mathematics
Mathematics at The Laurel Hill School emphasizes problem solving, mathematical reasoning, and real-world applications. All New York State standards are incorporated into our daily lessons and both tutorials and advanced study are available to our students.
Students enhance their problem solving skills by adding to their “Problem of the Day” book. Students use a variety of methods to approach each problem. Mathematical skills are introduced and enhanced. Classes are very interactive and involve constant participation. Individuals are given the guidance and attention needed to succeed. Lessons are designed to promote success and to increase self-confidence.
Math Lab is incorporated into the Mathematics Lessons. These “hands-on” activities enhance the students’ learning experiences. Students have opportunities to work individually, and in groups for cooperative learning experiences. Students practice their communication skills by reading to interpret directions, discussing possible solutions with their group, and in writing results and reasons explaining how they arrived at their solutions. Real life applications are incorporated into the projects. Technology is also used to investigate and explore possibilities. Creativity is always encouraged in ways to solve problems and in presentation of the final project.
Benchmark practice is used to reinforce learned skills. Spiral review is implemented for skill retention. The “Scholastic Math Magazine” is one source used for promoting real-life experiences involving mathematics problems while reviewing and enriching skills. Students use their emerging self-confidence to gain a deeper understanding of the mathematical concepts that have been previously introduced. They are able to appreciate and explore more complex concepts by using their developing critical thinking skills.
Overview of Concepts, Skills and Objectives
Number Systems and Operations:
- Evaluate expressions with integral exponents
- Read, write, and identify percents less than 1% and greater than 100%
- Apply percents to: Tax, percent increase/decrease, simple interest, sale price, commission, interest rates, and gratuities
- Estimate a percent of a quantity, given an application
Algebra: Variables and Expressions
- Translate verbal sentences into algebraic inequalities
- Write verbal expressions that match given mathematical expressions
- Polynomial Computations
- Factor algebraic expressions using the GCF; Factoring Trinomials
Algebra: Equations and Inequalities
- Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines
- Solve multi-step inequalities and graph the solution set on a number line
- Solve linear multi-step inequalities
Algebra: Patterns, Relations and Functions
- Understand that numerical information can be represented in multiple ways:
- Find a set of ordered pairs to satisfy a given linear numerical pattern then plot and draw a line
- Determine if a relation is a function
- Interpret multiple representations using equation, table of values and graph
Geometry: Constructions
- Construct the following using a straight edge and compass: Segment congruent to a segment; angle congruent to an angle; perpendicular bisector; and angle bisector
Geometry: Geometric Relationships
- Identify pairs of vertical angles as congruent
- Identify pairs of supplementary and complementary angles
- Calculate the missing angle in a supplementary or complementary pair
- Determine angle pair relationship when given two parallel lines cut by a transversal
- Calculate the missing angle measurements when given two parallel lines cut by a transversal
- Calculate the missing angle measurements when given two intersecting lines and an angle
Geometry: Transformational Geometry
- Describe, identify, and draw transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations.)
- Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation
Geometry: Coordinate Geometry
- Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change
- Determine the y-intercept of a line from a graph
- Graph a line using a table of values, and by the slope-intercept method
- Determine the equation of a line given the slope and the y-intercept
- Solve systems of equations graphically
- Graph the solution set of an inequality on a number line
- Distinguish between linear and nonlinear equations ax²+bx+c; a=1 (only graphically)
- Recognize the characteristics of quadratics in tables, graphs, equations, and situations
Measurement: Units of Measurement
- Solve equations/ proportions to convert to equivalent measurements within metric and customary measurement systems. Note: Also allow Fahrenheit to Celsius and vice versa
Column Content Areas
Number Theory
- Laws of Exponents
- Evaluate Expressions
- Apply Percents
Algebra
- Functions
- Translating Inequalities
- Multi-Step Inequalities
Polynomials
- Addition/Subtraction
- Multiplication/Division
- GCF Factoring
- Trinomial Factoring
Geometry
- Vertical Angles
- Complementary Angles
- Supplementary Angles
- Angles formed by Parallel Lines
- Constructions
Transformational Geometry
- Dilations
- Reflections
- Rotations
- Translations
Coordinate Geometry
- Linear
- Quadratic
Measurement
- U.S./Metric Conversion