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High School — Mathematics
Measurement

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    Measurement

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      Strategies: Help with Fundamentals

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

      Difficulty 1

      Students may confuse the process for finding surface area with area or volume formulas for various objects.

      • Help students understand the formula for the area of a triangle by having them cut out two congruent right triangles. Then have them put the two triangles together to form a rectangle. Since the area of the rectangle is length times width or base times height, students can see that the area of the triangle is half the area of the rectangle or . Extend students' thinking to non-right triangles by having them create parallelograms from two non-right, congruent triangles. Once students understand the area formulas for triangles and quadrilaterals, they are ready to apply these to finding the surface area of three-dimensional figures such as pyramids, prisms, or cylinders.

      • Deepen students understanding of area and volume formulas by having them create figures using graph paper, linking cubes or other materials. For instance, have students begin by drawing a square or rectangle on the graph paper. Students should understand the relationship between the number of squares inside the figure and the formula . Next have students use linking cubes to create a rectangular prism or a cube. Help them see the connection between the number of cubes used and the formula .

      Difficulty 2

      Students may write incorrect proportions for similar figures.

      • Give students several pairs of similar figures. Have students cut out the similar figures. Then have them write correct proportions by aligning the congruent angles and proportional sides.

      Difficulty 3

      Checking answers. Students should be able to determine if their answers to word problems are reasonable.

      • Have students estimate answers to problems before they actually solve the problem. Then have students compare the actual answer to their estimate.

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