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.

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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.

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A quadrilateral is 360 degrees and a triangle is 180 so …

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.

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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.

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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.

Angle Relationships

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My fourth graders are just about finished with their unit on geometry and measurement.  They classified angles earlier in the week and are now looking at angle relationships.  This is one of my favorite topics to teach as it involves logic and an understanding of basic geometry.  I’m finding that students are becoming better at measuring angles using a protractor.  Using Angle Tangle has helped in that process. They’re able to identify and measure acute and obtuse angles comfortably.  Reflex angles still give them issues, although this is improving as students are able to subtract an acute or obtuse angle from 360 to find the measurement.

Students then moved on to angle relationship skills. When asked to find the missing angle in a triangle they immediately started to look for their protractor.  Students wanted to find the actual measurement without looking at what types of relationships actually exist and if a protractor is needed.  So on Tuesday the class reviewed interior angles.  Students found through patterns that they could split a convex polygon into triangles and find the sum of angles.  This was eye-opening for some students and you could tell that they were relieved in seeing that they wouldn’t have to measure all of the interior angles.

One of the assignments called students to create  polygon and find the sum of angles without actually measuring each interior angle.  Some students were stumped while others students looked at how a triangle’s sum can aid in finding the sum of other polygons.  The student projects turned out well, although some had to redo them as the drawing actually started to get in the way of creating triangles.  This is one of the better projects.

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I could tell that students needed a bit more practice with using angle relationships to their advantage.  On Thursday I asked students to create a qudrilateral using a straightedge.  Students drew arcs to indicate the angles on each vertex.  The quadrilaterals were cut out and the sides of the shape were torn off.  Students lined up the sides and the class had a brief discussion on what they noticed.

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Right away, some students noticed that the arcs didn’t line up.  They also noticed that the four corners actually created a circle. Some even said that the total was 360 degrees. Students checked their work by using a compass to add all of the angles together.  Their prediction rang true.  This was a winning moment as I could tell that students were starting to grasp this concept better.  I gave each student some tape and they tapped together their circle to their folder.  I’m hoping it stays on their folder and in their memory banks.

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