In fifth grade, students investigate four major areas: the properties of whole numbers, two-dimensional geometry, fractions, decimals and percents, and an introduction to concepts in algebra. They study place value, number theory, including factors, multiples, primes, composites, and prime factorization. The unit on fractions, decimals, and percents focuses on the concept of equivalence - students move among fractions, decimals, and percents, and compare and order rational numbers. In the study of geometry, they learn about area and perimeter including calculating both, and are introduced to the concepts of surface area and volume. By solving open-ended problems about growth and change, students learn about variables and representations of relationships, including tables, graphs, words, and symbols. Reasoning and proof are established as classroom norms throughout the year. Students develop mathematical confidence and communication skills through the use of multiple models - visual, algebraic, numeric and physical - as well as group problem solving, discussion and writing exercises.