Exploring Dilations 2

On the second day of the Dilations lesson I begin by handing each student an Entrance Slip in the intent of applying some prior knowledge and preparing for the lesson's tasks. I ask that they quietly and independently complete the slip.

Questions 1 to 3 are multiplication questions involving fractions, which learners will be doing when muliplying using conversion factors. 

Just like the dilations, which students will be analyzing and performing in this lesson, questions 4 and 5 demonstrate change of size without change of proportions. 

Once all students are done, I ask volunteer students to explain their answers and I discuss any doubts or misconceptions students may have before going on to the next section of the lesson. 

To begin this section of our lesson I randomly pair students up and give each pair a Cat Dilations 2 Worksheet. I assign each pair of students one and only one of the four tasks on the sheet.  The goal of the task is to determine how the image was drawn from the pre-image. My plan is that towards the end, student pairs that have answered the same problem will group up to discuss their work. Calculators can be handy for this task.

Each partnership will determine how the image was produced from the pre-image based on the three points that are labeled on the cat. I give the class the following instructions:

1. Analyze the figures in your assigned coordinate plane. Make sure you know which figure is the image and which is the pre-image.
2. With your partner, discuss and determine how the image was created from the pre-image given the scale factor and center of dilation.
3. Write the procedures on your sheet such that another person can perform the dilation by following your procedures.

At this point I walk around aiding students but allowing them to tussle with the task pretty much on their own.  With students that verbally or non-verbally show they are struggling, I help by hinting things out like, “start by finding distances; see what you can do with those” or I’ll say “refer back to yesterday’s lesson….see if that can help you.”  I also advise all students to make a table to organize their data, and write the procedures as they go along.

I expect to see students undertaking the following procedures as they work:

1. Find the horizontal and vertical distances from the center of dilation to each of the 3 pre-image points
2. Multiply the distances found by the given scale factor. These will be the “new” distances.
3. Starting from the center of dilation point, use the “new” horizontal and vertical distances to plot each image point.

To avoid difficulty and confusion, I advise students to take care of one pre-image-image point at a time and literally write down what they do and what they calculate. Later, they can organize and “polish” their procedures.

To close the lesson, I ask each student to use the set of procedures his/her group concluded with to dilate the pre-image on this Exit Slip. I randomly assign each student one of the four tasks on the Exit Slip. I allow the large group to remain together but each student actually performs his/her own dilation. Students will always find someone nearby that is doing the same dilation and compare their result. This is fine actually because they can find possible mistakes, which usually is a minor math error or a wrongly plotted poing.

I ask that they put their names on the slips and I collect them. I like to hand them back the following day and I plan to ask that they correct any errors, if any.