Memorizing the multiplication tables: Does it have to be so tedious, difficult, and boring for our child?

Confession time. While I was at school, I hated the multiplication tables. I found memorizing them difficult and mind-numbingly dull. Even until today, I have not quite mastered the tables. Ask me, for example, what is 9 x 7, and I would answer 63, but only after performing some mental gymnastics. I know that 10 x 7 = 70, so 9 x 7 must be 70 – 7 or 63.

I do not want my five-year-old son, Zachary, to suffer the same experience as I did in memorizing the tables or end up fearing maths because of them. I wanted an easy but yet effective technique that Zachary could master the multiplication tables.

Memorizing the multiplication tables does not have to be dull and tedious (photo from www.cosmomagazine.com)

But why learn the multiplication tables?

Multiplication, together with addition and subtraction, are the foundation of more advanced mathematics a child would later learn and use. A child who fails to master these skills curses this child to a low self-confidence in learning.

A report in 2011 by Ofsted (The Office for Standards in Education, Children’s Services and Skills), UK argued that:

Confidence with numbers is an essential part of any child’s early learning.  Not only does it help them with day-to-day problem-solving and practical tasks but it also gives them the building blocks to acquire the later mathematical skills valued by the world of industry and higher education.

The Ofsted report further remarked that learning the multiplication tables by heart is an essential component in mathematics mastery, a task that a child must accomplish before leaving the primary school. It is often said that skipping learning the multiplication tables is like expecting a child to run without having to learn walking first.

Mastery of multiplication is the foundation leading to more advanced mathematics. Failure to master it leads to learning problems later. (photo from www.educationnews.org).

The internet offers many suggestions or techniques to aid memorization of the multiplication tables. Some of these techniques require rather abstract reasoning which my son would probably not understand or appreciate. Zachary is only five years old, not seven to ten years old for which some of these techniques seem to target.

Others techniques involve filling in, by rote, the answers in a 9×9 or 5×5 way multiplication table. Some even suggested that the child learns the multiplication by 5s and 10s first, followed by 2s, 4s, 6s, and 8s. None of these techniques, however, attracted me because they still involve boring and tedious memorization.

Computer games to aid memorization have even been developed where the child progresses through a game by answering multiplication problems. Again, I was not attracted to these games because I was looking for a simpler technique. Besides, I did not want Zachary to master the multiplication tables at the price of being addicted to computer games!

I then came across Alan Walker’s technique at multiplication.com. I was attracted to his technique because it involves memorization through pictures and stories. Each number from 2 to 9 is denoted by a picture, such as 2 is a “shoe”, 3 is a “tree”, and 4 is a “door”.

Every number from 2 to 9 is represented by a picture or character. These characters will interact with one another to create a unique and funny story to aid a child’s recall of the multiplication tables. (excerpt from “Memorize in Minutes: The Times Tables”)

When two numbers are multiplied together, such as 3 x 4, they are translated into their respective pictorial representation. In the case of 3 x 4, it is equivalent to “tree x door” which has the following unique story to aid the child in remembering the answer:

Once there was an elf. He loved the forest. He loved walking through the big tall trees. The elf decided he wanted to live in a tree because he loved the forest so much. The elf came up with a great idea. He found a great big tree, hollowed it out, and made his house inside the tree. He put a door on his house. The elf loved living in the tree with a door.”

What is 3 x 4? Translate 3 into “tree” and 4 into “door” and you have a story about an “elf” (or 12) who stays inside a tree with a big door leading to his home. (excerpt from “Memorize in Minutes: The Times Tables”)

And the answer to “tree x door” is “elf” which rhymes with 12. Thus, 3 x 4 = 12.

As another example, consider: 5 x 7 which translates into “hive x surfin’” (where 5 = hive and 7 = surfin’), and the story for this combination of 5 and 7 is:

A hive went to the beach. He was afraid of getting hurt on a rocky beach, and sandy beaches were too hot for his feet, so he went to a muddy beach. The hive had a funny way of surfing at the muddy beach. He would surf up to the beach and dive right into the mud. Soon he was very dirty! The hive loved doing the dirty dives.

A funny story depicting the characters of hive (5) and surfin’ (7) to give the answer as “dirty dive” or 35. (excerpt from “Memorize in Minutes: The Times Tables”)

And the answer to “hive x surfin’” is “dirty dive” which rhymes with 35. Thus, 5 x 7 = 35.

So, how effective was this technique on Zachary, my five-year-old son? See for yourself:

Zachary recalls his multiplication tables.

I taught Zachary slowly and incrementally. Each day for about a month, I would teach him two or three new multiplication problems, but with plenty of revision before I introduce new problems.

Zachary answers a few multiplication questions. Despite an initial hiccup, he was soon able to complete his task perfectly.

