1. Number, operations and quantitative reasoning 6.1Acompare and order non- negative rational numbers

2. Number, operations and quantitative reasoning 6.1Bgenerate equivalent forms of rational numbers including whole numbers, fractions, and decimals

3. Number, operations and quantitative reasoning 6.1Cuse integers to represent real- life situations

4. Number, operations and quantitative reasoning 6.1Dwrite prime factorizations using exponents

5. Number, operations and quantitative reasoning 6.1Eidentify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers

6. Number, operations and quantitative reasoning 6.1Fidentify multiplies of a positive integer and common multiples and the least common multiple of a set of positive integers

7. Number, operations and quantitative reasoning 6.2Amodel addition and subtraction situations involving fractions with objects, pictures, words and numbers

8. Number, operations and quantitative reasoning 6.2Buse addition and subtraction to solve problems involving fractions and decimals

9. Number, operations and quantitative reasoning 6.2Cuse multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates

10. Number, operations and quantitative reasoning 6.2Destimate and round to approximate reasonable results and to solve problems where exact answers are not required

11. Number, operations and quantitative reasoning 6.2Euse order of operations to simplify whole number expressions (without exponents) in problem solving situations

12. Patterns, relationships, and algebraic thinking 6.3Ause ratios to describe proportional situations

13. Patterns, relationships, and algebraic thinking 6.3Brepresent ratios and percents with concrete models, fractions and decimals

14. Patterns, relationships, and algebraic thinking 6.3Cuse ratios to make predictions in proportional situations

15. Patterns, relationships, and algebraic thinking 6.4Ause tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area

16. Patterns, relationships, and algebraic thinking 6.4Buse tables of data to generate formulas representing relationships involving perimeter, area, volume of a rectangular prism, etc.

17. Patterns, relationships, and algebraic thinking 6.5formulate equations from problem situations described by linear relationships

18. Geometry and spatial reasoning 6.6Ause angle measurements to classify angles as acute, obtuse or right

19. Geometry and spatial reasoning 6.6Bidentify relationships involving angles in triangles and quadrilaterals

20. Geometry and spatial reasoning 6.6Cdescribe the relationship between radius, diameter, and circumference of a circle

21. Geometry and spatial reasoning 6.7locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers

22. Measurement 6.8Aestimate measurements (including circumference) and evaluate reasonableness of results

23. Measurement 6.8Bselect and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight

24. Measurement 6.8Cmeasure angles

25. Measurement 6.8Dconvert measures within the same measurement system (customary and metric) based on relationships between units

26. Probability and statistics 6.9Aconstruct samples spaces using lists and tree diagrams

27. Probability and statistics 6.9Bfind the probabilities of a simple event and its complement and describe the relationship between the two

28. Probability and statistics 6.10Aselect and use an appropriate representation for presenting and displaying different graphical representations of the same data including line plot, line graph, bar graph, and stem and leaf plot

29. Probability and statistics 6.10Bidentify mean (using concrete objects and pictorial models), median, mode, and range of a set of data

30. Probability and statistics 6.10Csketch circle graphs to display data

31. Probability and statistics 6.10Dsolve problems by collecting, organizing, displaying, and interpreting data

32. Underlying processes and mathematical tools 6.11Aidentify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics

33. Underlying processes and mathematical tools 6.11Buse a problem-solving model that incorporates understanding the problem, making plan, carrying out the plan, and evaluating the solution to reasonableness

34. Underlying processes and mathematical tools 6.11Cselect or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem

35. Underlying processes and mathematical tools 6.11Dselect tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems

36. Underlying processes and mathematical tools 6.12Acommunicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models

37. Underlying processes and mathematical tools 6.12Bevaluate the effectiveness of different representations to communicate ideas

38. Underlying processes and mathematical tools 6.13Amake conjectures from patterns or sets of examples and nonexamples

39. Underlying processes and mathematical tools 6.13Bvalidate his/her conclusions using mathematical properties and relationships