Pre-Algebra Essential Curriculum
UNIT I:
STANDARD 6.0 – KNOWLEDGE OF NUMBER RELATIONSHIPS AND COMPUTATION/ARITHMETIC
Goal 1. The student will demonstrate the ability to apply knowledge of
rational numbers and place value.
Objectives - The student will be able to:
1. Compare, order, and describe rational numbers with and without relational
symbols.
2. Read, write, and represent rational numbers.
Goal 2. The student will demonstrate the ability to analyze number relations
and compute.
Objectives - The student will be able to:
1. Add, subtract, multiply, and divide integers.
2. Identify and use the laws of exponents to simplify expressions.
3. Calculate powers of integers and square roots of perfect square whole numbers.
4. Estimate the square roots of whole numbers.
STANDARD 1.0 – KNOWLEDGE OF ALGEBRA, PATTERNS, AND FUNCTIONS
Goal 1. The student will demonstrate the ability to write, simplify, and
evaluate expressions.
Objectives - The student will be able to:
1. Evaluate numeric expressions using the order of operations.
2. Evaluate algebraic expressions.
3. Write algebraic expressions to represent unknown quantities.
4. Describe a real-world situation represented by an algebraic expression.
5. Use properties of addition and multiplication to simplify expressions.
6. Simplify algebraic expressions by combining like terms.
Goal 2. The student will demonstrate the ability to identify, write, solve,
and apply equations and inequalities.
Objectives - The student will be able to:
1. Write equations to represent relationships.
2. Solve for the unknown in a linear equation.
3. Identify equivalent equations.
4. Apply given formulas to a problem-solving situation.
UNIT II:
STANDARD 1.0 – KNOWLEDGE OF ALGEBRA, PATTERNS, AND FUNCTIONS
Goal 2. The student will demonstrate the ability to identify, describe,
extend, and create patterns, functions, and sequences.
Objectives - The student will be able to:
1. Write inequalities to represent relationships.
2. Solve for the unknown in an inequality.
3. Identify or graph solutions of inequalities on a number line.
UNIT III:
STANDARD 1.0 – KNOWLEDGE OF ALGEBRA, PATTERNS, AND FUNCTIONS
Goal 2. The student will demonstrate the ability to identify, describe,
extend, and create patterns, functions, and sequences.
Objectives - The student will be able to:
1. Determine the recursive relationship of arithmetic sequences represented in
words, in a table, or in a graph.
2. Determine the recursive relationship of geometric sequences represented in
words, in a table, or in a graph.
Goal 3. The student will demonstrate the ability to locate points on a number
line and in a coordinate plane.
Objectives - The student will be able to:
1. Graph linear equations in a coordinate plane.
Goal 4. The student will demonstrate the ability to analyze relationships.
Objectives - The student will be able to:
1. Determine the slope of a graph in a linear relationship.
2. Determine the slope of a linear relationship represented numerically or
algebraically.
STANDARD 3.0 – KNOWLEDGE OF MEASUREMENT
Goal 2. The student will demonstrate the ability to analyze measurement
relationships.
Objectives - The student will be able to:
1. Determine whether relationships are linear or nonlinear when represented in
words, in a table, symbolically, or in a graph.
2. Determine whether relationships are linear or nonlinear when represented
symbolically.
UNIT IV:
STANDARD 6.0 – KNOWLEDGE OF NUMBER RELATIONSHIPS AND COMPUTATION/ARITHMETIC
Goal 1. The student will demonstrate the ability to analyze ratios,
proportions, and percents.
Objectives - The student will be able to:
1. Determine unit rates.
2. Solve problems using proportional reasoning.
3. Use proportional reasoning to solve measurement problems.
4. Determine the uses of percents, rates of increase or decrease, discount,
commission, sales tax, and simple interest in the context of a problem.
UNIT V:
STANDARD 2.0 – KNOWLEDGE OF GEOMETRY
Goal 1. The student will demonstrate the ability to analyze the properties of
plane geometric figures.
Objectives - The student will be able to:
1. Identify and describe geometric relationships between angles formed when
parallel lines are cut by a transversal.
2. Identify and describe the relationship among the parts of a right triangle.
Goal 2. The student will demonstrate the ability to analyze geometric
relationships.
Objectives - The student will be able to:
1. Determine the measurements of angles formed by parallel lines cut by a
transversal.
2. Apply right angle concepts to solve real-world problems.
3. Determine whether three given side lengths form a right triangle.
Goal 3. The student will demonstrate the ability to represent plane geometric
figures.
