Combining Transformations Formative Assessment Lesson Continued
Lesson 13 of 23
Objective: This lesson is intended to help you assess how well students are able to recognize and visualize transformations of 2D shapes. Also assess how well students can translate, reflect, and rotate shapes and combine these transformations.
I already completed the lengthy warm-up for the collaborative activity as scripted in the plan on page T4 of the lesson guide located at http://map.mathshell.org/materials/download.php?fileid=1368 on the day prior to this class period. I would not pass out the tracing paper and L shape transformations page again. Instead, I would start by putting students into their cooperative groups based on the pre-assessment results from the previous day and running through only a quick reminder of the lesson warm-up. Again, yesterday students took a pre-assessment and completed a hands-on warm-up for the collaborative activity. Today, students need to work in groups to complete card matches, so grouping students strategically is key as well as reviewing the main points from the lesson warm-up with the L shape as you noticed misconceptions on the pre-lesson assessment.
Environment – creating cooperative groups:
I like to give the pre-assessment at least a day in advance of beginning the activity because I use the pre-assessments to look for common misconceptions among my students and I develop guiding questions to ask throughout the activity that will address these common problems. The lesson plan has some suggested questions on page T3 of the lesson guide. I also use the pre-assessments to group students for the collaborative activity. I use partnerships for the activity and I group students homogeneously meaning, if two students struggled with the same content on the pre-assessment, then I put them together as partners. Sometimes, I group students who answered the same questions correctly through using two different processes and I want them to share their unique thinking with their partner. My goal with strategically grouping students is to put together groups who will work at the same speed, and work together to grapple with the same math content so they will learn together. I do not want to group students where one student knows everything and the second is extremely dependent or lazy.
I have a video of my students completing this section of the activity if you would like to watch us follow the plan outlined in the lesson on page T4 through page T5 from the lesson website located at http://map.mathshell.org/materials/lessons.php
To begin the card matching, put the matching cards directions slide from the PowerPoint presentation on the Shell website up on your board. (http://map.mathshell.org/materials/lessons.php?taskid=490&subpage=concept) Remind students that the directions say each partner is to find matches and then discuss their match with their partner to ensure both parties agree the cards are correct. Partners are not to make matches and just assume each other is correct. I even go further by saying that when disagreements occur, students are to be respectful and discuss their differences of opinion about the math in a productive manner.
As students worked to pair graphs and insert the correct transformation between them, I walked about the room formatively assessing their progress and providing feedback that moved their learning forward. Some of the feedback I provided included simply asking them to prove their matches by taking tracing paper to show me the transformation correctly mapped one shape onto the other. I noticed some very unique approaches to the reflections cards when my students began to fold the cards along the x or y axis to find a matching reflection image. I did not pass out the poster paper and glue sticks until the very end of the class period because I knew they needed to make a plan for the layout of the poster before gluing any cards in place. I gave poster supplies to students about 10 minutes from the end of the class period.
Several observations I made include: students assumed once they mad one set of matches they were finished, even though they still had several transformation arrow cards left over. I repeatedly had to encourage students to go beyond the first set of matches and begin to link cards even further in multiple matches using multiple transformation cards. Almost every group matched the reflection cards across either the x or y axis first. Almost every group left the reflections across the lines y = x and y = -x as the final matches they attempted and some groups did not use either of these cards in their final poster. Some of my groups wanted to get really creative and use two or three transformations between each match and I had to really stop these groups and ask them to use tracing paper to prove their transformations were correct, many were not. I passed out the extension cards in set C to about half the groups in each class. In talking to one group about finally using the card reflect across the line y=x I noticed they both saw the reflection at the same time. I took a picture of their match using my I-Pad and let them know that I wanted them both to present their “Oh I get it now” moment to the rest of the class on the following day.
Click below to see images of completed student posters. You will notice that many possible matches and layouts are possible. Do not worry about students creating perfect posters. The learning occurs through the discussions among each other and with you as the teacher. Misconceptions will still exist, but you should see growth over the lesson from pre to post assessment. Some of my groups did not even finish early enough to glue anything down, but again the learning was in the matching not the gluing.
Closing by Creating Posters
To close the lesson, I simply gave students glue sticks and poster paper to glue their matches and finish the collaborative activity.