Show the slide called a view around town. Have the students first identify the ordered pairs that belong to each location and how they know. Next, have the students find the Pool by telling them that the pool is located in the IV quadrant and is the same distance from the x axis as the school. What is the ordered pair and how do you know you are correct. (SMP 2 and 3)
During this section, students will be looking at ratio tables and discovering how to place the information from a table into the graph. Although this is primarily going to be working with quadrant I, it is still valuable information for their tool box because students will be graphing points from tables throughout several units.
During the direct instruction, I’m going to use a ratio that students deal with daily. I’ve chosen to represent how many days in a week. I’ve completed the table for them because the objective here is to get them to pull information from the table to put on to the grid.
I will set them up by asking them to identify the tool being used to represent this information? (Ratio table) and how do you know? Next, I’m going to ask them if they can see a connection between a ratio table and the coordinate grid? (SMP 2). I’m going to give students a moment to think about their answer and then have them share with the class. My goal here is to get them to see that a ratio table has ordered pairs and ordered pairs can be graphed in the grid. If students have difficulty coming up with a relationship, I may ask them to think about how many numbers are needed to start a ratio table, how many numbers do we work with when using the table and then ask them to think about the grid again.
Next, I will model how to set up the coordinate grid to graphically represent the information from the table. I’m going to set up days on the x axis and weeks on y axis because of the way the table is set up. When I get to placing the numbers on the x axis, I will be asking the students if it is important to represent all numbers? Is there a way to represent all numbers without actually writing them on the number line? My goal here is to get the student understanding that they can minimize their grid by skip counting with numbers, however, numbers need to be in order as this is part of a number line. Once the points are graphed, I’m going to have the students connect the dots. What is formed when the points are connected? (straight line) What can we predict about the next point on the line? What does the line tell us? (SMP 2)
Finally, I’m going to have the students predict and investigate what they think the line will look like if the ratio table compared weeks to days. Students can recreate the ratio table, plot the points and then tell whether their prediction was accurate. (SMP 8)
I used this lesson to teach the students about using the ratio table to graph the points on the grid. I followed this part of the lesson, using all the questions, and my students got it! They were able to answer all the questions including the prediction question about what will happen to the graph when we change the table around. It was amazing! My students are very low in ability so I took them through step-by-step on how to get the information from the table to the grid. I even spoke to them about how this connects to Algebra where they will be finding the equation of the line. I gave them some helpful hints when it came to understanding the x and y from the table. I used language like this number goes in: Independent variable and what comes out: dependent variable. I also explained to them that there will be times that the table may show different variables ie: m and n, s and t. These variables still represent our ordered pair (x and y).
This part of the lesson was awesome! It was thrilling to see them so very successful.
I’ve chosen 12 real life application problems to use for the around the room problems. Since this activity is to get the students to recognize the connection between the ratio table and coordinate grid, I’m going to start the tables for them. In some problems I will have them find missing numbers and then graph and in others, I will just have them graph. This activity is about creating experiences for them to deepen their understanding about the grid and its purpose.
During this time, I’m going to be placed near one of the questions. Each pair of students will have to sit down with me and process through the problem. While students are with me, I’m going to have them explain their solution. They will need to explain to me what they did first and why. What they did next and why and so on. To get both students involved in the problem, I will have them take turns explaining the step and the reasoning. (SMP 3)
To bring this lesson to a close, I want the students to demonstrate an understanding of the relationship between a ratio table and the grid. I’m going to have them fill in the missing pieces in the table, graph the points on a grid and have them explain to me what they did and why they did it. As a stretch question, I’m going to ask them what they notice about displaying the information from a ratio table on a grid. (SMP 7)
If 2 pints of blue and 3 pints of red make purple paint, create a ratio table to show how many pints of red will be needed if you have 16 pints of blue.