Commutative property of Addi-

    tion � a mathematical property that

    states that t he order in which quanti-

    ti es are added does not matter. For

    example 5 + 7 = 7 + 5

    Commutative Property of Mult ipli-

    cation � a mathematical property

    that states that t he order in which

    quantit ies are multiplied does not

    matter. For example, 5 x 7 = 7 x 5.

    Distributive Property � A mathe-

    matical property used to rewrite ex-

    pressions involving additi on and

    multiplication. For example,

    4(5 + x) = 4(5) + 4 (x) = 20 + 4x Expanded Form � x

    2

    + 7x + 12

    and x

    2

    + 2x.

    Factored Form � The form of an

    expression composed of products of

    factors rather than sums and differ-

    ences of terms. The expressions

    (x+3)(x +4) and x(x-2) are in factored

    form.

    Parabola � The graph of a quadratic f unction Roots � The roots of an equation are the values of x that make y equal 0.

    Say It With Symbols

    Glossary

    Connected Mathematics

    Project

    Everett Public Schools

    Mathematics Program

    Proposed Time Frame:

    Approximately 6 weeks

    Say It With Symbols

    Algebra

    Unit Goals:

    Making sense of symbols

    Using the appropriate order of

    operations in evaluating ex pressions

    Writing sy mbolic sentences, using

    parentheses and properties of real

    numbers, to communicate

    effectively

    Reasoning wi th equivalent expressions Solving linear and quadratic equations Modeling and solving problems

    Web Resources

    Algebra Tiles

    http:// www.coe.tamu.edu/~strader/Mathematics/Algebra/

    AlgebraTiles/AlgebraTiles2.html

     

    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: Order of Operations

    Make sense of symbolic expressions involvi ng addi-

    tion, subtraction, multip lication, division and expo-

    nents.

    Develop an understanding of the conventi onal order

    of operations rules by being attentive to the ways

    expressions are written and eval uated in a variety of

    settings

    Evaluate expressions by applying the rule s of order

    of operations

    Investigation 2: Equivalent Expr essions

    Informally articulate the distributiv e property

    Apply the distributive property to simplify and com-

    pare expressions

    Further articulate what it means for two ex pressions

    to be equivalent

    Judge the equivalency of two or more ex pressions by

    examini ng the reasoning that each represents

    Determine the equivalency of two or more ex pres-

    sions by examining tabl es and graphs

    Investigation 3: Some Important Properties

    Determine the impact of a negative quantity as a

    factor

    Use the distributive and commutati ve properties to

    show equival ence of expressions

    Solve a variety of problems using the di stributive and

    commutati ve properties

    Investigation 4: Solving Equations

    Apply the properties for manipulating ex pressions to

    solving li near equations

    Solve simple quadratic equations symbolical ly

    Connect the solutions of an equation to in formation

    about its tabl e and graph

    Investigation 5: W riting Expressions for Surface Area

    Find and compare equivalent expressions in a given

    context

    Evaluate expressions for a specific val ue of a vari-

    able

    Connected Mathematics Project

    Mathematics in

    Investigations

    Phone: 425-385-4062

    Fax: 425-385-4092

    Email: mstine@everett.wednet.edu

    Back to top