Mathematics and the World We Live In

 

Gateway Algebra

Gateway Mathematics

   

Standard Number:

  1.0  Number and Operations

 

   

Performance Indicators

Reporting As documented through state assessment  -

State:

Category  

 

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:

  2.0 Algebra

 

   

Performance Indicators

Reporting As documented through state assessment  -

State:

Category  

 

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

 

A

A

 

A

 

RW

GG

 

GG

At Level 3, the student is able to

          solve multi-step linear inequalities in real-world situations;

          recognize the graphical transformation that occurs when coefficients and/or constants of the corresponding linear equations are changed;

          determine the domain and/or range of a function represented by the graph of real-world situations,

          Domain and Range

*         Select the system of equations that could be used to solve a given real-world problem.

*         Find the solution to a quadratic equation given in standard form (integral solutions and a leading coefficient of one).

*         Quadratic Equation Tutorial

*         Select the solution to a quadratic equation given solutions represented in graphical form (integral solutions and a leading coefficient of one).

*         Graphically find Solutions of a Quadratic

*         Select one of the factors (x + 3) of a quadratic equation (integral solutions and a leading coefficient of one).

*         Select the discriminant of a quadratic equation (integral solutions and a leading coefficient of one).

*         Discriminant and Quadratic Review

*         Recommended by the 2003 committee as additional state performance indicators. Additional state performance indicators will begin to be assessed during 2005-2006.

Performance Indicators

 

As documented through teacher observation -

Teacher:

   
 

 

At Level 1, the student is able to

          analyze rational number patterns;

          describe in writing the pattern for real-world data listed in a function table.

 

 

At Level 2, the student is able to

          produce an equation to describe the relationship between data sets;

          explore patterns including Pascal's Triangle and a Fibonacci sequence;

          solve a system of two linear equations using the graphing, elimination, and substitution methods;

          defend the selection of a method for solving a system of equations;

          represent algebraic expressions and operations using manipulatives;

          model the steps for solving simple linear equations using manipulatives;

          write an equation that symbolically expresses a problem solving situation;

          justify correct results of algebraic procedures;

          distinguish between a function and other relationships.

 

 

At Level 3, the student is able to

          analyze "families of functions" using technology.

 

Standard Number:

  3.0 Geometry

 

   

Performance Indicators

Reporting As documented through state assessment  -

State:

Category  

 

A

 

GG

At Level 1, the student is able to

          identify ordered pairs in the coordinate plane.

          FREE GRAPH PAPER!!!

 

A

 

A

 

SSG

 

SSG

At Level 2, the student is able to

          apply the given Pythagorean theorem to a real life problem illustrated by a diagram (no radicals in answer);

          apply proportion and the concepts of similar triangles to find the length of a missing side of a triangle.

           

 

A

 

SSG

At Level 3, the student is able to

          calculate the distance between two points given the Pythagorean theorem and the distance formula.

Performance Indicators

 

As documented through teacher observation -

Teacher:

   

 

 

At Level 1, the student is able to

         describe real-world uses of geometric formulas and relationships;

         discuss issues related to estimating areas of irregular-shaped figures for real-world uses (i.e., fencing, painting, laying carpet, or purchasing wallpaper or border).

 

 

At Level 2, the student is able to

          explain how to determine if a triangle is a right triangle when given the measurements of all three sides;

          illustrate the Pythagorean theorem by measuring the length, width, and diagonals of rectangular objects; design area models to illustrate the Pythagorean theorem.

 

 

At Level 3, the student is able to

          determine the height of an object that is difficult to measure by using the properties of similar triangles.


 

Standard Number:

  4.0 Measurement

 

   

Performance Indicators

Reporting As documented through state assessment  -

State:

Category  

 

A

A

 

A

 

SSG

RW

 

SSG

At Level 1, the student is able to

          estimate the area of irregular geometric figures on a grid;

          calculate rates involving cost per unit to determine the best buy (no more than three samples);

          apply the given formula to determine the area or perimeter of a rectangle.

          Area and Perimeter

 

A

 

SSG

At Level 2, the student is able to

          apply the given formula to find the area of a circle, the circumference of a circle, or the volume of a rectangular solid.

          Area and Perimeter of a Circle

 

A

 

AE

At Level 3, the student is able to

          select the area representation for a given product of two one-variable binomials with positive constants and coefficients.

Performance Indicators

 

As documented through teacher observation -

Teacher:

   

 

 

At Level 1, the student is able to

          justify the selection of a unit of measure in specific situations;

          defend estimates of the perimeter and/or area of rectangles and triangles;

          discover and explain formulas used to compute area and volume.

 

 
At Level 2, the student is able to

          describe the procedure for determining the area of a composite shape in a real-world situation;

          generalize area formulas using manipulatives for a parallelogram, a triangle, and a trapezoid;

          defend an estimate for the volume of a container;

          relate the volume of a container to its shape;

          analyze precision, accuracy, tolerance, and approximate error in measurement situations.

 

 

At Level 3, the student is able to

          discover the dimensions of a rectangle when given its area and the relationship between two adjacent sides;

          describe how changes in the dimensions of figures affect perimeter, area, and volume.

 

Standard Number:

  5.0 Data Analysis and Probability

 

   

Performance Indicators

Reporting As documented through state assessment  -

State:

Category  

 

A

 

A

A

 

RW

 

RW

RW

At Level 1, the student is able to

          determine the mean (average) of a given set of real-world data (no more than five two-digit numbers);

          interpret bar graphs representing real-world data;

          interpret circle graphs (pie charts) representing real-world data.

 

A

A

A

 

GG

GG

RW

At Level 2, the student is able to

          choose the matching linear graph given a set of ordered pairs;

          make a prediction from the graph of a real-world linear data set;

          determine the median for a given set of real-world data (even number of data).

 

A

 

RW

At Level 3, the student is able to

          apply counting principles of permutations or combinations in real-world situations.

Performance Indicators

 

As documented through teacher observation -

Teacher:

   

 

 

At Level 1, the student is able to

          design a strategy for collecting real-world data for a scientific investigation;

          collect and organize real-world data.

 

 

At Level 2, the student is able to

          graph real-world data using a variety of representations;

          debate the selection of a graphical representation which best describes specific data;

          model situations to determine theoretical and experimental probabilities;

          judge the validity of claims made in probabilistic situations;

          defend the sampling method chosen to conduct a survey.

 

 

At Level 3, the student is able to

          debate possible conclusions that can be supported by given data;

          make predictions from real-world data using a line of best fit.

 

 

 


 
 

 

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Elementary Resources

Worksheets

Sixth Grade

Seventh Grade

Eighth Grade

Algebra I

Secondary Resources

Worksheets

Science Fair

Dynamic Curriculum

Math/Science Integration

Math Online