Building Understanding and Developing Culture

I have done this problem with first graders for the past couple years.  The first time I offered it to students, I was surprised by how difficult they found it (due to the majority of my experiences being with older students).  When I did it subsequent times, I offered a lot of "up-front" guidance to help them think about it, and I highly encouraged them to use manipulatives and images to help them make sense. However, they still struggled...

I have decided that if  I work in a first grade classroom next year, we will again do this problem. I have been pondering some different ways to approach it.  

I think it will make a great numberless word problem that we can do with a slow reveal in hopes that students work to make sense of it rather than just trying to solve it. Using the slow reveal will offer a great way to directly instruct the students in the process of notice/wonder and making sense of the problem before trying to solve it.  This use of numberless problems should help them as we continue to build understanding throughout the year.

Doing a general overview as a class, offering the students manipulatives and encouraging them to work with a partner to solve it.  Once they think they have solved it, they must find another pair who has a solution, and each group must convince the other that their solution is correct.  I like this idea, too, as it should help to build mathematical culture int the classroom--collaboration, sharing methods, convincing others of our solution... I think that the deliberate teaching of convincing others with math talk will need to come before this lesson, so that both sets of students don't just say the answer they got and move on.  

I could provide a picture of two spotless ladybugs and then have the students work to put the spots on to match the words in the problem. This one seems very direct, but it does emphasize the importance of using visuals to help us make sense of the problem. Again, I think partner work is a great way for them to approach this.

I think the sharing out of this problem is important and recognizing the different ways that students went about solving it. Determining as a class what we think the correct answer is and acknowledging how we worked with our partners to solve it.  Maybe a gallery walk of our thinking?  

A possible follow-up activity could include students writing their own kind of problems like this and then switching problems with others.

This problem is written with 1st grade in mind.  Certainly, this type of problem could be adapted for different grade levels:
* I have six pieces of candy in my purse.  There are four more pieces of gum than mints. How many pieces of gum do I have, and how many mints do I have?
* We have 27 students in our class.  There are 5 more girls than boys in our class.  How many boys and girls are in our class?
* There are 114 vehicles in the parking lot.  There are 72 more vehicles with 4 wheels than vehicles with 2 wheels.  How many vehicles have two wheels?  How many vehicles have four wheels?
* In my closet, there are 18 shoes on the floor. However, there are 2 more right shoes than left shoes.  How many complete pairs of shoes do I have in my closet?
* I found thirty-five coins in my car.  There were four times as many pennies as all of the other coins combined?  How many pennies did I find in my car?

What do you think?  How might you approach a problem like this with your students? Do any of the ideas I shared seem to be better than the others?  I'd love to hear your thoughts.