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Multiplication for Elementary School Students

Education is one of the chief obstacles to intelligence and freedom of thought.

---Bertrand A. Russell

Education is the process of instructions aimed at the overall development of children. It dispels ignorance. It includes moral values, character-development and strengthening of mind.

Education in a broad sense is an experience that affects an individual’s mind, character as well as physical ability. In a technical sense, it is a process in which the society’s accumulated knowledge, values and skills are been transmitted from generation to generation through various types of institutions. In other words, education is one of the most time-bound activities human participates in.

In our society, we get the education through schools and other institutions. Schools help us to build our character strong, increase our knowledge resulting us to be independent.

Elementary Education

Also known as Primary Education is the first phase of the formal education an institution offers. It starts at the age of five or six, which may vary from place to place and continues for the next six to eight years.

One of the basic areas which every institution involve in teaching a child from the very first day of his schooling is Mathematics.

Mathematics, derived from a Greek word ‘Mathematika’, is the study of numbers and quantities, their combinations and interrelations, their configurations and transformations, and their structure and generalizations.

Only professional mathematicians learn anything from proofs. Other people learn from explanations.

---R. P. Boas

Mathematics is all around us. We use it in our everyday, professionally as well as personally. We use mathematics to budget our money and time, balance our bank accounts, shop for groceries and other important items, file our taxes, and even to calculate tips in restaurants. To teach this subject to the children, we have keep this in our mind and show them that how our life relies upon our basic math skills. This will be the first step to help them to overcome the mathematics anxiety.

Once the child has increased his or her confidence level in mathematics skills, it is time to work on their test anxiety. Give the child some practice tests making sure that each mathematics concepts of their level is covered. At the same time, do not make the questions too difficult.

Success in mathematics improves the child’s self-esteem and confidence and paves the way for them to succeed in all facets of life.

Mathematics can be taught as well as learnt successfully by developing a specific analysis of the task. Every skill is built upon the previous skill which has been learned.

Following are the ways in which we can help the children to know the importance of mathematics in our everyday lives –

(1) Problem-solving

(2) Budgeting money (3) Time management

(4) Calculating taxes

(5) Estimating distances or weights

In elementary arithmetic, there are four basic operations – Addition, Subtraction, Multiplication and Division. Generally, students face more difficulty in performing multiplication and division than addition and subtraction. In fact, division seems to be one of the hardest mathematical concepts to be grasped. But when it is understood, it seems to be very easy. And to make it easy, the inverse of division (multiplication) should be understood thoroughly.

Mathematics at Home

Making the children do some mathematics activities at home will definitely encourage them to use their skills learnt at school. The children will earn appreciation from the family members as well as enjoy the moments. In the following ways the parents can help their children to enjoy mathematics –

1.Ask them to find out a particular range of number, for example, all the numbers between 20 and 50. This process can follow finding the odd or even numbers, prime numbers or multiplication facts of any number etc.

2.Ask them to tally the items purchased from the grocery-store as well as check out the total amount paid for the items.

While on long trip, ask them to estimate the distance travelled as well as how many more miles left to reach the destination.

Multiplication

Multiplication is related to addition. It is a quick way to add the numbers together. For instance, if you plan to prepare a glass of lemonade, it’s easy to determine the number of lemons to be used. But to make several glasses of lemonade, how will you know that how many lemons should you have? By multiplying!

The result of multiplication is the total number that would be obtained by combining several groups of similar size. The same result can be obtained by repeated addition. If we are combining 6 groups of 5 objects in each group, we could arrive at the same answer by addition.

Now this is the other way to understand –

2+2+2+2+2+2 = 12

6 multiplied by 2 means 6 times 2. You are adding the 3 four times.

Here, we are having 6 twos. The quicker way to find the answer is –

6×2 = 12

Following are some of the sums for practice –

Problem How many of the numbers? Multiplication Answer

6×6×6 3 6×3 18

7×7×7×7×7 5 7×5 35

4×4×4×4 4 4×4 16

2×2×2×2×2 5 2×5 10

9×9×9×9×9×9 6 9×6 54

Setting Up Numbers to Multiply

When we multiply, we can write the numbers in two ways using the times sign - X.

When multiplying small numbers, we can write them on the same line with the X in the middle -

6 × 4

However, we'll want to stack when multiplying with larger numbers -

40 ×6 240

Multiplication Terms

In the process of multiplication operation, several terms are used, which are as follows –

1.Multiplier – The number which do the multiplying.

2.Multiplicand – The number which get multiplied.

3.Product – The answer to a multiplication problem.

In the expression, 5 × 6 –

5 is the multiplicand.

6 is the multiplier.

5 × 6 = 30 is the product.

Multiplication can be symbolized in three ways –

1.With a ×, as in 5 6.

2.With a centered dot, as in 5.6.

3.By writing the numbers next to each other, as in (5) (6) or 5(6).

Different Approaches

Different civilizations opted for multiplication differently –

1.Egyptians – The Egyptians included additions and doubling in their method of multiplication. For instance, to find the product of 13×24, one had to double 24 three times, obtaining 1×24 = 24, 2×24 = 48, 4×24 = 96, 8×24 = 192. The full product could then be found by adding the appropriate terms found in the doubling sequence – 13×24 = (1+4+8) × 24 = (1×24) +(4×24) + (8×24) = 24+96+192 = 312

In other words, for the example 7x13 –

We make two columns. We start with 1 and 7 (one of the numbers we want to multiply). Then we double the number in each column, over and over until we get to a number just below the other number (13 in this case) in the left-hand column -

1 7

2 14

4 28

8 56

We have powers of two in the left column, and we have 7 times the powers of two in the right column. We can make 13 out of the left column, by 8+4+1. That is where the base 2 arithmetic comes in. We mark those numbers (8, 4, 1). And we add up the numbers in the second column, skipping the ones that are not next to a marked power of two -

/1 7

/2 14

/4 28

/8 56

2.Indus Valley – In this region, the early Hindu mathematicians followed various intuitive tricks to perform multiplication. The most popular was the Lattice Multiplication. In this, rows and columns are drawn labeled by the multiplicands. Each box was diagonally divided into two. The entries held the partial products written as decimal numbers. The final product could come up by summing up the diagonals of the lattice.

