Teach Your Children Tables

Bill Handley

• Publisher: Wiley
• Year: 2012
• Print ISBN: 9780731406647
• eBook ISBN: 9781742168869
• Edition: 2
• Topic: Education
• Subtopic: Teaching Mathematics

Bill Handley is well known for making maths fun! The first edition of Teach Your Children Tables challenged over 20000 readers -- and Bill has been inundated with letters of thanks since from parents whose children have quickly become proficient in maths and problem solving. This not only pleases their teachers but does wonders for a child's self-esteem. In this new, fully revised edition, rewritten for clearer understanding, Bill expands the sections on explaining multiplication to young children, on problem solving, and the correlation between the multiplication method and subtraction.

Chapter 1

Teach your child tables

What is multiplication? How can you teach your child what the word means? If you are going to teach your child the multiplication tables and how to multiply, it is necessary to first teach him what multiplication is.

This is a method that I have found useful. I begin by holding up one hand and asking the child how many hands. Then I hold up both hands and ask how many. Then I hold up three fingers on one hand and ask how many fingers.

Next I hold up three fingers on each hand and ask them how many fingers. I tell them they can count the fingers if they like. If they count correctly, they will get the correct answer of six. I explain that they can add the fingers on each hand—that three fingers plus three fingers makes six fingers. That is addition.

I tell them they can also say two hands with three fingers, or two lots of three fingers make six fingers. That is multiplication. So three plus three and two threes are both the same—they both equal six.

You could ask someone else to hold up three fingers on each hand, too, so there are four hands altogether. Then you could either say three plus three plus three plus three or, simply, four threes. The child could also count the fingers to find that four threes make twelve fingers.

It’s useful to point out that the more hands and fingers you have to count, the greater the chance of making a mistake. For example, when you have to count fingers on eight or nine hands it becomes hard work and you have even more chance of making a mistake.

You can use other examples. How many marbles in a glass? How many marbles do you have if you have three glasses with four marbles in each glass? This is all multiplication.

Multiplication is simply a short, easy way to write and do addition. It is addition written in shorthand. For instance, 3 times 7 means 7 plus 7 plus 7, or three sevens added together. Seven times 8 means 8 plus 8 plus 8 plus 8 plus 8 plus 8 plus 8, or seven eights added together. Two times 6 means two sixes added together, or 6 plus 6. A child needs to be able to understand this concept to use the methods taught in this book. That doesn’t mean she must know the answers to 6 plus 6 or 4 plus 4.

I was asked to teach maths to a 14-year-old boy and, at our first meeting, I asked him if he knew his tables.

He said, ‘Yes, up to the two times table’.

I said, ‘What are two eights?’

He shook his head and said, ‘I don’t know them that well’.

Within a week, he was multiplying 96 by 96 in his head. Because the methods were working for him, he practised them and so he learnt his two and three times tables. He asked me if I could teach him to beat his friends, who do their multiplication with a calculator.

So long as the child knows what two sixes means, and how to calculate two sixes, he will be able to make good use of the methods taught in this book. A five-year-old boy who hadn’t yet started grade one mastered multiplication using these methods. When he had to multiply two fours, he would extend four fingers on each hand and count the fingers. It wasn’t long before he knew two threes and two fours. But he was multiplying two fours to calculate 96 × 98 = 9408. Since learning this, he has been regarded as a maths prodigy at his school.

Using my methods, a child can memorise her tables up to around the thirteen or fourteen times tables in a couple of months through repetition. Not repetition in reciting the tables, which is boring, but repetition in calculating the answer, which is fun. It is fun because the child knows that no-one else in the class, or maybe even in the school, can do the calculation so easily. Certainly, the child wouldn’t expect that other children could multiply 96 times 96 and give an immediate answer off the top of their head.

We use maths every day

Some children have said to me, ‘When do we need this? When do we ever have to multiply or divide in real life?’

