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| Parent Letter |
Dear Family,
The next unit in your child's course of study in mathematics class this year
is Stretching and Shrinking. Its focus is geometry and it teaches students to
understand and to use the concepts of similarity Students look at what it means
for figures or shapes to be mathematically similar. The goals of the unit include
having students explore relationships among figures that have been stretched
or shrunk, and the resulting changes in properties of the figures, such as area
and perimeter.
In this unit, your child will use properties of similar figures to explore
reductions and enlargements made on copy machines. Similarity will also be used
to estimate the height of real objects (such as buildings and flagpoles) and
the distance across large areas (such as ponds).
By the end of this unit, your child will know how to create similar figures,
how to determine whether two figures are similar, and how to predict the growth
of the lengths and areas between two similar figures.
You can help your child with the ideas in this unit in several ways:
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Talk with your child about any situations that are like those your child
is encountering in the
investigations-places in the real world where items are reduced or enlarged,
such as models.
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Continue to have your child share his or her mathematics notebook with
you, showing you the different ideas about similarity that have been recorded.
Ask your child why these ideas are important, and try to share ways that reductions
or enlargements help you in your work or hobbies.
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Look over your child's homework, and help your child make sure all questions
have been answered and that all explanations are clear.
If you have any questions or concerns about geometry or your child's progress
in the class, please feel free to call. We are interested in your child's success
in mathematics and want to ensure that this year's mathematics experiences are
enjoyable.
Sincerely
Mr. John Hampshire
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| Topics |
Topics:
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Similarity
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Enlargement
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Scale drawing
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Geometry
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| Big Ideas |
Big Ideas:
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Enlarging and shrinking plane figures
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Identifying the corresponding parts of similar figures
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Describing and producing transformations of plane figures
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Analyzing scale factors between figures
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Applying scale factors to solve two-dimensional geometric problems
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Using the computer program Turtle Math to generate similar figures and
to apply properties of similar figures
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Applying properties of similar figures
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| Mathematics |
Mathematics:
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Enlarge figures using rubber-band stretchers and coordinate plotting
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Informally visualize similar and distorted transformations
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Identify similar figures visually and by comparing sides and angles
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Recognize that lengths between similar figures change by a constant scale
factor
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Build larger, similar shapes from copies of a basic shape
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Divide a shape into smaller, similar shapes
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Recognize the relationship between similarity and equivalent fractions
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Learn the effect of scale factor on length ratios and area ratios
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Discover that areas of similar figures are related by the square of the
scale factor
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Observe and visualize ratios of lengths and areas
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Recognize that triangles with equal corresponding sides are similar
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Recognize that rectangles with equivalent ratios of corresponding sides
are similar
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Determine and use scale factors to find unknown lengths
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Collect examples of figures and search for patterns in the examples
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Use the concept of similarity to solve real-world problems
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Draw or construct counterexamples to explore similarity transformations
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Make connections between algebra and geometry
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Use geometry software to explore similarity transformations
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| Tips |
Tips:
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Be sure to read the Mathematical Highlights on page 4. They give you a preview of the activities and problems.
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As you go through the unit, be thinking about your Unit Project on page 5.
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| Games |
Games:
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| Resources |
Additional Resources:
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