In other words, the lattice is filled in with 2-digit products of the corresponding digits labeling each row and column – the 10s digit goes in the top left corner. During the addition phase, the lattice is summed on the diagonals. Finally, if a carry phase is necessary, the answer is converted to normal form by carrying 10s digits.

3.Chinese Method – The Chinese mathematicians used abacus in hand calculations involving addition and multiplication. An abacus is a calculation tool, often constructed as a wooden frame with beads sliding on wires. It has sliding indicators to keep track of where we are, which are fast enough to use that they don’t really slow down your pace when multiplying. The two upper mini abacuses can also be used to help us remember the two numbers we are multiplying.

To multiply using an abacus, following points should be in mind –

1.If the numbers involved are decimals, count how many digits behind the decimal there is total for both the numbers.

2.Set the abacus to one of the numbers.

3.Add that number to itself for the number in that starting place.

4.The sum will be the final product.

4.Modern Method – Brahmagupta was the first to describe the modern method of multiplication based on the Hindu-Arabic numeral systems. He gave definite rules of all the four basic operations – Addition, Subtraction, Multiplication and Division.

Henry Burchard Fine, who was the Professor of Mathematics at Princeton University, quoted –

The Indians are the inventors not only of the positional decimal system itself, but of most of the processes involved in elementary reckoning with the system. Addition and subtraction they performed quite as they are performed now- a-days; multiplication they effected in many ways, ours among them, but division they did cumbrously.

Multiplication Chart

It is a tool to determine the product of two whole numbers. Following is a multiplication chart –

Multiplication Facts

1.Following are the facts of 0, 1, 2 and 3 –

0 × 1 = 0

0 × 2 = 0

0 × 3 = 0

0 × 4 = 0

0 × 5 = 0

0 × 6 = 0

0 × 7 = 0

0 × 8 = 0

0 × 9 = 0

0 × 10 = 0

1 × 1 = 1

1 × 2 = 2

1 × 3 = 3

1 × 4 = 4

1 × 5 = 5

1 × 6 = 6

1 × 7 = 7

1 × 8 = 8

1 × 9 = 9

1 × 10 = 10

2 × 1 = 2

2 × 2 = 4

2 × 3 = 6

2 × 4 = 8

2 × 5 = 10

2 × 6 = 12

2 × 7 = 14

2 × 8 = 16

2 × 9 = 18

2 × 10 = 20

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

3 × 6 = 18

3 × 7 = 21

3 × 8 = 24

3 × 9 = 27

3 × 10 = 30

2.Following are the facts of 4, 5 and 6 –

4 × 1 = 4

4 × 2 = 8

4 × 3 = 12

4 × 4 = 16

4 × 5 = 20

4 × 6 = 24

4 × 7 = 28

4 × 8 = 32

4 × 9 = 36

4 × 10 = 40

5 × 1 = 5

5 × 2 = 10

5 × 3 = 15

5 × 4 = 20

5 × 5 = 25

5 × 6 = 30

5 × 7 = 35

5 × 8 = 40

5 × 9 = 45

5 × 10 = 50

6 × 1 = 6

6 × 2 = 12

6 × 3 = 18

6 × 4 = 24

6 × 5 = 30

6 × 6 = 36

6 × 7 = 42

6 × 8 = 48

6 × 9 = 54

6 × 10 = 60

3.Following are the facts of 7, 8 and 9 –

7 × 1 = 7

7 × 2 = 14

7 × 3 = 21

7 × 4 = 28

7 × 5 = 35

7 × 6 = 42

7 × 7 = 49

7 × 8 = 56

7 × 9 = 63

7 × 10 = 70

8 × 1 = 8

8 × 2 = 16

8 × 3 = 24

8 × 4 = 32

8 × 5 = 40

8 × 6 = 48

8 × 7 = 56

8 × 8 = 64

8 × 9 = 72

8 × 10 = 80

9 × 1 = 9

9 × 2 = 18

9 × 3 = 27

9 × 4 = 36

9 × 5 = 45

9 × 6 = 54

9 × 7 = 63

9 × 8 = 72

9 × 9 = 81

9 × 10 = 90

4.Following are the facts of 10, 11 and 12 –

10 × 1 = 10

10 × 2 = 20

10 × 3 = 30

10 × 4 = 40

10 × 5 = 50

10 × 6 = 60

10 × 7 = 70

10 × 8 = 80

10 × 9 = 90

10 × 10 =100

11 × 1 = 11

11 × 2 = 22

11 × 3 = 33

11 × 4 = 44

11 × 5 = 55

11 × 6 = 66

11 × 7 = 77

11 × 8 = 88

11 × 9 = 99

11 × 10 =110

12 × 1 = 12

12 × 2 = 24

12 × 3 = 36

12 × 4 = 48

12 × 5 = 60

12 × 6 = 72

12 × 7 = 84

12 × 8 = 96

12 × 9 = 108

12 × 10 =120

Tips to memorize Multiplication Facts

Memorizing the multiplication facts makes multiplying small numbers easy. When multiplying with large numbers make sure to stack the numbers in their digit places. The traditional way to learn the multiplication facts is to read them aloud number of times. Not to say, it still works. Apart from this method, there are other tips which help the students to learn the facts. Following are few tips to learn the multiplication facts in an easy way –

1.As we know that any number times zero is zero, we can memorize the 0s first.

2.The 1s can be learnt quickly as any number multiplied by one will be equal to the number itself.

3.2s and 3s can be learnt by counting twos and threes respectively.

4.5s and 10s can be learnt by counting fives and tens respectively.

5.Rhyming times can be learnt easier too. For example, 6× 6 = 36,

6 ×4 = 24, 6× 8 = 48 etc.

