The way the order was entered, the customer was charged for a Double-Double plus 98 additional meat and cheese layers. Note that their answer should be the “Counter-Eat In” amount and not the “Amount Due” unless you want to have them factor 7.5% sales tax into the cost. When it is time to show students the actual cost of the 100×100 burger, use this picture below which shows a price of $90.85. What about the cost of the cheeseburger? Note that this is a discrete and not continuous function as you can only get whole number layers. For example, where do you see the cost of the extra layer mentioned in the words in the table, graph, and symbols. The most important part of the multiple representations is challenging students to explain connections between the representations. I have included an example of how that may look below. Something for students to aspire to would be to explain their solution using numbers (an input-output table), symbols (Algebra), pictures (graph), and words (a written explanation of how they approached the problem) which is CCSS F-LE.2. Note that these prices were from 2004 and were used so they matched the receipt that has the price of the 100×100 on it. We want them to make the assumption that perhaps $0.90 is the cost of one layer of beef patty and cheese slice. They can get $0.90 by subtracting the price of a cheeseburger ($1.75) from the price of a Double-Double ($2.65) using the menu below. You may have to ask them, “What are the differences between a cheeseburger and a Double-Double?” We want them to realize that they are the same except for an extra beef patty and cheese slice and a cost difference of $0.90. We then want to ask students, “How can we figure out how much an additional beef patty and cheese slice cost?” Hopefully they struggle with this question. There are no additional buns or toppings such as lettuce, tomato, onions, or spread. Essentially it is a cheeseburger with 99 additional beef patty and cheese layers or a Double-Double with 98 additional beef patty and cheese layers. Make sure to have a conversation about what is on a 100×100. Eventually you want them to be able to generalize the cost of a NxN burger.Īs much as possible, you want students to do all of the discovery. I have found that students with emerging skill sets need to begin with a 3×3 to establish that it is not the same thing as ordering 3 cheeseburgers or a Double-Double and a cheeseburger. You may choose to begin by asking students about the cost of a 100×100 or start with something smaller like a 3×3. I recommend beginning with exploring cost before calories because I have included a receipt that shows the actual price of a 100×100 burger. This awesomely gross lesson provides students with a real world context for building linear functions. How would your answer change if you had started with a Double-Double and added 98 layers versus a Cheeseburger and added 99 layers?.Where do you see the cost of the cheeseburger in the words in the table, graph, and symbols?.Where do you see the cost of the extra layer mentioned in the words in the table, graph, and symbols?.
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