You told me it’s important for children to memorize the times tables

Last week I revealed the results of the Maths Insider Times Tables survey, which showed that nearly all those surveyed felt that memorizing the times tables was an important skill as shown by these comments from the survey:

“need to rote memorize initially and then lots of practice worksheets – no easy way out there…”

“It is really important. If they crack these early it will give them confidence with division and enable them to see patterns in larger numbers.”

The results weren’t a surprise since I’ve spoken many concerned parents over the years as a maths teacher, a Kumon instructor and now as a maths blogger. Many of you have children who have passed the milestone of learning their times tables, but there are others of you who are worried that the whole memorization process is taking too long, is time consuming and is stressful.

Do you want your child to achieve faster, more confident times tables?

After listening to concerned parents and seeing what was already available on the market, I’ve developed a product that will help you guide your child to faster, more confident times tables in just 31 days.

The 31 Days to Faster Times Tables program is a mixture of worksheets, audio and practical activities, so if your child needs to spend time designing their online avatar before they’ll even consider doing any maths, then this product may not be for you.

However, if :

your child has 10-15 mins each day to spare

you want to be involved in their times tables learning

you want a flexible program where your child isn’t tied to one learning style

Last week I asked Maths Insider readers to fill a survey about how important learning the times tables is to your family. 71 people responded to the survey. Thanks to everyone who took the time to share their opinions! The winner of the $20 Amazon gift card was Gerda Rutherfoord from South Africa.

The results were interesting but I was blown away by the insightful comments that you made in the survey. I’ve shared the results below along with a selection of the great comments!

Make sure to sign up to the Maths Insider email list, so you don’t miss next week’s article where I’ll be revealing exactly how you can guide your child to faster, more confident times tables.

The Importance of Times Tables

97% thought that it was important to for children to memorize the Times Tables

However by what age? Some were in favour of early memorization: 5% said by 5 years old, 7% by 6years old, 14% by 7 years old.

The majority (27%) said by 8 years, 22% by 9 years and a generous 21% by 10 years old.

The percentages were similar for the questions “What age were you when you learnt your tables?” and “What age were your children when they learnt their tables?”

Some strong opinions about this:

Tables are vital basic skill needed for math at all levels to Gcse and beyond .Those who do not know them are much slower at completing exam questions, including things like factorising in algebra

Saying that this is unecessary just because you have a calculator is like saying writing is unnecessary just because you have a word processor. Basic numeracy is a valuable skill and times tables are an essential part of it.

A vital skill to be able to recall multipllication facts. As it is one of the four key mathematical operations, the earlier we can arm our kids with this one, the easier it is for them to move onto higher functions.

So valuable. If they don’t know TT they cannot do upper level math with the same ease and fluency. TT is foundation for math! If they were learning them in 3rd grade, we could move on much quicker in 5th. Some things just have to be memorized!

I think memorizing the times table is really important because I know (as a teacher) how difficult fractions and algebra are if you can’t mentally factor using the times table (factoring is more critical than multiplying, and it’s harder to do unless you have the times tables memorized).

I don’t understand why there would be any question about learning the times tables. Should be required!

Memorizing times tables makes it easier to move forward and solve problems later in math at a more efficient level… which is important for testing (especially college entry exams)

As a math tutor, I work with kids struggling in math. Most of my kids are not automatic with their multiplication facts and they lose focus as they attempt problems that require higher order thinking skills like reasoning. Students must know their facts from 1-12 and be able to answer each fact in 2 seconds or less in order for them to move successfully through solving problems with multiple steps

I believe times tables are important in life (how else do you successfully buy a house, manage finances, shop smartly, or even plan a party?), but I also believe times tables are satisfying to learn. In school there’s so much graded on subjectivity, at least in learning the times tables kids know there is a right or wrong answer, and once you know all the right answers it’s quite rewarding and satisfying to realize this goal has been achieved. Of course we can all use a calculator, but I think memorizing the times tables can be a confidence booster for kids as well.

I think it is critical. I am a senior school maths teacher and still see A level maths students that struggle because they don’t know their tables well enough. They must be memorized thoroughly by the time they get to senior school or will struggle with maths.

