Ratios on the Coordinate Plane

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Objective

Students will be able to represent ratio relationships on a coordinate plane.

Big Idea

Ratio GPS: How to represent ratios on the coordinate plane

Curriculum Reinforcer

5 minutes

The Curriculum Reinforcer is basically a quick three to five question quiz containing information from previously taught standards that will allow you to determine areas in which your students may need to review. When I create my Curriculum Reinforcers, I make sure to mix up the types of problems. I use multiple choice, open-ended questions, as well as questions that require constructed responses. I may provide a mixture all in one day or, I may have all multiple choice one day and a mixture the next. It all depends on what I am looking for my students to be able to do. Often times, I also mix the standards however, there are times when I don't. I mix them so that I can see how well my students are fairing in more than one standard. In those instances when I don't mix up the standards, I am trying to see if the students are able to understand the standard when it is presented in a variety of ways.

Engagement

5 minutes

 

To engage my students in today’s lesson, I will facilitate a discussion by asking the question, “Do you understand what a coordinate plane is?”

 

To clarify its meaning, the teacher will play a clip from the movie “Battleship.” The scene that will be played will show a digital screen where the characters in the movie are attempting to “hit” a target that is moving in a predictable pattern. The characters use coordinates to determine where to plan their next hit.

 

 

Using this clip, I will discuss the pattern displayed as well as what the coordinates meant… To deepen the understanding of the connection of the clip to the mathematics, I will ask the question, “How did the coordinates determine where the next hit would be?” (MP7)

 

Instruction & Teacher Modeling

10 minutes

The purpose of this lesson is to ensure that students are able to graph points on a coordinate plane. Furthermore, students should be able to see patterns and relationships between the points that are being graphed, as well as an overall trend in how the data presents itself on the coordinate plane. More specifically, students ultimately need to make the connection between proportional relationships and linear patterns on the coordinate plane. (MP4 & MP7)

To help my students to understand this concept of ratio patterns and the coordinate plane, I will demonstrate how to use ratio tables as ordered pairs and then how to take those ordered pairs and plot points on a coordinate plane. I will accomplish this by using the following scenario:

Joanna has created the perfect party mix. Her secret is that she makes sure that she has 2 cups of cashews for every 3 cups of pretzels. If she puts 12 cups of pretzels in a large bowl, how many cups of cashews will she need to make her perfect party mix?

  • Using this scenario the I will be sure to place emphasis on the following:
  • The data points of a ratio/proportional relationship create a straight line.
  • When the data points start or go through the origin and create a straight line, the relationship is called a direct proportion or a direct variation.
  • The line created by the data points can be used to make predictions or inferences about the information presented in the scenario.
  • There is a difference between discreet data and continuous data (categorical vs. numerical)

 

I will present this information using grid paper that will be presented under the document camera to make the presentation large enough for all students to see.

 

 

 

Try It Out

10 minutes

First, my students will practice representing ratio relationships on the coordinate plane. My students will also practice interpreting the ratio relationship between two variables when presented with a graph. (MP1, MP2, and MP4)

To do this, students will complete the problems presented in the document attached to this section of this lesson. This assignment contains three problems for the students to try.

  • The first problem has students plotting coordinates and describing the relationship between the coordinates when given a table.
  • The second problem requires students to compare two graphs when given two different tables.
  • The third and last problem requires students to describe the relationship between two variables when given a graph.

 

I will ensure students understand the concepts presented in this lesson selecting three students to present their solutions by placing their solutions under the document camera. While their work is under the document camera, they are to explain their solution using precise mathematical terminology. (MP1, MP3, & MP6)

 

Independent Exploration

20 minutes

To explore the concept presented in this lesson, my students will complete the worksheet attached to this section of this lesson. This worksheet requires the students to be able to recognize proportional relationships in tables and represent those relationships on a coordinate plane by plotting the coordinates that are represented in the table. The students also have to be able to describe the relationships that they see in the table and/or coordinate plane as well as compare relationships represented by two different tables or graphs. (MP1, MP2, MP3, MP4, MP6, & MP7)

 

Closing Summary

20 minutes

Using the document camera, teacher will select students to come up to the front of the room to present their solutions to the problems of the independent practice. (MP3 & MP6)

Ticket Out The Door: Students will answer the following question: How can the coordinate plane be used to help you solving real world problems involving proportional relationships?