Whether they’re just starting out with their tables, having trouble learning them or having trouble remembering them, this process suits everyone.

It gets away from those old traditional lists, which is very important. A child who has had heaps of trouble learning lists of facts needs a different, more modern approach. And this is it.

Using the very best practice teaching strategies, this e-book shows you how to teach your child easily, quickly and efficiently. Many children find it difficult to think in multiples, and need to see actual groupings of objects so they understand what times really means. This e-book focuses on helping your child develop this ability quickly through some hands-on grouping of common, everyday objects. At the same time, your child learns how to link sets of facts together to make them faster and easier to learn. It’s a fun new process. Your 8-12 year old, or older child, will love working through it with you.

Not only is it guaranteed to take care of learning the facts, it also teaches three important maths strategies that are REALLY useful in other areas of Maths.

AUD 34.95    Instant PDF download

Times Tables Remembered comes with a small practice workbook for your child. It contains easy to use blank grids that support what your child is learning at any time.

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Why do so many young children have difficulty with maths?

There’s a very simple reason why many young children just don’t ‘get’ maths. More often than not, problems arise when they are rushed into working with maths concepts in an abstract manner before they have spent enough time exploring them using very small numbers, hands-on materials and simple made-up maths stories they can relate to. Young children are not able to think about Maths concepts abstractly. In order to understand addition or joining, for example, they need to be able to hear simple addition stories about animals or familiar things, and they need to see these represented with real objects. They also need lots of practice themselves in laying out real objects to match stories they’re told, and lots of opportunities to experiment with making up their own.

There is a world of difference between presenting a child with an abstract pen and paper Maths problem, such as 4 + 3 = ?, and presenting them with a maths story such as:
Once upon a time there were 4 bears in bed sleeping. Later, 3 more bears came in the door and quietly hopped into bed as well (representing the story with little bears as you tell it).

With this story attached to the problem of 4 + 3 = 7, your child will be not only find it easier to tell you how many are in the bed altogether (because they can see it and count the bears if they need to), but they will also find it easier to tell you how many bears there were to start with and how many joined them, because the situation is now very ‘real’ to them. It’s important to talk about ‘one part’, ‘the other part’ and ‘the whole amount’ when pointing to the materials used to represent early addition and subtraction problems, as this helps prevent confusion with representing problems later on.

Also, children are often expected to work with numbers above 20 before they can explain and demonstrate (using any common old materials that are to hand) that they understand these the following things properly:

• One-to-one correspondence (they point to each thing once as they count it)
• Trusting the count (they know the amount of things stays the same if counted from the other end or even if the things are moved into a different arrangement)
• Counting on (they don’t have to start counting from the beginning again if more things are added…again, they trust that the first amount hasn’t changed)
• How to relate addition and subtraction to ‘real life’ contexts (they can represent simple situations or story problems…as already mentioned above)
• Simple number patterns (they can say what is happening in, for example, 1, 3, 5, 7)
• Some calculation strategies for addition and subtraction (they know, for example, how to jump along a number line to add things)

When working with numbers above 20, children should still use manipulatives (hands-on materials) as they need. They may need them in some contexts and not others. Because some children don’t need to use them, many people believe that their child shouldn’t need to either. Peer competition also feeds this stigma of low ability.

The truth is that your child WILL be able to work abstractly in the future if they use manipulatives now. But if they are pushed into the abstract world of Maths too soon, they will remain confused.

When a concept is demonstrated with manipulatives and small numbers, a child who is struggling to understand will start to see the light. Then with hands-on experience and practice, they will come to fully understand it.

Despite this, children are FREQUENTLY introduced to processes and concepts without any use of manipulatives. Many become very confused and may remain so for years. Adults who say ‘I was always hopeless at Maths’ were very likely expected to make these early gigantic leaps in understanding.

It doesn’t have to be this way. Everyone can understand Maths concepts if they have enough experience with them using manipulatives and small numbers.

When a child’s early issues (ie sticking points in understanding) are identified and dealt with, they can move forward confidently and are likely to have no further problems.

So how does this maths test help?

As a specialist in K-7 numeracy with over 20 years’ teaching experience, a large part of my work has involved explaining and discussing the teaching of primary maths with both teachers and parents.

