Building Number Sense in 4 Year Old Kindergarten

1. Building Number Sense in 4 Year Old Kindergarten “Concepts embedded in number sense may be as important to early math learning as concepts of phonemic awareness”- Gerslen and Chard 1999

2. Activity: Stranger in the Woods

3. Activity: Stranger in the Woods • Problem: Five animals investigated the stranger in the woods. Which animals investigated the stranger in the woods? • How many visited the snowman in our problem? • How could you show the animals to share your thinking with others?

8. Teacher Reflections…. • Who solved the problem accurately? Does the student understand the problem, does the student understand “five”? • What strategies did the students use- how do the examples compare and contrast? • If selecting a few pieces of student work to share with the whole class, what would you choose?

9. The Components of Number Sense • Quantity- value • Magnitude- relative size • Numeration- names and naming systems that are used in the spoken/written language for numbers • Different forms of number • Equality- being quantitatively the same • Language- what we use to describe number

10. What number is this? 3 What mathematical connections are being made that develops number sense in your students?

11. C-A-T is not a cat • learn to decode words • learn to attack words • Learn that words never are the things they describe – build background knowledge and supplied context of the word ? ? ?

12. 3 Not ‘three” Not the quantity Not We must consider if we have worked to develop an understanding of the concrete concept that this abstract orthographic symbol (3) represents. We want to show a true representation of arbitrary quantity. Are we neglecting to teach the “threeness” of three?

13. Point to remember…. • Think about math symbols in the same way as we think about letter symbols and words: • Helping children “break the code” with numbers allows them to understand how different forms of the number can come together

14. The Components of Number Sense • Quantity- value • Magnitude- relative size • Numeration- names and naming systems that are used in the spoken/written language for numbers • Different forms of that number • Equality- being quantitatively the same • Language- describe

15. Counting and Cardinality • Several progressions originate in knowing number names and the count sequence.

16. Pre-Counting • The key focus in pre-counting is an understanding of the concepts more, less and the same and an appreciation of how these are related. • Children at this stage develop these concepts by comparison and no counting is involved. • These concepts lay the foundation for children to later develop an understanding of the many ways that numbers are related to each other; for example five is two more than three, and one less than six.

17. From saying the counting words to counting out objects- building 1-to-1 correspondence • Number sense begins with early counting to telling how many in one group of objects. • Students usually know or can learn to say the counting words up to a given number before they can use these numbers to count objects or to tell the number of objects. 1,2,3 To count a group of objects, they pair each word said with one object.K.CC.4a Count to 100 by ones K.CC.1

18. Before we can break the code at the symbolic level (3), we must first ascertain that students “see” number in a way that will construct their understanding of compositions and decomposition of numbers.

19. Playdough Stamping

20. One-to-One Counting • Two skills are needed: • ability to say the standard list of counting words in order • ability to match each spoken number with one and only one object

21. Counting objects arranged in a line is easiest; - rectangular arrays (they need to ensure they reach every row or column and do not repeat rows or columns); -circles (they need to stop just before the object they started with); and -scattered configurations (they need to make a single path through all of the objects).K.CC.5

24. Counting Sets • develops children’s understanding of cardinality. • This means that children understand when you count the items in a set, the last number counted tells the size of that set. They also know that the number in a set will remain constant as long as no items are added to the set, or taken from the set.

25. Remember: Only the counting sequence is a rote procedure. The meaning attached to counting is key conceptual idea on which all other number concepts are developed.

26. Activities Make Sets of More/Less/Same Provide students with cards with sets of 4-12 objects, a set of small counters, and some word cards labeled More, Less, and Same. Next to each card have students make three collections of counters: a set that is more, one that is less, and one that is the same. The appropriate labels then can be placed on the sets. Have them show (Justify) how they know there are more in one group than another. Questions: How do you know five is more than four?

27. Video Clip- Pre Kindergarten Block Play • http://youtu.be/gsDY6qftzQk • http://youtu.be/gsDY6qftzQk

28. Meaning Attached to Counting • Van de Walle makes it clear that an understanding of cardinality and the connection to counting is not a simple matter for 4 year olds • Child learn how to count before they understand that the last count word indicates the amount or set or the cardinality of the set. Cardinality Principle • VandeWalle states by age 4.5 students have/should made this connection.

29. How many deer are there? 1, 2, 3, 4, 5 Are there 5 deer? 5 because I counted them! Student can use counting to find a matching set.

30. Fosnot and Dolk discuss a class of 4 year olds in which children who knew there were 17 children in the class however they were unsure how many milk cartons they should get so that each could have one. • To develop their understanding of counting, engage children in any game or activity that involves counts and comparisons.

31. Games

32. Activity: Counting Blocks • http://illuminations.nctm.org/ActivityDetail.aspx?ID=27

33. Relationships Among Numbers 1- 10 • Once children acquire a concept of cardinality and can meaningfully use their counting skills, little is to be gained from counting activities. • More relationships must be created for children to develop number sense, a flexible concept of number not completely tied to counting.

34. Subitizing- instantly seeing how many • Students come to quickly recognize the cardinalities of small groups without having to count the objects; this is called perceptual subitizing. • This develops into conceptual subitizing— recognizing that a collection of objects is composed of two collections and quickly combining their cardinalities to find the cardinality of the collection

36. We read 7 in stages; Stage 1 Working on correspondence and counting skills- one by one

37. Stage 2 • Students will need to be presented small numbers that they can subitize and begin to see quickly. • Once students subitize up to 4-5 they develop the ability to combine numbers into larger numbers

39. Stage 3 • 3+4=7 7=3+4 • 5+2 • 3+3+1 • Student has developed number sense through deeper understanding of quantity, number composition, different forms of a number and equality. • 3+4=34 8-5=8

40. Activities • Learning Patterns Provide each student with about ten counters and a whiteboard as a mat. Hold up a “dot plate” for about 3 seconds. Say “Make the pattern/draw the pattern you saw using the counters or on the whiteboard. Spend time discussing the configuration of the pattern and how many dots. Do this with a few new patterns each day. Questions: • How many dots did you see? • How did you see them? • What is a different way to see the total number of dots? http://teachmath.openschoolnetwork.ca/documents/dotplatepatternsVDW.pdf

41. Activities • Flash Cards Show a student a flashcard with, for example, 7 things in groupings of 5 and 2. Question: • How many things are there? • What helped you see how many there are?

42. Activities • Dice combinations Organize students into pairs. Give each pair two dice. Have students take turns to roll the dice and then say how many dots just by looking. Ask: How many dots are on the first die? How many dots on the second die? How many dots all together?

43. 3 • Some children develop the skill of “number calling”- without understanding • Subitizing is a fun early step in ensuring that our students are not “number calling” but understanding what is underneath the numeral.

44. Think about 5 • Teach quantity • Teach different forms of the number • Teach equality • Teach numeration • What is key? Make connections between these components

45. Activity: Stranger in the Woods • Problem: Five animals investigated the stranger in the woods. Which animals investigated the stranger in the woods? • Which animals visited the snowman? • How many visited the snowman in our problem? • How could you show the animals to share your thinking with others?