Equilateral Triangle � A trian-

    gle with all three sides the

    same length

    Isosceles Triangle � A trian-

    gle with two sides the same

    length

    Parallel Lines � Lines that

    never meet no matter how

    long they are extended. The

    opposite sides of a square or

    rectangle are parallel.

    Vertex � Angles are formed by tw o rays that have the

    same endpoint, this endpoint

    is called the vertex.

    Shapes and Designs

    Glossary

    Connected Mathematics

    Project

    Everett Public Schools

    Mathematics Program

    Proposed Time Frame:

    Approximately 6 weeks

    Shapes and Designs

    Two-Dimensional Geometry

    Unit Goals

    Understand the relationships

    between and among polygons

    Learn im portant properties of

    polygon

    Create and determine

    properties of shapes that tile a

    surf ace

    Explore symmetries in

    squares, rectangles,

    parallelograms, and equilateral

    triang les.

    Web Resources

    You will find web resources

    at:

    www.illuminations.nctm.org

    Investigating Properties

    of Triangles

    Exploring Properties of Rectangles and Paral-lelograms

     

    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 Bees and Polygons

    Discover which regular polygons c an tile a

    plane.

    Discover combinations of regular polygons that

    can be us ed to tile a plane

    Discover that some irregular poly gons can be

    used to tile a plane.

    Invest igation 2 Building Polygons

    Understand that triangle are st able figures that

    keep their s hape under stress

    Discover that the sum of the lengths of any two

    sides of a tr iangle is greater than the length of

    the third side.

    Discover that quadrilaterals and ot her polygons

    are not stable s hapes and become distorted

    under stress

    Discover that the sum of the lengths of any

    three sides of a quadrilateral is greater than the

    length of the fourth side.

    Investigation 3 Polygons and Angles

    Develop and understanding of what an angle is

    and find examples in the real world

    Understand the measure of an angle

    360�, is a full circle, 180� is a half circle, 90� is a

    quarte r circle

    Use angles and angle measures in real-life ap-

    plications

    Investigation 4 Polygon Properties and

    Tiling

    Use information about angles to test potential

    tiling patterns

    Show how regular hexagons can be us ed to tile

    Understand that most other polygons do not tile

    Understand that circular shapes do not tile

    Invest igation 5 Side-Angle-side Connec-

    tions

    Recognize and describe flips and tu rns that will

    return a triangle, square, rectangle, or parallelo-

    gram to its original orientation

    Understand the properties of side s and an-

    gels in isoscel es and equilateral triangles,

    squares, rectangles, and parallelograms

    Connected Mathematics Project

    Mathematics in

    Investigations

    Phone: 425-385-4062

    Fax: 425-385-4092

    Email: mstine@everett.wednet.edu

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