Year 4 very poor maths reasoning and problem solving skills

[Tead]

My son is in year 4 and whilst his arithmetic skills are fine his problem solving and reasoning skills are very very poor.
today with we’re doing this:
there are 26 crabs with 10 legs each and 12 cats with. 4 legs each. how many legs in total.

he added 26, 10, 12 and 4. He couldnt work out that you needed to multiply and then add.

I spent ages trying to break down the problem and giving his alternate examples etc. he just couldn’t work it out.

whenever he sees a worded maths problem he doesn’t know what operation to apply.
his class teach says his maths is fine, he sits on the table that are given the most challenging work.

any suggestions how I could improve these skills. Thanks

Practice!

Could he do just the cat part? Or simplify again, how many legs if you have 1 cat, 2 cats, 3 cats, 5 cats..... build it up.

Hide the numbers so he can't just add them together. Then draw a crab and a cat. Show how many lets each crab and each cat have and add that to the drawing/model (could be an actual crab and cat or a circle/rectangle to represent the crab and cat). Talk about how many leg's you'd have if there were 2 cats or 5 cats or 10 cats. Then show the actual number and work it out.

Eventually you want him to be drawing a bar model to represent the problem to help him decide which operation to use, but that will take time. It's really common for children to pick random numbers and add them together, which is why hiding the numbers so they can't do that really helps. They build the model (either drawn or using physical objects or in their heads) first, decide what they need to do to find the answer and then they can slot the numbers in.

I think the RUCSAC method of breaking it down might be helpful, along with looking at the problem pictorially as mentioned already.

I used RUCSAC in my classroom for years but over time realised there are lots of problems with RUCSAC. It doesn't tell you how to decide what the important information is when you read the question. It doesn't give you any guidance on how to understand the question ie how to decide what it is you need to find out. It doesn't help you to choose the operation - how do you know which the correct one will be?

I was then trained that children don't struggle with the maths in a word problem, they struggle with knowing what maths to do, which explained why RUCSAC isn't helpful - it doesn't help with that decision making. Children underline any number they see then pick some at random to add.

So often when adults help children with word problems, they end up identifying for them the calculation that they need (ie do the hard bit), leaving the easy bit (completing the calculation) for the child. That doesn't then help a child solve a different problem.

Could you please give an example of how the bar model would work. I have only seen the bar model when adding, using the part + part = wholemodel

He needs it breaking down further then. Keep practicing until he can increase the sum.

@Tead it sounds like your DS can do the actual math but having an issue with applying the operations when it comes to seeing a problem in words. would suggest going back to basics.

so for example, start with 1 dog with 4 legs, 2 dogs with 4 legs....you can draw it and show him...he may not be able to visualise the problem so it will help him 'see' the groups of animals and legs....then you can add a spider with 8 legs and ask him to count..or do with smaller numbers...I know it sounds simple - 'just' multiplying and adding but sometimes kids cannot decipher the words !

Can you change the numbers, make it like 4 crabs and 3 cats. Draw them out and have him count them. Then represent crabs as 10+10+10+10 and the cats as 3+3+3 . Then show him it's the same as 10x4 and 3x3 and add them together . Lots of repetition until he understands the process ,what it means ,why it is done that way .

Bar model it would be another visual interpretation and it could look like this.

@Tead - let's see if can do this in words - if it doesn't work I'll have to resort to a bit of paper and photographs...

So - there are 2 parts to this question - first we have to work out how many legs the crabs have and then how many the cats have. Then we can put them together to find out how many legs in total.

Let's start with the crabs. Draw a (small) rectangle to represent 1 crab and write 10 inside it. Now draw another rectangle to the right, joined onto the first one and write 10 inside that. So now we have 2 crabs. Add another rectangle for the third crab, and another.... until you have 26 in a horizontal line all joined on to each other. This is what we know - 26 crabs with 10 legs on each crab. Now you draw a long rectangle on top of your line of small ones to make a big bar across the top. This is empty because it shows us what we don't know. How can we work it out? At this point, you hope to goodness he recognises he can do 26 x 10 otherwise it's a very long addition. (Actually, you'd like to think he would have noticed before that it's a multiplication question because drawing 26 rectangles is very long winded. So I'd introduce this method with a question with a smaller number of parts to draw.)

Now we've worked out the number of legs the crabs have we can think about the cats. Repeat the process described above.

Now we know how many crab legs and how many cats legs we have, how can we find out how many we have altogether? If necessary you could draw this onto a bar model - you have the 2 parts and are trying to find the whole.

Bar models for multiplication work exactly the same as bar models for addition & subtraction - you just need to remember that the 2 numbers in a multiplication question mean something different. One of the factors tells you how many equal groups you have and the other tells you how many you have in each group. A common pitfall is to draw a multiplication bar model with 2 parts and put one factor in each part ie 26 in one part and 10 in the other part. As a teacher, that tells me the child is really confused about multiplication!!

Let me know if you want me to draw it.

@JustAnotherManicNameChange saved me hunting down my phone!

I think have concrete things. So get out a box of cars. Ask him how many wheels 1 car has - let him hold it and count. Then 2 cars. Ask him to guess how many 3 cars would have.

put smarties into piles of 3. Ask him how many is in 1 pile, then 2, 3, 4 (let him count and pick them up). You can the. Rearrange so they are in piles of 5.

you can do it with people and socks/gloves. How many socks would you need for 1 person? How about the total for everyone in the family? How about everyone in the family plus 2 dogs?

I'd ask him how many legs he has. How many you have. How many do you have together. How many legs if you added his dad in.

Then add in your pets legs.

Yes I'd agree with concrete objects. Then progress to pictorial. I ALWAYS encourage my maths students (I'm a tutor) to draw as much as they can with problems like this. Some can see that it needs to be multiplied. Others cannot but once it's drawn they can. So with that question I'd say first highlight the numbers then go back and look again at it to reread and think about how to represent the problem pictorially or in a concrete manner. THEN work out what the number sentence is and go from there.

Concrete -> pictorial -> abstract

does he understand that multiplication is a symbol for repeated addition? That seems the first idea to make sure he has grasped.