Unit Rates, k?

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Aim 1: SWBAT calculate unit rates in the context of different situations. Aim 2: SWBAT identify and calculate the constant of proportionality and the equation in the form y = kx

Big Idea

Students work in pairs and groups over two days to review proportional relationships and the constant of proportionality

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. Over the next two days we will be tackling a major concept in 7th grade math: unit rate and the constant of proportionality. These topics and skills are included in the “major cluster” of the test which will take up 70-80% of the test questions, including other key topics (i.e. the number system, expressions and equations).  

The Do now exercises over the next two days will include review topics in unit rate and identifying the constant of proportionality. In order to get brains warmed up, these topics will likely push students to access knowledge rather than other higher order thinking skills such as interpretation and analysis.

Students went on Spring Break prior to this lesson and took home their blue “Ready” books with review topics relevant to these clusters. The first lesson covered in this, unit rate, takes place the Monday upon their return. Thus, the Do Now assignment requires that they bubble their answer sheets so that I may check these and collect data. We have one week left before the state test, thus I will be using this data to inform my instruction for the remaining time.

On the second day's Do Now we review the constant of proportionality. Understanding its role in proportional relationships is complicated, thus it is important that students are able to calculate unit rates with ease so that our discussion on the second day can revolve more around higher levels of thinking (i.e. application and analysis of this topic). The Do Now on the second day tests students’ abilities to create proportions to find missing information within a proportional relationship (#1) and reviews number operations to continue spiraling and reviewing this key skill (#2).

Class Notes: Review

15 minutes

After reviewing Do Now answers or turning in work, students receive class notes. The following is a breakdown of the main ideas, topics, and essential questions reviewed each day:

Day 1: Unit Rate Class Notes

  • We divide to calculate the unit rate
  • Sometimes written as a fraction; other times as a whole number with two units (i.e. 0.5 miles/1 hour or ½ mph)
  • Unit rate is out of 1. Why?
  • Review dividing rational numbers (complex fractions) to calculate unit rate


Day 2: k, the constant of proportionality Class Notes

The notes for this day look slightly different. They include two paragraphs which students must read independently. Time should be giver after for questions or definition of misunderstood words/phrases. Then, 4 questions are included which review the following concepts/topics:

  • What is the constant of proportionality? The constant ratio between two quantities
  • What does it mean? When there are two quantities decreasing or increasing, they are doing so at a constant rate. For example, if apples cost $5 a pound, you will pay $10 for 2 pounds, $15 for 3 pounds, etc. If you are charged $20 for three pounds, the rate is no longer constant.
  • The unit rate is one way to represent the constant of proportionality
  •  What does a proportional relationship look like on a graph? a straight line that goes through the origin
  • How can you use the equation y=kx to identify the constant of proportionality? Or, if you know the constant of proportionality, k, how can you use it to write an equation?
  • Why would you want to write/use an equation? To calculate larger values. For example, if you want to know the amount of food a dog eats after a month, you can use the graph and equation to calculate

On this second day, there are two problems we review together and two others students must complete on their own. I begin by first reviewing both problems, then giving students 3 minutes to answer the bottom two on their own. As I walk around during this independent time, I am targeting a group of 6-8 students who ought to work with me on the class work as well as students who will be able to lead other peers to complete the class work. 

Class Work

20 minutes

On the first day students will be asked to work in pairs to complete their Classwork. They will be given 15 minutes and must complete at least 75% of the work. The last 5 minutes will be silent work time.

On the second day, students will be separated into groups around the room and given Classwork. They will have 15 minutes to work together. The last 5 minutes will be silent and independent. I make sure to pull my student leaders to remind them what good leadership looks like:

  • Your peers should not just be copying the work off your paper
  • You should not be giving out answers only
  • Explanations should be given by the leader, but he/she should also feel free to ask their peers to justify their thoughts/answers
  • Student leaders are responsible for the completion of at least 75% of the work
  • Student leaders ought to always be on task and try their best to encourage their peers to remain on task. Should there be any issues in misbehavior, they must tell me at the end of class and not fight with that teammate.

Though I will be working with a small group during this time, I also make time to circle around to other groups to ensure everyone is on task and to answer any lingering questions.


10 minutes

There will be an exit slip included in the classwork each day. Students will have the remainder of class to complete this exit ticket along with any unfinished classwork. These exit slips should inform the content to spiral in future classwork and homework. No student is to leave an exit ticket completely blank. They will be advised to ask as many questions as possible (at least 3) if they are unsure about solving. Homework will be distributed after exit slips have been handed to me.