Objectives - The student will be able to:
1. Draw quadrilaterals.
2. Construct perpendicular line segments.
3. Construct triangles.
Goal 4. The student will demonstrate the ability to apply the properties of
similar polygons.
Objectives - The student will be able to:
1. Determine similar parts of polygons.
Goal 5. The student will demonstrate the ability to analyze a transformation
on a coordinate plane.
Objectives - The student will be able to:
1. Identify, describe, and plot the results of multiple transformations in a
coordinate plane.
UNIT VI:
STANDARD 3.0 – KNOWLEDGE OF MEASUREMENT
Goal 1. The student will demonstrate the ability to estimate and apply
measurement formulas.
Objectives - The student will be able to:
1. Estimate and determine the circumference and area of a circle.
2. Estimate and determine the area of a composite figure.
3. Estimate and determine the volume of a cylinder.
4. Determine the volume of cones, pyramids, and spheres.
5. Determine the surface area of cylinders, prisms, and pyramids.
UNIT VII:
STANDARD 3.0 – KNOWLEDGE OF STATISTICS
Goal 1. The student will demonstrate the ability to organize and display data.
Objectives - The student will be able to:
1. Organize and display data to make a box-and-whisker plot and multiple
box-and-whisker plots.
2. Organize and display data to make a histogram.
Goal 2. The student will demonstrate the ability to analyze data.
Objectives - The student will be able to:
1. Analyze multiple box-and-whisker plots using the same scale.
UNIT VIII:
STANDARD 1.0 – KNOWLEDGE OF ALGEBRA, PATTERNS, OR FUNCTIONS
Goal 1. The student will demonstrate the ability to write, simplify, and
evaluate expressions.
Objectives - The student will be able to:
1. Evaluate numeric expressions using the order of operations with rational
numbers.
2. Evaluate algebraic expressions with rational numbers.
3. Translate verbal sentences into equations and equations into verbal sentences.
4. Write equations and inequalities that describe real-world problems.
Goal 2. The student will demonstrate the ability to identify, write, solve,
and apply equations and inequalities.
Objectives - The student will be able to:
1. Solve equations involving rational numbers with more than one equation.
2. Solve equations involving rational numbers with the variable on each side.
3. Solve equations for given variables and use formulas to solve real-world
problems.
4. Solve inequalities involving rational numbers with more than one operation.
Goal 3. The student will demonstrate the ability to analyze linear equations.
Objectives - The student be able to:
1. Determine the slope of a line given two points.
2. Analyze the slope as a rate of change in the context of a real-world situation.
3. Write and graph linear equations in slope-intercept form.
STANDARD 6.0 – KNOWLEDGE OF NUMBER RELATIONSHIPS AND COMPUTATION/ARITHMETIC
Goal 1. The student will demonstrate the ability to apply knowledge of
rational numbers and place value.
Objectives - The student will be able to:
1. Add, subtract, multiply, and divide rational numbers.
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QUARTER 1
Standard 6.0 Knowledge of Number Relationships and
Computation/Arithmetic-Students will describe, represent, or apply numbers or
their relationships or will estimate or compute using mental strategies,
paper/pencil or technology.
GOAL 1: The student will apply knowledge of rational numbers and place value.
GOAL 2: The student will be able to analyze number relations and compute.
Standard 1.0 Knowledge of Algebra, Patterns, and Functions- Students will
algebraically represent, model, analyze, or solve mathematical or real-world
problems involving patterns or functional relationships.
GOAL 1: The student will be able to write, simplify, and evaluate expressions.
GOAL 2: The student will be able to identify, write, solve, and apply
equations and inequalities.
