Let’s Talk Numbers

1. Let’s Talk Numbers The Importance of Number Sense

2. Just a little humor...

3. What is Number Sense? “Number sense can be described as a good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualising them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms”. (p. 11) Howden, H. (1989). Teaching Number Sense. Arithmetic Teacher, 36(6), 6-11.

4. Relationships What are those relationships? Spatial Relationships- recognizing how many without counting by seeing a pattern. One and two more, one and two less- this is not the ability to count on two or count back two, but instead knowing which numbers are one and two less or more than any given number. Benchmarks of 5 and 10- ten plays such an important role in our number system (and two fives make up 10), children must know how numbers relate to 5 and 10. Part-Part-Whole - seeing a number as being made up of two or more parts.

5. Relationships Spatial Relationship- gives children a visual to go along with a number instead of just the abstract numeral. 9 + 6

6. Relationships One/Two More and Less The spatial relationships helps build the idea of One/Two More and Less in this problem because it gives children a concrete way to see that 9 is just one less than ten. 9 + 6

7. Relationships Benchmarks of 5 and 10 Having the objects placed into the ten frame sequentially helps children develop an understanding of how that number relates to 5. No matter how objects are placed in a ten frame, the visual created helps children see how the amount relates to the benchmark of 10.

8. Relationships Part-Part-Whole There are too many children who only see 6 is just 6. They do not understand how it can be broken down into parts that create the whole six. http://www.mathcoachscorner.com/2015/01/developing-partwhole-thinking/

9. Relationships Why are these relationships so important to develop before we expect children to be fluent? • If we just allow students to memorize their math facts, then we end up with high school children still counting on their fingers. • It is important that children develop a conceptual understanding and their relationships before we ask them to compute.

10. Resources http://www.mathematicallyminded.com/free-downloads/ Dr Nicki Kindergarten Fluency pt 1 - YouTube Dr Nicki - CCSS Math 1st Grade Fluency pt 1 - YouTube Dr Nicki - CCSS Math 2nd Grade Critical Areas.mov - YouTube

11. Four Early Numeracy Counting The Importance of Number Sense

12. 4 Early Numeracy Counting • Subitizing • Verbal Counting • Object Counting • Counting and Cardinality

13. A few tools Use Your Classroom as a Math Toolkit - YouTube Beaded Number Line Pt 1 - YouTube

14. What Do You Think? Number Lines vs. Number Paths Many K5 and 1st grade classrooms have a number line along the classroom wall and/or on every child’s desk. New research has shown that number lines are conceptually too difficult for young children. Instead we should be using number paths; until a child is in 2nd grade (Fuson, et.al., 2009) Fuson, K.C., Clements, D.H, Beckman, S. (2009). Focus in Grade 1: Teaching with Curriculum Focal Points. Reston, VA: NCTM.

15. What Do You Think? Number Paths The number line is a length model; each number is represented by its length zero. With students using a number line, children have to count the length of the units and not the numbers. Whereas the number paths, the units are easy to recognize. A number path is a count model; the numbers are represented by a rectangle and each rectangle can be counted.

16. References Tondevold, C. (2015). 4 Relationships That Will Increase Your Students’ Number Sense, Boulder Drive, ID, www.mathematicallyminded.com

17. Presented by Edwina Perrin District Five Math Coach