I know all too well that early maths difficulties rarely fix themselves, so I devised this simple Maths Test For 6-8 Year Olds to show you how to help your child with maths. By checking all the important number concepts at the earliest level, the test uncovers and highlights any problem areas your child may be dealing with, and then shows you how to help your child get over them and steadily improve.

Is this maths test easy to carry out?

Yes! Unlike other basic number tests, Maths Test For 6-8 Year Olds is an informal, practical test that allows your child to use common household materials, such as straws, pegs or spoons, to explain and demonstrate certain situations. This hands-on approach ensures that not only is the test both interesting enough to engage their attention and challenging enough to get results, it is also easy for them to understand and fun for you both to do.

Maths Test For 6-8 Year Olds is not designed to place further stress on your child, or make them feel like a failure in any way. If at any point during the test your child does make a mistake, they are unlikely even to realise it. It will be obvious to you, however, and the suggested activities will show you what is needed in that particular area.

Also, if your child sails through a check easily, there are plenty of suggestions about what to do next to keep them moving forward to a higher level in that particular concept.

What will I need to do to help my child?

You will see exactly what each individual check is for, how to do it and what questions to ask. You will need to look out for certain things while your child does each task so that you can pinpoint any areas in which they may be unsure or struggling. There are photos to show you exactly what to look for.

If any problems arise, you use the quick and easy follow-up activities to fix them.

Maths Test For 6-8 Year Olds will help you gain a better understanding about how your child is doing, and enable you also to discuss vital information with their teacher.

Can the test also help older children?

Yes, absolutely. If your 9 or 10 year old has been struggling with maths for years, it’s likely they have missed out on developing some really early mathematical understandings. Maths Test For 6-8 Year Olds can help those long-term strugglers by pointing out their early sticking points and showing you how to help them go forward.

It’s extremely important to remember that NO child should ever be written off as a lost cause. They simply need a little extra help to get where they need to be, and this e-book is the perfect teaching tool when it comes to helping your child.

Will it also help with Maths word problems?

Yes! In the early years, when children are working on simple addition and subtraction story problems with very small numbers, they will often be great at calculating the answer in their heads, but totally unable to represent the story problem mathematically. It is much more difficult for young children to turn a story problem into a number sentence (ie write the numbers and signs in the correct order), than to do the actual calculation. This is because they can visualise simple problems in their heads and often ‘see’ the answer.

Later on, when the word problems become more advanced with words and numbers that don’t clearly indicate what to do, children can no longer visualise the problems in their heads. Their understanding (or lack of understanding) of operations and representing number situations then becomes very obvious. It takes considerably more time and effort to address this problem at this later stage.

I have often seen older children write the numbers and signs in the wrong order or choose the wrong sign, eg + instead of – when representing even very simple story problems involving very small numbers. To avoid this confusion, it is really important to start on the journey of representing story problems with numbers and symbols in the early years.

Maths Test For 6-8 Year Olds tells you exactly what you need to concentrate on to start improving your child’s skill in this particular area, as well as all the other areas relating to numbers. Once again, the checks and activities set out in this comprehensive e-book are as quick and easy as they are fun and highly effective.

Is this the right test for us?

Maths Test For 6-8 Year Olds is the perfect choice for you to make:

• If you are searching for ways to help your 6-10 year old child overcome their maths miseries, and turn from a reluctant learner into a happy student
  
• If you want to see if your 6-8-year old is on track with maths now, and prevent problems arising later on

Buy this e-book, and start building your child’s confidence in maths today.

AUD 34.95 Instant PDF download

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This will give you some indication of how well your child understands number for his age. It is not a complete test. If your child has difficulty with any of the questions, Maths Test for 6-8 Year Olds will test these and other early sticking points in greater depth, and give you strategies and activities to help your child.

Question #1

Say:

Write down the next number after one hundred.

Check:

Did they write 101 or 1001?

Question #2

Say:

Write the next number after 119.

(Write down 119 in front of your child so they can see it)

Check:

Did they write 120 or 200?

Question #3

Say:

Show me all the different ways 16 lollies can be shared between 2 kids.

