PRE NUMBER CONCEPTS

The Foundation of Numbers

Early Number Concepts

Classification

Seriation

Patterns

Comparisons

Conservation

Group recognition - subtilising

CLASSIFICATION

• Prerequisite to number work• Make sense of the things around them• Identify, Distinguish, Sort out• Decide on the given characteristics• Classifying objects in different ways fosters the

development of thinking skills• No counting words as more, few , many , most

and none used in describing the result• Allows pupils to reach general agreement

Classification

Classification skills are prerequisite to any meaningful number work.Before a child can count they must know what to count, and classification helps identify what is to be counted.

SERIATION

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

• Compare 2 objects so as to recognize different attributes and learn comparative terms. Then order larger sets with more than 2 items according to various attributes.

• Attribute such as length, size, capacity, mass, height

• Observe and assess how children’s observation skills, logical reasoning abilities and problem solving strategies are developing

PATTERNS

• Is a basic skill that enhances the development of mathematics concepts

• Based on geometrics attributes(shape, symmetry), relational attributes( sequence, function), physical attributes( color, length, number) or affective attributes(like, happiness).

• Based on combine patterns• Stack, arrange and order objects• Patterns helps pupils develop number sense ,

ordering, counting and sequencing• Exploring patterns requires active mental

involvement and often physical involvement

Patterns

CopyingFinding the next oneExtendingMaking their own

Copying

Find the next one

?

Extending a pattern

??

Make your own pattern

COMPARISONS

• Important part of learning to count and in developing number awareness

• Activities frequently provide opportunities for comparisons, with questions ask.

• Questions either directly or indirectly involve comparisons

• Pupils must be able to discriminate between important and irrelevant attributes

ONE TO ONE CORREPONDENCE

• Children can compare sets by using 1 to 1 correspondence before developing counting capabilities.

• Baroody and Benson(2001) instruction 1 to 1 begin by asking children to match 1 or 2 items, then 3 and later 4 and more.

• Need to learn the meaning of comparative terms such as “more than”, “fewer than”, “ the same number as” and “ as many as”. These terms should be used when comparing sets.

CONSERVATION• The ability to conserve number quantities

arranged in different ways marks a certain mental maturity. A child who cannot yet conserve large numbers will have difficulty making sense of number groupings.

• 2 blocks are arranged side by side• Pupils believe stretching out the row makes it

longer• Grouping of marbles has more than the other

Conservation

The phenomenon of conservation of number - that a given number does not vary - reflects how children think

Group recognition

The skill to instantly see how many in a group is called subtilising, from the Latin word meaning ‘suddenly’

Sight recognition;- saves time

- develops counting skills

- accelerates the development of addition and subtraction

COUNTING

• 4 principles

a) each object to be counted must be assigned one and only one number name. (one-to-one correspondence)

b) the number name list must be used in a fixed order every time a group of objects is counted (stable-order rule)

c) the order in which the objects are counted does not matter (order- irrelevance rule)

d) the last number name used gives the number of objects.(cardinality rule)

Counting Stages

• Rote counting

- knows some number names but not necessarily the proper sequence.

- count the same object several times and use different counting sequence each time. Children need to spend more time on the stable order rule.

-may not always able to maintain a correct correspondence between the objects being counted and the number names

• Rational Counting

- children gives a correct number name as the objects are counted in succession

- able to answer about the number of objects being counted.

- provide regular practice and encourage each child to count as fast as the child can.

Counting Principles Rational counter – uses all four

principles• They are able to recite the number – word sequence (

i.e one, two three...)• They make a one to one correspondence between the

items being counted and saying the number.( say one as they touched the first item)

• Count each object in the collection once only• they realize that the last number they say represents

the total number of objects in the set.(cardinality principle)

Counting Strategies

• Counting On

- child gives correct number names

- can start at any number and begin counting• Leads children to the discovery of many valuable

patterns and for developing addition• Counting Back

- child give correct number names as they count backwards from a particular point.

- helpful in developing subtraction, use calculator as a tool , calendar.

• Skip counting

- counts by twos, fives, tens or other values

- provides readiness for multiplication

Counting Practice

• Dice• Calendar• Hundred chart

Early Number Development

• Developing Number Benchmarks

- fingers, five frame, ten frame• Making connections

- linked model/visual representation to symbol/written representation and to words/oral

-Example three

-provide different objects, different form of numerals

- valuable concept one more, one less

- concept of zero – the absence of something

Cardinal, Ordinal and Nominal Numbers

• Cardinal numbers – how many? A correct number name for a given group.

• Ordinal numbers - Which one? Emphasizes arranging things in order. The order may be based on any criterion such as position in the race. First, Second, third and so on.

• Nominal numbers – provides a label or classification such as telephone number,

Cardinal, ordinal and nominal numbers`

Cardinal - Think “How many?”We have 4 cats

Ordinal - Think “Which one?” (order)Eliza was third in the race

Nominal - Think “Who?” (identification)Zola is number 25 for Chelsea

Writing Numeral

Activity:• Tracing the digits• Draw appropriate number of objects beside the

numeral• Cut out shapes of numerals• Trace the number in air• Write a numeral on the other child’s back

Number sense

• Number sense involves understanding numbers; knowing how to write and represent numbers in different ways; recognizing the quantity represented by numerals and other number forms; and discovering how a number relates to another number or group of numbers. Number sense develops gradually and varies as a result of exploring numbers, visualizing them in a variety of contexts, and relating to them in different ways.

Read more on TeacherVision:http://www.teachervision.fen.com/pro-dev/teaching-methods/48939.html#ixzz1Dup8kjDM

• In the primary and intermediate grades, number sense includes skills such as counting; representing numbers with manipulatives and models; understanding place value in the context of our base 10 number system; writing and recognizing numbers in different forms such as expanded, word, and standard; and expressing a number different ways—5 is "4 + 1" as well as "7 - 2," and 100 is 10 tens as well as 1 hundred. Number sense also includes the ability to compare and order numbers—whole numbers, fractions, decimals, and integers—and the ability to identify a number by an attribute—such as odd or even, prime or composite-or as a multiple or factor of another number.

• n teaching number sense, using manipulatives and models (e.g.,place-valueblocks,fraction strips,decimal squares,number lines, and place-value andhundreds charts) helps students understand what numbers represent, different ways to express numbers, and how numbers relate to one another.

• When students trade with place-value blocks they can demonstrate that the number 14 may be represented as 14 ones or as 1 ten and 4 ones. They can also demonstrate that 10 hundreds is the same as 1 thousand. By recording the number of each kind of block in the corresponding column (thousands, hundreds, tens, or ones) on a place-value chart, students practice writing numbers in standard form.

• Using fraction strips, students find that 1/4 is less than 1/3 and that it names the same amount as 2/8.

• Using decimal squares, students see that 8 tenths can be written as 0.8 or 8/10. By pairing upcountersto identify even numbers and marking these on a hundreds chart, primary-grade students discover that, beginning with 2, every other number is an even number.

• Intermediate-grade students can mark multiples of 3 and 6 on a hundreds chart and find that every number that has 6 as a factor also has 3 as a factor.

• Using a number line, students see how fractions with different denominators relate to the benchmark quantities of 0, 1/2, and 1.

• From these concrete experiences, students build the foundation for number sense they will bring to computation, estimation, measurement, problem solving, and all other areas of mathematics.