Hypotenuse The side of a right

    triangle that is opposite the right

    angle. The hypotenuse is the long-

    est side of a ri ght triangle

    Irrational Number � A number that

    cannot be wri tten as a fraction with

    a numerator and a denominator that

    are integers.

    Pythagorean Theorem � The theo-

    rem states that if a and b are the

    lengths of the legs of a right tri angle

    and c is the length of the hypote-

    nuse, then a

    2 +

    b

    2

    = c

    2

    Rational Number� A number that

    can be written as a fraction with a

    numerator and a denominator that

    are integers, for example 1/2.

    Repeat ing Decimal� A decimal

    with a pattern of digits that r epeats

    forever, such as 0.333333�. Re-

    peating decimals are rational num-

    bers.

    Square Root � If A = s

    2

    , then s is

    the square root of A. The positive

    square root of a number is the side

    length of a squar e that has that

    number as i ts area.

    Terminating Decimal� A decimal

    that ends, or termi nates, such as

    0.5 or 0.125. Terminating decimals

    are rational numbers

    Looking for Pythagoras

    Glossary

    Connected Mathematics

    Project

    Everett Public Schools Mathematics P rogram

    Proposed Time Fram e:

    Approximately 6 weeks

    Looking for Py thagoras

    The Pyth agorean Theorem

    Unit Goals:

    Calculate the distance

    between two points in the

    plane Understanding square root s as lengths as sides of squares Understand the Pythagorea n Theorem Use the Pythagorean Theo rem to solve problems

    Web Resources

    You will find the Factor

    Game and the Product Game

    at:

    www.illuminations.nctm.org

    Pythagorean Theorem

     

    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 Locating Points

    To review the use of coordi nates for specifying locations

    To use coordinates to specify di rection and distance

    To connect properties of geometri c shapes, such as parallel

    si des, to coordinate representations

    Investigation 2 Finding Areas and Leng ths

    To find areas of polygons draw n on a dot grid using various

    strategies

    To find the length of a line segm ent drawn on a grid by

    thinki ng of it as the side of a square

    To begin to develop an understandi ng of the concept of

    square root

    Investigation 3 The Pythagor ean Theorem

    To deduce the Pythagorean Theorem through exploration

    To use the Pythagorean Theorem to fi nd areas of squares

    draw n on a dot grid

    To use the Pythagorean Theorem to fi nd the distance be-

    tween two poi nts on a grid

    To determine whether a triangle is a right triangle

    To relate areas of squares to the l engths of the sides

    Investig ation 4 Using the Pythagorean Theorem

    To apply the Pythagorean Theorem in several problem

    situ ations

    To investigate the special properti es of a 30-60-90 triangle

    and an isosceles right triangle

    To use properties of special ri ght triangles to solve problems

    Investigation 5 Irrational Numbers

    To connect decimal and fractional representations of rational

    num bers

    To estimate l engths of hypotenuse of right triangles

    To explore patterns in terminati ng and repeating decimals

    Investigation 6 Rational and Irration al Slopes

    To review the concept of slope of a line

    To connect the concept of sl ope to the idea of irrational

    num bers

    To use slopes to test whether li nes are parallel or perpen-

    dicula r

    Connected Mathematics Project

    Mathematics in

    Looking for

    Pythagoras

    Phone: 425-385-4062

    Fax: 425-385-4092

    Email: mstine@everett.wednet.edu

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