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Stretching and Shrinking

Stretching and Shrinking. 5.1 Similar Triangles Using Shadows to Find Heights. ACOS 7 th Grade Math. 1 Demonstrate computational fluency with addition, subtraction, and multiplication of integers.

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Stretching and Shrinking

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  1. Stretching and Shrinking 5.1 Similar Triangles Using Shadows to Find Heights

  2. ACOS 7th Grade Math • 1 Demonstrate computational fluency with addition, subtraction, and multiplication of integers. • 5 Translate verbal phrases into algebraic expressions and algebraic expressions into verbal phrases. • 6 Solve one- and two-step equations • 8 Recognize geometric relationships among two-dimensional and three-dimensional object • 11Solve problems involving ratios or rates, using proportional reasoning. • 12 Determine measures of central tendency (mean, median, and mode) and the range using a given set of data or graphs, including histograms, frequency tables, and stem-and-leaf plots.

  3. Vocabulary Terms • Corresponding • Ratio • Similar

  4. Authentic Literature • My Shadow by Robert Louis Stevenson

  5. POD Shadow Math 3 Feet 20 Feet 2 Feet Shadowy Science By Jess Brallier

  6. POD Answer The flag pole is 30 feet tall. 3 = 2 X 20 X(2) = 60 2 2 X = 30 (3)20 = 60

  7. Real Life • Treasure Hunt Video Clip • Shadow Measurement Explanation Video Clip • Peter Pan’s Shadow

  8. Learning Experience • In your group, start at your assigned station. • Measure the shadow of the unknown in centimeters. (Twice) • Hold the meter stick steady. • Measure the meter stick shadow in centimeters. (Twice) • Record your measurements in your journal. • Use a proportion to figure the measurement of the unknown. • At the end of 5 minutes, rotate clockwise to the next station.

  9. Materials Needed for Each Group • Meter Stick • 4 Tape Measures • Journal • Pen/Pencil

  10. Illustrate Calculate Explain Yellow M & M Flag Pole Red M & M Tree Green M & M Light Pole ICE

  11. 5.1 Follow-up—LINE PLOT Flag Pole Height (centimeters)

  12. ACE In Journal complete ACE Questions 1-4 & 7 on pp. 64-67

  13. ACE Question 1 Answers • 1a Sides CD and XW, Sides DE and XY, Sides CE and XY are corresponding sides. • 1b Angles CDE and XWY, Angles CED and XYW, Angles ECD and YXW are corresponding angles (congruent angles).

  14. ACE Question 2 Answers • 2a Triangle PQR and Triangle PST are similar triangles. • 2b Sides PQ and PS, Sides PR and PT, and Sides QR and ST are corresponding sides for the similar triangles. • 2c Angles PQR and PST, Angles PRQ and PTS, and Angles QPR and SPT are corresponding angles (congruent angles) for the similar triangles.

  15. ACE Question 3 Answer • From the meterstick’s shadow to the backboard’s shadow, there is a scale factor of 3/2 ÷1/2 =3. Therefore, the top of the backboard must be 3 times the height of the meterstick or 3 x 1 = 3m

  16. ACE Question 4 Answer • From the meterstick’s shadow to the flagpole’s shadow, there is a scale factor of 38/5 = 7.6 times the height of the meterstick, or 7.6 m

  17. ACE Question 7 Answer • The scale factor from the stick’s shadow to the monument’s shadow is • 42.25 ÷ 0.5= 84.5 • Therefore, the monument is 84.5 times the height of the 2-meter stick, or 169 m

  18. Math Reflection • Use at least two vocabulary terms to explain what properties of similar triangles are useful for estimating heights. • Corresponding • Ratio • Similar

  19. Website Link • http://micro.magnet.fsu.edu/primer/java/scienceopticsu/shadows/

  20. Corresponding • Corresponding sides or angles have the same relative position in similar figures.

  21. Ratio • A ratio is a comparison of two quantities that tells the scale between them.

  22. Similar • Similar figures have the same shape. Two figures are mathematically similar if and only if their corresponding angles are equal and the ratios of all pairs of corresponding sides are equal. This ratio image length:original length compares a side in the image to a side in the original. This means that there is a single scale by which all sides of the smaller figure “stretch” or “shrink” into the corresponding sides of the larger figure.

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