Congruent Figures � Congru-

    ent figures have corresponding

    angles that are equal and cor-

    responding sides the same

    length

    Corresponds, Co rrespond-

    ing � Corresponding sides or

    angles have the same relati ve

    position in similar fi gures.

    Ratio � A ratio is a comparison

    of two quantities that te lls the

    scale between them

    Scale Factor � The scale fac-

    tor shows the ratio of the

    lengths of similar figures. If

    the scale factor is 3, all the

    lengt h measures in the image

    are three times the corre-

    sponding measures in the

    original Similar � Similar figures have t he same shape. Two figures

    are mathematically similar if

    and only if their corresponding

    angles are equal and t he ratios

    of all pairs of corresponding

    sides are equal

    Stretchi ng and Shrinking

    Glossary

    Connected Mathematics

    Project

    Everett Public Schools

    Mathematics Program

    Proposed Time Frame:

    Approximately 6 weeks

    Stretching and Shrinking

    Geometry

    Similarity

    Unit Goals:

    Enlarge and shrink plane

    figures

    Identify the corres ponding

    parts of s imilar figures

    Describe and produce

    transformation of plan e figures

    Analyze scale factors between

    figures Apply properties of simil ar figures

    Web Resources

    You will find the Factor

    Game and the Product Game

    at:

    www.illuminations.nctm.org

    Paper Pool

    Using Transformations

    and Interactive Figures

     

    Tips for Helping at Home

    Good questions and good listening w ill

    help children make se nse of mathemat-

    ics an d build self-confidence. A good

    question opens up a problem and su p-

    ports different ways of thinking about it.

    Here are some questions you might try,

    notice that none of them can be an-

    swered with a simple �yes � or �no�.

    Getting Started

    What do you need to find ou t?

    What do you need to know?

    What terms do you understan d or

    not understand?

    While Working

    How can you organize the inf orma-

    tion?

    Do you see any patterns or relation-

    ships that w ill help solve this?

    What would happen if�?

    Reflecting about the Solution

    How do you know your answer is

    reasonable?

    Has the question been answ ered?

    Can you explain it another w ay?

    At Home:

    1 Talk with your child about

    what�s going on in mathem atics

    class.

    2 Look for ways to link mathe-

    matical learning to daily activi-

    ties. Encourag e your child to

    figu re out the amounts for halv-

    ing a recipe, estimating gas

    mileage, or figuring a restau-

    rant tip.

    3 Encourage y our child to sched-

    ule a regular time for home-

    work and provide a comfortable

    place for their study , free from

    distractions.

    4 Monitor y our child�s home-

    work on a regular basis by

    looking at one problem or ask-

    ing your child to briefly de-

    scribe the focus of the home-

    work. When your child asks

    for help, work with them in-

    stead of doing the problem for

    them.

    At School

    1 Attend Open House, Back to

    School Nigh t, and after school

    ev ents.

    2 Join the parent-teacher organi-

    zation

    Investigation 1 Enlarging Figures

    Make enlargements of similar fi gures with a rubber

    band stretcher

    Describe in an intuitive way w hat the word similar

    means

    Consider relationships between l engths and between

    angles in simp le, similar figures

    Investigation 2 Similar Figures

    Locate points in a coordinate system

    Graph figures using algebraic rules

    Predict how figures on a coordi nate system are af-

    fected by a gi ven rule

    Experiment with exampl es and counterexamples of

    simila r shapes

    Investigation 3 Patterns of Similar Figures

    Recognize similar figures and be abl e to tell why they

    are similar

    Build a larger similar shape from copies of a basic

    shape

    Understand that the sides and perim eters of similar

    figures grow by a scale factor and that the areas

    grow by the square of the scale factor

    Find a missing measurement in a pai r of similar

    figures

    Recognize that triangles with equal corresponding

    angles are simila r

    Investigation 4 Using Similarity

    Use definition of similarity to recognize when figures

    are si milar

    Find the missing measurement in pai rs of similar

    figures

    Solve problems that involve scali ng up and down

    Investigation 5 Similar Triangles

    Recognize similar figures in the real worl d

    Find a missing measurement in a pair of sim ilar

    figures

    Apply what has been learned about simila r figures to

    solve real-world problems

    Connected Mathematics Project

    Mathematics in

    Investigations

    Phone: 425-385-4062

    Fax: 425-385-4092

    Email: mstine@everett.wednet.edu

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