At the heart of Prospect Sierra's K-4 Math Program is the recognition that the foundation of mathematics is rooted in the study of patterns and relationships. Throughout the grades, emphasis is placed on conceptual understanding providing students with the basis for seeing the connections among skills, problem solving, and mathematical ideas. Students develop a strong grasp of math facts and operations. Manipulative materials and group activities play an important role in the classroom.
Kindergarten
Kindergarten students experience math through hands-on exploration, inquiry, and games. They learn about patterns, counting, sorting, measuring, collecting and representing data, adding, subtracting, geometry, and time. Mathematical thinking is woven throughout the day in individual, small group, and large group activities to support different learning styles. Math activities are often integrated into daily morning meetings. In the course of the week, Math Workshops introduce students to new math concepts and games that are reinforced at regularly scheduled work periods and during choice time. Students are encouraged to come up with their own methods of solving problems, and to discuss their ideas with their peers. Through daily math lessons and routines, they develop number sense and become increasingly aware of math in the world around them.
-updated fall 2006
First Grade
Students in the first grade continue to build their understanding of number sense. They are introduced to basic computation, patterns and functions, place value, time, money, measurement, geometry, fractions, data collection, analysis, and logic. Through concrete explorations, using manipulatives and number games, students begin to develop their abstract mathematical thinking skills. They are encouraged to explore multiple solutions and explain their mathematical thinking in a variety of ways. The curriculum builds in a spiral fashion, deepening students' understanding of a concept each time it is reintroduced. Students work as a whole group, with partners, and independently during our daily Math Workshop. The goals of the workshops are that students will put their thinking into words, pictures, and numbers; begin to identify the strategies they use to solve problems; communicate what they are learning; and make everyday life connections with mathematics.
Second Grade
Second graders extend their understanding of place value and number sense by further exploring number patterns and relationships between numbers in the base-10 system. They commit addition and subtraction facts to memory and learn to regroup two- and three-digit numbers. Students investigate the connection between multiplication and addition, and are introduced to the concept of division in the context of problem solving. They expand their knowledge of money by adding and subtracting amounts and delve further into fractions, i.e. finding equivalent fractions. Students collect, organize, and interpret data by using tables, charts, and graphs. They also study two-and three-dimensional shapes and use tools to measure in both centimeters and inches. Manipulatives continue to play an active role in the development of computational and mental math skills. Logic and problem solving skills are developed throughout each unit.
-updated fall 2006
Third Grade
Students continue to develop their understanding of number and place value. Addition and subtraction facts are solidified as they move toward regrouping of multi (four or more) –digit numbers. Students continue to study money (including decimals), time, measurement (volume, weight, and mass), and fractions (addition and subtraction). There is a strong emphasis on problem solving – particularly in cooperative groups. Geometry and multiplication (including multi-digit numbers with a single digit multiplier) are explored in depth. Students are more formally introduced to division and probability. Emphasis is placed on mathematical communication, especially in writing, and on applying multiple strategies in problem solving.
Fourth Grade
In fourth grade mathematics, students continue developing their number sense, as well as delving into areas of geometry, problem solving, measurement, algebra, logic, pattern recognition, statistics, and probability. Students should be facile with the addition and subtraction number facts, and be able to multiply and divide single digits with ease. Fourth grade math concentrates on skills of estimating, rounding, reading and writing large numbers, recognizing and finding equivalent fractions, and further develop an understanding of decimals. Based on the Everyday Mathematics Program (University of Chicago), the math program emphasizes:
A problem solving approach based on everyday situations that develops critical thinking
Mathematical communication including understanding and evaluating the mathematical thinking and strategies of others
Frequent practice of basic skills
A spiral approach to teaching skills and concepts
A variety of activities to reach all types of learners
The comprehensive Middle School math program strikes a balance between concrete skill-building and systematic problem-solving. Continuing the spiral teaching method established in the elementary school with the Everyday Math program, students extend their search for patterns and connections between ideas and apply these ideas to real-world situations. Primary emphasis is placed on number sense and math reasoning. Students go beyond mastery of basic skills to achieve a deeper level of understanding. This rigorous math program culminates in the eighth grade Algebra 1 course, where students form a solid foundation for more advanced study in the future.
Fifth Grade
The Everyday Mathematics program continues in fifth grade and builds on the solid foundation provided in the elementary grades. Everyday Math students are expected to master multiplication and addition of fractions and decimals and the division of whole numbers. Mastery is developed through the repetition of concepts introduced in earlier grades and spiraled through this thoughtfully articulated curriculum. Understanding is fostered through cooperative hands-on activities and games. Students continue to make the connections between fractions, decimals, and percents. Other topics covered during the year include logic, statistics and probability, geometry, mental math and estimation, and consumer applications (discounts and tips). A monthly rendezvous with Everyday Math’s “American Tour” helps to integrate humanities and math.
Sixth Grade
In sixth grade students complete the Everyday Mathematics curriculum spiral and transition to the 7th grade pre-algebra course. Students are expected to become proactive in their own mathematical learning through exploration, cooperative activities, direct instruction, and concept reinforcement through games. Success depends on a home-school partnership and includes regular family communication and high expectations. The curriculum tackles the full mathematics spectrum, extending beyond basic arithmetic, with attention to mathematical reasoning and effective communication of thinking. Conceptual understanding is emphasized and basic skills are reinforced in order for each student to attain confident proficiency. Key mathematical themes include: algorithmic and procedural thinking, number sense and estimation skills, mental arithmetic, and problem solving.
Units of study are tied to the National Council of Teachers of Mathematics standards and include a selected balance among these topics:
Data collection, graphical display, and interpretation
Arithmetic operations with whole numbers and decimals
Variables, including expressions, introductory equations, and formulas
Rational number uses and operations
Geometry topics include: congruence, constructions and parallel lines, tessellations, symmetry, and topology
Number systems and introductory algebra concepts
Probability and discrete mathematics
Rates and Ratios
Seventh Grade – Pre–Algebra
Seventh grade math is a pre-algebra course that promotes the cognitive development from concrete to abstract thinking. The process of the study is as important as the content. Students engage in group work that requires individual accountability and cooperative learning. Students learn which tools will serve them best, whether it be mental math, pencil, calculator and/or spreadsheet. There is an emphasis on mastering the arithmetic of fractions and integers, and on showing work.
Curriculum themes and general topics include.
linear algebra
geometry
number theory
table-graph-equation
Pythagorean theorem
number patterns
single-variable
circles and π
base mathematics
use of formula
2D and 3D studies
irrational numbers
coordinate graphing
probability
Linear algebra includes an introduction to symbolic language interpretation. Geometry topics involve precision work with protractor, straightedge and compass. Number theory units develop number sense as well as specific problem-solving techniques. All topics offer opportunity for study beyond mastery of the basics.
Eighth Grade – Algebra 1
Algebra I is a stimulating and challenging course that uses traditional lecture, investigation, cooperative learning, graphing calculator technology, and discovery to develop abstract reasoning and problem-solving skills. The course provides students with the tools necessary to make the important algebraic connection between patterns, graphs, and equations, and enables students to justify their ideas while making sense of complex situations. Algebra I at Prospect Sierra accords with The Principles and Standards for School Mathematics set forth by the National Council of Teachers of Mathematics (NCTM) and the structure of the course prepares students for a variety of math programs and future challenges.
