### Mathematics Curriculum

A curriculum describes what students should be learning through the grades. It should give clear statements of goals and objectives and should leave to teachers the decisions about how to realize them. Our faculty is high professional, knowledgeable, caring and committed to the individualized development of the whole child, therefore each teacher must decide how best to deliver the academic concepts in his/her curriculum.

A good curriculum should be organized clearly and structured logically within and between subjects and from grade to grade. It must be standards based, student focused, and goal oriented to build the foundation for future learning. It should gradually become more complex and difficult in terms of skills and objectives.

While IAS is structured to assure that all students who attend can, go on to higher education, its primary aim is to develop all aspects of the individual student. We want our students to know and respect themselves and others, and to develop their individual strengths. IAS seeks to stimulate and develop intellectual curiosity, critical and analytical thinking, as well as develop a foundation for information processing at higher levels. It is our goal that our students would be life long learners and constructively question the world around them. We want them gain the ability to analyze critically and objectively. We encourage them to seek to change, to challenge themselves to make a difference

IAS expects its students to work hard and to meet these challenges. It is only through continued maintenance of its standards and of the full partnership of the IAS learning community that our students can fulfill these goals.

#### MATHEMATICS

The elementary program stresses the acquisition of mathematical power — the ability to use, explain, and justify mathematics. Students study the number system and the relationships of numbers and operations in that system. Fluency and accuracy are critical. The program values the arithmetic basics, and in addition stresses understanding of the underlying concepts that prepare students for higher mathematics. The foundational curriculum enables children to make and investigate mathematical conjectures, then develop and evaluate arguments and proofs. Students are encouraged to use various types of reasoning and methods; critical and analytical information processing is essential. The students develop flexible and resourceful problem-solving skills and learn the importance of being able to communicate their strategies and methods to others. There is flexibility in the program, to meet individual needs and abilities. Students can use strategies and tools that are appropriate for them, such as manipulatives to model the problem, or elegant mental strategies. Extensions enable students to further explore the mathematical ideas presented or connect the work to other areas of study. From the earliest grades, students learn to interpret data and graphs, learn the characteristics and relationships of geometric objects, and begin to understand and predict change in the world. Teachers consistently use concrete materials such as counters, pattern blocks, tiles, balance scales, interlocking cubes, attribute logic blocks, and coins, as well as calculators and computer software to clarify concepts. The curriculum reflects the standards established by the National Council of Teachers of Mathematics.#### KINDERGARTEN

Beginning in Kindergarten, the children are introduced to a way of approaching mathematics that emphasizes thinking, strategy use, communication, and collaboration. Daily routines include the attendance, calendar, and survey questions. Students create, compare, extend and shrink, record, and predict patterns. They count and compare various sets of items and play mathematical games that involve counting and accumulating amounts. They use pictures, numbers, and words to represent quantities. Measurement is introduced, as well as sorting and classifying by attributes. Children collect, record, and represent data in a variety of ways and solve problems based on data. They describe and explore relationships between 2-D and 3-D shapes, then combine them to make other shapes or fill an area. Students develop strategies for solving, combining, and separating story problems as they work to master combinations of numbers up to 10.#### GRADE ONE

In First Grade, students build their understanding of numbers and number relationships and use their growing understanding of the number system to solve addition and subtraction problems. Daily routines include counting in different ways, data exploration, estimation, time, money, and the concept of change over time. Students represent and compare larger numbers and work to master number combinations up to 20. They find the total of several single-digit numbers, count, read, write, and sequence numbers up to 100, and continue to develop strategies for solving story problems, including the writing of equations. The total of several 2’s, 4’s, 5’s, and 10’s is also found. Children invent and interpret representations for data they have collected, sorted, and categorized and begin to describe data in quantitative terms. Geometric patterns and the connections between two and three dimensions are explored. A hands-on approach with a variety of tools is used to develop language for describing weight, capacity, and length, and students learn to use units to measure and compare.#### GRADE TWO

Children look for patterns and relationships in the number system in Grade Two, deepening their understanding of how the system works. As they explore landmark numbers such as 5 and 10 and their multiples, they use those numbers to develop facility with addition combinations. They use doubles and the 100 chart as other tools for adding. The relationship between addition and subtraction is explored as students develop their own addition and subtraction problems that reflect a given equation. As they solve these problems, recording and communicating solution strategies clearly is emphasized. Multiplication concepts begin with skip counting by 2’s, 5’s, and 10’s and becoming familiar with the relationship between skip counting and grouping. Children learn coin equivalencies and use coins as a model for counting by 5’s, 10’s, and 25’s. Classification of data becomes more sophisticated with the use of Venn diagrams, which help students think flexibly about characteristics, use the idea of negative information to clarify a category, and build theories about data. Construction and deconstruction of 2-D and 3-D shapes is used to investigate rectangular arrays and how they relate to number, symmetry, and equal fractional parts. Students explore linear measurement by constructing paths on and off of the computer that are compared and measured using units of different sizes. They also study concepts of time and rhythm as they sequence events using timelines. Classroom routines include hour and half-hour intervals recorded in both analog and digital time and equations written to equal the number of days in school.#### GRADES THREE

