Whole Number Concept Development

Early Number Concepts  When we count a set, the last number we say names how many are in the set, or its cardinality.  Numbers are related to each other through a wide variety of relationships, including more, less and same.  Number have different values when connected to real objects and measures: when is 5 a large number; when is it small

Dot Plate Flash  I will hold up a plate for 1-3 seconds.  You will show me how many you saw using your fingers.  Be prepared to tell me how you saw the number.  Recognizing these dot configurations is called “subitizing”.

Dot Plate Flash Variation  Decide whether you want to play 1 more, 2 more, 1 less, 2 less, or double.  Flash the plate and ask the students to show you the predetermined more or less amount.

Developing Meanings for the Operations  Addition and subtraction are connected  Multiplication involves counting groups of the same size and determining how many are in all.  Multiplication and division are related.  Models can be used to solve story problems for all operations.  For all four operations, word problems and models (counters & number lines) are the basic tools for developing the concepts.

Part Part Whole Models

Helping Children Master the Basic Facts  Number relationships can be used to help remember basic facts  “Think addition” is the most important idea for subtraction facts  There are patterns and relationships in basic facts – you can figure out unknown facts from the ones you already know.  All of the facts can be learned when efficient strategies are employed.

Circles and Stars  Roll one number cube and draw that many circles on your paper.  Roll the cube again and draw that many stars in each circle.  Write the equation and find the product. 4 x 3 = 12

Whole-Number Place-Value Development  Sets of ten must be perceived as single entities which can then be used to describe how many.  The position of the digits in numbers determine what they represent-which size group they count.  There are patterns in the way numbers are formed.  Groupings can be decomposed in many ways.

Who Could They Be A B C D E 50200

Strategies for Whole-Number Computation  Flexible methods of computation involve decomposition and composition of numbers in a wide variety of ways.  All computational strategies are based on ideas in place-value and an understanding of the operations and how they are related.  Each traditional algorithm is simply a clever way to record the place value transitions (trades) to an adjacent position.

Number Sense and Estimation with Whole-Numbers  Multidigit numbers can be taken apart in many ways, including by decades (36 is 30 and 6), with place value concepts (36 is 2 tens and 16 ones), and other multiples (480 is 500 less 20). Numbers can be recombined when these parts are recognized.  Nearly all computational estimations involve replacing or substituting difficult to handle numbers with close or nice numbers, making mental computation easier.

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