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Math 412 Number Readiness.

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Presentation on theme: "Math 412 Number Readiness."— Presentation transcript:

1 Math 412 Number Readiness

2 Developing Number Concepts
What type of pre-number activities must children engage in to develop understanding of number concepts? What type of counting abilities are necessary for children to develop? What are several of the ways that children must be able to represent numbers? What types of number relationships are essential for children to understand?

3 Number Readiness Ages 3 to 6
Preoperational thought according to Piaget Understand best when they can invent meaning

4 Pre-number Concepts Classification Class inclusion Seriation
Number conservation Equivalence of sets

5 Classification Child must make a decision about certain attributes of objects and sort them based on the classification Earliest stage of logical thinking

6 Sample Activity Grades Pre-K-1
Identifying Attributes Materials: Classroom objects or toys Directions: Hold up an object and ask the children to describe it. The scenario may go something like this: What can you tell me about this? What properties does it have?

7 Sample Activity Grades Pre-K-2
Sorting Objects Materials: Attribute blocks or other objects that may be sorted Directions: Ask students to sort by color Ask students to sort by shape Ask students to sort by size or thickness Ask students what types of objects are sorted at home: Toys, mail, groceries, laundry

8 Class Inclusion The ability for a child to see relationships between different groups at different levels in the classification system For example, one group can be part of another group at the same time For example, the group of girls in a classroom can also be part of the total group(Ms. Smith first grade class)

9 Class Inclusion Show the child a box of twenty red beads and ten yellow beads. If you ask the child if there are more red beads or more plastic beads, a young child would say more red beads. It is difficult for a young child to see the relationship between the two classes

10 Number Inclusion This concept is directly related to the addition principle. Because addition is putting two sets together and naming it as a single number, this concept is difficult for a young child …. The child is not ready to add until they this skill is developed with practice

11 Sample Activity Grades Pre-K-1
Concept of Number Inclusion Materials: various objects Directions: Ask a child to count a number of objects, say 5, then add 3 more. Then ask how many things there are now. Most children will start counting the entire group beginning at 1, rather than starting at 5 They do not think of the relationship between five and the adjacent numbers

12 Sample Activities Whole to part and back to the whole activities will give children experience of putting sets together

13 Seriation This involves the ordering of objects and events
The child at this stage must be able to make comparisons and make decisions about differences

14 Sample Activity Concept of Seriation Materials: different size objects
Directions: Order the smallest block to the largest block Order the largest rock to the smallest rock What do you do first in the morning?

15 Number Conservation How the child perceives number invariance and the degree that the child is tied to perceptual cues Can the arrangement of a constant number of objects be changed without changing the number?

16 Sample Activity Grades K-2
Concept of Conservation Materials: Five red blocks and five blue blocks Teacher statement: On the table I have a row of red blocks and a row of blue blocks. Raise your hand if you think there are more red blocks than blue ones. Raise your hand if you think there are more blue blocks. Raise your hand if you think there are as many red blocks as blue blocks. What about now? (spread out the row of blue blocks) Then ask the same questions again…..

17 Conservation

18 Number Conservation Conservers do not see changes in configurations and counter suggestions This is developmental Piaget claims that without reversibility of thought and number conservation, addition cannot be understood – first operation

19 Equivalence of Sets A task associated with understanding numbers is equivalence of sets Perceptual cues may interfere with a young child’s understanding of number

20 Sample Activity Grades Pre-K-1
Concept of Equivalence of Sets Materials: Two glasses, one short, one tall filled with the same size and same number of beads Teacher statement: Are there the same number of beads in each glass?

21 Developing Meaning for Numbers
Once children become aware that the quantity in a set is named by a specific name, they begin to associate meaning to numbers

22 Building the Concept of Number
Patterns Number relationships One to one correspondence More, less, same Rote counting Rational counting (counting with meaning) Counting sets Numeral Set association (number, the number name, written symbol) three 3

23 Cardinal Numbers “Cardinal” numbers are used to designate the quantity of a set For example: If a child is asked to count the pieces of chalk in the chalk tray and counts to seven, then he is using the cardinal aspect of the number When a set is counted the last number named is the total number of objects in the set

24 Ordinal Numbers “Ordinal” means order.
Ordinal numbers are used to denote the order of an object For example: “ Michelle finished her test first”

25 Nominal Numbers “Nominal” means name. Numbers are used to name objects
Examples: a social security number, a postal code, a license plate, a house address

26 Readiness for Operations in this Order
Addition Subtraction Multiplication Division


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