MINGGU 2

PLACE VALUENILAI TEMPAT

Isi KandunganPerwakilan Nilai Tempat bagi Nombor◦Pengumpulan (Grouping)◦Penukaran (Trading)◦Membina idea Nilai Tempat◦Pengumpulan & Penamaan semula

Our numeration systemThe Hindu-Arabic numeration system has four important characteristics: place value : the position of a digit

represents its valueBase of ten : the system has 10

digits, ie 0 through 9Use of zero : allows us to represent

symbolically the absence of something.

Additive property: numbers can be summed with respect to place value

Thinking place value:

Which pile would you use to decide how many?

Ten-frame provide a convenient model for counting, grouping & eventually representing 2-digit number

Provides valuable mental imagery in naming & differentiating 2 numbers

Grouping or trading(Lesson Idea 8-1) provides some early guided practice in grouping by tens.

These models show how grouping by ten helps determine the number in the group more quickly.

Grouping or tradingTrading and grouping by tens provide problem-solving activities that contribute to number sense and provide opportunities for developing mental computation

(Lesson Idea 8-2) another grouping experience that further facilitates counting and trading.

Grouping & Trading

Modeling Place Value“Hands-on” experience using

manipulatives essential in establishing & developing place-value concept this process is called “modeling”

Research shows that instructions should focus on…

(Thompson, 1990; Wearne & Hiebert, 1994)

Concret

e Models

Oral description

s

Symbolic representations

Proportional & Non-proportional

Place-value models

Additional physical models that are effective in helping students understand place values especially those involving large numbers…

Skip beyond the teensNames for numbers 11-19 are not

consistent with the names for other numbers

Do not exhibit place value characteristics in their names like other numbers; e.g.◦ 21, 22, 23, 24,…◦ 31, 32, 33, 34,…◦ 41, 42, 43, 44,…

How to call the names of 11, 12, 13, 14, …?

It is important that children have the capability of thinking numbers in various ways:◦ 5 X 5◦ 2 RM10 + RM5◦ 2 dozen eggs + 1 egg◦ 4 six-packs of milk + 1 pack◦ 25 cm or 0.25m or ¼ m

If place value is needed, the tens & ones model is needed.

Progression from concrete model to symbolic representation

Tens

Ones

2 525

Concrete Physical models

Semi-concrete Organizational models

SymbolicRepresentational models

How many tens? [ 2 ]How many ones? [ 5 ]Name this number [ 25 ]

H T O

1 2 3

100 20 3+ + 1 0 02 0

3

= 123

Important for young children to observe what happens when the number after 9 (or 19, 29, 99, 109, 999, etc…) is modeled.

Trading occursBridging from one decade (ten) to

another should be recognized & clearly understood

RM1 10sen

2 9

RM1 10sen

2 10

RM1 10sen

3 0Regrouping is requiredso a trade is made

2 Rounding Rules for a number ending with 5:◦ Increase the previous digit by 1◦ If the digit preceding the 5 is even,

drop the value 5, if it is odd, increase the previous digit by 1

Example◦ 75 would be rounded to 80 according to

rule 1 & 2◦ 85 would be rounded to 90 according to

rule 1 & 80 according to rule 2.

Models for rounding

A roller coaster model◦Effective tool if children understand the number line

◦The coaster could go either way when you have a five

◦Attention is given to the back-end digit or digits

◦Refer to Fig 7-13

55

60

656357

750

800

850

Where do 784 slide to?Where do 757 slide to?Where do 843 slide to?

Find numbers that slide to: 700, 800, 900?

Using the hundred charts

Some Basic Rules…

Are symbolic activitiesShould follow much

modeling & talking about numbers

Avoid focusing reading, writing & ordering numbers symbolically only

Develop number sense

H T O

1 2 3

H T O

12 3

H T O

123

1 hundred 2 tens 3 ones

12 tens 3 ones

123 ones

H T O

3 8 0Reads: 3 hundreds 8 tensRealizes there are no onesRereads: 38 tens, which is 380

Not logical to write numbers as they sound

Example: ◦ Sixty-one -> 601◦ One hundred and twenty three ->

100203If a child makes this mistake,

teacher can use the place-value mats as a model

Tens Ones

6 1

H T O

6 0 1

Sixty-onerepresents

Not this

Modeling several numbers on the mat will help clarify this problem

What is three hundred fifty-six thousand, ninety-seven in symbol?

What is four hundred five and three tenths?

Sample of teaching aids

Comments?

TutorialShow how 201 & 120 would be

represented with three different place-value models.

Examine a primary mathematics text book. How many different place-value models are illustrated? Which model is used most? Comment if the textbook provides a good choice of models? Defend your answer.

AmaliMake a number expander (Reys,

pp176) or arrow cards for use in reinforcing reading and writing numbers.

Make hundred chart and carry out lesson Idea 8-3 (Reys; pp177) and Activity in the Classroom 8-3 (Reys; pp 182)

What have you learnt from these two activities?

Arrow Cards