Practice Fact Test

1.Find the product –

(1) 9 (2) 12 (3) 11 (4) 11 (5) 9

×3 ×4 × 2 ×8 ×8

(6) 8 (7) 5 (8) 3 (9) 2 (10) 9

×8 ×6 ×5 ×4 ×8

2.Count by twos up to the number 12.

3.Count by threes up to the number 15.

4.Count by fives up to the number 30.

5.Count by tens up to the number 70.

Activity

1. Join the factors to the correct product – 18 27 5 10 35 0 6 12 3 36

3×9 2×3 4×9 1×5 2×5 0×8 4×3 6×3 7×5 1×3

2. Find the missing number –

1) 72 2) 42 3) 63

× × ×

4608 3402 2835 4) 72 5) 58 6) 33

× × ×

6624 3364 231

3. There are 8 plates with 4 cupcakes and 7 scoops of ice cream on each plate. How many cupcakes are there in all? And how many scoops of ice cream are there in all?

4. Solve the following with the order of operations - (1) 7 + 3 x 2 = ____ (2) 13 + 4 x 2 = ____ (3) 17 + 0 x 8 = ____ (4) 2 x 5 + 5 = ____ (5) 43 - 7 x 1 = _____ (6) 27 - 1 x 4 = _____ (7) 33 - 5 x 3 = _____ (8) 62 - 4 x 7 = _____

Relationship between Multiplication And Division

Understanding multiplication and division is fundamental to mathematics. The relation between multiplication and division is an inverse one. Multiplication and division “undo” each other. For example, 6 multiplied by 5 is equal to 30, and 30 divided by 5 is equal to 6. For this reason, multiplication and division are known as “inverse” operations, meaning that they undo each other. Every multiplication fact has two division facts. For example,

8 × 9 = 72 - Multiplication Fact

72 ÷ 8 = 9 - Division Fact

72 ÷ 9 = 8 - Division Fact

7 × 6 = 42 - Multiplication Fact

42 ÷ 7 = 6 - Division Fact

42 ÷ 6 = 7 - Division Fact

Another concept presented is the idea of a “fact family”. A mathematical fact is a true statement like “six times five is equal to thirty” or 6 x 5 = 30. A fact family is the group of all the related multiplication and division facts, between three related numbers. With three numbers, there will be two multiplication and two division facts.

Rules of Multiplication

1.When two numbers are multiplied in any order, the product is the same. For example, 2×4 = 8 4×2 = 8 9×7 = 63 7×9 = 63

2.When any number is multiplied by 1, the product is the number itself. For example, 6×1 = 6 3×1 = 3

3.When any number is multiplied by zero, the product is zero. For example, 4×0 = 0 2×0 = 0

4.When three numbers are multiplied in any order, the product is the same. For example, 2×3×5 = 30 3×2×5 = 30 2×5×3 = 30 3×5×2 = 30 5×2×3 = 30 5×3×2 = 30

Exercise

Fill in the blanks by using facts about multiplication –

1.(a) 4×3 = ___ ×4 (b) 7× ___ = 8×7

(e) 6×3 = 3× ___ (f) ___ ×10 = 10×5

2.(a) 5× ___ = 5 (b) ___ ×1 = 9

(e) 8×1 = ___ (f) ___ ×1 = 1

3. (a) 9× ___ = 0 (b) 12×0 = ___

4. (a) 2×3×4 = 4×3×3 ___ (b) 3×4 ___ = 4×3×5

Methods of Multiplication

Following are the different methods used o perform multiplication –

1.Grouping – Under this method, following should be the steps for the example 24×8 –

a.Write the problem as 24 ×8

b.Eight times 4 is 32. Write down 2 and carry the 3.

c.Eight times 2 is 16. Add the 3 that was carried over from Step 1, and write the result 19, beside the 2 that was written in Step 1.

d.The final product is 192.

2.Partial Product - Under this method, following should be the steps for the example 6×8 –

a.Break 8 into 3 and 5, and write as (3+5).

b.Multiply each with the other factor, 6 - 6×3 + 6×5

c.Add the partial product, as 18+30 = 48

d.The final product is 48.

3.By using repeated addition on the number line - - Under this method, following should be the steps for the example 2×6 –

a.Draw a number line starting from 0 to 12.

b.6 jumps of 2 from the point 0.

c.The jumps end on the point 12.

d.The final product is 12.

4.By using patterns - Under this method, following should be the steps for the example 3×5 –

a.Draw 3 rows and 5 columns.

b.Count the total number of boxes.

c.The final product is the total number of boxes counted in Step 2, 15.

5.By using sticks - Under this method, following should be the steps for the example 3×2 –

a.Draw 3 horizontal sticks.

b.Draw 2 vertical sticks crossing the sticks drawn in Step 1.

c.Count the number of points where the sticks crossed.

d.The total number of cross points is 6, which is the final product.

6.End zeroes – The placement of partial products must be kept in mind when multiplying in problems involving end zeroes, as in –

27 ×40 1080

We have 0 units times 27 plus 4 tens times 27, as - 27 ×40 0 1080 1080

The 0 in the units place plays an important part in the reading of the final product. End zeroes are often called ‘place holders’ since their only function in the problem is to hold the digit positions which they occupy, thus helping to place the other digits in the problem accurately. The end zero in the foregoing problem can be accounted for very nicely, while at the same time placing the other digits correctly, by means of a shortcut. This consists of off setting the 40 one place to the right and then simply bringing down the 0, without using it as a multiplier at all.