School vs Parents

91.5% think that parents and teachers should be jointly responsible for helping children learn their tables. 1.4% think the school should be responsible and 8.5% think parents should be responsible.

More from Maths Insider readers:

Our daughter has learning disabilities so it may take her 12-18 months to memorize all times tables, but once learned they will benefit her for the rest of her life. I am appalled that our supposedly high flying school system in Massachusetts places little to no value in memorization of addition and multiplication facts.

Schools don’t do enough to teach them. We did lots at home. My kids know them much better than their peers.

my mum taight me all my times tables when I was primary age and I am grateful to her for this. Am trying to do the same for my 4 year old and funnily enough my 2 year old is picking it up better than the 4 year old!

I don’t think this is stressed enough at school or enough repetition is done with this.

Methods

74% think that worksheets work well. 83% think that oral questions work well. 90% think that games work well.

What you told me about times tables methods:

In Singapore,the children are taught 2, 5 and 10 tables by end of P1,then 3,and 9 mid P2, 4and6 by end P2 ,8yrs old.and rest after. By ‘taught’ I mean first the text books place huge emphasis on conceptual understanding ie multiplication as repeated addition.So far my daughter has enjoyed learning tables almost ‘naturally.’ parents should also assist for example I put charts up around the house and have played games which have helped I think.

Learning the times table is boring if we don’t incorporate some fun to it. There should be colors, games and appropriate activities so the children will be engaged and happy :^)

Forcing memorization does not help children. They need to know the underlying concepts.

I think the online games are fun for kids but my 8 year old agrees that writing out worksheets multiple times works best.

We learnt it parrot fashion and that was the best way now with all the new games and learning methods kids seem weaker in tables

Work on it a little bit every day.

I get my best results by tying times tables into games (e.g. football: get one right and score a goal).

Learning by song and repeating the tables is the best way. Also having the tables up on the wall as a visual aid is great.

I think repetition is important,whether that’s online games or worksheets.

I always found these difficult to memorize as a child (though I understood things well enough that this didn’t cause problems), so I believe multiplication practice should be as fun and low stress as possible.

Don’t forget to sign up to catch next week’s “faster times tables” announcement.

I’ve written before about the problem of innumeracy and about what problems this can cause for those who are maths illiterate. However the question still comes up on parenting forums “Is it really important for children to know their times tables?”

The following survey results show the problem;

In the UK:

A survey of 1,000 people over the age of 15 found that only 40% of those questioned could correctly answer a simple sum such as 8 x 9, but among the over-55’s in the survey, the number of correct answers rose to more than 60%

and

In the US

A survey of California Algebra I teachers report that 30% of their students do not know the multiplication tables.

So how important is learning the times tables to you and your family?

If you have a teenager (or a pre teen) at home, you’ll know that their willingness to discuss maths questions with their parents often decreases exponentially as their hormones levels increase! Even for those teens who like maths, it can become a become a subject full of complex equations and abstract ideas.

With my own pre teen in the house I wanted to explore how parents can use topical questions to sharpen their teens mental maths skills so I’ve asked the team of teachers and educators at Teachnology – the worksheet resource website, to share their ideas with Maths Insider readers:

Making mental math fun

Does your teenager like performing mental maths? It seems to be a dilemma, as students are given more opportunity to use calculators and computers in the classroom (Did we get to use a calculator?). For teenage math students to be truly well-rounded, they need the mental skills to perform basic math calculations without the aid of a calculator, pencil or paper. The problem is getting the students to take an interest. What if they actually enjoyed that aspect of math? It can be a lot of fun.

Real world math problems

One tool that is helpful is to use real world word problems. When teenage students are given problems that are applicable to their issues and interests, they demonstrate far more involvement than when asked, “What is 24+37?” Presenting problems on math worksheets and in class and homework around jobs, money, cars, music icons, mobile phones, etc. can really pique their interest and generate some conversation. What if we asked the same question in this format, “Two football leagues are going to merge into a single league. The Spanish football league consists of 24 teams. The English football league consists of 37 teams. How many teams will be in the new football league?” Which question do you think would motivate students more? Students frequently fail to see the applicability of their studies to the real world. Word the math problems so they do apply.

