Mathematics

Lower School

Kindergarten

An emphasis on the use of concrete experiences helps to develop an understanding of mathematics. Integrating activities across the content areas motivates students to use mathematical thinking as they process information and solve problems. The language of math resonates within the classroom as our students explore basic concepts such as quantity, number, size, and shape throughout the day.

Primary

Students encounter a wide variety of activities that improve their development of mathematical sense and content understanding. The main focus is the integration of math into the child’s everyday life. A large emphasis is placed upon numeration and counting: reading, writing, and verbal counting. Patterns and place value are discovered through hands-on games and activities. Students learn basic addition and subtraction facts through twenty. Measurement includes length, temperature, time, and capacity. Problem solving is threaded throughout each lesson. For example, students shop in the class store in order to apply money skills, add costs for items, and determine appropriate change.

Intermediate

Instruction encourages students to become life-long mathematical thinkers. A focus is placed on numeration and computation with an emphasis on geometry, data, and algebraic thinking. Students establish connections to past experiences, problem solve, and communicate explanations of solutions. Fast recall of multiplication and division facts is a focus so that multi-digit problem solving can occur more easily. Students also learn about fractions and decimals. Tools of measurement such as number lines, money, and clocks are used to draw comparisons and make connections between fractions and decimals.

Fifth Grade

The math curriculum is designed to give students the opportunity to use the solid math foundation from their kindergarten through grade Intermediate experience, moving from the concrete concepts they have already learned to the abstract concepts for which they must be prepared in Middle School. Students begin to apply algebraic logic to math problems using traditional algorithms, which are reinforced using hands-on activities. There is a focus on integrating the specific vocabulary inherent in math, such as equation, expression, equivalent, product, etc., with the higher-level critical thinking and language skills needed to solve word problems.

 

Middle School

DSCN3715The mathematics program is intended to imbue Trinity students with much more than proficiency in numbers. Through study and application, students are challenged to develop into critical and logical thinkers who can use problem solving skills to develop invaluable life strategies. Additionally, students benefit from the development of ordered, rational, and structured algorithms for framing their ideas and are encouraged to extend this method to other disciplines. This product of the mathematics curriculum finds its greatest utility in the sciences, but also applies to the presentation of coherent, persuasive ideas across the entire Trinity curriculum.

The mathematics curriculum is designed to function as an integrated effort, beginning with the Lower School grades and continuing through the Middle School grades. Students’ experiences are connected by a threaded curriculum. We believe successful instruction in mathematics is based upon individualized, differentiated instruction appropriate to a student’s demonstrated ability and potential. An assessment of the student’s skill level determines course placement beginning in grade six so that instruction is differentiated, and from that point on, the mathematics curriculum consists of separate, but connected, paths for students to follow. Trinity Middle School is compliant with Common Core Math Standards and rigorous private school math curricula. This allows for depth rather than breadth in each school year and compliments the mission and goals of Trinity.

6th Grade Math:

Students focus on improving and extending math skills in the areas of decimal and fractional math, ratios and rates, expressions and equations. In the areas of decimal and fractional math, students reinforce knowledge of multiplication and division with these types of numbers, as well as the relationships between them. In the areas of ratios and rates, students use real world examples to explore how these relationships are used in every day life. In the areas of expressions and equations, evaluating and writing expressions and algebraic solutions to linear equations are explored. Each of these main areas are connected to prior knowledge in geometry and measurement, number and operations, and data analysis. Problem solving strategies related to each area of math are emphasized. Big Ideas Math – Green : A Common Core Curriculum (2012) is used.

7th Grade Math:

In this course students expand upon prior skills and explore the areas of proportion and similarity, surface area and volume, rational number operations and linear equations.

In the area of proportions and similarity, proportional relationships are analyzed and used to solve real world problems. In the section on geometry, construction of and the relationships between various geometric figures is explored, and surface area and volume are calculated. In the area of rational number operations and linear equations, properties of operations and equivalent expressions are utilized to understand the foundation of algebraic solutions to linear equations. Fractions, decimals, and percents are utilized throughout to apply and extend prior understanding. Each of these main areas are connected to prior knowledge in geometry and measurement, number and operations, data analysis, and probability. Problem solving strategies related to each area of math are emphasized.

Big Ideas Math – Red : A Common Core Curriculum (2012) is used.

7th Grade Accelerated Math:

This course is designed as a bridge course for the accelerated student between Common Core 6th and Common Core 8th grade math. It replaces the Common Core 8th class entirely. The successful student will be prepared to take Common Core Algebra I in 8th grade upon completion of this course.

This course includes the topics from Common Core 7th with several additional topics. Emphasis is placed on the additional topics, which include: linear functions, equations and their graphs, radicals, and exponents. Each content area is connected to prior knowledge in geometry and measurement, number and operations, data analysis, and probability. Problem solving strategies related to each area of math are emphasized.

Big Ideas Math – Red Accelerated: A Common Core Curriculum (2013) is used.

8th Grade Math:

This course is designed to explore the relationships between linear functions and linear equations, analysis of figures by distance and angle, and the study of data sets and their representations. In the area of linear functions, students explore the relationship between different representations of linear equations including algebraic, graphic, and numerical. Systems of linear equations are also explored in depth. In the area of analysis of figures, similar triangles, angles formed by transversals, and the Pythagorean theorem are explored. In the data analysis section, graphical representation of the data as well as statistical significance is learned as well as how to construct a best fit line for a set of collected data.   All of these main areas are connected to prior knowledge in geometry and measurement, number and operations, and Algebra. Problem solving strategies related to each area of math are emphasized.

Big Ideas Math – Blue : A Common Core Curriculum (2012)

Common Core Algebra I:

The common core Algebra I course is designed to fully explore the algebraic and graphical representation of linear and nonlinear functions. Students build on prior knowledge of solving linear equations and inequalities, and extend it to compound inequalities with absolute value. Nonlinear functions including exponential growth and decay, radicals, and quadratics are fully explored. Multiple methods to describe and solve quadratic equations are used, including factoring and the quadratic equation. Rational functions and equations are simplified, solved, and graphed. Data analysis and probability are also explored on a more complex level. Each of these main areas are connected to prior knowledge in geometry and measurement, number and operations, data analysis, and probability. Problem solving strategies related to each area of math are emphasized. Students can earn high school credit upon successful completion of this course.

Big Ideas Math – Algebra 1 : A Common Core Curriculum (2013) is the text used.

Geometry:

In Geometry, students fully explore angle and line relationships, logic, polygon relationships, circles, and three-dimensional figures. These are explored both on the coordinate plane as well as with graphical representations. Construction of geometrical figures with a compass is used to draw graphical figures. In the area of angle and line relationships, students learn rigorous methods of measurement including the distance and midpoint formulas. They also learn the relationship between angles when parallel lines and transversals are present. Parallel and perpendicular lines are investigated, including the perpendicular distance from a point to a line.   Transformations on the coordinate plane are also discussed. Reasoning and logic are taught throughout the course, leading up to the creation of multiple types of proofs. Proofs are used to formally recognize and understand theorems as well as to find unknowns in real world situations. Polygon relationships are taught first from the perspective of congruence, and then followed up with the idea of similarity. Triangles and quadrilaterals are the shapes most commonly used to explore these relationships. Formal proofs of triangle relationships are developed and explored. During the unit on circles, students explore the meaning of Pi as well as calculate various attributes of a circle. The concepts of inscribed angles, central angles, tangents and secants are also fully explored. In the final unit on three-dimensional shapes, the concepts of surface area and volume are explored for both regular and composite figures. Glencoe Mathematics, Geometry (2010) is the text used.