Maths Test For 6-8 Year Olds is a unique e-book. It’s a test that becomes a tutor! It checks all the important number concepts at their earliest level and then shows you exactly how to help your child improve, according to his or her individual needs.

Maths Test For 6-8 Year Olds is largely a practical test, using common household materials you have to hand, such as pegs or spoons. You ask your child to show you certain situations using these materials. It’s fun to do!

Young children are often rushed on to abstract written calculation problems well before they’re ready…and this can lead to long-term difficulties. Parents worldwide are searching for help for this very reason. A child needs to know the principles of counting, how number patterns work and how to represent ‘real-life’ situations mathematically…as well as a variety of calculation methods using manipulatives…before being presented with abstract calculation problems in addition, subtraction, multiplication or division.

I’m a specialist in K-7 numeracy. The test is designed to show up problem areas. I tell you exactly what to look for while your child does each task.

The suggested follow-up activities are quick and easy to do and will fix any problems that show up.

If your child completes all the tasks easily and accurately, there are recommended strategies for improving maths at the next level.

If your 9 or 10 year old has been struggling with maths for years, it’s because he or she has missed out on developing some really early mathematical understandings. This test is designed for long-term strugglers also. It highlights the basic problems and shows you how to tackle them.

Until these issues are addressed, your child is likely to continue having maths difficulties. The sooner you find the problem or problems, the sooner your child will be on the path to success.

Click here to read more about Maths Test For 6-8 Year Olds

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How to help your child understand subtraction

Children need to understand what’s happening to the numbers when they are subtracting. The easy, best practice strategies below are highly recommended. Introduce a new strategy with small numbers that can be easily visualised, particularly if a child has maths difficulties.

Algorithms are now seen as just one way to calculate…not the only way. This is because they do not help children understand anything about numbers. All they do is provide an abstract process. Many children have no idea when they’ve made a mistake because they can’t determine the ‘reasonableness’ of an answer. Try some of these alternatives and notice how your child’s understanding grows.

Subtraction can be thought of as addition!

eg 21-18 = ?

If you think of this in terms of addition, then you would ask yourself what you’d have to add to 18 to get 21.  Much easier!

Add or subtract the same amount to each number to make the numbers easier to deal with!

By rounding one of them to the nearest 10 or 100, the problem becomes easily manageable.

eg 19 – 4 = ?

Round 19 up to 20 to make it easier. Also add 1 to the number you are subtracting (4) to compensate. The problem becomes:

20 – 5 = ?

= 15

Another example of rounding:

22 – 15 = ?

Round the 22 down to 20. Also take 2 away from 15 to compensate.

20 – 13 = ?

= 7

With larger numbers:

238 – 123 = ?

Round 238 up to 240. Add 2 to 123  to compensate.

240 -125 = ?

= 115

Make small jumps using easy numbers along a number line!

The number line can be real or imaginary. A real one is recommended for any child who is having a lot of difficulty with Maths.

It’s easy to draw one up on a piece of paper. Your child may be used to drawing them at school. If so, great. If he doesn’t know how, you can get him to help you to draw one. This will give him practice in numbering and labelling accurately. You can add to it as he starts working with higher numbers. Make sure the ‘easy numbers’ are highlighted, eg 0, 5 10 etc, and all the other numbers are also marked along it.

eg To solve the problem 27-19, you can start at 19 and make jumps to the easy numbers up to 27, or start at 27 and make jumps down to 19.

If you start at 27, the easiest jumps would be 27 t0 25 (=2), then 25 to 20 (=5), then 20 to 19 (=1)

Then add up the jumps: 2+5+1 = 8

If you start at 19, the easiest jumps would be 19 to 20 (=1), 20 to 25 (=5), 25 to 27 (=2)

Then add up the jumps: 1+5+2 = 8

Take away the hundreds, tens and ones in chunks

For children 10 years and older who are familiar with negative numbers on a number line.

eg:

408 – 351 = ?

Take away 300 from 400 (= 100)

Take away 50 (5 tens) from 0 (0 tens) (= -50)

Take away 1 from 8 (= 7)

= 100 – 50 + 7 = 57

eg 51-19 = ?

Take 10 (1 ten) from 50 (5 tens) (=40)

Take 9 from 1 = (-8)

40-8=32

eg 56-32 = ?