Practice Test

1.Multiply by Grouping method – (1) 36 (2) 85 (3) 96 (4) 53 (5) 82 ×5 ×3 ×8 ×4 ×7

(6) 63 (7) 11 (8) 95 (9) 56 (10) 75 ×8 ×8 ×5 ×7 ×6

2.Multiply by Partial Product method –

(1) 85 (2) 54 (3) 312 (4) 513 (5) 2015

×9 ×8 ×7 ×6 ×5

(6) 815 (7) 108 (8) 707 (9) 818 (10) 233

×4 ×3 ×4 ×2 ×5

3.Multiply by Repeated Addition method –

(1) 5 (2) 3 (3) 5 (4) 9 (5) 14

×3 ×4 ×4 ×2 ×2

(6) 12 (7) 15 (8) 13 (9) 17 (10) 14

×3 ×5 ×7 ×3 ×5

4.Multiply by Patterns method –

(1) 4 (2) 4 (3) 3 (4) 4 (5) 14

×4 ×2 ×4 ×5 ×2

(6) 3 (7) 2 (8) 1 (9) 5 (10) 8

×6 ×4 ×4 ×6 ×4

5.Multiply by Sticks method –

(1) 2 (2) 1 (3) 3 (4) 3 (5) 5

×1 ×2 ×3 ×2 ×0

(6) 6 (7) 5 (8) 7 (9) 8 (10) 6

×3 ×4 ×3 ×5 ×4

Multiplying 2-digit number with Single digit number

For the example, 28 × 2 –

1.Multiply 8 by 2.

2.It will give a partial product of 16.

3.Place 6 in the ones place of the product and carry the 1.

4.Now, multiply 2 × 2 to get 4.

5.Add 4 to 1 that have been carried in Step 3 to get the final product 56.

Practice Test

Multiply –

(1) 24 (2) 32 (3) 40 (4) 72 (5) 65

×2 ×3 ×2 ×5 ×6

(6) 94 (7) 33 (8) 47 (9) 22 (10)15

×4 ×4 ×5 ×6 ×4

Multiplying 2-digit number with 2-digit number

For the example, 64 × 46 –

1.Multiply 64 by 6 ones. 64 × 6 ones = 384 ones

2.Multiply 64 by 4 ones. 64 × 4 tens = 256 tens = 2560 ones

3.Add 384 and 2560. 384 + 2560 = 2944

So, 64 × 46 = 2944

Practice Test

Multiply –

(1) 18 (2) 27 (3) 35 (4) 45 (5) 52

×16 ×29 ×17 ×36 ×48

(6) 65 (7) 62 (8) 68 (9) 78 (10) 89

×15 ×11 ×42 ×53 ×75

Multiplying 3-digit number with single digit number

For the example, 221 × 4 –

1.Multiply 1 ones by 4 ones. 1 ones × 4 = 4 ones

2.Write 4 in the ones place.

3.Multiply 2 tens by 4. 2 tens × 4 = 8 tens

4.Write 8 in the tens place.

5.Multiply 2 hundreds by 4.

2hundreds × 4 = 8 hundreds

6.Write 8 in the hundreds place.

So, 221 × 4 = 884

Practice Test

Multiply –

(1) 132 (2) 309 (3) 932 (4) 102 (5) 211

×2 ×3 ×2 ×5 ×6

(6) 418 (7) 101 (8) 123 (9) 201 (10) 303

×2 ×7 ×3 ×4 ×3

Multiplying 3-digit number with 2-digit number

For the example, 212 × 26 –

1.212 × 6 ones = 1272 ones

2.212 × 2 tens = 424 tens = 4240 ones

3.Add 1272 and 4240 1272 + 4240 = 5512

So, 212 × 26= 5512

Practice Test

Multiply –

(1) 132 (2) 301 (3) 343 (4) 307 (5) 501

×16 ×19 ×26 ×31 ×15

(6) 611 (7) 215 (8) 687 (9) 109 (10) 799

×16 ×42 ×13 ×53 ×11

Multiplying 4-digit number with single digit number

For the example, 1396 × 4 –

1.4 × 6 ones = 24 ones 2 tens 4 ones

2.4 × 9 tens = 36 tens = 360 ones 3 hundreds 6 tens 0 ones

3.4 × 3 hundreds = 12 hundreds = 1200 ones 1 thousand 2 hundreds 0 tens 0 ones

4.4 × 1 thousand = 4 thousands = 4000 ones 4 thousands 0 hundreds 0 tens 0 ones

5.Add 24, 360, 1200 and 4000. 24 + 360 + 1200 + 4000 = 5584

So, 1396 × 4= 5584

Practice Test

Multiply –

(1) 3542 (2) 1685 (3) 1769 (4) 1048 (5) 1745

×2 ×3 ×4 ×6 ×5

(6) 1382 (7) 2573 (8) 1438 (9) 1253 (10) 1027

×6 ×3 ×6 ×6 ×9

Multiplying with 10s

For the example, 36 × 10 –

1.Place the decimal point one place to the left in the number ending in 0.

2.This means 36 × 1 = 36.

3.Place the decimal point of the product one place to the right.

4.This means 360 – the final product.

Multiplying with 100s

For the example, 21 × 100 –

1.Place the decimal point two places to the left in the number ending in 0.

2.This means 21 × 1 = 21.

3.Place the decimal point of the product two places to the right.

4.This means 2100 – the final product.

Multiplying with 1000s

For the example, 8 × 1000 –

1.Place the decimal point three places to the left in the number ending in 0.

2.This means 8 × 1 = 8.

3.Place the decimal point of the product three places to the right.

4.This means 8000 – the final product.

Practice Test

Multiply –

(1) 28 (2) 96 (3) 140

×10 ×90 ×20

(4) 2 (5) 70 (6) 85 ×100 ×400 ×600

(7) 5 (8) 9 (9) 6 ×1000 ×1000 ×1000

Multiplication Game

This is a very simple game which helps reinforces children's knowledge of their multiplication tables.

Materials

30 2" x 2" squares

Preparation

Decide on a times table (i.e. the 7X tables) Write each factor and product on one side of a card to make a match of an equation. For example, on one square write 7, the second square write 2 and on the third square write 14. That makes one equation. Then you would write 7 on the next square, 3 on another and 21 on the third. Continue this until you have all the 7X tables written.