Just estimate

Estimation can be a useful tool, and sometimes, estimating is enough. When a teenager is checking their answer, it can be useful to round to factors that are easier to deal with and then compare the results. For example, when attempting to multiply 48 x 103, by multiplying 50 x 100 = 5,000, the student is aware the answer should have 4 digits and be in the neighborhood of 5,000. Some real-world problems are too complex to be solved precisely and estimation is the only practical option. When comparing two options, the disparity between the two options may be great enough that estimation is sufficient to make an appropriate decision. Estimation is a frequently underutilized tool.

Develop some ideas around your child’s interests. Include the names of current movies, current bands, pop icons, etc. in your mental maths and watch your teenager’s interest soar. This is where some conversations with your teenager can really pay off. Ask them about their favorite music, favorite actors and movies. Really listen to the conversations between them and their friends. Any mental maths around mobile phone related issues are always popular.

Here are some examples to get the creative juices flowing:

1) Justin Bieber has asked Michael (your teen to dance in his latest music video. If Michael is offered $22,000 to dance in a 4 minute video, how much will he be paid per minute of video?

2) Your mobile phone provider has offered you the following options:

A) 500 free text messages per month, and each additional text is $0.10.
B) You also have the option of paying $0.01 for every text message.

C) If you send/receive 650 texts/month, which is the better plan? How many text messages would it take for both options to be equal?

3) LeBron James is paid $14,500,000 for an 82 game season, is that more or less than $150,000 per game?

4) Steve and Sarah (teens) start a dog walking business, charging $5.75 per dog walk. If each walk takes an average of 12 minutes, and the average travel time between customers is 18 minutes, how much would they earn (total) in 3 hours if they worked separately?

5) If Sandra Bullock drives a $175,000 Ferrari, and the insurance is $8,500/year, approximately what percentage is the insurance (per year) of the cost of the car?

6) If Emma Watson, (Hermione from the Harry Potter Movies) earns $13 million for a 120 minute film, how much does she earn per minute of screen time?

You now have enough information to develop mental maths that will increase the participation level of your teenager. Keep their interests in mind, and your child will have a great opportunity to round-out their math skills. Remember to consider estimation skills when developing your math problems; the applicability to the real-world is significant. “If it takes 17 minutes to develop 7 mental maths……”

Author Bio:

Teachnology helps 1 million teachers, homeschoolers and parents every month. They provide printable teaching resources and lesson plans.

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How do you get your teen excited about maths? Share your comments below!

Merry is a friend and fellow blogger at Merry Makes. She’s also a qualified Science and EFL (English as a foreign language) teacher and is in great demand around these parts to tutor. Previously, Merry gave us 5 Merry Maths Games which she had used with her reluctant learner. Merry couldn’t teach a boring lesson if she tried, so read on to find out how Merry used 4 different ways of teaching times tables using games.

Visual times tables

I asked my student to draw for me what 2 x 3 = 6 meant. I played the role of the student while he was the teacher. He drew 6 circles then crossed out 3, without explaining it to me. So I asked him to describe his drawings to me. He mumbled something and I managed to catch the ‘2’, ‘3’ and ‘6’ come out of his mouth, but not in any coherent sentence. The purpose of this exercise was to diagnose exactly what it was about multiplication he didn’t ‘get’.

As a result of this I let him experience multiplication visually. I took out coloured mathsticks and carefully counted out the matchsticks as I pointed to them. I pointed out the 2 groups of 3s, and then asked him to add them all up.

3D Times tables keyboard game

I have this cool piece of equipment I picked up in a Turkish market stall several years ago, which I used extensively for my own children. It is a 3D times table chart up to the 9 times table. Each button when pressed down reveals the answer behind the opaque button. You may well ask yourself, what is the advantage of this over a regular paper chart? Think ‘kinaesthetic learners’ and there you have the answer. Of course, pointing to a chart and chanting the sum is also kinaesthetic learning but this cool tool helps the child to be in control of their learning. And we all know how much fun it is to push buttons!