In Grade Three, students explore number relationships in the context of time, money, and linear measurement. They work with things that come in groups, patterns in the multiplication tables, and rectangular arrays as the model for multiplication. Arrays help to find factor pairs, and the children use their knowledge of factors and multiples to invent and solve word problems in multiplication and division as they explore the relationship between those two operations. Addition and subtraction strategies become more sophisticated with the use of landmark numbers in the hundreds and thousands and positive and negative net change. Children use subtraction to cancel addition as a strategy for solving long equations. Net change is also found on graphs. Halving and doubling as a means to solving multiplication equations is a natural outgrowth of their positive and negative change work. Students develop spatial visualization abilities as they investigate, compare, and measure area of shapes in units and half-units. They explore geometric motions — slides, flips, and turns — to determine congruence. The need for standard measurement is explored, and children learn to use different measurement tools and systems (standard and metric). They interpret and evaluate data they collect by measuring, with an emphasis on developing conjectures and predictions from data. Students explore problems involving paths, lengths of paths, perimeter, and turns. They become familiar with degrees as a measurement term, and understand that there are 360° in a full, 180° in a half, and 90° in a quarter turn. Definitions for various types of triangles are built. The students use fractions and mixed numbers as they solve sharing problems and build wholes from fractional parts. They connect fractions to division and use calculators to see fractions as decimals. Familiarity with common equivalents is built, and students begin to make exchanges, such as 1/6 + 1/3 = 1/2. Students learn about the sides, vertices, and angles of polygons, and then recognize how the components of polygons are put together to form solid shapes with faces, corners, and edges. Their solid geometry work extends to find the volume for boxes. Daily routines include probability discussion, estimation and mental math, creation of equations to equal the date, exploring alternative ways to arrive at the same numerical solution, and problem solving by multiple methods.#### GRADES FOUR

Fourth grade students gain fluency with multiples and factor pairs and learn to identify factors of numbers as large as three digits. They solve problems using their own strategies as well as by breaking problems into manageable components, such as using known multiplication relationships to solve harder problems. The children relate knowledge of factors to division notations and recognize prime numbers as those that have only one set of factors. They gain understanding of how division notation represents a variety of division situations (partitioning and sharing) and realize that what is done with leftovers depends on the situation. Working with factors of 100 and 1000, they explore the multiples of those numbers and get a sense of the magnitude of 10,000. They learn to solve double-digit multiplication problems. Students explore fractions by dividing rectangular areas into halves, fourths, eighths, thirds, sixths, and twelfths. Using both areas and numerical reasoning (an understanding of the meaning of numerator and denominator), they compare and order fractions, including fractions greater than one, and identify equivalent fractions. Using data they have collected, the children learn to partition a group according to a rule and then use fractions to describe and compare the categorizations. They are able to estimate the complex fractions they encounter using familiar ones, i.e., 12/25 is about one half. Money and distance measurement using scale on a map are used to familiarize children with decimal and fraction equivalencies. Coordinate grids are used to investigate 2-D geometry. Students use positive and negative ordered pairs to locate points. They calculate distances along grid lines and explore numeric patterns that represent geometric shapes. In 3-D geometry perspective is explored, and the students begin to visualize how solids project shadows with 2-D shapes, learn to visualize an object from different points of view to form a mental model of the whole object, and start to think about problems related to volume. In statistics, the students move from noticing individual features of the data to describing the overall shape of the distribution and realizing how that yields usable information. They learn to express what is typical, what kind of landmark the median is, and how to use that information to compare data sets. By examining real situations and events that show change, the students also investigate change over time, ways to describe and represent changes, continuous vs. separate changes, and how to get an overall sense of change from a graph. They learn to use curves to communicate information.#### GRADE FIVE

Fifth Grade builds on the foundations laid in earlier grades. The curriculum emphasizes computational competence, use of manipulatives, cooperative learning, and critical thinking. Students extend their knowledge of statistics through the use of more sophisticated graphs and surveys. Algebraic formulas, expressions, and functions are introduced. Fraction work includes review of least common denominator and is expanded to multiplication and division and the conversion of fractions to decimals and percents. Geometric constructions, measurement of angles, perimeter, circumference, area, volume, and the multiplication and division of decimals are also covered.Fifth Grade incorporates individual and group projects such as surveys and the Stock Market Game. These projects provide the opportunity for students to apply learned skills.