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1. Numbers and Operations |
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1. Encourage young children's exploration and understanding of relationships among numbers. |
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2. Encourage young children's understanding of addition and subtraction and how they relate to each other. |
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3. Encourage young children's fluent computation. |
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4. Encourage an understanding of the structure of numbers and relationships among numbers. |
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5. Encourage an understanding of the meanings of multiplication and division and how they relate to each other. |
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6. Encourage students to compute fluently and make reasonable estimates. |
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7. Encourage young children's systematic sorting and classification as they work with a variety of patterns, geometric shapes, and data. |
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8. Encourage young children's systematic exploration of the general principles and properties of operations such as addition and subtraction. |
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9. Encourage the expression and generalization of mathematics relationships. |
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10. Encourage further understanding of multiplicative structures through application and analysis of the distributivity of multiplication over addition. |
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11. Encourage young children's exploration of characteristics and properties of two- and three-dimensional shapes. |
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12. Encourage young children's application of similarity transformations to analyze geometric situations. |
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13. Encourage young children's use of visualization and spatial reasoning in their exploration of geometric shapes. |
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14. Encourage students' exploration and mathematical analysis of the properties of two-dimensional geometric shapes. |
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15. Encourage students' use of geometric transformations to analyze mathematical situations. |
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16. Encourage students' use of visualization, spatial reasoning, and geometric modeling to solve problems. |
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17. Encourage young children's exploration and understanding of measurement concepts and relationships. |
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18. Encourage young children to accurately apply appropriate tools and techniques to linear measurement. |
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19. Encourage students' exploration and understanding of measurement concepts and relationships. |
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20. Encourage students' appropriate application of conventional measuring tools in varied situations. |
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5. Data Analysis and Probability |
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21. Encourage young children's collection, display, and organization of objects and data. |
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22. Encourage the idea in young children that data, graphs, and charts give information. |
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23. Encourage young children's informal explorations of probability. |
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24. Encourage students to explore questions they find personally relevant and that can be addressed by data collection and analysis. |
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25. Encourage students to become more precise in their mathematical descriptions of data. |
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26. Encourage students to explore and evaluate issues of representativeness and inference. |
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27. Encourage students' exploration and quantification of simple probabilistic events. |
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28. Encourage young children to ask mathematical questions and to identify essential mathematical information. |
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29. Assess young children's abilities to solve problems through examination of student work and conversations. |
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30. Encourage students' development and application of problem-solving strategies. |
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31. Select rich, appropriate, and challenging problems and orchestrate their use. |
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32. Encourage young children to explain their thinking by stating their reasons. |
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33. Ask questions that encourage young children to make conjectures and to justify their thinking. |
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34. Encourage children to reason about the relationships that apply to the numbers, operations, or shapes that they are studying. |
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35. Focus on general mathematical structures and relationships. |
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36. Encourage young children's verbal and written communication of mathematics concepts and ideas. |
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37. Expect young children to explain their thinking and give them opportunities to talk with and listen to their peers. |
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38. Encourage students to share their thinking, to ask questions, and to justify their ideas. |
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39. Provide models for student dialogue about mathematics. |
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40. Encourage young children to make connections among mathematical ideas, vocabulary, and representations. |
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41. Make links between routine school activities and mathematics. |
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42. Encourage students to see that mathematics is a web of closely connected ideas. |
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43. Select tasks that help students explore and develop increasingly sophisticated mathematical ideas. |
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44. Encourage young children to represent their mathematical ideas and procedures in varied ways. |
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45. Create a learning environment that supports and encourages children's use of multiple representations. |
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46. Encourage students to use representations to support, clarify, and extend their mathematical ideas. |
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47. Choose tasks that embody rich and varied representational structures. |
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