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2. Objectives: Students will be able to:  Understand what scale drawings are.  Find the scale of a drawing  Convert map distances to actual disctances 6.R.P. 3.d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

3.  Solve each proportion 1. 6/30 = 4/x 2. 15/21 = y/35 3. 5/z = 145/174 4. 5/m = 12.5/ 5 5. n/16 = 4.5/72 20 25 6 2 1

4. What are scale drawings? Scale drawings are everywhere! Scale Drawings On Maps Footprints of houses Vehicle design Can you think of any more?

5. Scale drawings are SIMILAR to the original. To say that two objects are SIMILAR means that they are identical in shape, but not in size. In order for two shapes to be similar they must have the same angles and the sides must be in the same ratio. Example: Are these two shapes similar? Angles the same x2 Sides have the same ratio – x2 The two shapes are similar

6. Are these pairs of shapes similar ? 3cm 9cm 2cm 6cm 40° 50° 5m 6m 4m 10m 2m 3m 1m 1.5m 50° 60° 70°

7. All scale drawings must have a scale written on them. Scales are usually expressed as ratios. Normally for maps and buildings the ratio: Drawing length: Actual length For maps the ratio is normally in the ratio: Map distance: Actual Distance Example: 1cm : 100cm The ratio 1cm:100cm means that for every 1cm on the scale drawing the length will be 100cm in real life Example: 1:10000 The ratio 1:10000 means that the real distance is 10000 times the length of one unit on the map or drawing.

8. In the drawing, the height of the tree is 20 inches. The actual height of the tree is 260 inches. What is the scale of the drawing? Drawing Height Actual Height 20 inches = 260 inches 1 inch 13 inches The scale of the drawing is 1in to 13 in or 1:13

9. Straight line distances  Step 1: Use a metric ruler to measure the distance  Step 2: Write the scale as a ratio  Step 3: Find the distance by solving the proportion

10. Look at this scale map of Detroit. At the bottom of the map, what is the scale? It is shown to be I inch 10 miles If you measured the distance from Detroit to Mt. Clemons, estimate how many inches that would be. If you estimated 3 inches, how far is Detroit from Mt. Clemons in actual distance? X = 30 mi So Mt. Clemons is about 30 miles from Detroit.

11.  Another Example on Video  Distances Distances

12. Architecture: Gwen Uses a scale of 1in : 10 ft to build a model of the White House. The White House is 58 feet tall. How tall will her model be? Model (in) Actual (ft) Write the scale as a ratio Use x to represent the model Height Cross Multiply: 10x= 58 X = 5.8 Gwen’s model will be 5.8 inches tall

13.  Play this Landscape Mapping Skills game to help you learn more about the importance of Scale DrawingsLandscape Mapping Skills  Homework  Homework: Scale Drawing Handout