In sharp contrast to my experience, Zachary enjoys learning the multiplication table! How many children do you know who can say that? Not only did Zachary enjoy memorizing the tables, he could remember them more easily and effectively.

The success in Alan Walkey’s method is it adds context to each multiplication problem. Rather than memorizing boring and bare 3 x 4 = 12, Alan’s method translates 3 x 4 into “tree” and “door” characters, respectively. The child then recalls the story specifically involving tree and door, which ultimately gives the answer as “elf” (see above description), or 12.

Some people who had bought Alan’s method were initially skeptical because of the additional mental work the child has to do in recalling the multiplication tables. But they were converted into believers when they saw how effective this method was on their children. Instead of burdening the child with additional work of memorizing the pictures and stories, Alan’s method is actually simpler and more effective. Like watching a TV series with many interesting and funny characters that interact with one another differently, Alan’s pictures and stories help in recall, akin to recalling a particular funny TV episode.

Nonetheless, not all children would benefit using Alan’s method. Alan’s pictures and stories are explained in English, so children with poor command in English would probably find his method ineffective simply due to language barrier. This is particular true in Malaysia.

However, if your child reads English well, I strongly recommend this method. Alan’s book can be bought directly from multiplication.com. There is no need to get the Teacher’s manual, as the Student’s eBook is adequate for both child and parent. And the price of the Student’s edition? A steal at USD 4.99, and the result on your child’s education — priceless.

“Memorize in Minutes: The Times Tables” by Alan Walker. Published by Krimsten Publishing, Washington, 2000.




Electricity demand and supply in Peninsular Malaysia: Energy efficiency, renewable energy, or nuclear? (Part 3)

This is Ir. G. Lalchand’s third article in his series of Malaysia’s energy challenges.

Part 2 of this series showed that Malaysia may not need to add any nuclear (or other fossil-fuelled) power generation plant until after 2025 provided that the RE (Renewable Energy) development (even when moderated) and adoption of EE (Energy Efficiency) initiatives (even on a conservative basis) are pursued diligently.

This is of course subject to the potential retirement of existing fossil fuelled power plants, whether operated by IPPs (Independent Power Producers) or TNB (Tenaga Nasional Berhad) itself. The potential retirement of existing power plants would naturally warrant an earlier planting up of the new proposed power plants. I will address this aspect in a later episode in this series.

Initiatives from the Malaysian government to promote more energy efficient technology and its use (photo from www.saveenergy.gov.my)

Obviously, these projections also depend on the actual pace of adoption of EE practices and the rate of development of RE power generation under the RE Act and its FiT (Feed-in Tariff) mechanism. The development of RE in Malaysia is being handled by SEDA (Sustainable Energy Development Authority) under the provisions of the RE Act and its related FiT mechanism. There is no dedicated agency to implement EE&C (Energy Efficiency & Conservation) initiatives although SEDA is expected to do so when the EE&C Act is enacted.

So let us look at the possibilities, constraints and impact of pursuing the desired EE&C initiatives and assess the likelihood of achieving the target savings as mentioned earlier.

First of all, there is widespread public skepticism, at least in Malaysia, as to whether the frequently touted EE initiatives can really deliver the promises made for it. How difficult, or easy, is it to achieve the ambitious demand saving targets that are often announced by various authorities?

Secondly, even if the skepticism can be overturned, there would still be some doubt as to how much impact can EE have on the national power demand. The chart below, which is also shown in part 1 of this series, indicates a potential demand saving of about 826 MW by 2020, at a conservative demand saving rate of about 0.5% in demand per annum.

Fig. 1. Projected Electricity Demand (Business-as-usual, BAU, is at 3.2% p.a. growth rate)

A demand reduction of about 826 MW, together with a reserve margin of 25% equates to a generating capacity need of about 1,030 MW, which could need over RM 3.0 billion in capital investment, a tidy sum to save indeed.

What does this mean to an “ordinary consumer”? The typical consumer would probably say “So what! Even if EE is able to save 826 MW in demand by 2020, does it mean me having to pay more for my electricity?” This would be a fair response from a consumer, whose first preference would be “What is in it for me?”. So, let us look at the demand saving issue from a consumer’s perspective. A consumer would certainly be happy to help national EE objectives if by doing so he can also save his own electricity costs.

There are several EE initiatives that can be exploited by all categories of consumers and a few simple and easy initiatives are considered as follows.


One of the most widely implemented options is the use of 5-Star EE refrigerators (fridges), an initiative that was promoted by KeTTHA (Ministry of Energy, Green Technology and Water) from mid 2011 under its SAVE (Sustainability Achieved Via Energy Savings) programme. A 5-Star fridge is about 25% more efficient than a standard 3-Star fridge. The chart below shows the potential savings that consumers can gain from changing to EE type 5-Star fridges for a typical 400 litre fridge for which the price premium for a 5-Star fridge is less than RM 200.00.

