1. Understanding Numbers
Module 4
Understanding Numbers

2. Early Number Sense An intuition about numbers and their relationships.
Develops gradually as a result of exploring numbers.
Continues to develop as children begin to use numbers in operations, build an understanding of place value, and devise methods of computing larger numbers.

3. Counting and Number Sense
Counting is both complex & cognitively sophisticated.
“Counting is the successive assignment of a sequence of number words to items” (Fuson & Hall, 1983)

4. NCTM Objectives PK-2: 3-5 Count with understanding
Develop understanding of ordinal and cardinal
Develop sense of whole numbers
Connect number words and numerals
3-5
Place Value of Base 10
Recognize equivalent representations
Describe characteristics of number sets

5. (how to count principles)
5 Counting Principles
1. One-one Principle – each item counted is represented by one and only one counting word or symbol.
2. Stable-order Principle – the sequence of counting words or symbols must be repeatable & unchanging.
3. Cardinal Principle – the word or symbol for the last item in a counting sequence represents the total number of items.
(how to count principles)

6. 5. Order-irrelevance Principle – items may be counted in any order
4. Abstraction Principle – a variety of items may be collected and counted.
5. Order-irrelevance Principle – items may be counted in any order
(what to count)

7. Teacher asks, “How many are here?”
To determine if young children have the cardinality rule, listen to how they respond when you discuss counting tasks with them.
Teacher asks, “How many are here?”
The child counts correctly & answers, “Nine.”
Ask, “Are there nine?”
Before developing cardinality, children may count again or will hesitate.
Children with cardinality usually emphasize the last count & can explain that there are nine, “Because I just counted them.”

8. Counting On Strategy
A strategy for dealing with a change in the number that results in more.
Children start with a number and then count on through the number sequence. For example, to find 2 more than 5, a child might say, “Five, six, seven.”

9. Comparing Sets of Numbers
More than
Less than
Fewer than
Same as
Example: dominoes or cards with the same number of dots and one that is different. Which is not the same? Why?

10. Vocabulary Cardinal numbers: designate the quantity
Ordinal numbers: designate the order
Nominal numbers: name objects
Discrete: how many?
Continuous: how much?
Skip Counting: count by multiples

11. Activities Counting and writing numerals
Count objects in the room and write statements about findings
Square tiles – p. 86
Find manipulatives in backpack that can be used to represent numbers – p. 87
Create Bean Sticks
Adding Literature: Counting Crocodiles

12. Ordering Activities Ordering
Comparing: more than, less than, greater than, fewer than
Part-Part-Whole: p. 90
Pegboard – number patterns of 6
3D Cubes – use 2 colors to show a variety of ways to make up the number 6
10 Frame – find missing part

13. Estimation Activities Objects Covered or on Overhead
Jelly Bean Activity

14. A Collection of Number Relationships
Spacial relationships
One and two more, one and two less
Anchors or “benchmarks” of 5 and 10
Part-Part-Whole Relationships

15. Spacial Relationships Patterned Set Recognition
Dot Plates
Activities:
Learning Patterns: children replicate the pattern shown
Dot Plate Flash: children recognize & name amounts quickly (Around the World)
Dominoes: children play dominoes – matching patterns

16. One and Two More, One and Two Less
These activities encourage children to reflect on the relationship between two numbers.
Example: 6 and 8 are related by twin relationships. 6 is “two less than” 8 and 8 is “two more than” 6.
One-Less-Than Dominoes
Instead of matching ends, a new domino can be added if it has an end that is one less than the end on the board.
Make a Two-More-Than Set
Provide students with dot cards. Their task is to construct a set of counters that is two more than the set shown on the card.

17. Anchoring Numbers to 5 and 10
Fives Frame Tell About It
“There are 2 counters and 3 empty spaces.”
“I need three more.”
Tens Frame Activities

18. Part-Part-Whole Relationships
A major conceptual achievement of the early years is the interpretation of numbers in terms of part & whole relationships.
Basic Ingredients
Let the children focus on a single number for the entire activity.
Let children say or “read” the parts aloud & write them down on a recording sheet (reflective thought)
Important variation – missing part activities

19. Build It in Parts Activity
Children focus on the combinations.
Use two-color counters, snap cubes, colored rows of squares on grid paper
Vary the activity by adding a design component.

20. Counters under the tub “Four and _____ is six.” “I wish I had _____”
Missing Part Activities Two children working together. Teacher directed activity.
Counters under the tub
“Four and _____ is six.”
“I wish I had _____”
“I have five.”
“I need ____more.”