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:
- Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers)
- Write numbers in scientific notation and translate back into standard form
- Find the common factors and greatest common factor of two or more numbers
- Determine multiples and least common multiple of two or more numbers
- Determine the prime factorization of a given number and write in exponential form
- Simplify expressions using order of operations - Note: Expressions may include absolute value and/or integral exponents greater than 0.
- Add, subtract, multiply and divide integers
- Recognize and state the value of the square root of a perfect square (up to 225)
- Determine the square root of non-perfect squares using a calculator
- Identify the two consecutive whole numbers between which the square root of a non-perfect square whole number less than 225 lies
Algebra:
- Translate two-step verbal expressions into algebraic expressions
- Add and subtract monomials with exponents of one
- Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation
- Solve one-step inequalities (positive coefficients only)
Geometry:
- Calculate the radius or diameter, given the circumference or area of a circle
- Calculate the volume of prisms and cylinders, using a given formula and a calculator
- Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones and pyramids)
- Determine the surface area of prisms and cylinders, using a calculator and a variety of methods
- Find a missing angle when given angles of a quadrilateral
- Identify the right angle, hypotenuse, and legs of a right triangle
- Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle
- Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator
- Graph the solution set of an inequality (positive coefficients only) on a number line
Measurement:
- Calculate distance using a map scale
- Convert capacities and volumes within a given system
- Calculate unit price using proportions
- Draw central angles in a given circle using a protractor and display data (circle graphs)
Statistics and Probability:
- Convert raw data into double bar graphs and double line graphs
- Identify and explain misleading statistics and graphs
Column Content Areas
Operations with Integers
- Addition/Subtraction
- Multiplication/Division
Number Theory
- Prime Factorization
- Greatest Common Factor
- Least Common Multiple
- Order of Operations
Numerical Rational/Irrational Numbers
- Radicals
Exponents
- Rules of Exponents
- Scientific Notation
Geometry
- Closed Plane Figures
- Triangles
- Pythagorean Theorem
- Solids
- Classification
- Volume
- Surface Area
- Coordinate Plane
Algebra
- Equations
- One Step/Multiple Step
- Inequalities
- Solving/Graphing
- Related Word Problems
Measurement
- U.S./Metric Conversion
Statistics
- Data/Graphing/Central Tendency