less than, fewer than

[joysworld]

I visited this with ds earlier in the school year, and he didn't get it, so we took a break. He'll be 7 next month, and he is extremely good at math. And yet, he can not wrap his head around 'fewer than' 'less than'. You are using MM, and he's to write out the correct amount of items from 'Jim has 2 fewer than Ann' or 'Jess has 5 more than Ted.' We had to just give up doing it for the day because he was sooo frustrated. I have no idea how to help him with the concept. I've tried phrasing it different ways, showing him different ways, and then I just asked him 'if Jess has 5 more than Ted, who has the most?' He would answer Ted because the picture shows Ted having 2 items, and Jess is blank because he is suppose to draw the items.

 

So then, I took the paper away, and I asked him 'if mommy has 2 fewer cars than ds' who has more?' He said mommy. But then I asked if mommy has 2 cars, and I have 2 fewer than ds, then how many does ds have?' He screeched in frustration 'I don't know.' I really don't know how to help him get this concept.

Edited April 17, 2012 by joysworld

[Lucy the Valiant]

Could you offer him 2 piles of M&M's and ask which pile he'd rather have? :001_smile:

[Greta]

Could you offer him 2 piles of M&M's and ask which pile he'd rather have? :001_smile:

 

:iagree: I'd say give up on doing it in abstract ways like on paper and orally, and just use manipulatives for awhile: an abacus, some pebbles, candy, whatever you have handy. JUST use something concrete like this for a good long time, until you're sure he's got it. And maybe take a short break from it entirely first.

[blondeviolin]

I agree to go back to something concrete. You might set out two piles of candy and show how one has more, then line up the pieces until its obvious that pile A has more by so many pieces. You might also check out MEP, which really hits this early on, but in a very developmentally appropriate way. It might be nice for him to work with y1, which would be easy for him and confidence-building.

[Tanikit]

I would also get out the manipulatives and forget that type of wording for now. First make sure he understands more than and less than (not 5 more than) MEP 1 covers this very early on mostly in picture format so you could also try that though I would still use manipulatives.

 

When saying 5 more than when dealing with elementary students it is not usually algebra (x + 5) with (x) - they usually do give you the original number - so Anne has 5 more sweets than Bill WHO HAS 2 SWEETS. So make your son start with what he knows - Bill has 2 sweets. So Anne has 2+5 (5 more than) Don't allow him to do this without giving all the numbers - he needs to be able to see it in action without the algebra. Mom must have a certain number of cars for him to have fewer - make sure you tell him how many cars Mom has!

[jennynd]

miquon is really good with concept like that. but DD did learn the concept through M&M :)

[joysworld]

He definitely understands the concept of more than, less than. He has no problem doing 'alligator' math. I think the visual is throwing him off as well as the word 'fewer'.

 

How could I do this more concretely? I get I can give him some, give me some, and ask how many more does one have, etc. But what beyond that?

[momofsbandeg]

I told her the arrow (< >) always points to the "smaller" number.

 

She understands the concept, just doesn't always know when to say "less than" or "greater than" when it comes to the arrow (< >) part of the problem.

[Greta]

He definitely understands the concept of more than, less than. He has no problem doing 'alligator' math. I think the visual is throwing him off as well as the word 'fewer'.

 

How could I do this more concretely? I get I can give him some, give me some, and ask how many more does one have, etc. But what beyond that?

 

I'm sure others will have more creative ideas, but one thing that comes to mind is to start with two equal piles, take a couple away from one, and tell him that it now has fewer. Do that a few times, then change it to ask him which has fewer. Then change it again where you are starting with unequal piles to begin with.

 

Just a thought.

[Bang!Zoom!]

Check out a picture of a pac man and try to see if they can tie in the visual of the open mouth being "more" <

[joysworld]

Maybe I didn't explain well. He has no issues with < or >. For math, he always tells me what to write, and I write it. He will tell me 'less than' more than' when he wants me to write < or >. That's not the issue.

 

The issue is when the problem states 'Jan has two fewer than Jack.' Then it has a picture of Jack with 8 items, and he has to figure out how many Jan has. Or 'Steve has 3 more than Dan' with a picture of Dan with 7 items and he has to figure out how man Steve has. He is having a hard time with those.

 

Now, if it has a picture of Jan with 5 items and a picture of Ben with 8 items. He can answer 'how many fewer does Jan have' or 'how many more does Ben have. He has no problem answering those questions.

