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Background For Teachers:
Ways to Gain/Maintain Attention (Primacy):
Lesson Segment 1: Similar figures are a different size but the same shape.
Have students trace their hand on a piece of paper. Q. Is the tracing exactly the same size as your hand? Q. Is the tracing the same shape as your hand “Similar” in conversational language has a different meaning than similar in a mathematical sense. To illustrate this, have the students compare their tracing with those of other team members asking them to suggest whether or not the tracings seem congruent or similar. No two people have hands that are exactly the same shape. Discuss that even though hands may look like hands, they are still not exactly the same shape, so they are not similar in a mathematical sense.
Give students the Congruent and Similar Figures worksheet and have them work with a partner to complete a-h. Have each pair then compare with another pair to see if they all agree. As they compare ask them to discuss the following question:
Q. How did you know which were congruent? Which were similar? Why are B and D neither congruent nor similar? Discuss this as a class.
Lesson Segment 2: How can I identify corresponding parts in similar figures?
One of the most difficult things for students to do when working with similar figures is to identify corresponding parts. The Patty Paper activity will help them begin to do this.
Patty Paper Corresponding Triangles Activity: Have student fold hamburger patty paper or other very thin paper in quadrants as shown on the worksheet. Have them sketch a small right scalene triangle in quadrant II. They should then fold vertically to sketch another right scalene triangle in quadrant I by tracing just about a half centimeter larger frame around the original triangle. Next, fold the paper horizontally to sketch a right scalene triangle in quadrant III by tracing just about 1 cm larger frame around the perimeter over the original triangle. Last, fold diagonally to trace a figure about 1.5 cm larger around in quadrant IV.
Label each angle of each triangle using a different number, so you have 1, 2, 3, on the smallest, 4, 5, 6, on the next larger, 7, 8, 9 on the next larger, and 10, 11, 12 on the largest triangle. Don’t place every third number purposely on a corresponding angle, or students will look for number pattern rather than looking for corresponding sides. Help student identify the corresponding angles by looking for angle measures as well as length of sides included sides. List the 4 corresponding sets of angles.
Label each side of each triangle using a different letter, so you have a, b, c, on the smallest, d, e, f, on the next larger, g, h, i on the next larger, and j, k, l on the largest triangle. Don’t place every third letter purposely on a corresponding side, or students will look for letters pattern rather than looking for corresponding sides. Help student identify the corresponding sides by looking for side measures: shortest, middle length, and longest. List the 4 corresponding sets of sides.
Have student pairs work together to list the corresponding parts asked for in # 3 then measure the angles for # 4. They should compare with the other pair of students on their team. Then, do Think-Write-Share for #4. Have them repeat this routine, labeling the sides for question # 5 and 6. In Think-Write-Share, students think about a question individually, write about that item on their own, and then check with their team to discuss differences. One or two students are chosen to describe what they have done and explain why for the class.
Lesson Segment 3: What is the relationship between the corresponding angles in two similar figures? What is the relationship between the corresponding sides in two similar figures?
Lesson Segment 4: Summary and Practice:
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