The third-grade standards place emphasis on developing an understanding of, and solving problems that involve multiplication and division through 10 × 10 (fluency and automatic recall is not expected until the end of fourth grade). Students will apply knowledge of place value and the properties of addition and multiplication as strategies for solving problems. Concrete models and pictorial representations will be used to introduce addition and subtraction with fractions and the concept of probability as the measurement of chance. Students will use standard units (U.S. Customary and metric) to measure temperature, length, and liquid volume. Properties of shapes, points, line segments, rays, angles, vertices, and lines will be explored and students will identify polygons with 10 or fewer sides, combine and subdivide polygons, and name the resulting polygon(s). Students will continue to develop more sophisticated ways to communicate and represent their mathematical thinking. Problem solving, reasoning, exploration, and connections are essential components of instruction so that students develop a deep understanding of concepts.