I demonstrated the 3D grid and asked him to use this to test me, first! You may be wondering, well, who’s teaching who, here? I have always found that children take great joy in testing adults, and even more joy if we get stuck or get one wrong. In this case, I wanted to show the student that the task I was asking from him is one I have achieved myself, also to make it less daunting for him. From a child’s point of view, it is extremely stressful to be the only one under scrutiny, to be the one expected to know the answers, the only one getting things wrong. So to provide them the opportunity to turn the table on the adult brings down barriers, increases willingness to participate in the learning process. Needless to say, my student loved asking me my multiplication tables.

Times tables games with answers

I drilled him for the 2-times table and made sure I asked the sums in both serial and random order. All the while he was allowed to use the grid to provide answers. You may think, surely he should know the answers without looking. Well, if you provide the opportunity to drill whilst armed with answers, it sets up the model for what you want. Secondly, the child practices under ‘safe’ conditions i.e. safe in the knowledge that he cannot fail: all he has to do is take a look. Later you can take away the information, in this case, the grid, and you will find that the child will have picked up a lot of the correct answers through repetition. As before, I asked him to test me on some easy and ‘hard’ sums too. It gave him great pleasure, and took down another wall between us.

Times tables flick cards

In the next session, I made some “quick flick cards” which are basically flashcards which have the multiplication sum on one side, with the answer on the other side.

When I show my student the sum he reads it out loud. I give him a moment to answer it (about 5 secs) but if it takes him longer than that, I quickly flick the card with a movement of my wrist and let him see the answer, making sure I flick back to the sum. If he watches carefully, he can see the answer and it turns into a fun way to get him repeating his timestable. In later sessions, I will gave him less than 5 seconds to respond, and when he fails to answer, cards are set aside to drill again. All cards which he gets correct, he can win off me, so he can see his achievements in a tangible form, which is a great motivator for learning.

Then I set some follow-up tasks for him to complete at home:

A a few multiplication sums from his grade 3 workbook,

B drilling his 2 and 3 times table with his father (also testing his father),

C counting out beans or pasta to write out his 2 and 3 times tables, under mother’s supervision.

5 take away tips

It is vital for the child to feel that he is supported at home in all aspects of his learning, and the involvement of parents is often enough motivation for a reluctant child. And finally, it is extremely important to acknowledge his progress and successes. After all, what is a moment of triumph without a loved one to share it with?

1 Take an active part in your child’s learning process

2 Show your child what you expect from him by modelling it

3 Praise when he succeeds

4 Encourage when he struggles

5 Set targets and provide another opportunity to succeed when he fails.

After just 4 sessions with me, he brought me this door-knob hanger (a present from me for spotting one incorrect sum on the 3D grid).

It totally made my day when I read what he’d painted on it: ‘Mathmatison Working’ !!

Big punch in the air from me! He’s gone from being a reluctant math-student to ‘Mathmatician’ in just 4 sessions. That is why I love teaching.

Merry blogs at Merry Makes where she inspires and delights readers with discoveries and tutorials spanning crafts, recipes, gardening and more!

For those of you not able to get to a Turkish Market, Amazon has a similar 3D Times Tables Keyboard!

Multiplication facts are essential for every student.

As students move forward in mathematics into high school and college math, they will rely heavily on their multiplication and division facts. Students start to learn these facts around the age of 7 and it can be a challenge for some. Many teachers simply suggest that students “memorize” all the facts. This is challenging and many children are unable to do this.

The multiplication facts strategy

Eventually we hope that students will just “know” their facts, but when first learning multiplication facts, it is best to teach students strategies for finding the facts, so that they always have a way to find the fact if they forget it.

It also makes them quicker to learn.

Teaching facts should be taught in a particular order, so that the student doesn’t get frustrated, and so that they can rely on their “partner fact” (3X4=4X3) for some of the harder facts.

Before multiplication facts

Before starting, let me stress a prerequisite that must be accomplished before starting multiplication. Students must be adept at addition without counting on their fingers prior to starting multiplication. Specifically, they need to know their doubles.

