(NB: Contingent on physical or other limitations.)

Mathematics curriculum at any grade level or for any topic identifies what students should know and be able to do at a particular grade level or course. However, intricately connected to and supporting all mathematics content and curriculum are mathematical processes that are common to all strands and specific expectations. Students at all levels need experiences with and growing proficiency in these practices. Educators and parents keep these in mind and integrate them constantly into mathematics instruction. These processes describe ways that students need to engage with mathematical subject matter increasingly as they progress through the grades.

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Source: National Council of Teachers of Mathematics process standards, National Research Council’s report on helping children learn mathematics, Adding It Up.

The Next Generation Science and Engineering Standards (developed in 2013 in a joint collaboration among the American Association for the Advancement of Science, the National Research Council, the National Science Teachers Association, and Achieve) describe scientific practices that scientists use as they investigate the natural world and engineering practices that engineers use as they design and build models and systems. In addition, they present seven crosscutting concepts that apply across all the topics and fields of science. The teaching of science topics and the corresponding standards at all grade levels K-12 are intricately interwoven with these practices and crosscutting concepts. Students need consistent experience and connection with these two dimensions of science education (practices and cross-cutting concepts) as they work with the third dimension (core science content topics).

Science and Engineering Practices

1. Asking questions (science) and defining problems (engineering)

2. Developing and using models

3. Designing and carrying out investigations

4. Organizing and interpreting data

5. Using mathematics and computational thinking

6. Constructing explanations (science) and designing solutions (engineering)

7. Engaging in argument from evidence

8. Obtaining, evaluating, and communication information

Crosscutting Concepts

1. Patterns

2. Cause and effect

3. Scale, proportion, and quantity

4. Systems and system models

5. Energy and matter: Flows, cycles, and conservation

6. Structure and function

7. Stability and change

1. These ten themes of social studies serve as a background framework for the teaching of the social sciences at all grade levels. They weave through all content and are interrelated with one another. Students need exposure to and development of these themes throughout the grades.

Source: National Council for the Social Studies

Ten Themes of Social Studies

1. Culture

2. Time, continuity, and change

3. People, places, and environments

4. Individual development and identity

5. Individuals, groups, and institutions

6. Power, authority, and governance

7. Production, distribution, and consumption

8. Science, technology, and society

9. Global connections

10. Civic ideals and practices

2. In addition, there are social studies practices and habits and literacy skills that should be fostered and integrated with all social studies content. Students at all levels need grade-level appropriate experiences that develop and polish these practices.

1. Gathering, interpreting, and using evidence from various sources

2. Applying critical thinking skills to organize, use, and evaluate information

3. Problem solving and decision making processes

4. Chronological reasoning and understanding of causation

5. Comparing and understanding events and relationships in context

6. Communicating knowledge, research conclusions, and ideas in written, oral, and visual forms

7. Geographical reasoning and use of geographical tools (including maps and timelines)

8. Describing and explaining economics and economic systems

9. Civic participation and understanding