Counting and Cardinality

Counting and Cardinality

Children’s first experiences with numbers will influence the way they deal with mathematics for the rest of their lives.

Pre-Number Concepts

Early experiences that lead to the development of counting skills are known as pre-number concepts. They include

Sorting and ClassifyingSubitizingComparingPatterns

Sorting and Classifying

Sorting and classifying activities in children’s mathematical development is critical.

Through these activities children learn to think analytically and develop logical thinking.

Sorting and Classifying

In order to sort and classify a group of objects, child must recognize what is called an attribute.

Children begin sorting and classifying by focusing on one attribute.

They need to describe the attribute with words that label the groups that have been sorted and placed together.

Subitizing

Subitizing is a way of instantly counting.

Perceptual subitizing – seeing a small group of items and knowing how many without counting.

Conceptual subitizing – recognizing the whole as a sum of its parts

The ability to subitize can be developed, and uses a student’s pattern recognition.

Dot plates, ten frames, dice, and dominoes are good tools to help students develop subitzing.

Subitizing

Comparing

Comparing two objects helps students recognize different attributes and learn comparative terms.

This pencil is longer than that pencil This chair is taller than that chair The red paper is larger than the yellow paper This book is heavier than this book

Comparing

The concepts of “more”, “less”, and “the same” are basic relationships students must understand to mathematics.

Which group of toys has more?

Seriating is the process of focusing on an attribute and then arranging or ordering a set of objects according to that attribute.

Before asking children to order a set of three or more objects, you should have them compare two objects so as to recognize different attributes and comparative terms.

Seriating

Patterns

Children need the opportunity to explore all types of patterns that occur around them.

Patterns

Repeating Patterns

Patterns

Growing patterns

Estimating

Estimates are approximations rather than exact quantities.

The meaning of the term estimate can be developed by referring to the word about.

“About how many gumballs are in the jar?”

Early Counting

One to one correspondence – the matching of one counting word with one object.

Prior to developing counting capabilities, children can compare sets by using a one-to-one correspondence strategy.

This involves learning to pair up objects such as 1. Putting one cookie on each plate

2. Finding out if there is enough books for each student in the class

3. Drawing tally marks for each object

Early Counting

Conservation of Number – the number of objects does not change when the objects are rearranged.

Counting on – continue counting up from a given number

Counting back- continue counting down from a given number.

Skip counting – sets stage for multiplication

Early Counting

When the children count, do they use the appropriate counting sequence?

Do their errors appear to be random or to they consistently make the same errors?

Do they count each object once and only once, or do they lose the idea of one-to-one correspondence as they count?

Do they remember the number they counted to?When asked to get a certain number of objects, do they

count correctly or do they count past the number they need?

Representing Numbers

Numbers can be represented in four ways:1. Concretely2. Pictorially3. Symbolically 4. Orally – using number words

Learning to write numerals is similar to learning to write the letters of the alphabet.

Representing Numbers

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Number Sense

Number Sense is “good intuition about numbers and their relationships”.

As students work with numbers they gradually develop flexibility in thinking about numbers which is a hallmark of number sense.

Number Sense

Number sense develops as students Understand the size of numbers Develop multiple ways of thinking about and

representing numbers Use numbers as referents Develop accurate perceptions about the effect of

operations on number.

Number Sense

It takes time and lots of experiences for children to develop a full understanding of number that will grow and develop into more advanced number related concepts.

Number concepts are intimately tied to the world around us. Application of number relationships to real world settings marks the beginning of making sense of the world in a mathematical manner.

Number Sense

Teachers support the development of understanding number by presenting planned and focused experiences and by interacting with the children as they work.