Geometry and Spatial Reasoning


 Chad Freeman
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1 Mathematics TEKS Refinement Tarleton State University Geometry and Spatial Reasoning Activity: TEKS: Creating Venn Diagrams with Quadrilaterals (6.6) Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. (A) use angle measurements to classify angles as acute, obtuse, or right; (B) identify relationships involving angles in triangles and quadrilaterals; (6.10) Probability and statistics. The student uses statistical representations to analyze data. (D) solve problems by collecting, organizing, displaying, and interpreting data. (6.11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. (6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. (B) validate his/her conclusions using mathematical properties and relationships. Measurement Connection: (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight; (C) measure angles; Overview: Students will construct Venn diagrams according to given attributes of quadrilaterals and use rulers and protractors to justify placement on the Venn diagrams. Creating Venn Diagrams With Quadrilaterals Page 1
2 Mathematics TEKS Refinement Tarleton State University Materials: Grouping: Time: Chart paper 1 polygon sheet per task assigned Scissors Glue Rulers Protractors Overhead of polygon sheet 34 students per group 60 minutes Lesson: Procedures 1. (5 minutes) Have students cut out the polygons from backline master #1. 2. (20 minutes) Write these attributes on the board: Task 1: At least one right angle No acute angles Task 2: Opposite sides congruent, At least two pairs of adjacent sides congruent Place the appropriate quadrilateral pieces in groups according to the attributes given. Glue them in place. Students must use all nine of the quadrilateral pieces 3. (1015 minutes) Justify placement by measuring the angle measures and length of sides. Students will write the measures directly on the polygons. A summary statement/paragraph must be written by each group member supporting the placements. Notes Have students give definitions of the following: right, acute, and obtuse angles; adjacent; congruent. Briefly discuss with students how groups may be formed by having a few students place an example on the overhead of 2 polygons that could be grouped together according to the attribute of having an acute angle and no parallel sides. Discuss how the groups will be shown by drawing circles and placing the shapes in the appropriate circles. Ask students to consider what to do when a shape will fit into more than one circle. Allow them to come up with suggestions on how to show membership in more than one group. What happens when there is a polygon that fits neither attribute? Where may we put it? It must be shown on the chart paper. Watch for misreading of the protractor. Have students measure side lengths in cm units. Creating Venn Diagrams With Quadrilaterals Page 2
3 Mathematics TEKS Refinement Tarleton State University Procedures 4. (10 minutes) Post the Venn diagrams about the room. Students conduct a Gallery Walk to compare the results. Notes As they walk (57 minutes), they must take notes where there are answers with which they may not agree. Students reconvene in their groups (about 5 minutes) to discuss their findings. Give students an opportunity to revise/edit their Venn diagram if there is a need. Conduct a brief discussion using some of the student comments as they reconvene. 5. (3 minutes) Student Reflection: What did you find to be challenging? Is there any thing that is still not clear? What did you like most about this activity? Homework: Assessment: Extensions: Provide additional attributes and have students construct Venn diagrams by drawing the pictures of the appropriate polygons. Use the Gallery Walk results as well as the Venn diagrams 1. Students create additional attributes for the Venn diagram rings with and without overlap as well as having to place a polygon on the outside of the rings. Attributes to be used must include comparisons of lengths of sides, angle measures, and adjacent angle or side comparisons. 2. Use backline master #2 for additional practice. Students must have a ruler to determine the lengths of the sides since these shapes are not drawn on a grid. 3. Use backline master #3, triangles instead of quadrilaterals. Provide students with attributes according to angle measures and/or relationship among the sides. For example, one label may read contains right angles while the other label reads two sides congruent. Students must use rules and protractors to justify placements according to side lengths and angle measures. Creating Venn Diagrams With Quadrilaterals Page 3
4 Mathematics TEKS Refinement Tarleton State University Blackline Master Creating Venn Diagrams With Quadrilaterals Page 4
5 Mathematics TEKS Refinement Tarleton State University Blackline Master 2 Creating Venn Diagrams With Quadrilaterals Page 5
6 Mathematics TEKS Refinement Tarleton State University Blackline Master Creating Venn Diagrams With Quadrilaterals Page 6
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