It is a fair question and should be answered. In fact, it must be answered if you want to keep the child motivated. Following are some situations you can present to children where basic maths skills are needed:

• Situation one—if three children get $5 pocket money each week, how much do they get all together?
  To solve this easily, they need to be able to multiply. This might be important if they want to pool their money to buy something. The answer is $15.
• Situation two—if you want to buy 16 DVDs at $14 each, how much will you need to buy them?
  If they learn the simple method to multiply numbers in the teens taught in these first few chapters, they will be able to give an immediate answer of $224.
• Situation three—if we are driving towards a town 240 km from home and we have driven 60 km, how far do we still have to drive? The answer is 180 km.

Encourage children to use the methods when they are shopping, cooking or making models. Show them it is difficult to go through a whole day without using some maths.

Working with your child

The best way to teach your child basic maths and the tables is to do the exercises together. If you get excited about what you are doing, this will in turn excite the child. Ask how many children in their class could do the problem so quickly in their head. Ask if their teacher could do the problem.

Don’t make firm rules. Don’t say, ‘You are going to spend fifteen minutes each night after school doing these tables’. This makes it sound like work for the child. On the other hand, you can say, ‘Let’s do this together each night for about fifteen minutes. I want to learn this. If you are willing, so am I’.

In one case, a father told me he couldn’t get his daughter to cooperate. I told him to learn the methods himself and then show his daughter what he had learnt. He did so. She asked him, ‘How did you do that? Teach me’. He said, ‘No, you will have to wait until I have finished’. She pleaded with him until he relented. She was desperate to begin.

The methods are fun because the results seem unbelievable. If you suspect your child might be reluctant to work with the methods, don’t offer the book, simply ask, ‘How would you like to master your tables in the next ten minutes?’ Or you could say, ‘I learnt a great way to learn the multiplication tables today. You can master your tables in five minutes. Let me show you this great trick’. That is a good, positive approach. (Actually, I dislike people calling these methods a trick. To me, a trick implies deception; you aren’t really doing what you appear to be doing. In this case, you are doing exactly what you appear to be doing.)

Spend fifteen minutes a day

When the child is working with the methods and seeing results, you can then ask, ‘How would you like to spend fifteen minutes a day, three or four days a week, working on your tables?’ Get the child’s cooperation and give plenty of encouragement. These methods are very easy to learn and to use.

As you learn with your child, you will be motivated to play and experiment with the strategies as well. This will also help to keep your child motivated.

Now, turn to the next chapter and become a mathematical genius.

Key points

• Multiplication is a short, easy way to write and do addition.
• We use maths every day.
• Parents should learn these methods with their children.

Chapter 2

Multiplication—part one

How would you like to master your tables, up to the ten times table, in around fifteen minutes? And your tables up to the twenty times table in less than half an hour? Using the methods I explain in this book, it is possible to master the multiplication tables, up to the ten times tables, in one lesson. I only assume you know the two times table reasonably well, and that you can add and subtract simple numbers.

Multiplying numbers up to ten

We will begin by multiplying numbers up to 10 times 10. Let’s take a look at an example—7 × 8.

Write ‘7 × 8 =’ on a piece of paper and draw a circle below each number to be multiplied, as shown overleaf.

Now go to the first number to be multiplied, 7. How many more do you need to make 10? The answer is 3. Write 3 in the circle below the 7. Now go to the 8. What do we write in the circle below the 8? How many more to make 10? The answer is 2. Write 2 in the circle below the 8. Your work should look like this:

Now subtract diagonally. Take either one of the circled num...

Table of contents

• Cover
• Contents
• Title
• Copyright
• Preface
• Introduction
• Chapter 1: Teach your child tables
• Chapter 2: Multiplication—part one
• Chapter 3: Using a reference number
• Chapter 4: Multiplying numbers above and below the reference number
• Chapter 5: Checking your answers
• Chapter 6: Multiplication—part two
• Chapter 7: Mathematical short cuts
• Chapter 8: Multiplying using two reference numbers
• Chapter 9: Direct multiplication
• Chapter 10: Alphametics—fun with numbers
• Chapter 11: Factors that determine intelligence
• Chapter 12: Helping your child develop intelligence
• Chapter 13: How to use this book
• Afterword
• Appendix A—solutions to alphametic problems in chapter 10
• Appendix B—solutions to puzzles in chapter 12
• Appendix C—practice sheets
• Index