This lesson introduces students to the idea of a scaled copy of a picture or a figure. Students learn to distinguish scaled copies from those that are
not—first informally, and later, with increasing precision. They may start by saying that scaled copies have the same shape as the original figure, or that they do not appear to be distorted in any way, though they may have a different size. Next, they notice that the lengths of segments in a scaled copy vary from the lengths in the original figure in a uniform way. For instance, if a segment in a scaled copy is half the length of its counterpart in the original, then all other segments in the copy are also half the length of their original counterparts. Students work toward articulating the characteristics of scaled copies quantitatively (e.g., “all the segments are twice as long,” “all the lengths have shrunk by one third,” or “all the segments are one-fourth the size of the segments in the original”), articulating the relationships carefully (MP6) along the way.
The lesson is designed to be accessible to all students regardless of prior knowledge, and to encourage students to make sense of problems and persevere in solving them (MP1) from the very beginning of the course.
- Describe (orally) characteristics of scaled and non-scaled copies.
- Identify scaled copies of a figure and justify (orally and in writing) that the copy is a scaled copy.
Let’s explore scaled copies.
You will need the Pairs of Scaled Polygons blackline master for this lesson. Print and cut slips A–J for the Pairs of Scaled Polygons activity. Prepare 1 copy for every 2 students. If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.
- I can describe some characteristics of a scaled copy.
- I can tell whether or not a figure is a scaled copy of another figure.
A scaled copy is a copy of an figure where every length in the original figure is multiplied by the same number.
For example, triangle \(DEF\) is a scaled copy of triangle \(ABC\). Each side length on triangle \(ABC\) was multiplied by 1.5 to get the corresponding side length on triangle \(DEF\).