(Give them counters or clothes pegs, real lollies and pen and paper. They can use any of these to show you.)

Check:

They should know most of the16 ways.

Question #4

Say:

Tell me how to double a number.

Check:

They say, for example, Double 2 = 4 or You add the same amount again… or something similar.

Then say:

What’s double 1?

Do they know their doubles facts?

Check:

Can they go on to double all the numbers 1-10, and 20, 50, 100?

Question #5

Say:

Take turns with me to skipcount by 5s from 1 to 36

(Don’t start at zero or five. Take turns to say the numbers.)

Check:

Do they get the pattern quickly? 1,6,11,16,21,26 etc

Question #6

Say:

Write a number sentence to match this story I’m going to tell you:  Dad had some chocolates. Mum ate 6. There are 14 left.

Check:

You should get: ? – 6 = 14

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Yes. Multiplication facts are enormously helpful in Maths calculation.

Nothing has changed.

Some children have great difficulty committing these facts to memory.

Nothing has changed here either.

So… what’s the best way to help a child learn times tables?

1 Make sure they understand what they mean

We often take this for granted because as adults we think it’s obvious. For many children, however, it isn’t obvious at all. So, when working on a table, it’s really important to check that your child can represent some of the facts within it using hands-on materials. Does he know that 5 times 3 means 5 lots of 3, and can he show you this with pop-sticks, pegs or something else you have to hand?

2 Make sure they can skip-count in the table pattern

If a child has not had practice skip-counting, eg in threes from 0 to 36, learning the three times table is very abstract, and although he may be able to say the pattern in the short-term, he is likely to have trouble remembering it. Use a number grid so he sees the number pattern in a table while skip-counting. There are downloadable grids here. Take turns with him to say the next number in the pattern.

3 Make sure they learn the easier tables first

The easiest tables to learn are 1s, 2s, 5s and 10s. This is because the numbers have a nice, easy-to-see pattern.

The rest have more obscure patterns and will require extra skip-counting practice.

Help your child by taking turns to say the facts. Not only does it help model the pattern and keep on track, it also removes a great deal of stress, and can change your child’s attitude about tables from negative to positive.

Work on the first 4 facts in one table until your child can remember them:

Take turns to start so your child doesn’t always get the same facts. When he can do this with you confidently, give the challenge of saying the 4 facts by himself. Then move on to the next 4 facts in the table, and finally the last 4.

The great thing about the 2 times table is that it makes the 4 times table very easy to learn. You just double the answers. This is something you should point out, providing you’ve worked on points 1 & 2 above in relation to the 4 times table.

The next table to focus on is the 3 times table. Work on points 1 & 2 and then work on the table in chunks of 4 facts as above. When that one has been learned, point out that he now knows the 6 times table. Show him that you can just double the answers after you’ve worked on points 1 & 2 to make sure he understands.

That leaves 7s, 8s and 9s.

The 8 times table is double the 4 times table. Brilliant! Use a 0-100 number grid to point this out.

The 9 times table has its own distinctive patterns. It’s a really fun table!

1×9=      9

2×9=   18 (1+8=9)

3×9=   27 (2+7=9)

4×9=   36 (3+6=9)

5×9=   45 (4+5=9)

6×9=   54 (5+4=9)

7×9=   63 (6+3=9)

8×9=   72 (7+2=9)

9×9=   81 (8+1=9)

10×9=90 (9+0=9)

11×9=99 (9+9=18, 1+8=9)

12×9=108 (10+8=18, 1+8=9)

One column of digits goes up 0123456789 and the other goes down 9876543210. They also pair off 09 90, 18 81, 27 72, 36 63, 45 54.

Now for the 7 times table.

Make the facts and skip-count using a number grid 0-100. Teach it in chunks of 4 facts also.

One last thing…

Point out the commutative nature of multiplication facts, eg 2 x 4 has the same answer as 4 x 2. However it does not mean the same thing, and you should get your child to make these facts with materials so this is clear.

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There’s no better way to help your children develop their maths skills and understanding than by encouraging them to use them in everyday contexts.

There are great opportunities to do this in the car.

It’s easy to keep an old calculator, a few small notebooks and some pencils in the glove box.

