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5 pencils cost $0.60. How much is each pencil? Warmup: 5 pencils cost $0.60. How much is each pencil? Remind students that we solved this question yesterday and ask a student to explain how we solved it. The point is to draw out that in this problem, we could simply divide 0.60/5

A bus with 4 people on it weighs a total of 29,440 lbs. The same bus with 11 people on it weighs a total 30,735 lbs. On average, how much does each person weigh? Ask a student how we solved this question. They should say (30735 – 29440)/(11 – 4). Remind them that we used this to invent the formula m = (y2 – y1)/(x2 – x1).

A bus with 4 people on it weighs a total of 29,440 lbs. = 7360 Does each person weigh 7360 lbs? 4 Why does this method give us the wrong answer? When you divide up the picture into 4 pieces, what does each piece represent? Ask a student to refresh for the class WHY we could not simply do 29440/4 in this problem. Hopefully, the student will say that the bus is something extra and you can’t just divide when you have something extra in the situation. Then pose the main question for today: how do you know when there is something extra in the problem that makes it so you can’t just divide? How do you know when you have to use the slope formula?

Pizzas are $5 each, and delivery is $4 C = 5p + 4 pizzas Cost Try just dividing to find the rate. Total cost # of pizzas Try to get students to come up with the function rule before clicking it up on the screen. Then prompt the class to generate values for the table, such as (1 pizza, $9 total) and (2 pizzas, $14 total). Come up with at least 4 ordered pairs. Then ask whether we can just divide “dollars/pizzas” to find the cost per pizza in this case. For example, for the ordered pair (1,9), can we just divide 9/1? For the ordered pair (2, 14), can we just divide 14/2? The class should see that we cannot, because we get a different answer every time, and none of the answers is $5. Ask WHY we can’t just divide. Someone should say that the delivery fee is something extra in the problem, like the weight of the bus was something extra in the last problem.

Pizzas are $5 each, and delivery is FREE C = 5p pizzas Cost Try just dividing to find the rate. Total cost # of pizzas Go through this slide with the same approach as the previous slide, except that students should see that in this case, you can simply divide “(total cost)/(pizzas)”. Ask why. Someone should say that it’s because there’s nothing extra in this problem, i.e., no y-intercept. You can introduce the vocabulary term of “proportional” to codify this knowledge.

Image credit of bus (from Wikimedia Commons): “This image has been released into the public domain by its author, Radagast. This applies worldwide. http://commons.wikimedia.org/wiki/File:Grt_nova_bus.png