Students work in pairs on the Think About It problem.
Many pairs will incorrectly conclude that Deal 2 is the better deal. I take the time to hear from many students about their thinking.
I make sure I ask students why we can't simply say that Deal 1 is better because it costs less money.
Before concluding this warm-up, I frame the lesson by telling students that the better deal is Deal 1 because the cost per chicken nugget is cheaper. This is known as a special kind of ratio, called a unit rate. I suggest that we can use unit rates to make valid comparisons.
During the Intro to New Material, the key idea for students to reflect on is that a unit rate is a ratio of two values in which the second term is one. Because of this, unit rates make it easy to compare values that are originally given in different (non-unit) ratios.
In raising this idea for my students, I guide them through the examples following these steps:
In this lesson I allow my students to use calculators, if they choose. My goal is for students to master how to find and use a unit rate to make comparisons. I don't want division to stand in the way of internalizing the idea of using unit rates to make comparisons efficiently. In future lessons, once students have a firm grasp of this idea, I will combine unit rate with division practice.
Students work in pairs on the Partner Practice. As students are working, I circulate around the classroom. I am looking for:
I ask students:
Students independently complete the check for understanding problem. I have students clap out their answer choices, and share a student work sample on the document camera. I then also go through each answer choice and discuss with students its reasonableness. Choice A in in terms of hours per mile. Choice B is far too slow, given the distance for 5 hours is over 2,000 miles. Choice D is more than 2000, which does not make sense for one hour given what the problem tells us. I want students to analyze the answer choices.
Students work on the Independent Practice problem set.
After independent work time, I bring the class back together to discuss problem 4. Students should recognize that John's thinking is incorrect because he did not find a rate in terms of 1 hour. I show student work on the document camera, and students give feedback about the work. A student work sample is here.
Problem 11 is also a good problem to discuss because it requires students make sense of the problem, organize their work, and analyze their answers.