Stretching and Shrinking
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InStretching and Shrinking, your child will learn the mathematical meaning of similarity, explore the properties of similar figures, and use similarity to solve problems. Your student will learn how to:
- Identify similar figures by comparing corresponding sides and angles
- Use scale factors and ratios to describe relationships among the side lengths, perimeters, and areas of similar figures
- Construct similar figures (scale drawings) using informal methods, scale factors, and geometric tools
- Use algebraic rules to produce similar figures and recognize when a rule shrinks or enlarges a figure
- Predict the ways that stretching or shrinking a figure will affect side lengths, angle measures, perimeters, and areas
- Use the properties of similarity to find distances and heights that cannot be measured directly
- Use scale factors or ratios to find missing side lengths in a pair of similar figures
When your child encounters a new problem, it is a good idea to ask questions such as:
- What determines whether two shapes are similar?
- What is the same and what is different about two similar figures?
- When figures are similar, how are the side lengths, areas, and scale factors related?
- How can I use similar figures to find missing measurements?
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Last modified: Monday, 31 August 2015, 09:36 PM
Stretching and Shrinking
Similarity, corresponding angles, corresponding sides, scale factor, ratio, Rep-Tiles, triangles, parallelograms.
Overview of Changes
Detailed Description of Changes
CMP 2 Stretching & Shrinking addresses the 7th grade Common Core State Standards for 7th grade for similarity and for proportional reasoning. It also promotes algebraic thinking with the use of algebraic rules to produce similar or non-similar figures. In the CCSS, the word similarity is not mentioned. Instead, CCSS ask students to create scale drawings and use these drawings to investigate the relationship between lengths, perimeter, and area of two scaled drawings. In this unit we use the words similar figures and scale drawings interchangeably.
Very little change has been made to the original content of this unit. The original five investigations have been arranged into four investigations. The fifth investigation in CMP 2 had three problems on finding indirect measurements. One of these problems has been transferred to Investigation 3 as an application for finding missing side lengths in similar triangles. One of the other two problems, which uses the shadow method, has been moved to the end of Investigation 3. The other problem, which uses mirrors, has been moved to the ACE. At this point in their mathematical understandings, students are ready to use ratios or equivalent fractions to find missing measurements. The number of investigations shrunk by one; the number of problems shrunk by one.
|New Investigation||Changes in CMP2 Investigation|
|Investigation 1 Enlarging and Reducing Shapes||Investigation 1.1 from CMP2 is used as a launch or introduction to 1.2 which is now 1.1 in CMP3.|
|Investigation 2 Similar Figures||Investigation 2 is very similar to Investigation 2 of CMP2.|
|Investigation 3 Scaling Perimeter and Area||Investigation 3 is very similar to Investigation 3 of CMP2 with the addition of 3.4 which is the 5.3 from CMP2.|
|Investigation 4 Similarity and Ratio||Investigation 4 is very similar to Investigation 4 of CMP2 with the addition of 4.4 which was 5.1 in CMP2|