UNIT 1
Instructional Objective(s): The student will be able to:
1) Compare, order, and describe rational numbers with and without relational
symbols - Use no more than 4 integers (-100 to 100) or positive rational
numbers (0-100) using equivalent forms or absolute value
2) Add, subtract, multiply, and divide integers Use one operation (-1000 to 1000)
3) Evaluate numeric expressions using the order of operations Use no more than
5 operations including exponents of no more than 3 and 2 sets of parentheses,
brackets, a division bar, or absolute value with rational numbers (-100 to 100)
4) Evaluate algebraic expressions- Use one or two unknowns and up to three
operations and rational numbers (-100 to 100)
5) Write algebraic expressions to represent unknown quantities - Use one
unknown and no more than 3 operations and rational numbers (-1000 to 1000)
6) Describe a real-world situation represented by an algebraic expression
7) Identify and use the laws of exponents to simplify expressions - Use the
rules of power times power or power divided by power with the same integer as
a base (-20 to 20) and exponents (0-10)
8) Read, write, and represent rational numbers Use exponential notation or
scientific notation (-10,000 to 1,000,000,000)
9) Use properties of addition and multiplication to simplify expressions -Use
the commutative property of addition or multiplication, associative property
of addition or multiplication, additive inverse property, the distributive
property, or the identity property for one or zero with integers (-100 to 100)
10) Simplify algebraic expressions by combining like terms - Use no more that
3 variables with integers (-50 to 50), or proper fractions with denominators
as factors of 20(-20 to 20)
11) Write equations to represent relationships Use a variable, the
appropriate relational symbols and no more than 3 operational symbols (+, -,
x) on either side and rational numbers (-1000 to 1000)
12) Solve for the unknown in a linear equation Use one unknown no more than 3
times on one side and up to 3 operations (same or different but only one
division) and rational numbers (-2000-2000)
13) Identify equivalent equations - Use one unknown no more than 3 times on
one side and up to three operations (same or different by only one division)
and integers (-2000 to 2000)
14) Apply given formulas to a problem-solving situation Use no more than four
variables and up to three operations with rational numbers (-500 to 500)
15) Calculate powers of integers and square roots of perfect square whole
numbers - Use powers with bases no more than 12 and exponents no more than 3,
or square roots of perfect squares no more than 144
16) Estimate the square roots of whole numbers Use whole numbers (0-100)
QUARTER 2
Standard 1.0 Knowledge of Algebra, Patterns, or Functions- Students will
algebraically represent, model, analyze, or solve mathematical or
real-world problems involving patterns or functional relationships.
GOAL 1: The student will be able to identify, write, solve, and apply
equations and inequalities
GOAL 2: The student will be able to identify, describe, extend, and create
patterns, functions, and sequences.
GOAL 3: The student will be able to locate points on a number line and in a
coordinate plane.
GOAL 4: The student will be able to analyze linear relationships.
Standard 6.0 Knowledge of Number Relationships and
Computation/Arithmetic-Students will
describe, represent, or apply numbers or their relationships or will estimate
or compute using mental strategies, paper/pencil or technology
GOAL 1: The student will be able to analyze ratios, proportions, and percents.
UNIT 2
Instructional Objective(s)
The student will be able to:
1) Write inequalities to represent relationships - Use a variable, the
appropriate relational symbols and no more than 3 operational symbols (+, -,
x) on either side and rational numbers (-1000-1000)
2) Solve for the unknown in an inequality - Use a one-or-two operation
inequality with one variable on one side no more than 3 times whose result
after combining coefficients is a positive whole number coefficient with
integers (-100 to 100)
3) Identify or graph solutions of inequalities on a number line - Use one
variable once with a positive whole number coefficient and integers (-100 to 100)
UNIT 3
4) Determine the recursive relationship of arithmetic sequences represented in
words, in a table, or in a graph. Provide the nth term no more than 10 terms
beyond the last given term using common differences no more than 10 with
integers (-100 to 5000)
5) Determine the recursive relationship of geometric sequences represented in
words, in a table, or in a graph. Provide the nth term no more than 5 terms
beyond the last given term using the recursive relationships of geometric
sequences with whole numbers and a common ratio of no more than 5:1 (0-10,000)
6) Graph linear equations in a coordinate plane a) Use two unknowns having
integer coefficients (-9 to 9) and integer constants (-20 to 20)
7) Determine the slope of a graph in a linear relationship - Use an equation
with integer coefficients (-9 to 9) and integer constants (-20 to 20) and a
given graph of the relationship
8) Determine the slope of a linear relationship represented numerically or
algebraically
9) Determine whether relationships are linear or nonlinear when represented in
words, in a table, symbolically, or in a graph. Use a graph to determine if a
relationship is linear or nonlinear
10) Determine whether relationships are linear or nonlinear when represented
symbolically
UNIT 4
11) Determine unit rates - Use positive rational numbers (0-100)
12) Solve problems using proportional reasoning Use positive rational numbers
(0-1000)
13) Use proportional reasoning to solve measurement problems - Use
proportions, scale drawings with scales as whole numbers, or rates using whole
numbers or decimals (0-1000)
14) Determine or use percents, rates of increase and decrease, discount,
commission, sales tax, and simple interest in the context of a problem
QUARTER 3
Standard 2.0 Knowledge of Geometry- Students will apply the properties of one,
two, or three-dimensional geometric figures to describe,reason, or solve
problems about shape, size, position, or motion of objects.
