# Middle School Mathematics Department

## Phillipsburg Middle School Mathematics Department

**6th Grade**

**6th Grade Big Ideas and Big Ideas Advanced 1**

This course is designed to review the basic principles of mathematics while gradually incorporating the components needed to understand the elements of pre-algebra. Learning targets and activities in the course include: Using estimation to find sums, differences, products, and quotients and rounding to an indicated place value or use compatible numbers to estimate an answer to a problem; Learning to solve equations and determining if a specific value is a solution of an equation; Learning about decimals and decimal applications such as using decimals to express large numbers in scientific notation; Studying fractions while converting between decimals and fractions and writing equivalent fractions; Using place value concepts to convert between decimals and fractions; Multiplying and dividing fractions, as well as solving equations containing fractions; Multiplying fractions by whole numbers; Interpreting and constructing different types of graphs used to display data. Some of the graphs the student will be creating are: bar graphs, double-bar graphs, line graphs, double-line graphs, histograms, and stem-and-leaf plots; Learning how percents, decimals, and fractions are related; Modeling percents by shading in portions of a 10-by-10-square grid; Learning about the properties of various triangles and other polygons; Learning to find the perimeter of different figures; Learning about three-dimensional figures and studying them from different views. When presented with three different views of an object (front, side, and top) the student will be able to visualize and draw the three-dimensional object; Performing the basic operations of addition, subtraction, multiplication, and division with integers; Relating the concepts of probability to application problems. Sometimes the student may need to make an organized list to find all the possible outcomes of an event; Extending his or her knowledge of equations and how to solve equations.

**7th Grade**

**7th Grade Big Ideas**

This course is designed to further review the basics of arithmetic concepts, while continuing to build a strong foundation in the principles of pre-algebra. Learning targets and activities in the course include: Working with the basic building blocks of algebra, beginning with recognizing the difference between a constant and a variable; Evaluating an algebraic expression by substituting a given value for a variable and following the order of operations; Learning divisibility rules; Finding the prime factorization of a composite number is one way to find its prime factors; Finding the prime factorization of a number by using a factor tree and a step diagram; Applying the four basic operations to fractions, starting with addition and subtraction; Finding a common denominator by either multiplying the denominators or finding the least common multiple (LCM) of the denominators; Learning about customary and metric measures and unit conversion factors; Learning about linear equations and linear functions; Learning to find percent of change; Displaying and analyzing data that changes over a period of time in a line graph or a doubleline graph; Learning about circles and polygons; Finding the square of a number, as well as the square root of a number; Finding the surface area of three-dimensional figures, such as prisms, cylinders, pyramids, and cones; Applying the concepts of probability; Learning about inequalities and how to solve them.

**7th Grade Pre-Algebra Big Ideas Advanced 2 **

This course is offered to advanced seventh grade math students as identified by student performance and teacher recommendation. Pre-algebra will help prepare students for the demands of Algebra 1 in eighth grade. The course combines a review of arithmetic concepts with an introduction to basic algebra. Topics include: variables, solving equations, signed numbers, rational numbers, ratio, proportion, percent, geometry, and the coordinate plane.

**8th Grade**

**8th Grade Big Ideas**

This course is designed to review arithmetic concepts while introducing basic algebraic strategies in order to prepare students for Algebra 1. Learning targets and activities in the course include: Solving equations and inequalities by learning the four equality properties: addition, subtraction, multiplication, and division. These properties will be used to isolate the variable in order to solve an equation; Solving equations that involve rational numbers; Learning what a function is and how to graph a function on a coordinate plane; Learning relations, or sets of ordered pairs, and how to tell if a relation is a function; Learning about squares and square roots, and learning how to recognize a perfect square while using this knowledge to evaluate expressions and estimate the square roots of numbers that are not perfect squares; Studying similar figures, figures that are the same shape, but not necessarily the same size; Solving different application problems that involve percents and begin to apply geometric properties to solve problems. One such property addresses congruent figures; Writing congruence statements for pairs of polygons by writing the second polygon in order of correspondence, or matching up the corresponding vertices between the two polygons; Drawing and identifying three-dimensional figures; Interpreting and constructing many different types of graphs used to display data; bar graphs, frequency tables, and histograms; Learning how to apply the concepts of probability; Learning how to use the Fundamental Counting Principle to find the total number of ways that two or more separate events can happen; Using direct variation to relate two variable quantities, graphing inequalities in two variables, and solving systems of equations by graphing; Learning about various types of functions and how to differentiate between the types of functions and how to graph each type of function; Adding and subtracting polynomials, and multiplying polynomials by binomials. In learning how to multiply two binomials, the student will learn the FOIL method.

**8th Grade College Algebra 1 **

This course is offered to advanced eighth grade mathematics students as identified by student performance and teacher recommendation. This course includes such topics as: variables, solving equations, signed numbers, polynomials, factoring, Algebraic fractions, and functions, graphing systems of linear equations, inequalities, and radicals. The emphasis is not only on algebra skills, but on developing the ability to solve problems within mathematics and in other subject areas, to reason and think critically, and to use mathematics in the world beyond the classroom through the use of textbooks, calculators, and computers.

**8th Grade Honors Algebra 1**

This course will be offered to students who qualify based upon several criteria including the test average in Pre-Algebra, the score on a district placement test, the score on constructed response tasks and a teacher recommendation. This accelerated program is designed to challenge students, and the curriculum will extend beyond the College Algebra 1 course. The course is taught at Phillipsburg High School by High School mathematics teachers.