If you say, 8 + 8, they should immediately know the answer is 16. 9 + 9 = 18. If these doubles are not automatic, start drilling these and then come back to multiplication.

You will also want your child to be able to double twice for the X4 facts, so they should be able to do problems like 14 + 14 and 16 + 16 in their head. The 16 +16 is a harder one since it requires you to carry, I accomplished this one with a song that goes like this: “2 and 2 is 4, 4 and 4 is 8, 8 and 8 is 16; 16 and 16 is 32.”

Use a sing-song voice and the kids learn these doubles quickly including the hard one 16 + 16 = 32!

Some multiplication facts to get you started

Here are some methods for each fact:

X0 Fact: Anything X0 is 0. This is a very easy fact since students just need to learn that anything times 0 is 0. Remind them that 0 sets of something is 0.
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X1 Fact: Anything X1 is itself. Again, another very easy fact. For example, 1 X 7, this means 1 set of 7, which is just 7 items.
_____________________________________________________________________
X2 Fact: Circle the number that is not 2, double that number. Since the student is good at doubling, this is an easy fact.
____________________________________________________________________
X4 Fact: Circle the number that is not 4, double the number and double again. The student should have doubling down well before starting, so X4 facts will come very easily to them. The only one that might be difficult is X9 – tell them that they can wait and use the “9’s trick” on that one instead of the 4’s trick if they don’t know 18 + 18 since we didn’t really drill that double.
___________________________________________________________________

If you look at the above chart, the only one’s that requires total memorization with no help at all are 6 X 7 and 7 X 7.

Once students get a handle on multiplication facts they can start looking at the concepts of divisibility and division.

Dr. Lynne Gregorio’s Apex-Math website offers additional articles and great value workbooks, games, and practice for students to explore multiplication concepts in greater depth; in a progressive manner; and without being overwhelmed with too many concepts at one time. Visit the website and see how she can help!

Share your multiplication facts ideas in the comments below!

If finger counting is an issue for your child, it’s worth reading the whole thread.

However, the most eloquent of the pro finger counters was “Musician Dad”.

I present a selection of his quotes below, in green, from the mothering.com forum, with my responses in black :

Regarding Finger counting as a visual starter

Using a different set of items is still using a visual representation of numbers, the only difference is you have your fingers with you at all times. You can’t misplace them, and taught properly, you can do larger number equations as well. You won’t need a whole bag of them to do 233 + 432.

If you have your fingers with you all the time, and use them all the time, there is no incentive to try to memorise and figuring out how to do more than basic arithmetic can be harder than using other visual or memory based techniques.

Regarding Finger counting disadvantages a child

Someone who can figure out a complex math problem using their fingers can still figure out a complex math problem. Failing them because they can’t do it fast enough is just plain dumb.

I finger count at times, I have friends that finger count at times. Many of us have excelled in math intensive studies in spite of (or maybe because of?) this.

I agree that lightening speed is not necessarily the main objective (but it’s cool!), especially if accuracy suffers. I’ve seen 10 year olds take 20 seconds to work out 13 + 9 because they’re counting out 13 fingers, then adding another 9. (very uncomfortable!)

Mathematics is actually a broad subject, so it’s true that you can excel at higher level maths without memorising basic facts as it’s often the deep understanding of mathematical concepts that elevates mathematicians who solve the worlds most complex mathematical problems.

There are people, the more times they count on their fingers to figure out the equation, it puts the equation into the “I did it myself, so I have an easier time remembering next time” category.

One day while out with his dad, who knew he was working on multiplication, a father asked his son a question.

“Son,” the dad said, “can you tell me what 2 x 6 is?”

Without even looking at his hands the boy announced “It’s twelve, right?”

“That’s right,” the dad replied. “You are very good at math, aren’t you.”

“I guess, but mostly I just figured it out on my fingers so many times that I had no trouble remembering it now.” The boy told him. And it’s true, he had counted by twos on his fingers so often that by that time he just knew what the answer was.

This can also be true if you ask a child to visualise counting their fingers or other objects in their head.