How to Play

In groups of 2-4 have students turn over the number squares and mix up. Then place them in rows and columns still numbers facing down. The first student will turn three squares over. If it makes a true 7X equation the student keeps the set and gets another turn. If it is not a match, the squares are turned over and the next player turns three over. Play continues until all cards are matched. The winner is the student with the most matches.

Bingo Card - Materials Bingo card templates Flash cards How to play Make copies of Bingo card templates for each students. Students choose any of the 25 numbers at the bottom of the card and write one in each square. When the students are done, use a set of flash cards to randomly choose a multiplication fact. Remove all the zero flash cards except one. Read the problem aloud. Any student with the product puts a marker on it. Continue until someone gets bingo.

Team Tag - Materials Flash cards How to play

Divide the students into two groups. Have them form two single file lines facing forward. The first student should be about 10 feet from the front of the room. Put two equal stacks of flash cards on a desk in the front of the room.

When play starts, the first person in line races to the desk, takes the first card in his or her pile, holds it up, announces the answer to the class, places the card in a discard pile, and then races to tag the next person in line. If the student does not know the answer or gives the wrong answer, he or she puts the card on the bottom of the pile and selects the next card. This student keeps selecting cards until he or she knows the answer to one or until five cards have been selected.

The two teams play simultaneously. The first team to correctly give the answer to all the multiplication facts in its pile wins.

Shortcut Tips of Multiplication

We all want to know the way we can do the multiplication work quicker and easier, then why not our students know? Following are some of the multiplication shortcuts –

Multiplying 2-digit number with 11 –

To find the final product of a 2-digit number and 11, we have to add the 2 digits among themselves and write the sum between the two.

For example, 34 × 11 –

1.Add the two digits. 3 + 4 = 7

2.Place 7 between the two (3 and 4).

3.It will give the answer 374.

So, 34 × 11 = 374

Note – This shortcut can be applied only if the sum of the two digits is less than 9.

Multiplying Single digit number with 9 –

Shortcut 1

To find the final product of a single digit number and 9, we have to subtract 1 from the single digit number, which will give us the first digit of the final product. To get the second digit, we have to subtract first digit from 9.

For example, 5 × 9 –

1.Subtract 1 from 5. 5 - 1 = 4 (First digit of the product)

2.Subtract 4 from 9. 9 - 4 = 5 (Second digit of the product)

The final product is 45.

Shortcut 2

For example, 6 × 9 –

1.Write the single digit number 6 and place 0 after it, which will give 60.

2.Subtract the original single digit number from the new number. 60 – 6 = 54

The final product is 54.

Practice Test

1.To use the shortcut for 11, to multiply 32 × 11, you should first add 3 + ____.

2.To use the shortcut for 9, to multiply 3 × 9, place the 0 to the right of ____.

3.Kevin earns $ 5500 per month. How much will he earn in a year?

4.Rose has a monthly mortgage payment of $ 1500. How much money will she pay in 12 months?

5.To use the shortcut for 9, to multiply 8 × 9, subtract 8 from ___ to get the answer.

Common Errors in Multiplication

Students commit different types of errors while solving a multiplication problem, which may or may not be detected. Either their error be due to carelessness or wrong multiplication fact or even misunderstanding the basics of multiplication. In any case, the teacher has to be very careful while analyzing any calculative work. Following example can help to develop to understand the common error patterns seen among children –

1.To multiply 35 × 3, a student solved it as –

35 ×3 125

Here, he recalled the fact of 3 × 3 as 12 instead of 9. And he didn’t carry the 1 of 15 while multiplying 5 × 3.

2.To multiply 27 × 15, a student solved it as –

27 ×15 255 270 525

Here, he recalled the fact of 2 × 5 as 22 instead of 10 and added the carried 3 to it resulting 25 of 255.

3.To multiply 28 × 14, a student solved it as –

28 ×14 112 580 692

Here, he committed the error while multiplying 28 × 1. The answer should be only 28, which he had written as 58.

4.To multiply 27 × 43, a student solved it as –

27 ×43 81 1280 1361

Here, he multiplied 27 × 4 wrongly. It should be 108.

5.To multiply 432 × 28, a student solved it as –

432 ×28 876

Here, he misunderstood the whole method of multiplying 3-digit number to 2-digit number.

6.To multiply 54× 23, a student solved it as –

54 ×23 162 108 270

Here, he placed the partial products in a wrong manner, which gave the sum wrong.

7. To multiply 802× 15, a student solved it as –

802 ×15 4060 8120 12180

Here, he misunderstood the multiplication rules which says that any number multiplied by 0 gives 0, and any number multiplied by 1 gives the number itself.

8.To multiply 207 × 6, a student solved it as –

207 ×6 1302

Here, he recalled the facts wrongly.

Examples of Word Problems

In daily life, we come across many situations where multiplication is involved. Following are few examples to solve the word problems -

1.In a function, 25 chairs were placed in arrow. If there were 42 rows, find out how many chairs were used in the functions? Solution Number of chairs in a row = 25 Number of rows = 42 Therefore, total number of chairs = 25 × 42 25 × 2 ones = 50 = 50 25 × 4 tens = 25 × 42 = 1000 Total 1050

2.There are 12 erasers in one packet. A shopkeeper has 125 packets of erasers in his shop. How many erasers does he have in his shop? Solution Number of erasers in one packet = 12 Number of packets in the shop = 125 Total number of erasers in the shop = 125 × 12 12 × 5 ones = 60 ones = 60 12 × 2 tens = 24 tens = 240 12 × 1 hundred = 12 hundreds = 1200 Total 1500

3.A truck can carry 140 bags of grains. How many bags of grain can 25 such trucks carry?

Solution

Number of bags of grain that a truck can carry = 140 Number of bags of grain that 25 trucks can carry = 140 × 25 140 × 5 ones = 700 ones = 700 140 × 2 tens = 280 tens = 2800 Total 3500

Practice for Word Problems

1.There are 4 baskets. There are 12 apples in each basket. How many apples are there altogether?

