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High School — Mathematics
Geometry and Spatial Sense

Overview

Core Resources

    Geometry and Spatial Sense

    Strategies

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      Strategies: Additional Instruction and Practice

      The following activities are suggestions for working with students who need additional instruction and practice. We hope that the activities spark ideas and conversations among teachers about useful classroom strategies that can supplement existing curriculum.

      Activity 1

      Have students use appropriate tools to construct the centroid, incenter, orthocenter, and circumcenter of acute, right and obtuse triangles. Have students label each point of concurrency and compare their location. Discuss such questions as, "Is each point inside or outside the triangle? Are any always inside or always outside the triangle? How can we tell the points apart?"

      Activity 2

      Have students define various quadrilaterals in terms of other quadrilaterals. For example, a square is a rhombus with four right angles. Have students defend their definitions or critique each others arguments using counterexample, inductive reasoning or deductive reasoning.

      Activity 3

      Have students draw a picture on the coordinate plane using only straight line segments. To emphasize coordinate geometry, have them calculate the slope of each line segment, and require them to include at least one pair of perpendicular and/or parallel line segments to reinforce the relationships of their slopes.

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