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 realworld 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 realworld 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 realworld situation. 
Performance Indicators 

As
documented through teacher observation  
Teacher: 




At Level
1, the student is able to
·
connect a variety of
realworld 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
·
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 realworld 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
twostep 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
slopeintercept form;
·
Slope Intercept Tutorial
·
solve multistep
linear equations (more than two steps, variables on only one
side of the equation);
·
Example Problems of Two Step Equations
·
solve multistep
linear equations (more than two steps, with variables on both
sides of the equation);
·
Example Problems of Variables on Both Sides Equations
·
solve multistep
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
realworld situation described in a narrative (no data set
given);
·
select the linear
graph that models the given realworld 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 realworld problems;
·
select the
appropriate graphical representation of a given linear
inequality;
·
Tutorial on Graphing Inequalities
·
select the nonlinear
graph that models the given realworld situation or vice versa;
·
identify the
graphical representation of the solution to a onevariable
inequality on a number line.
·
Solving Inequalities 
A
A
A 
RW
GG
GG 
At Level 3, the student is able to
·
solve multistep
linear inequalities in realworld 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
realworld situations,
·
Domain and Range
*
Select the system of
equations that could be used to solve a given realworld
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 20052006. 
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 realworld 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 realworld
uses of geometric formulas and relationships;
·
discuss issues
related to estimating areas of irregularshaped figures for
realworld 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 onevariable 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
realworld 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. 


·
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 realworld data (no more than five
twodigit numbers);
·
interpret bar graphs
representing realworld data;
·
interpret circle graphs
(pie charts) representing realworld 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 realworld linear data set;
·
determine the median for
a given set of realworld data (even number of data). 
A 
RW 
At Level 3, the student is able to
·
apply counting
principles of permutations or combinations in realworld situations. 
Performance Indicators


As documented
through teacher observation  
Teacher: 




At Level 1,
the student is able to
·
design a strategy for
collecting realworld data for a scientific investigation;
·
collect and organize
realworld data. 


At Level 2, the student is able to
·
graph realworld 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
realworld data using a line of best fit. 




Kindergarten
First Grade
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Elementary
Resources
Worksheets
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Algebra I
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Resources
Worksheets
Science Fair
Dynamic Curriculum
Math/Science Integration
Math Online
