Module 4 Understanding Numbers Early Number Sense An

Module 4 Understanding Numbers

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.

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)

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)

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)

To determine if young children have the cardinality rule, listen to how they respond when you discuss counting tasks with them. l l 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. l Children with cardinality usually emphasize the last count & can explain that there are nine, “Because I just counted them. ”

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. ”

Sample Activity Fill the Chutes Children roll die & collect the indicated # of counters. They place the counters in one of the chutes. The object is to fill all the chutes with counters. 7 7

Sample Activity l Mat’ls: deck of cards numbered 1 – 7, a die, a paper cup, counters, record sheet l Turn the first card & place the indicated # of counters in the cup l Roll the die and place that many counters beside the cup l Decide how many counters in all & record In Cup On Side In All 4 3 7

Watch how children determine the total amounts in this activity. Children who are not yet counting on may want to dump the counters from the cup or will count up from one. Permit any strategy. As they continue to play, they will eventually count on as the strategy becomes meaningful and useful.

A Collection of Number Relationships 1. Spacial relationships 2. One and two more, one and two less 3. Anchors or “benchmarks” of 5 and 10 4. Part-Whole Relationships

Spacial Relationships Patterned Set Recognition Dot Plates Activities: 1. 2. 3. Learning Patterns: children replicate the pattern shown Dot Plate Flash: children recognize & name amounts quickly (Around the World) Dominoes: children play dominoes – matching patterns

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.

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

Part-Whole Relationships A major conceptual achievement of the early years is the interpretation of numbers in terms of part & whole relationships. Basic Ingredients 1. 2. 3. 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

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

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