Students work with contexts and models that represent the place value structure of the base-10 number system to build and visualize how two-digit numbers are composed. Students’ work with place value becomes the basis for developing strategies for adding and subtracting two-digit numbers. The relationship between addition and subtraction is used to solve subtraction problems and to develop fluency with the subtraction expressions related to the addition combinations. Students develop an understanding of what fractions are and how they can be used to name quantities. They learn how fractions are expressed in words and represented using numbers, and learn the notation for mixed numbers through dividing sets. Students classify data with many different values by grouping the data into categories and use a variety of representations for the data. By comparing different representations, they learn how different representations can make different aspects of the data set more visible.

Students continue to develop their understanding of length and how it is measured. As students begin to measure objects using standard tools of measurement such as rulers and yardsticks, the emphasis is on making sense of length as an attribute of objects. Students practice naming, notating and telling time on digital and analog clocks. They work with timelines, associating events with a particular time and determine intervals of time with an emphasis on starting and ending times on the hour or half-hour. Students study quadrilaterals and polygons and consider which properties are important when describing these shapes. They combine and decompose both 2D and 3D shapes and explore the relationships between shapes.