The notebooks can be used to jot down results and the calculator can be used for checking answers.

Many maths games focus on calculating but it’s important to remember that calculation is just one aspect of maths. Here are some purposeful maths games that help develop some of the other important aspects of maths, such as understanding numbers and representing problems accurately.

1 minute games

Read and say numbers around you, eg in the car, or on road signs, other vehicles or buildings

Ask one child to be the time-keeper, a second child to keep a tally, and a third child to read and say all the numbers he can see within a minute. Give everyone a turn to do each of these.

Counting forwards

Choose a starting number that’s manageable for everyone and take turns to say the next numbers as far forwards as possible within a minute.

Counting backwards

Start a bit lower and see how far backwards you can get within a minute, taking turns to say the numbers.

Skip counting

Decide what to skip count by (eg by 2s), a direction (eg forwards) and a starting point (eg 10).
Ask one person to be the timer. Take turns to say the next number as you skip count as far as possible within a minute.

3 minute games

Explore combinations to 10 (for 5-7 year old children)

Ask each child to hide his hands behind his back. Then ask him to tuck some fingers in and leave the rest stretched out, eg 2 fingers stretched out and 8 fingers tucked in. When everyone is ready, ask, eg ‘Who has 2 fingers stretched out?’ Whoever has this arrangement shows his hands, and the other children have to work out how many of his fingers are tucked under.
Then repeat from the start & ask, eg ‘Who has 3 fingers stretched out?’

Special numbers (for 8-12 year old children)

Ask each child to choose a number they have seen somewhere along the way and write down as many partitions of that number as they can within 3 minutes.
eg If a child chooses 35 as his special number, he might write some or all of patterns such as 34+1, 33+2, 32+3, 31+4 etc

or 10+10+10+5, 10+10+10+4+1

or 36-1, 37-2, 38-3

or any other number facts they come up with about his special number.

Give younger children a one-minute headstart. Ask one child to use the calculator to check the winner’s partitions are correct.

5 minute games

Which is the most popular car colour?

Allocate one car colour per child, and give each child a notebook and pencil. Ask them to record their cars for 5 minutes, using a tally. Then ask the eldest to draw a simple column graph showing each person’s result.

Making up story problems

Make up an easy addition or subtraction word problem about the things you’re seeing on your journey.
eg There were some sheep in a paddock. 9 more jumped over the gate to join them. Then there were 13. How many were there to start with?
Ask one child to turn that story into a representative number sentence, ie  ? + 9 = 13, and another child to tell you how they’d calculate the answer, eg 9 + (4) = 13 (counting on from 9) or 13 – (4) = 9 (counting back from 13)…or any other way.
Then give one of the children a turn at making up a similar type story about something else they see, and choose someone else to turn it into a representative number sentence, and another person to say how they’d calculate the answer.

How many windows?

When you’re parked in the city, there are usually plenty of windows to count, and it can be a good way to introduce the idea of arrays. Ask how many windows there are in a row, and how many in a column. Ask how many windows are in a building. A child with early maths understanding will count each window. A child at a slightly higher level will count the number in one row and add this number repeatedly for the each of the rows (repeated addition). A child with reasonably developed primary maths understanding will multiply the number of windows in a row by the number of windows in a column, using his knowledge of multiplication facts.

Please share any maths games you enjoy playing while you’re out in the car!

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‘Trusting the count stays the same’ is an important early understanding your young child needs to develop before number facts will make real sense.

Children have to understand that 9 objects will still be 9 no matter what, as long as nothing is added to or removed from that particular group of objects. When they understand this, and can count on, learning addition and subtraction number facts is easy.

The child in the clip counts on from 10 when the extra pegs are added. She does not need to count the 9 again first. She trusts her first count.

Check out Maths Test For 6-8 Year Olds here

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Tables are just number facts (addition or otherwise) arranged in a logical order. Children should only be expected to try and memorise tables of facts if they understand them. When number facts are clearly understood, they are easy to memorise and apply in mathematical situations.

Is your child really ready?