2.Kim bought 3 cartons of eggs to cook breakfast for some guests. Each carton contains 10 eggs. How many eggs does she have?

3.Steve drives 9 miles every day to get to and from work. He works 5 days a week – so can you tell how many miles he drives for his job?

4.Barbara also plans to bake 2 pans of blueberry muffins. Each pan will hold 9 muffins. How many muffins will she bake?

5.A shopkeeper has 7 boxes of chocolates. If each box contains 6 chocolates, how many chocolates are there altogether?

6.A child has 5 books. How many books have 8 children?

7.There are 3 bumper cars. Each car holds 2 people. How many people altogether?

8.8 boys have 5 marbles each. How many marbles do they have altogether?

9.At an airport, 8 planes land everyday. How many planes land at the airport in 7 days?

10. Number of working days in a week is 6 days. If the school works for 41 weeks in a year, find the number of working days of the school.

11. The monthly fee of a school is $ 150. Eighty five students paid their fees on one day. Find out the total amount collected on that day.

12. 675 bicycles can be parked in a cycle stand. How many bicycles can be parked in 14 such stands?

13. There are 45 seats in a row. How many seats will 24 such rows have?

14. 24 tins of cocoa can be packed in one box. How many tins can be packed in 75 such boxes?

15. In a office building, there are 15 offices on each floor. The building has 45 floors. How many offices are there in the building?

16. There are 11 shoes in a pair. How many shoes are there in 4 pairs?

17. How many minutes are there in the month of April?

18. There are 2120 students in a school. Each student contributed $ 75 to the Prime Minister’s Relief Fund. How much did the students contribute to the Fund?

19. A factory produces 6750 buckles per day. How many buckles will it produce in 4 weeks, if every Sunday is a holiday?

20. There are 5 sections in a library. 30 shelves are arranged in each section. Each shelf contains 250 books. How many books are there in all in that library?

More Practice of Word Problems

1.A classroom has 4 rows of tables. If each row has 12 tables, how many tables are there in the classroom?

2.Mia used 3 matchsticks to form a triangle. If he made 23 triangles, how many matchsticks did he use?

3.Each student was asked to donate 2 cans of food to the poor. There were 56 students. How many cans of food did they donate?

4.There were 7 stalks of flowers in each vase. If there were 3 vases, how many stalks of flowers were there?

5.Jackson bought 14 packets of sweets. There were 13 sweets in each packet. How many sweets did he buy?

6.Each class has 58 children. There are 12 classes having 3 sections each. How many children were there altogether?

7.Emily bakes 15 cakes everyday. How many cakes can she bake in a week?

8.There were 8 boxes of blue pens and 6 boxes of black pens. There were 27 pens in each box. How many pens were there?

9.A bus can carry 52 passengers. It makes 8 trips everyday. How many passengers can it carry at the most in a month of 31 days?

10. In an orchard, there are 58 rows of mango trees. If the number of mango trees in one row is 29, how many trees are there in all?

11. Mike wants to buy 6 pairs of trousers at a cost of $ 26. How will he spend?

12. Angel buys 9 boxes of printer paper at a cost of $ 22 per box. How much does she spend?

Role of a teacher

The whole art of teaching is only the art of awakening the natural curiosity of young minds for the purpose of satisfying it afterwards.

---Anatole France

Teaching is a personal activity where different instructors take different approaches to teach their students. Broad issues associated with teaching – Preparation, respect, adjusting students’ expectations, time management, use of technology, clarity, demonstrating the applicability of mathematics etc.

Teaching is an on-going learning experience. Preparation, effort and a good attitude are the main requirements of good teaching. A teacher requires charisma and a genuine interest to teach, so that the students can enjoy the teaching simultaneously.

A teacher must keep a balance between teaching skills, concepts and problem solving. To convey the essence of a subject, a teacher needs to understand it deeply. The main objective of teaching is to establish a sound knowledge base on which students will be able to build as they are exposed to different life experiences. The passing of knowledge from generation to generation helps the students a lot to grow as useful members of the society.

The teacher can translate information, good judgment, experience and wisdom into relevant knowledge that a student can understand, retain and pass to others.

Teaching Multiplication

The idea of multiplication should be introduced to a child when he can count objects up to 100 properly. The next step should be to let him count objects in groups, beginning with 2. After this, he should be given higher order of objects in a group at a time.

And this way he gets an idea of repeated addition, which is the base of multiplication.

Lesson Plan

A good lesson plan is based upon how the teaching material can be matched to the level of the students. It should be presentable in such a way that it seems to be challenging and interesting.

The main aim of preparing a lesson plan is to match the teaching efforts to the learning objectives. It helps the teacher to make consistency in his or her focus to give quality knowledge. A good lesson plan helps to be on the right track so as to accomplish the pre-determined goals.

Lesson plan is basically a thinking process, which consists of four parts –

1.Determining what the students will learn and what they can do after learning the specific lesson.

2.Determining the knowledge level of the students for the specific lesson.

3.Determining the different ways to assist as well as evaluate the students in their learning.

Following are the main points to be included in a written form of a lesson plan –

1.Objectives – The objectives of the specific lesson should be clearly defined. While determining the objectives, students’ age as well as their ability to grasp should be kept in mind.

2.Anticipatory Set – Before starting a topic, the standard of the students’ should be tapped. This will help to handle their queries smoothly.

3.Main Content – In this section, the definite description of presenting the main concept of the lesson should be given. The presentation can be oral, or with an introductory worksheet, or some sort of interactivity.

4.Guided Practice –The students are given a chance to practice whatever they have learnt in the lesson under the supervision of the teacher.

5.Closure – The best way to wrap up a lesson is to give the students a brief summary of the lesson concepts.

6.Independent Practice – Now its time to work without the supervision. Through homework assignments or other independent projects, the teacher can let them practice independently.

7.Required Material – This section is to mention the materials which are required during the teaching session of the lesson.

8.Assessment – After the guided and independent practice, its time to evaluate the students.

