Adjusting Drawing Dimensions for a New Scale
Adjusting Drawing Dimensions for a New Scale is a Grade 7 math skill in Reveal Math Accelerated, Unit 6: Congruence and Similarity, where students recompute the dimensions of a scale drawing when the scale factor is changed, using proportional reasoning to find how each measurement must change to match the new scale. This practical skill is used in architecture, mapmaking, and engineering.
Key Concepts
Property Sometimes you need to update a blueprint to a new scale without calculating the real world massive dimensions first. You can find the new drawing dimensions directly using a "Linear Scale Factor" between the two scales: Linear Scale Factor = $\frac{\text{Old Real per Unit}}{\text{New Real per Unit}}$.
Examples Changing the Map: A map has a scale of 1 in = 10 mi. A road is drawn 4 inches long. You need to redraw the map at a scale of 1 in = 20 mi. Linear Scale Factor = $\frac{10}{20} = 0.5$. New Drawing Length = 4 in 0.5 = 2 in. Changing the Blueprint: A blueprint scale is 1 cm = 5 m. A room is drawn 6 cm wide. Redraw it at 1 cm = 2 m. Linear Scale Factor = $\frac{5}{2} = 2.5$. New Drawing Width = 6 cm 2.5 = 15 cm.
Explanation Think of this as a shortcut. When the real world size per unit gets bigger (going from 10 miles to 20 miles per inch), your map actually gets smaller, which is why we multiply by 0.5. The real road didn't shrink, your paper just got "zoomed out." If this shortcut feels too confusing, you can always do it the long way: use the old scale to find the real world miles, then use the new scale to convert those miles back into paper inches. Both ways work perfectly!
Common Questions
How do you adjust drawing dimensions for a new scale?
Find the ratio between the new scale and the old scale. Multiply each current drawing dimension by this ratio to get the new drawing dimensions. For example, if the scale changes from 1:50 to 1:25, all dimensions double.
What is a scale factor in a drawing?
The scale factor is the ratio of a length in the drawing to the corresponding actual length. A scale of 1 cm = 2 m means the scale factor is 1:200.
Why might an architect or engineer change the scale of a drawing?
Scale changes occur when a drawing needs to fit a different page size, when more or less detail is required, or when a drawing is being reproduced at a different size for printing or display.
What is Reveal Math Accelerated Unit 6 about?
Unit 6 covers Congruence and Similarity, including scale factors, scale drawings, proportions, geometric transformations, and applying similarity to real-world contexts.