Decimals

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DECIMALSDECIMALS

Put on your thinking hatWhy is there a need for decimal to exists

in our daily life?Sketch figures that would help a child to

understand that 0.5 = 0.50How could play coins be used to

demonstrate 5 – 4.21 = 0.79?

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Basic Facts of DecimalsBasic Facts of Decimals Decimal number is a representation of fraction

whose denominator is the multiple of 10 Example: 7 = 0.7 12 = 0.12 246 = 0.246 10 100 1000 Decimal numbers can be represented by

number lines Decimal numbers can be converted to fractions

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Basic Facts of DecimalsBasic Facts of Decimals Fractions whose denominators are multiple of

10 can be converted to decimals Every digit in a decimal number has its own

place value Number of decimal place for a decimal number

can be determined by the number of digit at the right hand side from the decimal point.

Estimation of a decimal number is determined by the value of the first digit at its right hand side. If the digit is 5 or more, the estimation will add 1; if less the estimation will add 0

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Basic Facts of DecimalsBasic Facts of Decimals Addition and subtraction of decimal numbers

can be done by arranging the number vertically with the decimal points arranged in the same column

Multiplication of decimal number with 10,100,1000 can be done by moving the decimal point to the right according to the number of 0 digit

Division of decimal number with 10,100,1000 can be done by moving the decimal point to the left according to the number of 0 digit

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Basic Intrepretation of decimalsAs special fractions with denominators of

some multiples of 10As an extension of base 10 place value

system

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Place values in decimalPlace values in decimalThousands Hundreds Tens Ones Tenth Hundredth Thousandth

5 4 3 2 4 6 7

5432.467

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Decimal IllustrationDecimal Illustration

1 41.4

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Decimal IllustrationDecimal Illustration

1 4 7

1.47

Relation of decimals to whole numbers Decimal numeration comes from a combination of

fraction concept and whole-number numeration. The major sequence to get right is the transition from whole numbers to decimal numbers.

The whole-number numeration system has the following principles:

(i) GROUPING BY 10s (ten ones is a ten, ten tens is a hundred, etc.);

(ii) LEFT x 10, RIGHT / 10 (multiplicativity); (iii) 10 IS 10 ONES, 100 IS 100 ONES AND 10

TENS (24 ones = 2 tens and 4 ones); (iv) PLACE VALUE POSITIONS (Ones, Tens,

Hundreds, ... - moving to the left); (v) ONE IS RIGHT HAND POSITION (200 - 2

hundreds, 0 tens and 0 ones); and (vi) VALUES RELATE TO THE ONES (and increase

to the left as move away from ones).

As the whole-number system is extended to decimal numbers, most principles remain fairly much the same as follows: (i) GROUPING BY 10s REMAINS - PARTITIONING

BY 10s ADDED (now the place values go in both directions from ones);

(ii) LEFT x 10, RIGHT / 10 REMAINS (multiplicativity remains and is across a wider range of place values);

(iii) WHOLE NUMBER PLACE VALUE POSITIONS (..., Hundreds, Tens, Ones) REMAIN - NEW DECIMAL POSITIONS ADDED (tenths, hundredths, ...);

(iv) SHOWING WHERE THE ONES ARE REMAINS CENTRAL (now shown by the decimal point - not the right hand position); and

(v) VALUES RELATE TO THE ONES REMAINS (still increase to the left).

There are of course some new ideas (as there has to be when a whole new section is added):

(i) PARTITIONING FROM ONES FOR DECIMAL PLACE VALUES (we now move to the right from the ones by dividing by 10 as well as moving to the right by grouping by 10s);

(ii) PLACE VALUES INFINITE IN BOTH DIRECTIONS (before it was only infinite to the left);

(iii) PLACE VALUE NAMES BASED ON SYMMETRY ABOUT ONE (tens/tenths. hundreds/hundredths, etc.);

(iv) DECIMAL POINT (should not take a position) (this has been added to show the ones position as the right hand position now could be anything); and

(v) TENTHS ARE DIRECTLY FRACTIONS (10 PARTS), HUNDREDTHS ARE DIRECTLY FRACTIONS (100 PARTS) AND TENTHS OF TENTHS (thus 23 hundredths is 23 out of 100 parts of a whole, but it is also 2 tenths and 3 hudredths).

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EXAMPLE OF DECIMAL TEACHING STRATEGYLEARNING AREA: Subtraction of Decimal Numbers

LEARNING OBJECTIVE - Pupils will be taught to:(i) Subtract two decimal numbers up to two decimal

places

LEARNING OUTCOMES - Pupils will be able to:(i) Subtract any two decimal numbers up to two

decimal places by converting into fractions

(ii) Subtract any two decimal numbers up to two decimal places by using standard form

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Teaching Aids: Place Value Chart, 100 grid chart, scissors

INDUCTION SET:Teacher shows place value chart as

illustrated below.Teacher asks pupils to fill in the correct

decimal numbers such as 0.23, 1.46, 2.08, 14.67, 104.58

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hundreds tens Ones Tenth hundredth

0.23

1.46

2.08

14.67

104.58

PLACE VALUENUMBERS

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TEACHING DEVELOPMENT

• Subtract decimal number from decimal number up to two decimal places without regrouping

• Teacher use 100 grid chart to explain subtraction of decimal numbers

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Ask pupil to colour 25 parts from the 100 grid chart 100

Ask pupils to take out 12 part from the 25 100 100 coloured parts by cutting with scissors

Ask pupils to count coloured parts left

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Guide the pupils to write mathematics sentences using the previous activity

25 - 12 = 13 100 100 100

0.25 - 0.12 = 0.13

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Guide pupils to do subtraction in standard form

One Tenth hundredth

00

21

52

0 1 3

0.25 - 0.12 = 0.13

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ENRICHMENT ACTIVITY15.43

-1.02

- 2.17

- 4.22 =- 5.16

-1.89

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TASKTASKWork individually or in pairChoose one/more learning outcome

from the topic DecimalsPrepare a complete lesson plan using

the given format