Subtraction and maths word problems

[dandelionsticks]

My 6yo (Y1) just doesn't get them no matter how many times we explain it to him. We use Squeebles and Doodlemaths for practice and we use counters and other visual aids. But they confound him. The kind of word problem I'm talking about is one like this: John has 10 books. Emma has 8 books. How many fewer books than John does Emily have? Or Bob has 11 pens. Zoe has 13 pens. How many more pens than Bob does Zoe have?

Adding/subtracting isn't an issue if you present it as a straightforward sum. As soon as it's in a word problem, child is stumped. In the above example, my child will know that Zoe has 2 more pens, but isn't able to reason that to get this answer one must work out 13 minus 11.

It's so frustrating. Unfortunately, we can't avoid as they are in the classwork they get. Is it just the case that some kids just don't get it? Is it a sign of dyscalculia? Any tips? Asking as we're still stuck on this weeks later. We keep explaining also that it's the difference between two numbers and that the smaller number must be taken away from the larger number but child still isn't getting it.

Do some children just find this hard and get it at some point? Do I just need to keep repeating and repeating and hope that one day it will click?

I'm assuming that its age appropriate as the school is setting the work and I also see it in Y1 workbooks.

Definitely not a sign of dyscalculia - that would be the opposite, ie finding it difficult when it's presented in numbers rather than words.

I don't teach maths at primary level, so I'm not sure exactly when I'd expect him to 'get' this, but my feeling is that 6yo is still very young for it. Lots of good maths students find word problems much harder than the equivalent sum. Maybe have a chat with his teacher if you're worried though.

I would try using objects and make it a game. He's not ready for abstract problems. I'd try involving his toys, this Teddy is Zoe and this one is Bob, give them the props to help them see how it works

Interesting that you call your second example a subtraction but it's actually an addition! Quite confusing! I think both of your examples are very wordy. Are they in a book? When reading them try leaving out the 'than John ' and 'than Bob' to start with. Make sure he knows that you are looking for the 'difference' in both examples. Lay counters out in 2 lines and emphasise what is the same ((11) and what is different (2). Does he know the word fewer? It is correct but I've heard it being taught as less because that is a word that children hear more frequently. E.g. greater than, less than.

Hang on I'm a bit confused so if for example you said "Bob has 5 pens, John has 12 how many more does John have?" would he be able to answer that John has 7 more but wouldn't justify it as "12 -7 = 5". If that's the case I really wouldn't worry a lot of quite bright students jump straight to the answer so automatically they find it difficult to justify how.

If he can't answer and doesn't know what calculation to do it's more tricky and what you need to do is try different methods - for example draw pictures of both sets of pens one below the other then count on or if he's still struggling simply break the word problems up into different classes (e.g. how many more does X have -> subtraction.) Some children find it helpful to circle the numbers as they read then circle certain key words to help them.

Does he understand subtraction as the inverse (perhaps not using that word) of addition?

So if for example you're given that 23+45 = 68
what is 68 - 45 = ?

And maths is all about word problems these days! I work with Yr1 and some find it hard to work independently as they are unable to read parts of the question. This is our LA's own scheme and is a bit disheartening sometimes

Could the problem actually be simply that your child isn't reasoning in the way that you want them to (or the way that you do)? I say this because you state that they knew the answer to the second question. That answer can be reached either by addition or by subtraction, since the two operations are reciprocal. So working out what you need to add to 11 to get 13 is just as valid a strategy as subtracting 11 from 13. Could this be the source of confusion?

Or it may simply be that they can easily "see" the answer. It's obvious to most adults that the difference between the numbers is 2. If your child has a good grasp of numbers, it is likely they are reaching the answer without conscious reasoning and so only struggle when you ask them to explain why that is the answer. ("It just is - it's obvious" is what we heard a lot.) Learning to explain why is important, but for children who don't have to consciously think through the steps, it sometimes actually takes longer to be able to do that.

We used to tackle word problems like this by asking "what sum will help you with this problem?" or "how can we turn this in to a sum with just numbers?". There will usually be more than one correct way of reaching the same answer, which is an additional value of such questions as it reinforced how different operations are linked.

Teacher here. You have to explicitly teach the language associated with each operation.

Eg
Addition- total, altogether
Subtraction--how many left, how many more (confusing one that many children don't recognise as subtraction)
Multiplication- if there are... groups of... How many altogether
Division- shared between

Etc

It's not really the reasoning, if he's not reasoning that way. Tell him 13-11 is just a code. I presume that's what you want him to write as the "answer"? ie translate this word problem into maths code.

It really is like a language, or a code. So just tell him, the code is: write the big number, then a minus, then the small number. And what was the answer? Yes, it is 2, so then we write =2.

This is for key stage 2 but some words will be met in ks1

DS is 8 and finding the verbal reasoning questions a struggle. Some of them are "how would Emma do this in her head" for example where the whole point of the exercise is to move away from long multiplication methods and look at separating hundreds, tens and units but DS will always default to long multiplication, even in his head. I do exactly the same and I remember sobbing with shame and frustration at school because I knew the answer and I'd done it the way my brain automatically did it but it wasn't what they wanted.