GOAL 1: The student will be able to analyze the properties of plane geometric
figures.
GOAL 2: The student will be able to analyze geometric relationships.
GOAL 3: The student will represent plane geometric figures.
GOAL 4: The student will apply the properties of similar polygons.
GOAL 5: The student will analyze a transformation on a coordinate plane.
Standard 3.0 Knowledge of Measurement- Students will identify attributes,
units, or systems of measurement or apply a variety of techniques, formulas,
tools or technology for determining measurements.
GOAL 1: The student will be able to estimate and apply measurement formulas.
UNIT 5
Instructional Objective(s)
The student will be able to:
1) Identify and describe geometric relationships between angles formed when
parallel lines are cut by a transversal - Use alternate interior, alternate
exterior, or corresponding angles
2) Determine the measurements of angles formed by parallel lines cut by a
transversal - Use alternate interior, alternate exterior, and corresponding angles
3) Identify, describe, and plot the results of multiple transformations on a
coordinate plane - Identify or plot the result of two transformations on one
figure using translations (horizontal or vertical), reflections (horizontal or
vertical), or rotations about the origin (90° or 180°)
4) Draw quadrilaterals Provide given whole number dimensions in inches or
centimeters or angle measurements
5) Construct perpendicular line segments - Provide a given point on a given
line segment
6) Construct triangles. Construct a triangle congruent to a given triangle
.
7) Determine similar parts of polygons - Use the length of corresponding
sides or the measure of corresponding angles and rational numbers with no more
than 2 decimal places (0-1000)
8) Identify and describe the relationship among the parts of a right triangle
- Use the hypotenuse or legs of right triangles
9) Apply right angle concepts to solve real-world problems - Use the
Pythagorean Theorem
10) Determine whether three given side lengths form a right triangle
UNIT 6
11) Estimate and determine the circumference or area of a circle - Include
circles using rational numbers with no more than 2 decimal places (0-10,000)
12) Estimate and determine the area of a composite figure - Include composite
figures with no more than 6 polygons (triangles, rectangles, or circles) by
measuring, partitioning, or using formulas with whole number dimensions
(0-10,000)
13) Estimate and determine the volume of a cylinder - Use cylinders, the given
formula, and whole number dimensions (0-10,000)
14) Determine the volume of cones, pyramids, and spheres
15) Determine the surface area of cylinders, prisms, and pyramids
UNIT 7
16) Organize and display data to make a box-and-whisker plot and multiple
box-and-whisker plots using the same scale
17) Analyze multiple box-and-whisker plots using the same scale
18) Organize and display data to make a histogram
19) Interpret a histogram
20) Organize and display data to make a scatter plot
21) Interpret the line of best fit for a scatter plot
Quarter 4
Standard 1.0 Knowledge of Algebra, Patterns, or Functions- Students will
algebraically represent, model, analyze, or solve mathematical or
real-world problems involving patterns or functional relationships.
GOAL 1: The student will be able to write, simplify, and evaluate expressions.
GOAL 2: The student will be able to identify, write, solve, and apply
equations and inequalities
GOAL 3: The student will demonstrate the ability to analyze linear equations.
Standard 6.0 Knowledge of Number Relationships and
Computation/Arithmetic-Students will describe, represent, or apply numbers or
their relationships or will estimate or compute using mental strategies,
paper/pencil or technology.
GOAL 1: The student will apply knowledge of rational numbers and place value.
UNIT 8
Instructional Objective(s)
The student will be able to:
1) Add, subtract, multiply, and divide and rational numbers
2) Evaluate numeric expressions using the order of operations with rational
numbers
3) Evaluate algebraic expressions with rational numbers
4) Translate verbal sentences into equations and equations into verbal sentences
5) Write equations and inequalities that describe real-world problems
6) Solve equations involving rational numbers with more than one operation
7) Solve equations involving rational numbers with the variable on each side
8) Solve equations for given variables and use formulas to solve real-world
problems
9) Solve inequalities involving rational numbers with more than one operation
10) Determine the slope of a line given two points
11) Analyze the slope as a rate of change in the context of a real-world situation
12) Write and graph linear equations in slope-intercept form
