# Mathematics

## Mathematics in the PYP

Where appropriate, mathematics is integrated into the transdisciplinary units of inquiry.  This is particularly true of the data handling, measurement, shape and space, and pattern and function strands. Emphasis is placed on the explicit teaching of numeracy in relation to both number knowledge and strategy. A number framework is used to track student progress in numeracy and inform teaching practice. The framework enables teachers to know their students accurately, and to develop numeracy through detailed assessment and explicit identification of key developmental milestones. It stresses differentiated learning and the development of both knowledge and strategy across addition and subtraction, multiplication and division, and ratio and proportion domains. Students are encouraged to engage in mathematical discourse through the sharing of their solutions, proving the validity of their answers and engaging in discussions with teachers and peers, which allow them to construct new learning.

Typically students work in small groups during math sessions on experiences, which are targeted at their stage of knowledge or strategy development.

The aims of PYP mathematics are to encourage and enable students to:

• collect, organize and display data for the purposes of valid interpretation and communication
• use the mode, median, mean and range to summarize a set of data
• understand that probability can be expressed on a scale (0–1 or 0%–100%) and that the probability of an event can be predicted theoretically
• understand that a range of procedures exists to measure different attributes of objects and events (e.g., the use of formulas for finding area, perimeter and volume)
• decide on the level of accuracy required for measuring and using decimal and fraction notation when precise measurements are necessary
• demonstrate an understanding of angles as a measure of rotation
• understand the properties of regular and irregular polyhedra, and of 2D shapes, and understand that 2D representations of 3D objects can be used to visualize and solve problems in the real world (e.g., drawing and modeling)
• develop an understanding of the use of scale (ratio) to enlarge and reduce shapes, including the application of the language and notation of bearing to describe direction and position
• understand that patterns can be represented, analyzed and generalized using algebraic expressions, equations or functions
• use words, tables, graphs and, where possible, symbolic rules to analyze and represent patterns
• develop an understanding of exponential notation as a way to express repeated products, and of the inverse relationship that exists between exponents and roots
• continue to use their understanding of pattern and function to represent and make sense of real-life situations, and to solve problems involving the four operations
• understand that the base 10 place value system extends infinitely in two directions
• model, compare, read, write and order numbers to millions or beyond, as well as model integers
• develop an understanding of ratios
• understand that fractions, decimals and percentages are ways of representing whole-part relationships, and work towards modeling, comparing, reading, writing, ordering and converting fractions, decimals and percentages
• use mental and written strategies to solve problems involving whole numbers, fractions and decimals in real-life situations, using a range of strategies to evaluate reasonableness of answers

## Mathematics in the MYP

The MYP mathematics programme is tailored to the needs of students, seeking to intrigue and motivate them to learn its principles by providing authentic examples of how mathematics is useful and relevant to their lives. Students in the MYP are encouraged to use ICT tools to represent information, explore and model situations, and find solutions to various problems. These are skills that are useful in a wide range of arenas. MYP mathematics aims to equip all students with the knowledge, understanding and intellectual capabilities to address further courses in mathematics, as well as prepare those students who will use mathematics in their studies, workplaces and lives in general. The emphasis on understanding increases as students work towards developing a strong mathematical knowledge base that will allow them to study a wide range of topics. Through this process they also work on communicating their ideas in ways that allow others to understand their thinking. Students in Year 9 are placed after careful assessment into either MYP standard or extended mathematics.

The aims of MYP mathematics are to encourage and enable students to:

• enjoy mathematics, develop curiosity, and begin to appreciate its elegance and power
• develop an understanding of the principles and nature of mathematics
• communicate clearly and confidently in a variety of contexts
• develop logical, critical and creative thinking
• develop confidence, perseverance, and independence in mathematical thinking and problem solving
• develop powers of generalization and abstraction
• apply and transfer skills to a wide range of real-life situations, other areas of knowledge and future developments
• appreciate how developments in technology and mathematics have influenced each other
• appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics
• appreciate the international dimension in mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives
• appreciate the contribution of mathematics to other areas of knowledge
• develop the knowledge, skills and attitudes necessary to pursue further studies in mathematics
• develop the ability to reflect critically upon their own work and the work of others

## Mathematics in the DP

The knowledge, skills and attitudes that students develop in mathematics courses provide a meaningful foundation for further study and help to prepare students for careers in fields such a climate research, actuary and insurance work, public-policy development, engineering, financial analysis and economic development, research and analysis, software development, biostatistics and epidemiology, law, and medicine.

The diploma mathematics programme offers three courses: mathematical studies standard level (SL), mathematics SL and mathematics higher level (HL). MYP students enrolled in extended mathematics generally elect to take HL mathematics courses in the Diploma Programme.