Based off of my analysis of yesterday's exit tickets, I felt it was important to get a better grasp of what my students know and are able to do with division as of today. For the the students that did not show proficiency in using the area model for division on their exit tickets, I wanted to be able to determine if they could use the place value chart strategy to be successful in division. Since Common Core Standard 4.NBT.6 states that students will use properties of operations and strategies based on place value, my goal was to find out if either the place value chart strategy or the area model strategy is working for my students. As long as students have a place value strategy that works for them right now, I can continue to guide students thinking and learning progressions.
Students work for about half an hour on this division quiz - division quiz. You can check out my reflection to read how my students performed.
CCSS 4.G.A.3 states that fourth grade students recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Students will identify line-symmetric figures and draw lines of symmetry. Students explore symmetry in this exploration activity with an inquiry based approach.
Symmetry is a fundamental part of geometry, nature, and shapes. It creates patterns that help us organize our world conceptually. We see symmetry every day but often don’t realize it. People use concepts of symmetry, including translations, rotations, reflections, and tessellations as part of their careers. Examples of careers that incorporate these ideas are artists, craftspeople, musicians, choreographers, and not to mention, mathematicians. It is important for students to grasp the concepts of geometry and symmetry while at the elementary level as a means of exposing them to things they see everyday that aren’t obviously related to mathematics but have a strong foundation in it.
The idea in this exploration is to let students create snowflakes that are symmetrical but by doing it on their own, learning as they go. I give students about four pieces of paper each, and ask them to create snowflakes. I do not give them limitations or directions, but allows them to explore and create. I always have several students that cut through the fold and end up cutting their paper into half, fourths, or more, but this is a good learning opportunity for them. I don't tell them why, I let them explore and figure that out.
I begin by showing this video.
I ask the students to identify the lines of symmetry and draw them directly on at least one of their snowflakes. (in the past, students don't want to "ruin" their snowflakes by drawing on them, so I only ask them to do it on one. ) Then I explain the differences between line symmetry, which occurs when the papers are simply folded in half, and rotational symmetry, which is when the patterns look the same while rotating the snowflake.
I chose to do a snowflake activity for several reasons today. First, the highest temperature it has been here all week is 1 degree Fahrenheit. My students have spent their entire day, for five days, inside! Students have not been outside and are a bit stir crazy. I needed an activity that was engaging, math related, but a change of pace from the division that we've been doing.
You can see in this video a student struggling to make a snowflake. Notice how I do not step in and "rescue" this student or tell him how to fold the paper. For this lesson to be exploratory, I have to give him opportunities to try something and make changes as necessary in order to succeed. You can hear him at the end of the video say that he is going to try different folds for his next snowflake.
I was overall surprised with how few of my students had made paper snowflakes before and how many needed this exploratory lesson in order to learn about paper folding symmetry.