By: Patti Huberty Grade Level – These ideas apply to, and have been used with, grade K-5
Objective- For students and teachers to understand the meaning of problem solving and to be able to create their own bank of word problems from a set of given information.
Materials- Individual bags of M&M’s, skittles, fruit loops, or whatever item they are planning to create a graph for. Also graph paper and notebook paper
Word Problem or Problem Solving?
by Patti Huberty
In my opinion, most of the word problems in the textbook are not really problem solving situations, they are equations written in words. That said, I think what makes these types of problems difficult for young children is that they are still struggling a little with text (reading). I believe because of this minor hurdle we have turned to a way of teaching children how to solve word problems that actually causes more confusion than anything else. The traditional method I’m referring to is the “key word” approach, teaching them to listen for certain words. When using this method, the focus of successful problem solving turns to teaching vocabulary, like "all together, in all, how many more, what's the difference between, etc” in an effort to teach kids which words require which operations. I am skeptical of the "key words" approach for two reasons. First, I think when we teach children to focus on key words we are forcing them into solving a problem one particular way. I have seen this mostly with subtraction problems where the kids have actually figured out the answer using addition (counting on) rather than subtraction to solve the word problem. Secondly, there are many situations where children can get faked out, like "how many more than?" sounds like you might be adding instead of subtracting. I do think that recognizing the importance of certain key words is very important in order for children to have success with textbook word problems. However, I think the focus needs to first be on where these problems come from (how to write them) and what they actually mean.
When introducing word problems I like to start by presenting some information, a situation or graph, and then have the students tell me what kinds of questions they can ask based on the given information. I feel very strongly that when we make children the authors of word/story problems we introduce two very important concepts; understanding the origin of word problems and why the vocabulary for these problems is important. This type of approach gives the students the opportunity to decide which words are important (key), hence leading to an understanding of the use/need of certain words and the action (operation) they require. They also have ownership over these problems and therefore are much more interested in solving them!
So, how do we create this type of lesson? I think bar graphs are a good place to start. Give the students something they can create a graph for, like colors of M&M’s.
Have the students graph their bag of M&M’s
Each student then writes 2 or 3 problems they can ask from their graph. Typical questions they may write are: Which color was there the most/least of? What two colors have the same amount? How many more blue than yellow?
Have students switch with a partner and solve their problems.
Then, using the teacher’s example graph, create some questions as a whole class that deal with a specific operation (but, don’t tell them what the operation is).
“We have five green and seven blue in this graph. Can anyone think of a question that would make us compare (subtract) the green to the blue?” Talk about how to solve the problem and get the students to tell how they knew what to do. Listen very carefully for them to say something about the words in the problem!
Then ask, “What about one that would have us combine (add) the green and the blue?” Again talk about how to solve the problem and how they knew what to do (focus on the words they use). Also ask them how this question is different from the first one.
“Did any of you write or solve problems that were similar to this?” Allow plenty of time for them to share their work and make sure to let them explain what they did and why. Focus on the vocabulary they use and take this opportunity to help them see the connection between their words and their actions (the operation they used to solve the problem).
Finally ask, “How about one that has us EAT the green or the blue?”
This last question should illicit lots of discussion! I think discussion about how the kids solved the problems, whether in their head or on paper with pictures or numbers, is THE most important part of problem solving. We need to allow the children the opportunity to talk and REALLY LISTEN to what they are saying. By doing this they will discover what they need to look for (key words) when presented with problem solving situations.
*Another variation using M&M’s (or any other attention grabbing/eatable manipulative)
You could have the M&M’s represent kids on soccer teams and compare the size of teams, balance teams, and figure out how many more on one than the other, how many kids could get playing opportunities on a given day if everyone is there or if certain ones are absent. Use certain colors for boys and others for girls (use Red and Black –UGA… or Orange and Blue -Cedar Shoals) and compare the components of each team or all the teams in a league.* When dealing with word problems that have already been written (in the text) I think the main focus needs to be on making sense of the information given. Every text I have seen has some 4 or 5 step method for doing this…ugh! No wonder kids hate problem solving! So let’s break it down to what is most important. Personally, I don't see how there could be any way around solving word problems without these two steps;
1) Actually understanding the situation of the word problem
2) Figuring out what the problem is asking them to do.
I know many teachers have children draw pictures and act things out with objects when they are dealing with word problems, and I think this is an excellent approach. However, we need to remember that these problems are very abstract to the children. They have no ownership of them and therefore do not see the importance or excitement of figuring out whether Bobby has more trains than John. That’s why I like to begin with children being authors of word problems. Also, keep in mind that most of the word problems in the text are not really problem solving scenarios. Be selective, just because they are in the book does not make them good problems! An example of a typical textbook word problem might be, “Billy has four pigs and Sara has seven chickens. Who has more animals? How many more?” We can change this typical word problem into one that actually requires some problem solving strategies by writing “Billy saw four pigs and Sara saw seven chickens. Who saw more legs? How do you know?”
Try to use everyday situations when making up your own word problems, or simply modify the ones in the book. Just keep in mind that whatever the problem is about, make sure the subject matter is interesting to kids; i.e. cookies are good but monsters are better!
Here are a few examples of word problems that will usually require the students to use some type of problem solving strategy to solve, rather than just writing down an answer on paper. In each case be sure to encourage the students to use a problem solving strategy like drawing a picture and/or using objects to "act out" the problems. And remember to substitute your student’s names in the stories to make them more appealing.
1) There were 12 monsters in the park. Josh scared 1/2 of them away. Then Amy scared 1/2 of the monsters that were left. How many monsters are still in the park for you to scare away?
2) (Super challenge!) There were some monsters in the park. Antonio chased 1/2 of them away. Then Maria chased 1/2 of the monsters that were left. Now there are only 5 monsters running around. How many monsters were in the park in the beginning?
3) Annie has 4 packages of crackers. Each package had 6 crackers in it. Annie opened one of her packages and ate 3 of the crackers. Now how many crackers does Annie have?
4) Nadia has 3 more jelly beans than Brian. All together, Nadia and Brian have 15 jelly beans. How many jelly beans does Brian have? How many jelly beans does Nadia have?
5) Julie went to the farm and saw 10 animals, some were pigs and some were chickens. She counted all the legs and got a total of 28. How many of the 10 animals were chickens and how many were pigs? 6) Four raccoons went to the pond for a drink. Two got their back feet wet and one got his front feet wet. How many dry feet are there?