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

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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.

Arrow Math

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