Geometry – Educational Aspirations

Polygon Hierarchy

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My fourth grade class has been exploring geometry and polygons. They’ve been comparing polygons and looking closely at how to classify them. Students are familiar with these shapes and can classify them by their looks. Students were confident early in the week as they were able to label polygons based on side length, angles, and sides. Things started to change when the word hierarchy was introduced. The word is new to most of my students so the class first reviewed the term.

Students were then given a paper full of shapes. They cut out the shapes and used their desk to classify them. Students classified the shapes according to their attributes. Some students sorted the polygons by angle size, while others used symmetry or side length.

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Students were finished in about ten minutes. The class took a gallery walk and reviewed all the other ideas. Students discussed which polygons met or didn’t meet the category title. Students then went back to their seats and reviewed the term hierarchy again.

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The class took the cards and taped/glued them to make their own hierarchy. Students are starting to see the characteristics of polygons in a different light. This is good news as later on in the year students will use polygon characteristics to find area measurements. They’ll also be transforming the polygons on a grid in about a month.

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I’m looking forward to the polygon discussion tomorrow.

Side note: This is my 300th post. I had no idea that I’d be writing so much over the years, but it’s been an amazing journey.

Two Different Camps

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My school has six days of school left before break. Between now and then I’ll be giving a unit assessment to my fifth grade crew. We’ve been studying angle relationships for the past few weeks. To be honest, it’s been a great unit but it’s also been challenging. There’s been a good amount of struggle in this unit. It’s the good type of struggle. Right now I feel like students are in one of two camps.

One camp is focused on the measurement and precision component. When given a question about angles they want to take out a protractor and start measuring. They want to be precise and get an exact answer. I’d say that some in this camp perceive this type of geometry as a measurement skill, rather than a looking at it as a problem associated with angle relationships.

screen-shot-2016-12-13-at-6-38-09-pm — Where’s my calculator?

The other camp is all about looking at the angles and the relationships that exist. They’re at the point of not even bothering to use their protractor. They also look at the lines, rays and line segments that make up the construction of a shape.

Getting both of these camps on the same page has been an interesting adventure. Both have positive aspirations and have been showing a tremendous amount of effort. I believe it’s important for students to use mathematical tools to solve problems, but that’s not what this unit is about. For so many years students have been asked to be specific and precise when calculating and finding math solutions. This is still the case, but students are now asked to use their understanding of angles and shapes to come to conclusions.

We had a classroom discussion last week about this very issue. I asked students to put away their protractors and calculators. They were asked to identify specific shapes and describe the characteristics of them in detail. The class then explored the different polygons on the Illuminations site. Click on the image to visit the actual site.

Students were allowed time to play and create connections. The focus of the exploration was targeted towards sum of the angles in polygons. The students in the first camp started to put their protractors away while the students in camp two looked at how the angle measurements changed when the triangle was stretched. Looking back, this was such an important period of time. Afterwards, students were given time to review angle relationships without using a measurement tool. They were using their prior knowledge of shapes and relationships solve problems. This was a bit of shift. So, I decided to build upon the first task and added a reasoning component.

screen-shot-2016-12-13-at-6-56-59-pm — Getting camp one and two on the same page

I’ll be grading the task above tonight. Including an “explain your reasoning” component added a bit for vigor to the task. Based on the class conversations I heard today I’m thinking that students looked at precision as well as angle relationships while tackling the problem. After grading them at some point tonight, I’ll review the results with the kids tomorrow.

Student Shape Books

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Last week I introduced one second grade class to Christopher’s Which Shape Doesn’t Belong book. After hearing about its success on Twitter I decided to use it with one of my classrooms. After downloading the pdf I displayed the images in front of the class and asked the students to think of which shape didn’t belong. Just about everyone in the class raised their hands. Students overwhelmingly decided that the unfilled shape didn’t belong. Students were ready for the next page of shapes when I saw a hand raise from the back of the classroom. That particular student said that wasn’t the only answer. Quite a bit of the class raised their eyebrows and their voices in saying that the unfilled shape was the answer. The student raising his hand said that the triangle doesn’t belong because it only has three vertices. Other students started to raise their hands with additional solutions. Through this process students started to find more solutions. The student input became contagious. I would sum up what happened during the next 10 minutes here. Words like vertex, diagonal, side, symmetry, and angles were starting to be part of our class conversation. I also was able to identify misconceptions and ask questions to think about their responses. This led to more student responses and questions. This conversation wasn’t planned but I felt like it was worth the time and fit in perfectly with my geometry unit. I was going to move to the second page of the book when our class ran out of time.

So the next day the class started the day off with page two of the book. Again, students found different solutions and the class continued the conversation. After a brief amount of time I introduced a shape book activity.

For this activity students were asked to create a personal shape book similar to Christopher’s book. In addition to creating a which shape book, students were asked to include particular shapes in their book.

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Students were given guidance on the first page. I explained the directions, what was expected for the assignment and answered a few questions. I included a formative assessment on the last page of the booklet. Students worked diligently in creating the initial parts of their books for the rest of the class. Most of the time was spent on the reasoning pages. The gallery below will show some of our progress from last week.

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I’m planning on having students share their books with the class next week.