[Tanikit]

Has your son done subtraction of small numbers - if not then back up and do subtraction first. This is a subtraction word problem and may just be a terminology problem for him - he doesn't understand what is being asked.

 

I would first make sure he understands the term fewer - if he can do less than, just make sure he knows that fewer means less.

 

Then do the problems he can do: Jane has five, Jack has 8 - and ask which has FEWER.

 

Then ask: How much less does Jane have than Jack and make sure he can do that (by counting the manipualtives.)

 

Then show Jack with 8 (use manipulatives) and tell him that poor Jane has fewer than Jack. Then ask him to show you how many he thinks Jane has - he can give ANY number so long as it is less than 8. Praise him and keep doing this.

 

Now try to get him to realise that less than can be any number less than - when you say Jane has fewer than Jack and he says she has 4 praise him and say: that was the case on Monday, but today is Tuesday and poor Jane only has 2 - is that still less than 8? What else can be less than 8?

 

And now do it again only this time when he says she has 4 say: Oh poor Jane she has 4 fewer than Jack. What if Jane has 7 - then she would have 1 less than Jack. How about 3 - that's 5 fewer than Jack.

 

And after all this: Jane has 2 fewer than Jack. Jack has 8 how many has Jane got. This is teaching subtraction and not greater than less than so has he done subtraction as if not you may have a problem with this. But he needs to see it all in all its forms with manipulaives.

Edited April 17, 2012 by Tanikit

[MomatHWTK]

Have him draw the problem.

 

Draw Jess with 5 apples (or just the apples).

 

Now draw Dave with 5 apples. Then draw "two more" for Dave.

 

 

 

Be sure to explain that even if the problem doesn't say, "Dave has the same amount of apples as Jess plus two more," that is what it means. See if that can solidfy it.

 

If that's not working, ask him to start with Dave. How many apples does Dave have? "He has two more than Jess."

 

Ok, so we know Dave has at least 2 because he has 2 more than Jess.

 

What do we need to know to figure out how many he has? The "than Jess" part. So Jess' apples plus 2 are Dave's.

 

I'm sure you've already done some of this. But be sure to draw lots of pictures as you are talking. I use a dry erase board- a lot. ;-)

 

And sometimes it still doesn't click. :banghead:

[almondbutterandjelly]

It doesn't sound like it's an inequality issue. It sounds like it's not understanding the language for subtracting. Can you read him some books about subtraction? I'm sure there's a Mathstart book about it. Livingmath.net has a whole category on addition and subtraction books.

 

Something I did with my dd that helped was that we looked up the "confusing" words like "fewer" in the dictionary. Make them understand that it's a language issue. They know how to do the math. They just need to figure out the story to know exactly what math to do. We also acted out the word problems literally for awhile, with teddy bear counters or polly pockets or what have you. He needs to understand the story of the word problem. Then he'll get the math.

[Classical Katharine]

I'd write out these equivalences (below) and illustrate them each with objects. Very tidy rows or stacks so they line up against each other till the top where they are different heights. Use smallish numbers so it's easy to take in at a glance. In other words I wouldn't confuse it by making it so you have to count a messy pile till you can even start thinking about the real issue you want to focus on.

 

I think the first set is easier linguistically so I'd start there. I s/ not have used two names w/ "J"--I'd make them very different.

 

Joy has two more than John.

If John has so many, and Joy has two more, add two to get Joy's. (You add because Joy has more.)

If Joy has so many, subtract two to get John's. (You subtract b/c if Joy has more then John has less.)

 

Joy has two more than John (which your son just did) is the same as John has two fewer than Joy. They are just two ways of saying exactly the same thing. Once your son understands that he may be happy to discover he now knows just what to do. He can just change the harder phrasing, "fewer," into the easier phrasing, "more" and then do the operation he did above. So it's still

 

If John has so many, add two to get Joy's. (You add because Joy has more.)

If Joy has so many, subtract two to get John's. (You subtract b/c John has less.)

 

(It's sort of like a seesaw--if one side is down the other is up! You could even draw a seesaw above your stacks.)

 

HTH. I agree w/ going to objects and then going back to paper. He may be so confused by the language issues of "fewer" etc. that he can't deal w/ the paper issue also, with the why the paper isn't showing a number of objects. That's a separate issue, an abstraction and memory issue, which you can tackle once he has the objects-and-language issue down first.

 

Isolating always helps . . . Not to mention a night of sleep and a promise that Mommy has a new way to do it tomorrow, so it will be O. K.