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Exploring Scale Drawings with Ratios

Learn to create scale drawings, determine scale factors, and solve problems involving geometric figures and scale. Practice enlarging and reducing figures, compute areas and lengths. Understand similar and congruent figures.

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Exploring Scale Drawings with Ratios

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  1. Lesson 4.1.1 – Teacher Notes • Standard: • 7.G.A.1 • Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. • Section 9.3 – asks students to create scale drawings and convert between measurements. • Lesson Focus: • The focus is to have students understand and apply scale drawings and scale factors by reproducing scale drawings.(4-2 and 4-5) • I can identify corresponding parts of similar geometric figures; and construct a proportion to solve for unknown quantities. • Calculator: Yes • Literacy/Teaching Strategy: Teammates Consult(4-1); Pairs Check (4-4); Walk and Talk (Closure)

  2. Bell Work Markus ran a total of 16.25 meters on Monday in 4.2 hours. How many meters did he run in 1 hour? How many meters could he run in 25 hours? What makes a table proportional? Draw an example. What makes a graph proportional?

  3. Today you will extend your study of ratios by looking at enlargements and reductions of geometric figures.  Think of a copy machine and what it does to a picture when the “enlargement” button is selected.  The machine makes every length of the picture larger or smaller by multiplying it by the same number, called the multiplier.  That multiplier is also called the scale factor.   Multiplier: The number you can multiply by in order to increase or decrease an amount. Scale Factor: A ratio that compares the sizes of the parts of one figure or object to the sizes of the corresponding parts of a similar figure or object.

  4. What is a pre-image? What is a post-image? Pre-image: is the original shape or condition before anything is done to manipulate it’s size or distance Post-image: is the image after a sort of transformation has taken place (in our case after the scale factor has been done to it) Pre-image Post-image

  5. 4-2. Karen wants to try scaling the figure shown below by 50%.  What do you think will happen to the figure? • Sketch the figure shown at right on your dot paper.

  6. Locate at least three pairs of corresponding sides. There are nine in all. Then write and simplify the ratio of each pair of corresponding sides in the order         . • Compare the ratios from each pair of corresponding sides with the scale factor. What do you notice? How do your ratios compare to the scale factor?

  7. Some things we need to know • If the scale factor is less than 1, the post-image will shrink. • If the scale factor is greater than 1, the post-image will enlarge. • If the scale factor IS 1, then the post-image and the pre-image will be identical. • If the SCALE PERCENTAGE is greater than 100 (meaning the scale factor is greater than 1) the post-image will enlarge. • If the SCALE PERCENTAGE is less than 100 (meaning the scale factor is less than 1) the post-image will shrink. • Angle measurements in pre-images and post-images are EXACTLY THE SAME. • Similar figures: figures that are the same shape but not necessarily the same size. The measurements of corresponding angles are equal and the ratio of the corresponding sides lengths are equal. • Congruent figures: two shapes are congruent if they have exactly the same shape and size. Congruent shapes are ALSO similar and have a scale factor of 1. ALL CONGRUENT FIGURES ARE SIMILAR BUT SIMILAR FIGURES ARE NEVER CONGRUENT

  8. 4-4. Similar figures are figures that have the same shape but are not necessarily the same size. One characteristic of similar shapes is that ratios of the sides of one figure to the corresponding sides of the other figure are all the same. Another characteristic is that the corresponding angles of the two figures are the same. • Patti claims she made a similar copy of each of the original figures shown in parts (a) and (b). For each pair of figures, write and simplify the ratios for each pair of corresponding sides in the order         .  • Compare the ratios.  • Are the figures similar? That is, did Patti really make a copy?

  9. 4-5. Draw a rectangle on dot or graph paper. Then enlarge the sides of the rectangle using a scale factor of 3. • Compute the perimeter and area of both the new and enlarged rectangles. • Write and reduce each of the following ratios: • How does each ratio compare with the scale factor?

  10. Practice Determine the scale factor for each pair of similar figures in problems 1 & 2. • A triangle has sides 5, 12, and 13. The triangle was enlarged by a scale factor of 300%. • What are the lengths of the sides of the new triangle? • What is the ratio of the perimeter of the new triangle to the perimeter of the original triangle? 1. 2.

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