"How many more?" Problems and introducing Math conflict

[Justified]

"Julie has 20 apples and Mary has 10 apples. How many more apples does Julie have than Mary?"

 

We are really struggling with this problem. There isn't a conflict needing to be solved in this problem above. Instead, the problem is asking the child to extract information. When I introduce a conflict by saying "Mary wants to have the same amount as Julie, how many more does she need?", my DD is able to find the answer by counting forward. Without the conflict, she just can't grasp it. In fact, if any problem is introduced without a conflict and it is just asking her to extract information she gets lost. How do I help her bridge this gap? Or is it okay for me to use the method of introducing a conflict until the gap is bridged naturally? Is there a reason why math books don't introduce conflict but instead want the child to learn to simply extract information without purpose? We are using MM1B. We have had many problems like this throughout the book, and as we come to the end, I would have thought by now that these problems would be a breeze. She isn't struggling on anything else. Hopefully my terminology is easy to understand. Thanks for any help.

[MotherGoose]

I think it's a developmental thing and she'll get it. I sometimes reword things too--as in if your sister has 20 pieces of candy and you only have 10, how many more does she have? Or having her match up objects--a line of 20 counters and a line of 10 counters, which ones don't have partners, that's how many more there are of one than the other. HTH

[Lori D.]

Yes, that's it exactly -- it is HARD for children to work with word problems -- understanding terminology, understanding what you know, and what you need to figure out -- and then what steps will get you there.

 

You might try ALSO using the terms and ways of phrasing from other math programs, so DD gets used to hearing several different types of terminology, and can then have a mental file she can run through and use whichever one "clicks" for her to understand what steps she needs to do to solve.

 

In this case you want to connect the idea of "how many more" (wording of the problem) with "difference in amount", as "difference" is a key word connected to the process of subtraction. That's what you're trying to do, is guide towards what process needs to happen. I REALLY like this quick little video that helps you Solve Subtraction Problems By Identifying Key Phrases.

 

The video says, "We subtract when...

… an amount is taken away."

… we are comparing two amounts."

… we are finding a distance."

 

She also goes on to show how to be careful to not be tricked, as ALL the wording of the problem is important. At this early stage for your DD, the problems will be very straightforward, so not going to be tricked yet. ;) At this stage, it really helps to talk your student through the process. Example (with answers you are trying to get from the student in parentheses):

 

Original problem: "Julie has 20 apples and Mary has 10 apples. How many more apples does Julie have than Mary?"

 

How many does Julie have? (20)

How many does Mary have? (10)

What is that second sentence asking us to find? (how many more apples does Julie have)

What does that MEAN? (comparing two amounts, or, difference in amount)**

How do we find the difference between 2 numbers? (subtraction)

 

** may need some leading questions here to get to the answer of "difference"

- So, the problem tells us Julie and Mary both have apples, right? (yes)

- Do they have the SAME amount? (no)

- So they have DIFFERENT amounts? (yes)

- That means one has MORE and one has LESS? (yes)

- What can we do to find out the DIFFERENCE between the MORE amount that Julie has and the LESS amount that Mary has? (subtract)

 

Another way is to use the Singapore "bar" method for visually comparing what you have, which helps you see what you need to find. A lot of times, once the student draws it out, they can SEE what they need to do to solve the problem:

 

20 = |--------------------| = Julie's amount of apples

10 = |----------|___?___ = Mary's amount of apples

_? = |----------|__?___| = how many MORE apples does Julie have than Mary

 

By lining everything up, it even LOOKS like a subtraction problem (20-10=?). Cuisenaire rods or other manipulatives are very handy for lining up and doing that visual comparison. In the video, she shows that very simply with the picture of known quantity + (unknown) quantity = known total. Visually you can see you know the total and one of the amounts, so you can see you have to subtract the one known quantity from the total to get the other unknown quantity.

 

Patient, gentle perseverance! This is HARD mental work and having to make a jump from straight algorithm to having to figure out WHICH algorithm and HOW to apply it, will solve the problem! Hang in there! :) BEST of luck! Warmly, Lori D.

 

[Cosmos]

Can she go in the other direction, as in a problem like this:

 

John has 25 apples.

David has 10 more apples then John. How many does David have?

 

I would start with that kind of problem first before the "how many more" kind of question. And when you do "how many more" start with a situation where the difference is just 1 or 2, such as this:

 

Sarah has 10 apples.

Elizabeth has 11 apples. Who has more apples? (Elizabeth.) How many more?

[Justified]

Thanks for the suggestions. Really awesome ideas. I knew I just needed a fresh perspective and the encouragement that we will get pass this eventually.

