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### NCTM Number and Operations

• 1. NCTM Strands Number and Operations Algebra Geometry Measurement Data Analysis & Probability
• 2. NCTM Strands Strand 1 Number and Operations Algebra Geometry Measurement Data Analysis & Probability
• 3. Number and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand meanings of operations and how they relate to one another. Compute ﬂuently and make reasonable estimates.
• 4. Number and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand meanings of operations and how they relate to one another. Compute ﬂuently and make reasonable estimates.
• 5. Number and Operations 1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand meanings of operations and how they relate to one another. Compute ﬂuently and make reasonable estimates.
• 6. Number and Operations 1 Understand numbers Count with understanding and recognize "how many" in sets of objects Know names of numbers 2 =
• 7. Number and Operations 1 Understand numbers Count with understanding and recognize "how many" in sets of objects There is an order to numbers
• 8. Number and Operations 1 Understand numbers Count with understanding and recognize "how many" in sets of objects There is an order to numbers 0123456789
• 9. Number and Operations 1 Understand numbers Count with understanding and recognize "how many" in sets of objects One-to-one correspondence
• 10. Number and Operations 1 Understand numbers Count with understanding and recognize "how many" in sets of objects Subitizing (instant recognition of quantity)
• 11. Number and Operations 1 Understand numbers Count with understanding and recognize "how many" in sets of objects Subitizing (instant recognition of quantity)
• 12. Number and Operations 1 Understand numbers Use multiple models to develop initial understandings of place value and the base-ten number system We use base-10 system
• 13. Number and Operations 1 Understand numbers Use multiple models to develop initial understandings of place value and the base-ten number system Not binary, not hexadecimal
• 14. Number and Operations 1 Understand numbers Use multiple models to develop initial understandings of place value and the base-ten number system Show them concretely/physically what 4 looks like
• 15. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Do you know the magnitude of 15?
• 16. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Give them a reference (in relationship to other numbers) -2 -1 0 1 2 3 4
• 17. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Ordinal
• 18. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Ordinal order
• 19. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Cardinal
• 20. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Cardinal counted
• 21. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Have examples up all around the class to quickly point to
• 22. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections How many letters in your name?
• 23. Number and Operations 1 Understand numbers Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections How many letters in your name? B i l l 1234
• 24. Number and Operations 1 Understand numbers Develop a sense of whole numbers and represent and use them in ﬂexible ways, including relating, composing, and decomposing numbers 5 Little Monkeys Jumping on the Bed 5 Green & Speckled Frogs
• 25. Number and Operations 1 Understand numbers Develop a sense of whole numbers and represent and use them in ﬂexible ways, including relating, composing, and decomposing numbers Decomposing. 5 can be: 1,1,1,1,1 2,3 1,4
• 26. Number and Operations 1 Understand numbers Connect number words and numerals to the quantities they represent, using various physical models and representations Find/Make poster with: 1) numeral 2) quantity 3) number word all in one place
• 27. Number and Operations 1 Understand numbers Connect number words and numerals to the quantities they represent, using various physical models and representations They need to count it before you can add the symbol, number or the number word
• 28. Number and Operations 1 Understand numbers Connect number words and numerals to the quantities they represent, using various physical models and representations Connect numeral (0-9) to quantity
• 29. Number and Operations 1 Understand numbers Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2. "Pour 1/2 glass of milk."
• 30. Number and Operations 1 Understand numbers Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2. Talk about fractions during snack time.
• 31. Number and Operations 1 Understand numbers Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2. Talk about fractions during snack time.
• 32. Number and Operations 1 Understand numbers Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2. Give non-examples.
• 33. Number and Operations 1 We haven't even talked about adding yet!
• 34. Number and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand meanings of operations and how they relate to one another. Compute ﬂuently and make reasonable estimates.
• 35. Number and Operations 2 Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand meanings of operations and how they relate to one another. Compute ﬂuently and make reasonable estimates.
• 36. Number and Operations 2 Understand meanings Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations. Fact family 2+3 = 5 3+2 = 5 5-2 = 3 5-3 = 2
• 37. Number and Operations 2 Understand meanings Understand the effects of adding and subtracting whole numbers. Adding
• 38. Number and Operations 2 Understand meanings Understand the effects of adding and subtracting whole numbers. Subtracting
• 39. Number and Operations 2 Understand meanings Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally. Equal sets during snack.
• 40. Number and Operations 2 Understand meanings Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally. Equal sets for backpacks.
• 41. Number and Operations 2 Understand meanings Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally. Equal sets: number of students in the playhouse.
• 42. Number and Operations 2 Make it relevant to them!
• 43. Number and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand meanings of operations and how they relate to one another. Compute ﬂuently and make reasonable estimates.
• 44. Number and Operations 3 Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand meanings of operations and how they relate to one another. Compute ﬂuently and make reasonable estimates.
• 45. Number and Operations 3 Compute Fluently Develop and use strategies for whole-number computations, with a focus on addition and subtraction. Teach a strategy: "I can move this counter to this compartment to help me count."
• 46. Number and Operations 3 Compute Fluently Develop ﬂuency with basic number combinations for addition and subtraction. Memorize it. (Don’t get lost in 5th grade.)
• 47. Number and Operations 3 Compute Fluently Develop ﬂuency with basic number combinations for addition and subtraction. Avoid math anxiety by developing a good foundation of the concept.
• 48. Number and Operations 3 Compute Fluently Develop ﬂuency with basic number combinations for addition and subtraction. Observe students in the classroom before you start lesson planning.
• 49. Number and Operations 3 Compute Fluently Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. Add this into your daily routine
• 50. Number and Operations 3 Compute Fluently Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. Practice estimating numbers, distance, & size
• 51. Number and Operations 3 Compute Fluently Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. Introduce calculators photo by Jason Toal
• 52. Number and Operations 3 Compute Fluently Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. Put numbers and rulers in writing center.
• 53. Number and Operations 3 Compute Fluently Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. Variety of manipulatives (many, many!)
• 54. Number and Operations 3 It needs to make sense to them!

### Editor's Notes

1. Who is first in line? The order depends on direction (face the other way in line)
2. &amp;#x2022;the last number I counted is how many I have altogether (1,2,3,4... I have 4 total)
3. Y.C. Ch.2 Principles in teaching math
4. Y.C. Ch.2 Principles in teaching math
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