Determine and Interpret Proportionality through Table and Graphs - Day 95

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SWBAT determine proportionality and interpret the constant of proportionality in tables and graphs.

Big Idea

Students work in pairs with materials from the NY State CCSS website to interpret proportionality in tables and graphs

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. Their Do Now includes one question where students must determine the best buy. Students will be given 5 – 6 minutes to complete the question. The directions on the board read as follows:

  1. You have 5 minutes to complete the problem in your Do Now.
  2. You must show the work in the form of a proportion, calculated unit rates, or a table.
  3. IF you finish before time is up you’ve earned a booth! Raise your hand for this opportunity.
  4. Show your solution using the chart paper and markers.

In the last 4 – 5 minutes of this section students will bring their displayed work to the front of the room to explain how they solved. Most likely there will only be time for one problem, but I make sure to dedicate space in the classroom to other appropriate solutions.

Most of the materials used in class today come from the NY State website dedicated to the Common Core curriculum.

Class Notes

15 minutes

Based on Exit Tickets and other forms of assessment, my students continue to need practice toward master of identifying and interpreting the constant of proportionality in tables and graphs. Thus, I begin the class notes section with a Cornell Notes style sheet that reviews:

  • How to calculate the constant of proportionality given x and y values k=y/x
  • How to write an equation in the form y = kx
    • This is a good opportunity to review manipulating literal equations to show how we can get the formula from the value of k



  • Given a word problem , determine whether a relationship is proportional using a table, the constant of proportionality and an equation  



  • Given a word problem , determine whether a relationship is proportional using a graph (will need to use the points generated in the table to draw a straight line)


After reviewing each example and answering student questions, students will be paired up for the classwork. 

Paired Practice

20 minutes

Class work is distributed. Teacher copies and other resources aligned with this material may be found on the EngageNY website for Common Core Curriculum.

A timer is set for 10 minutes. I inform students that after these 10 minutes they will be asked to start putting work up on chart papers. Any class work that is not completed during class must be completed for homework, and there will be an additional homework sheet. The motivation is for students to complete as much work as possible during class so that they don’t have to take it home. I like to celebrate kids who are “diminishing their work load” by announcing that they are finished. This usually motivates others to kick it up a notch and continue working toward completion.

As I walk around giving students feedback and ensuring they are on task, I am also making sure that they are following the directions given and determining proportionality using a table or graph, depending on what the question states. The first question may confuse students as they may try to put together a table with four different column, including one for the number of hours worked. This is why I will have a white board to show students templates of tables and graphs if they need them.

At ten minutes left I will begin to hand out chart paper to pairs of students who showed neat and organized good work so that they can copy it on their chart paper. As I narrate examples of quality work, “I love the way you organized your table and included your units”, I will also be giving out achievement points. I am looking for quality work in terms of neatness and organization, not full accuracy. If there is a common error being made my most groups, I prefer to have this mistake on a chart paper so that we may all review it. This idea also reinforces the effort more than the accuracy of the work. 


10 minutes

In the last 10 minutes of class I ask students who were able to display their answers on chart paper to walk us through the solution.  When selecting work with common errors I make sure to only sample 1 - 2 examples to conserve time. Any other examples of common errors we do not get to review will be spiraled into future homework assignments and Do Now activities.

My students have mostly been struggling with the interpretation questions such as question d on problem 3 which includes a graph. The question asks students to “describe what the point (0, 0) on the graph represents in terms of the situation being described by the graph”. This question has also taken different forms in prior examples:

  • What does the ordered pair represent in the context of the situation?
  • What is the constant of proportionality? What does it represent in the context of the situation?


For these questions, my students are struggling to understand what the question is asking of them. This is a classic struggle for them this year and this new curriculum. I use MP2 to push their understanding of the structure of a linear relationship within the situation being described by the word problem. Their struggle to understand is also rooted in the same struggles they endure in reading. To help, I like to ask students what strategies they are learning in Reading class to break down questions. This question can go two ways: either students get upset that I am “forcing them” to think about reading in math, or they are excited to share something they are good at and shine in my class. I obviously, choose to spotlight the positive thinkers and do my best to ignore the pessimists. Eventually they jump on the bandwagon. Beyond using MP2 mentioned earlier, students are also using MP1 throughout today’s lesson.

After reviewing the answers to the class work, students receive their homework and pack up to depart for their next class.