DS ended up yelling "I don't know what's in Emma's head, only what's in my head" yesterday. Quite.

ShowOfHands my dc3 is the same! He knows but doesn't know why he knows.

Getting him through teacher set work at home has explained why his teacher thinks he's explosive and volotile and unable to concentrate while O think he's bright, sweet, cooperative and obliging! He doesn't think the same way that the teacher explains, so he starts of understanding and ends up utterly confused! (We've been told to watch specific explanatory videos and these have highlighted the fact).

It's a problem though because children have to show their working as they get older.

I think more like my dc1 who used to need me to put "naked" sums into "real life" order to understand - so the opposite to DC3!

Once you know how a child thinks you can work around it, but generic and full class materials and explanations are obviously geared towards the way the majority of minds work, which confuses those equally able but with minds that get there a different way.

It's a tricky one with the 'explain your thinking' questions.

Some children know how the answer is found but don't have the knack of putting it into words.

Some children can put it into words verbally but can't write at a high enough standard to articulate it in paper.

Some children are just naturally good at mental calculations so can check it themselves without using any reasoning.

Some children need to draw pictures or use apparatus to show how they know.

The way the mastery curriculum progresses within each year group (concrete, pictorial, abstract, fluency, reasoning) means that reasoning is highly valued in able children (greater depth or exceeding the age related expectation) but reasoning is hard to teach and is more of an inherent skill, in my opinion. The children who can't access reasoning for any of the reasons I've listed, or more, get frustrated being constantly set reasoning type problems because they are high ability children.

Sorry, rambling.

ON paper.

Honestly, its like a verbal reasoning challenge on its own.

DS, how would Emma do this sum in her head?
I don't know, I'm not Emma
Can you describe how to work out the answer?
The answer is 615
Okay, can you describe how you know that?
Long multiplication
Emma didn't use long multiplication, is there another way she can do it?
if she wants, it's slower though and the answer is the same
Can you tell me or write it down?

DS knows exactly why he knows and can't see the merit of unknowing it just to know it again using a different method. DD used to struggle because she is exceptionally good at maths and kept using methods they hadn't been taught yet. She was more efficient and more accurate than her peers but kept being told to use simpler methods or visual aids or grids. She was much more placid though and saw it as a challenge to list ever single way you could do a single sum, with detailed descriptions and added notes. DS is just pleased he can get the right answer and feels demoralised and cross and frustrated when he has to do it again. It's necessary and it will make him a better mathematician but he gets so frustrated.

ShowOfHands at least he's shrugging and can see the other way. Maybe you could ask him how he'd explain it to someone who couldn't do long multiplication and needed an easier way.

My dc3's problem is that he knows the answer but as soon as a different method of reaching the answer is presented to him he despairs and thinks he was doing it wrong (even though his answers were right) and often something seems to say"does not compute" in his brain and he thinks he "can't do" something which he was able to do without conscious thought ten minutes earlier.

I suspect this is actually the key to the fact that before lockdown I got several calls to fetch dc3 from school because he'd apparently walked out in a temper! This is so utterly out of character that I thought something was going on with other children in the class, or that the teacher was having some kind of breakdown!

I now think the problem was that the "talky bit" (whole class presentation/ explanation of tasks) has been confusing dc3 to the point he just can't figure out what he's meant to do with tasks which are actually easy for him. He must feel as though he's going mad!

I've found I have to work out how dc3 understood the question unconsciously and reexplain that to him so he understands consciously what he was doing unconsciously.

Then I have to reassure him that that is an excellent method.

Then I can explain that some people can't do it that way and do it the way the video/ teacher/ workbook does. Then sometimes he can start to use that method too, but other times we're too wrung out (especially if I've just done a night shift) by that point and decide he should just write the answers his way but at least be aware that his way works and the other way works and both are good

This is laborious and obviously his teacher can't do it with a class of 27 in normal circumstances... Not sure what can be done about that.

The skills you are talking about need to be explicitly taught, he won't just 'get' it because he can add/subtract. I would recommend acting it out or doing it very practically. He may be using other strategies such as counting on rather than taking away. This all links back to using inverse operations and fact families.(google this and if he doesn't know these facts or cant tell you then inverse of say 13+3=16 then it needs to be taught)

Today we had a tantrum over converting mm to cm and meters and back.

What's 1427mm in meters and cm? - 1 meter 42.7 cm

How do you know that? No idea!

Ok, your teacher wants you to watch this jolly explanation video with a cartoon character...

Now, let's look at the next question: what's 1345mm in meters?

I don't know, I have no idea! I don't understand, it's impossible...

Thanks to everyone who posted a response. Reading through the responses, it's made me realize (a) I'm probably not explaining it very effectively (but then I'm not a teacher trying my best to home school on top of working), and (b) that it's a skill and I need to give him more time and opportunities to practice so he gets better at it.

I will re-read all the above suggestions tonight and take on board the tips given. Thanks again everyone. Massive respect to those who teach or who are teachers!

Can you write them out and get him to underline the relevant words? So under line the 11 then the minus then the 3 for example then slowly work back to adding names and items in?
Because he will need those skills for further on so can’t be ignored.