand slope and yintercept and in this case cost per topping and the cost of cheese pizza (we even had a great discussion about whether or not cheese counts as a topping). In order to get there, students need to understand the unit rate and rate of change. We also needed to revisit collecting data, making a table, and graphing the results appropriately. Even the concept of mathematical patterns was challenging for many students. We followed up with the “Goose Egg” problems which were great for identifying the rate of change and starting value. The numbers were easy to work with and the pictures made it easily accessible for all.
Something that came up that was a little surprising was how repeated addition and multiplication are the same things. Many of the students relied on repeatedly adding the cost per topping rather than simply multiplying by the cost per topping. I did my best not to tell them to multiply but certainly asked questions to steer them in the right or better direction (how about a pizza with 37 toppings?)
Tomorrow we literally start with abstract linear equations. Something else we will need to discuss more indepth is the independent and dependent variables and just how “y” is a function of “x”. Of course, the slope will be a fraction eventually and that will add another layer of complexity for those who struggle with multiplying fractions.
Looking forward to it!