Put it Together - Equations y = kx

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Objective

SWBAT identify k for a function in the form y = kx and use a table of values to represent word problems.

Big Idea

Students play a game matching word problems, values of k, data tables, and functions in the form y=kx.

Do Now

7 minutes

Students enter silently according to the Daily Entrance Routine. Do Now assignments are passed out with bubble sheets printed on the back.

Teacher's Note: I am using illuminateed.com for many assignments. It allows students to approach the computer at the front of the room, show their bubble sheet to the camera and get immediate results including a percentage score.

Today's Do Now is a spiraled review of skills required to identify operations from a given word problem. The first question is a multiple choice set that asks students to identify the equation which fits the word problem. The second problem includes skills in identifying division as the operation and dividing by a decimal to solve. The third question asks students to identify a correct ratio statement given piece of information. All of these skills are meant to warm up student thinking about word problems and the connection to an equation as a way to describe the context in today's lesson.

After scoring the assignment students still do not know which problems they answered incorrectly. They only know what percentage are correct. My students check their scores return to their seats to find and correct mistakes. Students who receive a 100% the first time are offered three choices: achievement points, points on their paychecks, or a choice of a piece of candy.

Review Class Notes

15 minutes

Students are asked to take out their notes from last Friday. This was assigned to be completed for homework. We review by displaying appropriate work and answers on the board. Whenever I review work this way, I like to Cold Call students to give me their answers. I make sure to include a warning at the beginning of this section that I will be cold calling. The following are some cold calling techniques I often use from the book Teach Like a Champion by Doug Lemov.

  • Make it predictable – Lemov explains that the cold call should be predictable by infusing it into the everyday fabric of class so that students learn to expect it. I admit, I don’t use it every day which is why I warn students when I will be doing it. This is an aspect of my teaching I am working to improve.
  • Make it systematic – everyone has an equal opportunity to be called. I call on students at varying levels of achievement.
  • Make it positive – the purpose is to build up the student positively, not to catch them not paying attention. Call on students who seem to be paying attention and come back to students who did not know the answer so that they can restate it
  • Scaffold – For this review I make sure to cold call students at lower mastery levels (for skills) to remind me of definitions by looking back at their notes. The students with higher mastery levels are asked to answer the application questions such as #3 on the back of the notes. For this question, students must tie together their understanding of the constant of proportionality, its location and meaning in the function y = kx, and apply these concepts to solve this problem.

This is a good time to put assessment data to work! I'm always thinking about which students need to continue spiraling through. I sue this information to guide my selection of students to Cold Call. I also know that some students do not like being put on the spot. So, I make sure to prep these students, giving them a heads up about when I will be calling on them and what question I will be asking.

Some important questions and concepts I want to review today include:

  • How does the equation y = 5x represent Jainney's allowance per week?
    • why do we use the number 5? 
    • why do we multiply it by x?
    • what does x represent?
    • what does y represent?
    • which is independent/dependent variable and why?
  • Where is the constant of proportionality in the equation y = 3.5x? 
  • In Nicholas's problem, what is the dependent/independent variable?
    • how do you know?
    • what does x represent? what does y represent?
    • how do we calculate the constant of proportionality? 
      • where does it go in the equation?
      • why is it multiplied by x?

Task

20 minutes

For the next activity my students each receive a different Puzzle Card on a rectangular piece of paper. Each card includes one of the following:

  • a value for k, the constant of proportionality
  • a data table with a linear pattern
  • a word problem
  • an equation in the form y = kx

I have printed these cards on colorful cardstock, so each student with a word problem has the same colored piece of paper. Each student with a data table has a different colored paper than a student who has a different representation.

Once the above information is shared, each student searches out students whose card contains information that matches the representation on their card (i.e., they are searching for the three matching cards). Usually this goes smoothly, but I have some hints prepared to share in response to questions that sometimes come up:

  • Matching the constant of proportionality, k, with the  function (or equation): if you’re looking for your match, think about the location of k within the equation.
  • Matching a word problem and with a data table: make sure that you know the unit rate for your data table or word problem because it will help you locate the other people from your team
  • No groups will have multiple cards of the same color.
  • Pay attention to the font

Once each foursome has found each other, they are to come see me for a piece of chart paper to display their cards on a poster about their problem. I also provide a sheet with visual guides and directions about where and how to show work in their solutions (see Directions Sheet).

This sheet details the responsibility of each student within the solution. For example, the student who received the word problem is responsible for copying the questions in the chart paper, the student who received the table has to find the missing values in the table, etc. The expectation is that students set up the problem as displayed and fill out their table of values. They will be told that there will be more time to display solution to the questions in tomorrow’s class. Here are some examples of student work:

Closing

10 minutes

Since poster days are sometimes messy, with ten minutes to go before the end of class students I will ask students to start cleaning up. Tasks will be divided up among the groups:

  • One student will be assigned to bring markers to the front.
  • One will be assigned to help re-arrange any merged tables used in the activity.
  • The other two group members will be asked to post the group's poster so that they can be viewed by the class.

Once cleanup and posting is complete, all students will receive a copy of Writing functions given k or a table. This resource includes all six problems from the previous activity. As I distribute this handout I tell the class that they will complete the handout and I will correct their work and assign them a grade. Then, I say, "I would like you to respond to the questions for each problem in class tomorrow." Once this information has sunk in, I will ask my students to have their handout and a pencil ready for a 5-minute Gallery Walk.  For the walk, students will process in a silent line around the room to complete and copy the k-values and the functions for all six problems.