[Alte Veste Academy]

That particular phrasing almost killed one of my kids. For real. I just rephrased until development caught up. And this was a kid who is GREAT at math. This is also a kid who abhors ambiguity. LOL

[EndOfOrdinary]

I used to teach my algebra kids to ask five questions for every story problem.  They would roll their eyes because they were always genius high school students who never needed to be taught anything, let alone ask questions, but soon I would catch them doing it.

 

1) What is going on?

2) What do you know?

3) What is the question being asked?

(Normally if they cannot find it, I ask them to physically touch the question mark and move backwards till they get to the beginning of the sentence.)

4) How would the problem look to answer the question?

(FIrst just using words: "Mary's Apples + Extra apples = Julie's Apples" or something else. This is hard for some kids, even in high school.  Do not worry if she cannot put words or symbols behind this part)

5) Which numbers can you fill in to get an equation?

(Many kids just jump here without the words step back at 4.  The words are not necessary at this point, but if they can learn them now it can really help later.)

 

I don't know if any of that helps.  It basically uses steps to walk through the process of decoding the story problem.  Some kids fly with this, some kids need manipulatives.  You can use both strategies together, but if your student just looks lost, bail on the 5 questions!  Their brain just doesn't work that way.

[crazyforlatin]

DD had major problems with those types of word problems, and it took time for me to see that it was all about development. I wasn't on this board in those days and was pretty much trying to figure out things on my own. I rephrased, drew pictures, took out manipulatives. She's now using AOPS Algebra. Don't worry too much it - it'll click with your child when the time is right.

[letsplaymath]

Echoing everyone else, this is a development question. It's much easier for young children to figure out what to do in a problem where stuff is moving, where we are putting things together or taking things apart. The comparison aspect is much more difficult---but you don't want to sidestep the issue, because it's important for them to learn. Therefore, rather than teaching them to memorize "key words" which will have a tendency to trip them up later in other, more complex situations (comparing and distance are NOT always subtraction, especially in middle school and beyone), I prefer to help them analyze the story:

• MaryAnnA's suggestion: Get some blocks, pennies, or whatever to represent each person's stuff. See how many blocks you can match up and how many extras don't match. Eventually the child will be able to imagine the items without something tangible.
• Or ask: Who has fewer? How many would we have to give them to make it even?

The one thing you DON'T want to do is to see this as an example of "story problems are too hard" and start focusing only on number calculations. For young children, story problems are mental manipulatives that lead them to conceptual understanding. Abstract, number-only calculations lead to rote procedures (follow the steps and get it over with). Both types of math are useful, but if you had to choose one, word problems are by far the more important.

[Justified]

Echoing everyone else, this is a development question. It's much easier for young children to figure out what to do in a problem where stuff is moving, where we are putting things together or taking things apart. The comparison aspect is much more difficult---but you don't want to sidestep the issue, because it's important for them to learn. Therefore, rather than teaching them to memorize "key words" which will have a tendency to trip them up later in other, more complex situations (comparing and distance are NOT always subtraction, especially in middle school and beyone), I prefer to help them analyze the story:

• MaryAnnA's suggestion: Get some blocks, pennies, or whatever to represent each person's stuff. See how many blocks you can match up and how many extras don't match. Eventually the child will be able to imagine the items without something tangible.
• Or ask: Who has fewer? How many would we have to give them to make it even?

The one thing you DON'T want to do is to see this as an example of "story problems are too hard" and start focusing only on number calculations. For young children, story problems are mental manipulatives that lead them to conceptual understanding. Abstract, number-only calculations lead to rote procedures (follow the steps and get it over with). Both types of math are useful, but if you had to choose one, word problems are by far the more important.

I agree. I feel word problems are very important. I knew this issue was important, and I am thankful for all the great feedback. I found some great word problem apps on the ipad that I think I am going to add to our program that include a lot of the techniques you all have given. I think this one will help especially and it is free. Maybe some else can benefit too so here is the link. https://itunes.apple.com/us/app/thinking-blocks-addition/id668450919?mt=8

[fdrinca]

For us, the magic solution to this problem was using the number line. Where are Julie's apples? Where are Mary's apples? What's the difference? Subtraction is just the distance between two numbers on the number line. 

 

Number line literacy will be very useful as your DD transitions to adding and subtracting negative numbers, too.

[wendyroo]

I would start finding similar situations in real life and talking them through using story problem language.

 

Daddy has 5 pancakes.  You have 2 pancakes.  How many more pancakes does Daddy have than you?

 

There are 10 plates in the dishwasher and 4 bowls in the dishwasher.  How many more plates are in there than bowls?

 

I have on two shoes and you have on two shoes.  How many more shoes am I wearing than you?

 

Wendy