Fig. 2. Savings from 5-star refrigerators

This chart shows that even on the present subsidised tariff, the consumer will recover the premium price for the 5-Star fridge in a few years and will continue to make “profits” over the rest of the fridge life. If the fuel subsidies are reduced and the electricity tariffs increased, then the payback period for the price premium will be shorter and the “profits” would start earlier.

Another attractive option would be the replacement of typical window or split type air-conditioners (A/Cs) with their 5-Star or “Inverter type” equivalent models. These EE A/Cs provide savings of between 10% to over 50% (for the inverter type units). These replacement initiatives by consumers will benefit them directly through energy and cost savings as shown in the chart below, which shows the savings for a typical 1 HP household A/C operated for an average of about 6 hours a day. Obviously, the savings would be proportionally higher if the A/C use is for longer periods.

Fig. 3. Savings for EE split type A/C

A simpler and frequently used option in Malaysia is the replacement of incandescent lamps with CFLs (Compact Fluorescent Lamps). KeTTHA has mandated the phasing out of incandescent lamps by 2014. Many users have already “cottoned-on” to the cost savings these CFLs provide and their use is rapidly displacing the traditional incandescent lamps

As a corollary, tubular fluorescent lamps, which are commonly used for commercial and residential use, also have more energy efficient alternatives. The traditional T-8 type of tubes can be replaced by the more efficient T-5 tubes which give the same lighting level with about a one-third reduction in the energy used (a T-8 tube of 36 watts can be replaced by a T-5 tube of about 28 or 24 watts).

The chart below shows the costs and savings from the use of CFLs to replace incandescent lamps. It is clear that the higher cost of a CFL is recovered from the energy savings within the first 1,000 hours of use.

Fig. 4. Comparative costs – lighting


These examples show that electricity consumers can derive cost savings for themselves by adopting EE initiatives for their own benefits. In the process they certainly also contribute to helping to achieve the national energy savings and carbon reductions promised by our Prime Minister at the COP (Conference of Parties) 15 in Copenhagen in December 2009.

Can they contribute to the demand reduction mentioned earlier? Let us look at the numbers involved.

A fridge has a power demand of over 100 watts, but its energy saving equates to only between 25 and 33 watts. It is estimated that there about 9 million fridges of these types in operation in Malaysia (about 7 million for domestic consumers and about 2 million for the other commercial and industrial users, not counting the heavy duty large commercial and industrial units). Thus a change of all refrigerators can contribute to a demand saving of between 225 MW and 297 MW.

Money savings from energy efficient technology applied, in this case, to refrigerators (photo from www.energystar.gov)

Similarly,1-HP A/Cs have a power demand of the order of 0.9 kW each but the equivalent saving demand reduction would be of the order of  25 to 70 watts (for the inverter type). The total number of such A/C units in operation may be of the same order as fridges (9 million units comprising say 25% of residences with an average of 3 A/Cs each, and about 700,000 commercial consumers with an average of about 5 units each). Hence the demand reduction from changing to EE A/Cs can be of the order of 225 MW to over 600 MW.

Where A/Cs are used for cooling, the inclusion of roof insulation can further help to reduce the cooling power demand. This is because many premises in Malaysia, whether residential, commercial or industrial, are not equipped with adequate roof or wall and window insulation. Anecdotal evidence indicates that the rains in the Klang Valley reduces power demand by about 3% for Peninsular Malaysia. This is equal to a demand reduction of about 450 MW on a maximum power demand of about 15,000 MW. Again, only a part (say 50% or 225 MW) of this reduction may be achieved with enhanced roof, wall and window insulation.

These three simple initiatives indicate a potential demand reduction of the order of between 675 MW and about 1,100 MW. No account is taken for any “demand reductions” from conversion to EE lighting loads for domestic premises as these reductions occur during the evening, or “off-peak” periods, even though the consumers will themselves save energy and costs.

These simple options have not even touched on the far more substantial savings that may be derived from the large commercial and industrial facilities where the lighting, A/C and industrial process loads provide the opportunity for much more significant demand reductions.

So, it seems clear that the demand reduction projection of about 826 MW by 2020 is relatively easy to achieve. What is needed to do so is to have the relevant government agency to conduct sustained promotion efforts to convince users to adopt these energy saving initiatives.

But we, as consumers, do not need to wait for the government to convince us. The monetary savings shown above should be sufficient incentive for us to take the initiatives ourselves, and in the process help reduce the need for more coal fired, or god-forbid, nuclear power plants to be developed in Malaysia.

For the record, I am not anti-nuclear power as it may be needed ultimately (but certainly not as early as 2021 or so). I choose to consider nuclear power as a “choice of last resort” if we are not able to satisfy our power and energy needs by more traditional and safer alternatives.