The idea of ‘tables’ will only begin to make sense when your child has reached a certain level of understanding…

He trusts the ‘count’

He knows that when he counts 5 objects, and then adds 2 more objects and wants to count how many altogether, he doesn’t need to count the 5 all over again because it hasn’t changed. It’s still 5. He counts on from there.

He knows number facts stay the same

This is more advanced than just trusting the ‘count’. He knows that, eg 5+2=7 is true in any context. That is, he knows that 5+2 will give the same result whether it’s 5+2 cars, dogs, peas…or anything, and he doesn’t need to work it out all over again just because the objects change.

If he ‘gets’ these two ideas it’s fine to start thinking about developing his understanding of number facts and then ordering them logically.

Getting started

Choose a low number, eg 5, to ‘make’ addition facts about.

These are the facts: 0+5=5, 1+4=5, 2+3=5, 3+2=5, 4+1=5, 5+0=5.

BTW if your child has been presented with a list of addition facts like this about 5 (or any number) and expected to learn them by rote, beware. A list of number facts is way too abstract for kids at this level.

Your child needs to find out for himself the different combinations that add up to 5. He needs to experiment with ‘hands on’ materials and record his findings as he goes, either on individual cards or pieces of paper that can go up on a wall somewhere.

For example:

Say

‘Here are 5 cars and 2 garages. Put some cars in one garage and the rest in the other.’ (He does eg 3 and 2)

‘Let’s describe the number fact for this situation…three and two makes five’ (You’re modelling this)

‘I’m going to check this quickly with my fingers too. Three fingers and two more…yes, that’s five.’

‘Three is one part, two is the other part, and five is the whole amount of cars.’

‘Now I’m going to write it down like this…3 + 2 = 5′ (You write 3 + 2 = 5 on a card and put it up somewhere.)

‘Now have a go yourself.’

‘Here are 5 horses and 2 paddocks. Put some in one paddock and the rest in the other.’ (If he does 3 and 2 again that’s fine…any combination is fine)

Prompt him to describe the number fact.

Prompt him to check if it’s true on his fingers.

Prompt him to tell you about the two parts and the whole amount of horses.

Prompt him to write it down on a card and put it up. It’s important that HE does the writing.

Next question to ask is ‘Is there another way you could share them between the 2 paddocks?’ (BTW ‘sharing’ is not the same as ‘sharing equally’.)

If he can’t think of another way, show him one. Go through the process as before and leave it at that for now.

If he can show you another way, get him to record it on another card and put it up on display. Then ask him to show you one more way if he can. If he wants to explore more possibilities…that’s great.

Continue making number facts about 5 in different ‘real life’ situations for a few minutes over a few days. Be as creative as you like in coming up with different situations.

Over time his cards will show all the number facts he’s discovered in a random order. Some will be repeated…that’s good.

The ‘Aha!’

This is where he notices there’s a pattern… without you saying a thing.

0+5=5

1+4=5

2+3=5

3+2=5

4+1=5

5+0=5

Ask him to describe the pattern to you.

Helping the ‘Aha!’ to happen

If he’s ‘made’ lots of number facts over and over about 5 but hasn’t noticed the pattern yet, you can ask him to put the cards under each other in a list. This might be enough to help him notice it. It’s better if he ‘discovers’ it by himself.

If not, ask him to remove any double-ups and say ‘Let’s just keep one example of each fact in this list.’

Order the first four in front of him without saying anything. Then ask him if he’s noticed anything about how you’ve rearranged them.

If not, explain, and see if he can do the last two.

Repeat the process over time to ‘make’ and order number facts about 6, 7, 8, 9, 10 (one at a time!)

Memorizing number facts

‘Making’ the facts and understanding them doesn’t mean your child will remember them. Whether you use songs, stories, software or charts to help with memorizing, it’s best to focus on a just few actual facts at a time and take turns to say them afterwards (you say one fact, he says the next, etc). Stay on these until he knows them and continue to practise the old ones even when you’ve moved on.

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Download these number charts, then print, laminate and put them on your fridge.

Download here

1 First, check that your child can SAY the numbers 0 to 50 in order forwards, and the numbers 20 to 0 in order backwards. Do this by taking turns to say each number without using the number chart. If he can do this, he’s ready to skip count.

