Constant Term � A number in an

    algebraic expression that is not mul-

    tiplied by a variable

    Expanded Form � the form of an

    expression composed of sums or

    differences of terms rat her than

    products of fact ors

    Function � the relationship between

    two variables in which t he value of

    one va riable depends on the value

    of the other variable.

    Like Terms � Terms with the same

    variable raised to the same power.

    Line of Symmetry � a line that di-vides a graph or drawing into two

    halves that are mirror images of

    each other Linear Term � A part of an algebraic ex pression in which the variable is

    raised to the first power. Parabola � the graph of a quadratic f unction. Quad r atic Term � A part of an alge-braic ex pression in which the vari-

    able is raised to the second power. Triangular Number � A quantity that c an be arranged in a triangular

    pattern. The first four triangular

    numbers are 1,3,6, and 10.

    Frogs, Fleas and Painted C ubes

    Glossary

    Connected Mathematics

    Project

    Everett Public Schools

    Mathematics Program

    Proposed Time Frame:

    Approximately 6 weeks

    Frogs, Fleas, and Painted

    Cubes

    Algebra

    Quadratic Relationships

    Unit Goals:

    Analyzing quadratic

    relationships by exami ning

    tables, gra phs, and equations

    Comparing characteristic s of

    tables and gr aphs for quadratic

    relationships

    Understanding the signifi cance

    of x� and y� intercepts

    Understanding the equival ence of two or more symbolic forms Attaching contextual mean ing to equations

    Web Resources

    Algebra Tiles

    http:// www.coe.tamu.edu/~strader/Mathematics/Algebra/AlgebraTiles/ AlgebraTiles2.html

    Graphing the Situation www.illuminations.nctm.org

     

    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: Introduction to Quadra tic Relationships

    Develop an awareness of quadratic f unctions and how

    to recognize t hem from patterns in tables and graphs

    Describe patterns in tables of quadr atic functions and

    predict subsequent entries

    Recognize the characteristic shape of the graph of a

    quadrati c function an observe such features as as lines

    of symmetry, maximum points, and intercept s.

    Use tables and graphs of quadratic r elationships to

    answer questi ons about a situation

    Represent some quadratic relationshi ps with equations

    Investigati on 2: Quadratic Expressions

    Develop an awareness of quadratic f unctions and how

    they can be re cognized from patterns in tables, graphs

    and equations

    Recognize a characteristic shape of the graph of a

    quadratic functi on and identify its line of symmetry,

    vertex, and intercepts

    Develop an understanding of equival ent expressions,

    that is, of tw o expression that model the same relation-

    ship

    Recognize a quadratic function from an equation

    Investigation 3: Quadratic Patterns of Change

    Observe and describe patterns of r egularity and

    change in data

    Express data from a problem situati on in tables,

    graphs, and equati ons

    Make predictions based on data

    Observe the pattern of change in a quadratic relation-

    ship

    Understand that the same equation ma y model differ-

    ent situations

    Investigation 4: What is a Quadratic Function:

    Predict from tables, graphs, and equations whether

    quadratic functions have maximum or minimum values

    Find and interpret maximum and minim um values from

    tables, graphs, and the factored form of equations

    Describe patterns of change in tabl es and graphs of

    quadratic relati onships

    Make predictions based on data

    Investigation 5: Painte d Cubes

    Observe patterns in tables of data

    Express data from a problem situati on in tables, graphs

    and equati ons

    Make predictions based on data

    Develop a deeper sense of the pr operties that charac-

    terize t he quadratic relationships by comparing quad-

    ratic relationships to linear and cubic rel ationships

    Connected Mathematics Project

    Mathematics in

    Investigations

    Phone: 425-385-4062

    Fax: 425-385-4092

    Email: mstine@everett.wednet.edu

    Back to top