Open Ended Problem Solving

UPDATED

Problem solving encompasses an important set of skills for young learners. For students, being able to find a solution to a problem and explain how they came up with their answer utilizes higher order thinking skills especially when the problems posed have many possible solutions. These types of problems require children to be creative with their answers and provide them with opportunities to think outside of the box. 

I recently started a session during math which I call "whiteboard review." During this time, we focus on whatever num

ber is that day's date. For 

today, our focus number was 26. We use this number to do a variety of math operations and then culminate with an open ended problem to solve. Each day we do the following:

• write addition or subtraction equations that equal the date
• write the date in tally marks
• tell whether the date is an odd or even number
• draw the date in tens and ones (we use rectangles for groups of ten and circles for ones)
• ***"purchase" candy using the number of cents that matches the day

*** The last activity is the newest that I have introduced and the kids really like it. I purchased three types of candy at the store; a Hershey bar, a pack of gum, and a Tootsie roll.  I put magnet strips on the back so that they can stick to the whiteboard. Under each type of candy I listed a price. 

Tootsie rolls: 1 cent

Gum: 5 cents

Hershey bar: 10 cents

**3/17/09 Candy types have changed since I last posted, but I wanted to update with a photo**

I wrote the problem on the board and change the amount of money each day to match the date:

I tell my students they should spend the exact amount of money that they have. The problem gets harder as we get closer to the end of the month. When we began, the solution was simple. On the first few days of the month, there was only one way to solve the problem each day. As we reached numbers like 10, there started to be more possible answers and it is interesting to see how the kids think it out and how they come up with all the possible solutions. It was actually a nice progression so the kids could get used to what I was asking before the solutions got complicated. 

Take, for example, the 10th of the month. Possible solutions include:

10 Tootsie rolls

2 packs of gum

1 Hershey bar

5 Tootsie rolls and 1 pack of gum

The students draw representations, shapes, letters, and words on their whiteboards and they came up with the coding of H for Hershey bar, G for Gum, and T for Tootsie rolls. I write all their ideas on the board in the code: 

10 T

2 G

 1 H

 5 T & 1G

My favorite part is that no two whiteboards look the same. It is not like asking for the solution to 2 + 2, it allows for more creativity and individual differences.

I also have large cardboard coins that I purchased at the Learning Palace that I use with the problem as well. I laminated the coins and put magnet strips on the backs, so that they too, can stick to the whiteboard. When I tell the students how much money they have to spend, I ask them to show me different combinations of coins that would add up to that number of cents. This is a great way for students to practice recognizing coins and adding mixed coins (both first grade math skills).

I started this activity at the beginning of February, but I do not want it to get old and boring, so I added a little motivation by telling my class that I will purchase different items for the month of March and that I will give away the candy on the last day of school in February to students who consistently demonstrate responsibility and appropriate behavior at school. Next month, I might get different types of candy or possible change the amounts that each costs.