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1.0 THE DEFINITION OF ALGORITHM

An algorithm is step-by-step procedure to solve a problem. The word

derives from the name of the mathematician, Mohammed Ibn - Musa al-

Khwarizmi, who was part of the royal court in Baghdad and who lived from about780 to 850. Al-Khwarizmi's work is the likely source for the word algebra as well.

(http://whatis.techtarget.com/definition/0,,sid9_gci211545,00.html ).

An algorithm is used because:

i) Always work to builds confidence in students

ii) Trains students to become fast in counting - mentally

iii) To complete the topic in syllabus and to establishes the potential in each

of the students fairly.

Say that everyone in the class can +, -, x, ÷

2.0 THE ALGORITHM OF ADDITION

The addition algorithm consists of adding ones, tens, hundreds, and so

on, regrouping any sum greater than 9 in each place. The reason the addition

algorithm works can be illustrated by examining the numbers in their expanded

form. There are many ways in algorithm of addition. Let¶s go through each of the

method. Let¶s say that the example is 68+94 for each of the method.

2.1 Expanded algorithm

68+94 =

Tens ones

(60+90) + (8+4)

150 + 12

=162

In the expanded algorithm, the order in which the numbers with a

given place value are added doesn¶t matter because all partial sum are

recorded.



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2.2 Standard algorithm

68+94=

1

6 8

+ 9 4

1 6 2

TENS ONES

16 2

In the standard algorithm usually we start to calculate with the ones.

Whenever we use this algorithm and there are 10 or more ones, we regroup 10ones as 1 ten and then add the tens altogether.

2.3 Left-to-right algorithm

68 + 94 =

6 8

+ 9 4

1 5

1 2

1 6 2



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In the left-to-right algorithm we must definitely start from left (tens) first,

sum up the tens and then sum up ones. Finally sum up the sum of tens and the

sum of ones.

2.4 Alternative algorithm (Lattice method)

68 + 94 =

6 8

+ 9 4

1 1

5 2

1 6 2

In the Lattice method, the answer for ones and tens columns writes in

vertical. Then to get the answer make a inclined line as shown to get the sum of

the equation correctly. Then sum up the number according to the line make.

2.5 Estimating sums

Estimate 68 + 94 =

68 70

94 90

160

In the estimating method, the most common method of estimating sums is to

round each add to a specific number near it and then add the rounded numbers. Thismethod is suitable to question that does not need the exact answer.



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3.0 MANIPULATIVE MATERIALS

Manipulative materials are any concrete objects that allow students toexplore an idea in an active, hands-on approach. Manipulative can be almostanything ± blocks, shapes, spinners, or even paper that is cut or folded.

(http://www.mathatube.com/glo-manipulatives.html ).

The manipulative materials help the students to understand faster aboutthe mathematics concept. The manipulative materials also use as a tool for students to solve problems. By using real tool to represent their thinking, theyseem to have many methods in order to solve the problem. They explore thematerials to the max. It happens in real life when the architects often make amodel of prototype first before they build the real one.

After some times searching for the information about the manipulativematerials, I found that using the colorchips is the best but I use the idea of it butusing candy which is µsmarties¶. I think this is very interesting manipulativematerial.

As we all know smarties is the famous candy brand. The children lovethem. They taste delicious and colorful. I sure the children will love it if we usesmarties as a manipulative material in mathematics.

From all of the method of algorithm shows in previous page, I prefer the

standard algorithm to explain with my manipulative material (smarties).



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68 + 94 =

1

6 8

+ 9 4

1 6 2

Let¶s say that : Red smarties tens

Blue smarties ones

10 ones 1 ten

10 ONES

1 TEN

16 2

TENS ONES

TENS ONES



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Using this manipulative material, we use two colors of smarties which red and blue.

They are place in two bowls like in previous page. First step is to two take out ten blue

smarties because the more than nine number must be place in tens bowl. Then take

the new red smarties to replace the ten red smarties and put it in the tens bowl. Count

the smarties remains and add. Make sure to place the tens and ones correctly when

adding.

Example tens ones

16 2

So the answer is 162

y The blue smarties that been take out from the bowl can be eaten. The students

can eat candy while making the calculation. This is fun!



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Appendix



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Regrouping With Addition

The addition algorithm consists of adding ones, then tens, then hundreds, and so on, regrouping any sumgreater than 9 in each place. The reason the addition algorithm works can be illustrated by examining thenumbers in their expanded form. For example, have children consider 58 + 36.

58+ 3650 + 8+ 30 + 680 + 14 = 80 + (10 + 4)= (80 + 10) + 4= 90 + 4= 94

The standard algorithm takes place in two stages and provides a shortcut for recording the renamingprocess.

When a vertical addition problem is presented to children, be sure to emphasize the need to correctlyalign the digits before completing the addition.

Estimating Sums

When an exact answer is not necessary, an estimate can be used. The most common method of estimating sums is to round each add end to a specific place and then add the rounded numbers. In this

chapter, children round numbers to the nearest ten with the help of a number line.

Estimate:48 + 31

48 50+ 31 + 30 Round each number to the nearest ten.80 Add the rounded numbers.

Mental math can often be used to complete estimates. At this grade level, however, explain that errorscan be more easily identified if children write down their work when estimating answers.

Teaching Model 10.3: Regroup Ones as Tens



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