1. Number and Operations Standard Grades Pre-K-12 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 Principles and Standards for School Mathematics National Council of Teachers of Mathematics 2000

2. Excerpts of Expectations from the Number and Operations Standard Grades Pre-K-2 Principles and Standards for School Mathematics National Council of Teachers of Mathematics 2000

3. Understand numbers, ways of representing numbers, relationships among numbers, and number systems Count with understanding and recognize “how many” in sets of objects Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections. Connect number words and numerals to the quantities they represent, using various physical models and representations

4. Number sense is an intuitive feel for numbers and their various uses and interpretations.

5. Examples of Number Sense Observing and using relationships Using patterns Using thinking strategies Recognizing different forms Judging unreasonableness Using numbers flexibly Using referents and benchmarks

6. Groups of 5 counters are arranged in the following 3 patterns

7. Student A T: Are there more red, blue, or yellow counters? S: More blue. T: How do you know? S: I can tell by looking. T: How many of each? S: One, two, three, four, five... five red. One, two, three, four, five...five blue. One, two, three, four, five...five yellow. T: Five of each? S: Yes. T: Do you still think there are more blue? S: Yes, I can just see there's more blue.

8. Student B T: Are there more red, blue, or yellow counters? S: They're the same. T: How do you know? S: I counted them. T: How many of each? S: One, two, three, four, five...Five red. Five blue. Five yellow. T: Five of each? S: Yes.

9. Counting Principles: Student A T: Here are some blocks in a row. Start with this one on the end and count them. S: One, two, three, four, five, SIX. There are six blocks. T: What if you start at the other end of the row and count them? S: One, two, three, four, five, SIX. There are six.

10. Counting Principles: Student B T: Here are some red blocks in a row. Start with this one on the end and count them. S: (Touches each of the 5 blocks) One, two, three, five, six. Six red blocks T: Now count these blue blocks. S: (Touches each of the 4 blocks) One, two, three, five. Five blue blocks.

11. Counting Principles: Student C T: Here are some blocks in a row. Start with the one on this end and count them. S: One, two, three, four, five, six. There are six. T: What if you start at the other end of the row and count them? S: I already counted them! There are six!

12. Counting Principles: Student D T: Here are some red blocks (4) in a row. Start with this one on the end and count them. S: (Points to each but says two numbers with each point) One, two, three, four, five, six, seven, eight. Eight red blocks.

13. Construct a Pattern The color spinner will be used to select the colors to be used in constructing the pattern. Using the colors chosen, make a pattern that repeats at least twice in the time allotted. When the time is up, compare patterns with others. Did you come up with a unique pattern idea?

14. Construct a Pattern Try another pattern with new colors or different types of manipulatives. Why should students have an opportunity to participate in patterning activities? Do you have other suggestions for patterning activities?

15. Chad: Third Month of Kindergarten

16. Cody: Third Month of Kindergarten

17. Steven: Third Month of Kindergarten

18. Elizabeth: Third Month of Kindergarten

19. Andrea: Third Month of Kindergarten

20. Jason: Third Month of Kindergarten

21. Joshua: Fifth Month of Second Grade