Take 30 (3 tens) from 50 (5 tens) (=20)

Take 2 from 6 (=4)

20 + 4 = 24

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Do children need to learn times tables?

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 tables?

1 Make sure he understands 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 he 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 he learns 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.

Use a 0-120 number grid for points 1&2 and see if your child starts noticing the patterns.

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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Fun maths games to play in the car

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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How to improve your child’s skip counting

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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Try this early maths check to see if your 6-8 year old counts on

‘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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Children with maths difficulties

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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Maths test for 6-8 year olds…

and older children with maths difficulties

Why test maths at home?

It makes sense to find out if your 6-8 year old is getting a good start in maths, and help prevent problems arising later on.  Or, if you have a 9-10 year old who really doesn’t ‘get’ maths at all, finding out where the problem lies is essential.  Maths Test For 6-8 Year Olds checks all the important number concepts at a very early stage.

Is this maths test easy to do?

I’ve had 20 years’ experience in teaching children and, as a K-7 maths numeracy specialist, I explain and discuss the teaching of primary maths with teachers and parents.  I’ve made sure the checks are easy to understand and easy to do. They’re also fun. All you need are some manipulatives, eg straws, pegs and counters… or any small things you have to hand at home.

Why do so many children have maths difficulties?

There’s a simple reason why many children just don’t get maths. Maths understanding builds as you go.  Children who miss out on certain early maths experiences often find the leaps in understanding they face to be overwhelming. They can be stuck at a much earlier point than people think and remain there until somebody helps them. Ongoing maths problems won’t fix themselves. They need to be identified and dealt with.

How will this test improve my child’s maths?

It will help you find any early understandings your child lacks and show you how to give the right help to move him on. The knowledge you gain from using it will also help you communicate with your child’s teacher.

The test checks for understanding of the number concepts at a fundamental level. It tells you exactly what each individual check is for, how to do it and what questions to ask.  Each check has a different purpose and there are photos to show you what to look for.

The checks definitely will make your child think, but if he makes a mistake he is very unlikely to realise it or feel as if he’s failed.

If he does something incorrectly, there are suggested activities to help him develop the basic understanding he needs in that particular concept. The activities are easy, interesting and fun.

If he sails through a check easily, there are suggestions about what to do next to keep him moving forward to a higher level in that concept.

Interesting facts that will help you improve your child’s maths

About algorithms:

eg

Algorithms have been used for centuries to help with calculation. But if you look at an algorithm as a ‘process’ (which is what it is) you realise that it is just about WHAT TO DO WITH THE NUMBERS, and has nothing to do with REALLY UNDERSTANDING THE NUMBERS OR THEIR PLACE VALUE.

Children who understand virtually nothing about numbers can use algorithms quite successfully because they can memorise the processes. It’s quite easy to recognise these children because they never check their answers to see if they’re reasonable. The converse is true too…they don’t see gross mistakes in their answers as unreasonable.

For example,

A child who’s just using a process (and has got it wrong) isn’t thinking about the size of the two numbers he’s adding together, so probably won’t notice the error.

These days we look at the use of algorithms as just one way to calculate…fine, as long as you understand that algorithms don’t help a child understand numbers. There are plenty of other strategies taught that DO promote understanding of numbers.

This is an example of one change in maths teaching over the last 10 years or so.

About word problems:

Children actually have more trouble figuring out how to represent a ‘real life’ or word problem in a mathematical way (ie get the numbers and signs right) so that an answer CAN be calculated, than in doing the actual calculation.

In early maths, when we’re still focused on interpreting addition and subtraction problems with small numbers, children will often be great at calculating the answer in their heads but unable to represent the problem mathematically. It’s important to work on this because later, when the words don’t clearly indicate what to do, or the size of the numbers in the problem doesn’t give any clue as to what to do with them, children can get very confused.

This e-book tells you exactly what to do to get the show on the road in these two areas, as well as all the other areas to do with number. The checks AND activities are quick and easy, as well as fun and effective.

If you want to help fix your child’s current problems and gain a happy maths student instead of a miserable one, or if you want to help prevent future problems for your 6-8 year old, buy this e-book and get started today.

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Starting out with addition facts

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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Why a child can’t remember a particular ‘times table’

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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