The document outlines the five strands of the National Council of Teachers of Mathematics (NCTM): Number and Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability. It focuses on the first strand of Number and Operations, which has three main components: understanding numbers and relationships, understanding the meanings of operations, and computing fluently using a variety of tools and methods. It provides examples of how to teach these concepts to elementary students in meaningful, relevant ways.

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!