Tag Archives: Equal and Unequal Parts

Week 13 – Mathematics – Finishing 2D Shapes

The end of the year is fast approaching and I am just so thankful for all of the opportunities that I have had in the Residency (UTRPP) Program. I am so glad that my collaborating teacher has provided me with the opportunity to continue to take the lead on teaching and planning in all subject areas so I can continue to gain more experience in front of the classroom.

I have many chances to experience guiding students through multiple units and on Monday we finished our 2D Shapes unit. The students took the assessment and based on what I observed, many of the students understood the content. There are still many students (about 6) who were unable to take the test because they were absent but I am eager to see their scores because I think they will show a good understanding of the content. One of the great things about teaching and planning math for the entire unit was that I am able to see the growth of my students and help address misconceptions and alter lesson plans to meet their needs.

For example, when teaching about equal parts, my students were confusing about whether or not certain squares were split into fourths. The students were able to recognize that four small squares or four rectangles that all looked the same are fourths but they were unable to make the connection when looking at a square split in half where the two halves are split in different ways.

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In the top squares, each piece is the same size. (I apologize that the rectangular pieces are not perfect on the second square but I wanted to show a pictorial representation of a misconception that my students had.) The third square, however, looks as if the four parts are no equal. But each side of the square (shown below using colors) is half of the square. Since these two pieces are cut in half each of the four parts are equal.

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This was a difficult concept for my students to grasp so I used actual paper that I cut up in front of the students along with drawings on the white board to help them understand. By providing this realia, I was able to bridge the gap in my students’ knowledge and allow many of them to grasp the idea. I felt like this was an important part to teach to help build their conceptual knowledge of splitting shapes into equal and unequal parts because my students made the assumption (which is a misconception) that when a 2D shape is split into parts of different shapes, that the parts are unequal.

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For example the fourth shape is split into rectangles and squares as taken from the other shapes on top. The parts are all equal even though they are different shapes because they are all half of half of the original shape. Although this terminology seems confusing, this conceptual knowledge can be helpful in the future, especially when students have to discuss fractions using ½ and ¼ and multiplying fractions to find half of a half or ½ x ½ = ¼.

I am approaching the final days of my internship, which is exciting because of the new opportunities that await me in the future but also a bit sad because I will really miss my classroom and my students. I have made so much growth and progress over the course of this year and I just cannot believe everything that has happened to me throughout my experience in the Residency Program. I can definitely say I would not trade this for anything.