2 Start working on skip counting by 2s from 0 using the chart and some manipulatives such as pegs, counters, toothpicks, pasta shells or anything you have to hand. Take turns to say 0, 2, 4, 6 etc, making the amount each time with the manipulatives and circling the number on the chart using a non-permanent marker.

3 In the same way, take turns to skip count by 2s starting from 1. (1, 3, 5, 7 etc)

4 Skip count by 2s backwards from 20 to 0, and then 19 to 0.

5 Write a starting number for any of these patterns in the correct place on the blank grid using a non-permanent marker. Ask him to fill in the rest of the pattern by himself.

6 Help him practice saying, reading, making and writing the numbers forwards and backwards.

7 Ask if he notices anything about the numbers. When he sees (by himself) that the last digit repeats as part of a pattern, it’s time to move on to skip count by 5s and 10s, starting from 0.

When he is confident with 2s, 5s and 10s like this, it’s time to expand by varying the starting number.

Skip count by 5s starting from 1

Skip count by 10s starting from 1

Remember to go forwards and backwards, saying, reading, making the amounts and writing.

By doing this you are building up a thorough understanding of skip counting. This is invaluable, not only as a solid basis for seeing patterns in number but also as a precursor to understanding multiplication facts and times tables.

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People we consider ‘numerate’ understand all the number concepts at a reasonably high level.

We usually begin learning about these concepts as toddlers, and then gradually learn more and more about them as we progress through school.

But sometimes this nice, tidy progression in learning goes wrong.

Children learn really well when the maths they’re taught is just a small jump beyond their current point of understanding. They learn best when 95% of any learning experience involves practice in something they truly understand, and 5% involves some sort of challenge.

It’s easy to see that children with maths difficulties continually face challenges that are way more than 5%. They cannot possibly learn at the level they’re being presented with. Somehow, they have missed out on one or more earlier building blocks in understanding number concepts and this has not been dealt with.

They will continue struggling to understand until someone finds out exactly what point they’re stuck at in their thinking and teaches them the very next step after that point.

Often a child is actually at a far lower level than anyone expects and isn’t tested appropriately. There may be teaching and learning adjustments as a result of testing, but the challenges they’re presented with may still be too high. The outcome is usually the same as if they’re higher, ie continued difficulty in understanding the concepts.

Children can be checked for early sticking points in maths number concepts from the age of 6. Then if there’s something that needs to be worked on, it can be addressed sooner rather than later, and future difficulties avoided.

9-11 year olds who’ve experienced ongoing difficulty with maths should be checked at the same level to make sure their earliest gaps in understanding are identified.

See Maths Test for 6-8 year olds to improve maths.

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When we think of ‘times’ tables we usually think of lists, eg

0×2=0

1×2=2

2×2=4

etc

I’ve worked with many children who can’t remember these. This is because they don’t understand them! ‘Times’ tables involve multiplicative thinking (or thinking in ‘lots of’) and this is something that we often expect children to be able to do before they are actually able to do it.

‘Times’ tables are multiplicative number facts arranged in logical patterns. Each number fact is a ‘number situation’ that can be trusted to stay the same. For example 5 x 6 (5 lots of 6) is always 30, no matter whether it’s 6 rabbits, rockets or radishes.

A child who find it very difficult to remember these number facts (or apply them) needs to use materials to explore what they mean. He needs to ‘make’ the facts with counters, pens, pasta or anything. He may only then discover that ‘times’ means  (in this case) ‘repeated addition’.

He may also need much more practise in skip-counting and this is easy to work on.

When you ‘make’ a number situation, let’s say 2×3=6, you put your counters or whatever into two ‘lots of’ or ‘groups of’ three  and write the corresponding number fact down (2×3=6). If your child can ‘make’ similar number situations and write matching number facts you are on the road to success.

It’s entirely possible that your child is not able to do this. He may not understand repeated addition yet, ie use materials to make a situation such as 3+3+3 = 9 and write it down using these numbers and symbols.

Check!

If he can’t do this, find out whether he knows his addition tables to 20 yet.

As in

0+1=1      or   2+1=3

0+2=2             2+2=4

0+3=3             2+3=5

He needs to know these first. See here.

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