Unit 3 - Stretching and Shrinking

By the end of this unit, students are expected to:

Similar Figures:

• 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

• Generalize properties of similar figures

• Recognize the role multiplication plays in similarity relationships

• Recognize the relationship between scale factor and ratio in similar figures

• Use informal methods, scale factors, and geometric tools to construct similar figures (scale drawings)

• Compare similar figures with nonsimilar figures

• Distinguish algebraic rules that produce similar figures from those that produce nonsimilar figures

• Use algebraic rules to produce similar figures

• Recognize when a rule shrinks or enlarges a figure

• Explore the effect on the image of a figure if a number is added to the x- or y-coordinates of the figure’s vertices

Reasoning With Similar Figures:

• Use the properties of similarity to find distances and heights that cannot be measured directly

• Predict the ways that stretching or shrinking a figure will affect side lengths, angle measures, perimeters, and areas

• Use scale factors or ratios to find missing side lengths in a pair of similar figures

• Use similarity to solve real-world problems

Helping At Home

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?

Stretching and Shrinking - Explanation of Concepts for Those Helping at Home - Connected Mathematics 3 Resource