1. Number Sense

2. The term "number sense" is a relatively new one in mathematics education. It is difficult to define precisely, but broadly speaking, it refers to "a well organized conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms" (Bobis, 1996). The National Council of Teachers (USA, 1989) identified five components that characterize number sense: number meaning, number relationships, number magnitude, operations involving numbers and referents for numbers and quantities. These skills are considered important because they contribute to general intuitions about numbers and lay the foundation for more advanced skills.

3. What teaching strategies promote early number sense? Learning to count with understanding is a crucial number skill, but other skills, such as perceiving subgroups, need to develop alongside counting to provide a firm foundation for number sense. By simply presenting objects in various arrangements, different mental strategies can be prompted. For example, showing six stamps in a cluster of four and a pair prompts the combination of 'four and two makes six'. If mental strategies such as these are to be encouraged then an element of speed is necessary. Seeing the objects for only a few seconds challenges the mind to find strategies other than counting. It is also important to have children reflect on and share their strategies (Presmeg, 1986; Mason, 1992). This is helpful in three ways: verbalizing a strategy brings the strategy to a conscious level and allows the person to learn about their own thinking; it provides other children with the opportunity to pick up new strategies; the teacher can assess the type of thinking being used and adjust the type of arrangement, level of difficulty or speed of presentation accordingly.

4. Researchers have found that children arrive at school on the first day of Kindergarten with wildly different levels of math knowledge. For example, some six-year-olds have not acquired mathematical knowledge that other children acquire at three years of age. These differences in children’s initial understanding of math have long-term implications for their success in school and in life.

5. The good news is that researchers have identified a specific, well-defined set of concepts and skills that can make the difference between children’s success and failure in mathematics in the early years. This knowledge is anchored in three key insights: – 1) Numbers represent quantities – 2) Spoken number names (“one,” “two,” etc.) and formal written symbols (1, 2, 3, etc.) are just different ways of referring to the same underlying quantities – 3) The quantities represented by the symbols have inherent relationships to each other (7 is more than 5, for example) and it is this property of the quantities that allows us to use the symbolic number representations to solve certain kinds of problems (putting objects in order, counting to determine how many objects are in a set, etc.)

6. This network of concepts and skills constitute what is called Number Sense. Happily, these research-based insights are embodied in the most recent guidelines for teaching mathematics in both the Common Core State Standards (National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010) and the Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics (2000).Common Core State Standards Principles and Standards for School Mathematics

7. Sub-skills developed in Number Sense are: Number Concepts: Connect number words and numerals to the quantities they represent Number Relations: Develop a sense of whole numbers and their relations, across different representations (“one”, 1, one turtle, etc.) Number Ordering: Understand relative position and magnitude of whole numbers Counting – Understand ordinal and cardinal numbers and their connections – Count with understanding and recognize “how many” in sets of objects

8. Here are some examples……

9. What Number am I? Tell me some things about the number 10. Tell me some things about the fraction ½.

10. Let’s play….What Number am I? - I am between 1 and 20. - I am less than 10. - I am odd. - I am prime. - I am a factor of 20. WHAT NUMBER AM I?

11. Let’s play….What Number am I? - I am odd. - I am less than 50. - I am a square number. WHAT NUMBER AM I?

12. Let’s play….What Number am I? - I am a square number. - I am a multiple of 2. - I am less than 100. - My digits add to less than 9. WHAT NUMBER AM I?

13. Common Property Patterns Look at the numbers. What do the numbers have in common? 36 9 45 60 24 30 15

14. Common Property Patterns Look at the numbers. What do the numbers have in common? 27 81 63 90 9 72 36 54 45 99 18

15. Which of these numbers would fit inside the bucket? 49 6650 29 23 77 64 81 88 80 21 62 40 35 36 28 6 31 71 11 7 3 5 19 17 13 2

16. Which of these numbers would fit inside the bucket? 49 6650 29 23 77 64 81 88 80 21 62 40 35 36 28 6 31 71 9 1 25 16 4

17. Today’s Target Today’s target is 8. Try to make today’s target in each of these ways.  Adding two numbers  Finding the difference of two numbers  Multiply two numbers  Adding three numbers  Adding and subtracting  Multiplying and adding  Multiplying and subtracting  Using a fraction  Using a decimal  Doing it an unusual way

18. Today’s Target Today’s target is 10. Try to make today’s target in each of these ways.  Adding two numbers  Finding the difference of two numbers  Multiply two numbers  Adding three numbers  Adding and subtracting  Multiplying and adding  Multiplying and subtracting  Using a fraction  Using a decimal  Doing it an unusual way

19. Number Club http://edweb.sdsu.edu/courses/edtec670/Cardb oard/Card/N/NumberClub.html

21. Name of ItemQuantityPrice Total Cost of item You and your friend are going out to eat at one of your local restaurants. Use the menu provided to select items that you and your friend would like to eat. Name of Restaurant: ______________________________________ Total Cost of Dinner:$ ________________________ *Remember: It cannot be lower than $30 nor can it exceed $34.67 You and your partner will share this with the group.