Common Mistakes in a Lesson Plan

Great teaching requires knowledge, dedication, and a lot of planning. Even the most talented teachers can fall short when their lesson plans are ineffective. Here are some of the most common mistakes teachers make when planning their lesson plans –

1.A student who is missing a valuable concept can find even the simplest lessons difficult to complete.

2.An unclear objective can mess up the whole lesson plan.

3.If students don't have their tools to be used, then concepts are unreasonable to them.

4.Every student has his or her own unique learning style.

5.A student cannot be expected to master a complicated concept in just one session.

Tips to teach Multiplication Tables

Following are the tips to teach the multiplication tables to the elementary students –

Step 1 – Multiplication is a quick way to add a series of numbers.

5 × 3 means to add 5 three times 5 + 5 + 5 Quick Practice – 4 × 2 = ___ 6 × 3 = ___ 5 × 9 = ___ 7 × 2 = ___ 4 × 6 = ___

Step 2 – The product will not change even if we change the order of the factors. It doesn’t matter which factor comes first. The answer will be same. 2 × 4 = 8 4 × 2 = 8 Quick practice – 4 × 6 = ___ 6 × 2 = ___ 8 × 7 = ___ 3 × 9 = ___ 7 × 6 = ___

Step 3 – The rules of multiplication - - When any number is multiplied by zero, the product is zero. - When any number is multiplied by 1, the product is the number itself.

Step 4 – There are 100 facts to learn. After going through the Step 3, only 64 facts left to learn.

Step 5 – After going through the Step 2, only 36 facts are yet to be learnt.

Step 6 – 2 Facts – Because of the base of multiplication (repeated addition) any number times 2 is the number doubled. 2 × 6 = 6 +6 = 12

Step 7 – 4 Facts – To multiply 4 with a number, double it twice and the answer will be there. 4 × 2 Double 2 = 2 +2 = 4 Double 4 = 4 +4 = 8

Step 8 – 5 Facts – To multiply 5 with an even number, halve the number and put 0 after it. 5 × 8 ( even number) Half of 8 = 40 To multiply 5 with an odd number, subtract 1 from the odd number, halve the difference and put 5 after it. 5 × 7 (odd number) 7 – 1 = 6 Half of 6 = 35

Step9 – 9 Facts – To multiply 9 with a number, subtract 1 from the number to be multiplied with. This will give the first digit of the product. The two numbers (the difference and the number itself) will be combined to get the answer. 9 × 5 5 – 1 = 4 (first digit) Two numbers = 4 and 5 Answer is 45

Step 10 – Remember the facts based on series. 12 = 3 × 4 56 = 7 × 8

Multiplication Strategies

There are various strategies followed by the teachers to teach multiplication. Few are as follows –

1.Rote memory – This is the most common and popular used strategy, which is traditional too. It is basically just repeating a particular concept again and again until it is learnt. It can be followed orally as well as written. The drawback of this strategy is that it takes lot of time and it may not be effective to some students.

2.Music – As everyone love to work with relaxation and ease, teaching the students with the help of music is one of the enjoyable way. It is better than the rote memory method of teaching. But here also, this way does not work with all students. And the main drawback is that after learning the whole song for a fact family, we have to sing the entire song just to remember one single fact.

3.Rhymes – This strategy works well if we combine it with some other way. It is similar to songs. The only difference is that it is shorter than a song and can be learnt quicker. For example, 2 × 2 = 4 (Two shoes kicked the door, two times equals four)

4.Pictures – This strategy is also becoming popular among teachers. In this method, the student remembers the picture reminding the fact, instead of the numbers. For example, students can draw pictures out of the numbers one to nine. And using those pictures, they can draw a picture with the answer as a part of the picture.

5.Games – In this world of internet, teachers are too taking help of it. Thousands of games can be downloaded and be a part of the teaching.

Rhymes – Learn with Fun

1.4 × 4 – A 4 by 4 is a mean machine I’m gonna get one, when I’m 16.

2.6 × 6 - 6 cold 6 packs 36 chicks will have for snacks.

3.7 × 7 - 7 and 7 made with lines Bend ‘em up and down to make 49.

4.4 × 6 - I’m hatching baby chicks Ooops! I dropped them on the floor Would have been eggs – actly 24.

5.6 × 6 - Chicks, chicks, dirty chicks 6 times 6 is 36.

6.7 × 4 - The animals are coming Better open the gate There’s 28!

7.4 × 8 - Clean your plate I ate the ‘goo’ Now I’m 32.

8.7 × 7 - 7 times 7 is 49 You are cool, you are fine!

9.6 × 7 - Happy B’day to Kevin He’s 6 and 7 He blew and blew ‘Coz he’s 42.

10. 7 × 8 - 7 packs of gum Each with 8 sticks Open up, Big mouth Can you chew all 56?

11. 6 × 8 - Flight 6 to 8! Don’t be late! Leaning at gate 48.

12. 7 × 7 - 7 times 7 is 49 Don’t bend down You’ll hurt your spine.

13. 8 × 8 - 8 times 8 is 64

Close your mouth and shut the door.

14. 3 × 3 - 3 times 3 is 9 Swing from tree to tree on a vine.

15. 6 × 7 - Hello, how are you? 6 to 7 is 42.

Multiplication Test

1.Fill in the blanks – (1) 7 + 7 + 7 + 7 + 7 = _____ (2) 8 × 5 = 5 _____ (3) 12 + 12 + 12 + 12 = _____ (4) 5 × 7 × 8 = 7 × 8 _____ (5) 23 × ____ = 23 (6) 51 × ____ = 0 (7) 15 × ____ = 120 (8) _____ ×4 = 52 (9) 43 × 10 = ____ (10) 75 × 100 = _____

2.Find - (1) 36 × 30 (2) 132 × 50 (3) 8 × 400

(4) 803 × 12 (5) 245 × 39 (6) 408 × 21

3. Find - (1) 46 (2) 225 (3) 1608 ×54 ×22 ×5

4. There are 68 parts in a machine. What is the total number of parts

In 12 such machines?

