Assignment 2EDX 1280

Foundations of Numeracy Whole Numbers Whole Numbers

Theoretical BackgroundsTheoretical Backgrounds

1. Whole Numbers

2. Pre-numbers

3. Early Numbers

4. Number Sense

5. Place ValueBy:By:

00610019110061001911

Whole Numbers:Whole Numbers:Jamieson-Proctor, R. (2012)

• The whole numbers are the counting numbers and 0.

The whole numbers are 0, 1, 2, 3, 4, 5, ...

• One of the numbers 1, 2, 3, ... also called the counting counting

numbers numbers or natural numbersnatural numbers. 0 is sometimes included in

the list of "whole" numbers (Bourbaki 1968, Halmos

1974), but there seems to be no general agreement.

Some authors also interpret "whole number" to mean "a

number having fractional part fractional part of zero," making the whole

numbers equivalent to the integers.

Set Name Symbol…, -2,-1, 0, 1, 2,3 Integers Z

1, 2, 3, 4, ….. Positive Integers Z^+

0, 1, 2, 3, 4, … Nonnegative Integers Z^*

0, -1, -2, -3, …. Nonpositive Integers

-1, -2, -3, -4, …. Negative Integers Z^-

Different Types of Integers: Different Types of Integers: Bourbaki 1998

Pre-numbers:Pre-numbers:Jamieson-Proctor, R. (2011)

• It’s early concepts and beginning processes (skills) which includes:

3. Determining attributes

4. Matching by attributes

5. Sorting by attributes

6. Comparing attributes

7. Ordering attributes

8. Patterning

1. Determining attributes

- Shapes- Sizes- Weight- Sound

Leading children using five senses which taste, smell,

touch, visual and hearing to recognize and to be aware

of the similarity and differences according to attributes

between objects.

2. Matching by attributes

Leading children to recognize and to be aware of

matching 2 objects for their likeness of attribute and

describe it.

3. Sorting by attributes

Sorting by attributes are involve 3 or more objects.

Children have to group objects according to their defined

attributes.

4. Comparing attributes Leading children compare more or less of a

mathematically significant attribute between 2 objects

at a time such as big or small, more or less, long or

short.

5. Ordering attributes Ordering is leading children to arrange more than two

objects in the increasing or decreasing sequence of an

attribute. It should begin to order with children’s

familiar objects such as ruler, from long to short or

from short to long.

6. Patterning Patterning includes matching, sorting, comparing and

ordering skills. It is based on repetition of some

recognizable feature.

Big

Small

Early NumbersEarly Numbers

• After knowing the pre-number concepts, children will get into early number.• According to Van De Walle, Karp and Bay-Williams (2010) described early

number sense are elaborate as children understand: The size numbers Various ways of thinking about the representing numbers Precise of perceptions about the effects of operations on numbers

The 5 counting principles in early number are:The 5 counting principles in early number are: Jamieson-Proctor, R. (2011)

• One to one correspondence (counting one by one)

• Stable order (know the order of numbers)

• Cardinal principle (the last number counted names the quantity in the set)

• Abstraction (what is countable and uncountable)

• Order irrelevance (from left to right)

Number SenseNumber Sense

• It is develop to visualize numbers in variety contexts, explore numbers and relate them in different ways which have no traditional restriction (Van De Walle, Karp and Bay-Williams, 2010).

• Howden (1989) described it as “good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.”

• According to Marilyn Burns(1999): Understanding the relationships between and among numbers Having the ability to think flexibly about numbers and to break numbers

apart and put them back together Being familiar with the properties of single digit numbers and using this

information to calculate efficiently using larger numbers Having the ability to manipulate numbers in their head Having effective ways to estimate

Place ValuePlace Value

• According to Mathisfun.com (2011), place value is the position of each digit in the number, it shows what the digits represent and which group they count. For example, unit, ten, hundred. Place value is the value of a digit as determined by its position in a number, the name of the place or location of a digit in a number.

Example: Example: 234

The common place value system is base-ten place value system.

Base 10Base 10

Hundreds Tens Ones

2 3 4

Hundreds Tens Ones Tenths Hundredths

10² 10¹ 10º 10 ¹﹣ 10 ²﹣

10×10 = 100 10 1 1÷10= 0.1 1÷10×10= 0.01