Gateway Mathematics

Standard Number:

Performance Indicators

State:

A

A

A

A

A

A

NS

NS

NS

AE

NS

NS

At Level 1, the student is able to

·          select the best estimate for the coordinate of a given point on a number line (only rational);

·          Rational Numbers on the Number Line and other information

·          identify the opposite of a rational number;

·          determine the square root of a perfect square less than 169;

·          Tutorial on Square Roots

·          use exponents to simplify a monomial written in expanded form;

·          apply order of operations when computing with integers using no more than two sets of grouping symbols and exponents 1 and 2;

·          Interactive Sample Problems on Order of Operations

·          select a reasonable solution for a real-world division problem in which the remainder must be considered.

·           

A

A

A

A

A

A

NS

NS

AE

NS

NS

NS

At Level 2, the student is able to

·          order a given set of rational numbers (both fraction and decimal notations);

·          Examples of ordering Rational Numbers

·          identify the reciprocal of a rational number;

·          Interactive site on Reciprocals

·          add and subtract algebraic expressions;

·          Adding and Subtracting Algebraic Expression

·          multiply two polynomials with each factor having no more than two terms;

·          use estimation to determine a reasonable solution for a tedious arithmetic computation;

·          Estimate

·          select ratios and proportions to represent real-world problems (e.g., scale drawings, sampling, etc.).

·          Ratios and Proportions

A

RW

At Level 3, the student is able to

·          apply the concept of slope to represent rate of change in a real-world situation.

Performance Indicators

As documented through teacher observation -

Teacher:

At Level 1, the student is able to

·          connect a variety of real-world situations to integers;

·          use manipulatives to represent commutative and associative properties of addition and multiplication;

·          investigate alternate algorithms that show the relationship of division to subtraction and multiplication to addition;

·          analyze prime and composite numbers;

·          Prime and Composite Numbers

·          compare and contrast the GCF and LCM of a set of numbers;

·          GCF and LCM

·          refine strategies for estimating whole numbers, fractions, and percentages.

·          Fractions, Decimals and Percents

At Level 2, the student is able to

·          probe the relationships among various subsets of the real number system;

·          compare and contrast the GCF and LCM of a set of algebraic expressions;

·          construct a number line to describe the absolute value of a number as distance from zero;

·          model operations using real-world situations and physical representations;

·          perform operations on matrices using appropriate technology (addition, subtraction, and scalar multiplication);

·          explore various representations of absolute value.

At Level 3, the student is able to

·          research the history of prime numbers and their uses;

·          scrutinize approximate values of real numbers such as pi and the square root of two.

·          Pi and Pi Day Activities

Standard Number:

Performance Indicators

State:

A

A

A

A

A

SSG

AE

AE

AE

EI

At Level 1, the student is able to

·          extend a geometric pattern;

·          extend a numerical pattern;

·          translate a verbal expression into an algebraic expression;

·          evaluate a first degree algebraic expression given values for one or more variables;

·          solve one- and two-step linear equations using integers (with integral coefficients and constants).

·          Interactive Equation Game ( 1 and 2 Step)

·          Solving One Step Equations with Multiplication and Division

·          Solving One Step Equations with Addition and Subtraction

·          Solving Equations Matching Game

·          Equations Quiz

·          Equation Aquarium

A

A

A

A

A

A

A

A

A

A

A

A

A

A

EI

EI

GG

EI

EI

EI

GG

GG

AE

GG

RW

EI

GG

EI

At Level 2, the student is able to

·          select the algebraic notation which generalizes the pattern represented by data in a given table;

·          translate a verbal sentence into an algebraic equation;

·          select the graph that represents a given linear function expressed in slope-intercept form;

·          Slope Intercept Tutorial

·          solve multi-step linear equations (more than two steps, variables on only one side of the equation);

·          Example Problems of Two Step Equations

·          solve multi-step linear equations (more than two steps, with variables on both sides of the equation);

·          Example Problems of Variables on Both Sides Equations

·          solve multi-step linear equations (more than two steps, with one set of parentheses on each side of the equation);

·          select the linear graphs that models the given real-world situation described in a narrative (no data set given);

·          select the linear graph that models the given real-world situation described in a tabular set of data;

·          evaluate an algebraic expression given values for one or more variables using grouping symbols and/or exponents less than four;

·          determine the slope from the graph of a linear equation (no labeled points);

·          Slope Tutorial              

·          apply the concept of rate of change to solve real-world problems;

·          select the appropriate graphical representation of a given linear inequality;

·          Tutorial on Graphing Inequalities

·          select the nonlinear graph that models the given real-world situation or vice versa;

·          identify the graphical representation of the solution to a one-variable inequality on a number line.

·          Solving Inequalities