I ended with this quote:

“Musiciandad, your arguments are both reasoned and persuasive, but if we return to the OP’s(Original Poster’s) question, her child only recently started finger counting and was previously able to recall number facts to 10. What I want to draw attention to is the unspoken idea that not only is it ok not to be able to recall number facts with ease but that as a parent, the OP shouldn’t try to help her child memorise these facts.

Yes, I’m sure her child could still become a great mathematician even if she continued finger counting, but let me support the OP in her attempt to help her child”

The full debate continues on the mothering.com forum!

Yes there are calculation methods which use the fingers to work out calculations at super fast speed, which is great if you’re going to train your child to do this;

But if you’re not, don’t let your child finger count

Here are my 4 reasons why you should wean your child from using their fingers;

1 Finger counting is just a visual starter

Finger counting is an introductory skill, in order for children to have a visual understanding of number facts, not the final method to be used for calculations. According to mathematical development research, ” children generally move from the less-efficient strategies using their fingers, to the more efficient strategies without finger use (Geary, Hoard, Nugent, & Byrd-Craven, 2007).”

2 Finger counting discourages memorisation of maths facts

Many things in life will need to be memorised in the future by your child, finger counting closes their mind to this essential skill. According to mental maths research, “When Chinese children could not retrieve an addition fact directly from memory, they tended to count verbally, whereas the American children tended to count on their fingers or guess.” The Chinese children scored better in addition facts tests.

3 Finger counting slows down the whole calculation process.

Further adult numeracy research “noted that those who consistently relied on finger-counting were unable to increase their speed and/or were unable to complete of the problems within the time constraints.” Fast recall of of arithmetic facts are essential for questions from “There are 8 eggs in a basket and 3 are taken out. How many are left?” through to “Solve 7x + 3 = 52” and beyond.

4 Finger counting puts them at a disadvantage in the class

Leaving your child to finger count while her classmates move ahead because they have memorised the arithmetic facts is just not fair.

Use other physical objects when introducing the concept of counting and adding on. I’m a great fan of using chocolate chips or raisins as a tasty prop when practicing preschool number facts.

We all want our kids to be happy, confident, well rounded individuals who excel at every subject at school and who will contribute fully to society, but all those dreams fall apart after asking them,

” Sara, what’s 15 + 17?”

As patient and loving parents we can deal with the long pause, but, if after that the answer is still wrong, then we wonder what have they been learning at school for the past 2, 5, or even 10 years! Have they never studied mental maths?

All is not lost

In this series I will show you what you (yes you, not the tutor, not their teacher, not the local Kumon centre) can do to rescue the situation.

If you can set aside 2 minutes a day for at least 4 months, your child’s mental maths problems will slowly but surely melt away.

Before we get started, make sure you’ve read my post about the importance of daily practice.

Confused?

Don’t worry, I’ll be there to hold your hand (and I’m hoping others will share their mental maths strategies as well).

Want to know what’s coming up in the rest of the series?

I’ll show you how the starting point is crucial to improving your child’s mental maths confidence (but you don’t necessarily need to start the very beginning)

In the introduction I promised to guide you through a method which will help your child become lightening fast at Mental Maths. I’ve made 2 short videos to show you a simple method which, with just a few minutes a day will improve your child’s Mental Maths skills.

Where to Start?

So you’ve asked a mental maths question or 2, you’ve got some serious pausing or hesitation, you’re not going to get mad or even because you’ve got Maths Insider to guide you to a solution.

Watch the video for full instructions and an explanation of where to start. A summary of the video is shown below:

Video Summary

Find your child’s weak points by asking increasingly more difficult questions such as 3+1, 7+1, 9+1, then some +3’s, then +5’s etc

If your child pauses or struggles with any of the answers, this is their weak point.

Choose a starting point 2 steps easier than their weak point. If they struggle at +3’s start at +1’s, if they struggle at +7’s start at +5’s etc.

In Part 2, I’ll show you a website where you can make free mental maths worksheets and how to use these worksheets to help your child become faster at Mental Maths.

Did you try this yet? Was it easy to find your child’s mental maths weak spot?