5. Multiply - (1) 215 by 42 (2) 687 by 13 (3) 109 by 53 (4) 799 by 11

6. Find - (1) 12 times of 21 (2) 67 times of 49 (3) 23 times of 49 (4) 76 times of 92 (5) 57 times of 34 (6) 25 times of 72

7. Fill in the blanks - (5 × 8) + (5 × 7) = _____ + _____ = _____ (3 × 8) + (4 × 9) = _____ + _____ = _____ (8 × 7) + (8 × 10) = _____ + _____ = ______ (9× 6) + (7× 8) = ______ + ______ = ______ (6 × 8) + (6 × 7) = ______ + ______ = ______

8. Fill in the blanks - 9 × 10 = ____ 4 × ____ = 20 ____ × 100 = 400 4 × 100 = _____ ____ × 5 = 20 8 × _____ = 16 ____ × 2 = 8 2 × _____ = 6 11 × ____ = 55 7 × _____ = 21 2 × 3 = _____ _____ × 3 = 6 3 × _____ = 6 10 × _____ = 40 10 × 4 = _____ 12 × 4 = _____

Fun Activities

1.In a flag hosting ceremony, children are standing in the form of a square with the flag in the centre. There are 5 children standing along each side of the square. Can you count how many children are attending the flag hosting ceremony?

2.A boy has as many sisters as brothers, but each sister has only half as many sisters as brothers. How many brothers and sisters are there in the family?

3.Find the missing number - This number increased by 5 is 10 ………… This number increased by 3 is 52 ………… This number increased by 132 is 492 ………… This number increased by 40 is 98 ………… This number increased by 70 is 210 …………

4.Match the factors with the products - 7 × 9 56 7 × 3 42 7 × 2 49 7 × 8 63 7 × 6 21

7 × 7 14

5.Complete the following –

×1

×2

×4

6. Circle the multiples -

7. Use the suitable sign - 3 ___ 3 = 9 6 ___ 6 ___ 6 ___ 6 = 24 5 ___ 5 = 25 8 ___ 1 = 8 7 ___ 7 ___ 7 ___ 7 ___ 7 = 35 0 ___ 3 = 0 4 ___ 4 = 8 2 ___ 2 ___ 2 = 6 9 ___ 0 = 0 1 ___ 4 = 4

8. Match the following numbers having equal products -

A B 4, 5, 9 6, 8, 5 2, 4, 7 1, 2, 6 3, 2, 6 7, 8, 2 4, 5, 6 1, 4, 7 5, 6, 8 6, 8, 4 2, 7, 8 4, 7, 2 4, 6, 8 5, 1, 7 7, 1, 4 2, 6, 3 6, 1, 2 5, 9, 4 7, 5, 1 5, 6, 4

9. Multiply each of the following by 60 -

(1) 26 (2) 58 (3) 85 (4) 46 (5) 74 (6) 96 (7) 47 (8) 25 (9) 32 (10) 18

Ways to make Multiplication Easy

After going through various methods existing, following two methods make the students feel burden-free from the ‘most serious subject’ – Mathematics: 1. Show the funny side – Teach the topic through a game. For instance, Monopoly. We can write the mathematical operations as well as problems on paper and stick them on the bulletin board. We can ask the child to solve them, and if he does them correctly, he will get that space of the board to stick his or her creative art work. We can make the subject fun by connecting it to the activities the child has fun doing.

2. Show the real world - Children understand math better when they can see how it works. This is easy to do at a grocery store. For example, if we are buying 5 packs of burgers, let the child figure out how many buns we need. Since a burger need 2 buns, the child will have to solve a simple multiplication problem to get the answer.

Links to Multiplication Games, Quizzes and puzzles

Following are some of the websites which can help us to have an idea of presenting games, quizzes and puzzles to the students –

1.http://www.gamequarium.com/multiplication.html

2.http://www.padring.com/soft/Education/Mathematics/MathGamesMultiplication.html

3.www.helpingwithmath.com/by_subject/multiplication/mul_games.htm

4.www.mathsisfun.com/games/mathionaire-multiplication-quiz.html

5.quizhub.com/quiz/f-multiplication.cfm

6.memorizeinminutes.com/quizzes.htm

7.www.thegreatmartinicompany.com/Math-Quick-Quiz/decimal-multiplication-quiz.html

8.www.mathworksheetscenter.com/mathskills/multiplication/multimathpuzzles/

9.www.teach-nology.com/worksheets/math/puzzles/

10.edhelper.com/multiplication.htm

Conclusion

After going through the elementary classes, a child should be able to do the simple arithmetic operations mentally. He should have firm understanding of all the four operations without having any doubt, which will help him to understand as well as solve the word problems with ease.

Often children come across the typical mathematical conceptions such as accurate numerical computations, tables and logical reasoning etc. These are due to lack of fundamental ideas. To overcome this, children should focus more on primary mathematics. By doing this, they can develop the qualities like logical thinking, proper application of concrete concepts into general problems of everyday life, enhancement of intuitive powers etc.

But generally children do not take the basic mathematical concepts such as multiplication or even just learning the facts as a must-to-do activity. Only teachers and parents can motivate them in more constructive ways. Innovative methods can enable them to comprehend the concept of multiplication and how it is used in numerical operations.

A few incentives can be offered in this process of motivation such as a big hug, a trip to their favourite amusement park, or just words of appreciation in front of guests.

These methods do not seem enough to help the children, but anything they learn is that much less to learn later. The most important thing is to encourage as much as possible and keep them from being overwhelmed. The mathematics will sink in their minds eventually.

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WHO MADE IT?

The MULTIMONSTER was originally designed by a physician to teach his second grader daughter the multiplication facts. Later it was professionally re-designed and created by a team of programmers and graphics artists over a six month period.

HELP YOUR CHILD MASTER MULTIPLICATION FACTS EASILY AND FAST.

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