An Ill-Defined Problem

The problem above was:

One year in Mr. Creahan's class there were 6 students who traveled to another state over our February break. Eight students stayed overnight with their grandparents. How many students just stayed home?

In our chart, we first asked ourselves, "What did we notice?"

We noticed that some students traveled, (6.)

Some students stayed at their grandparents, (8.)

These students went AWAY.

Next, we asked, "What do we wonder?"

How many students stayed home?

We think we need more information... how many students in all?

How many students are in the class?

Then, " What is our plan to solve?

What tools, or models might we use to solve?"

Since we discovered we were missing information, we needed more facts before we could continue.

We could use ten frames to help us show our work.

Solve:

Once we found out that there were 20 students in the class , we could get to work solving the problem.

We figured out that we needed to add the 6 students who traveled, and the 8 students who went to their grandparents together. All these students went away.

6+8=14 students went away.

Now we took the 20 students who were in the class, and subtracted the 14 students who went away. This would leave us with the number of students who stayed home.

So,

20-14 = 6 students stayed home.

Now, we needed to check~

Did our answer make sense?

Was it a reasonable answer?

Yes, our answer made sense because 6 + 8 = 14 and 14 + 6 = 20.

Our ten frames showed 6 cubes in one frame, we added 8 more cubes. Now we have 14 cubes. ( 1 full ten frame and 4 in the other.)

If there were 20 students, then we can see there are 6 empty spaces in our second ten frame.

Those 6 empty spaces show the 6 students who stayed home.

So, our answer statement was:

6 students stayed home during February break in Mr. Crehan's Class.

Feedback for Parents:

• This was purposely a "tricky" problem. It is called an ill-defined problem.

• Students needed to use their reasoning skills and logic to think through the problem before they could solve it.

• By creating opportunities where students need to truly reason through the given situation before they can solve the problem, we notice students are more thoughtful about the process.

• This thoughtful behavior tends to allow students to actually use the appropriate numbers to solve, rather than just taking numbers in the problem and adding or subtracting just "to get an answer." For example, without carefully thinking through what is being asked in the problem; students may simply take the 6 students who traveled, and the 8 students who went to their grandparents and add them together. So 6 + 8 becomes their answer. (Yikes!)

• The ill-defined part of the problem, (the missing information) needed to be asked for in order for our students to go about truly solving this problem. Students needed to rely on their sense of reasoning and logic to know to ask for it.

• Often, in "real life" situations, we need to search or hunt to gather all the information we need to accurately solve problems. Using our sense of reasoning, and logic is a huge help to us all. It is a "life long" skill!