# Problem Posing Fun in Fourth

Recently, I have been learning a lot about problem posing from my friend Jinfa Cai, in particular how to infuse these opportunities within the use of curriculum materials. Because, while there are rich problem solving experiences in a good curriculum, we do not often see explicit use of problem posing, especially in K–5. The Notice/Wonder routine is probably as close as it gets.

Since I am in classrooms this year, I get to try some problem posing around curriculum activities and follow up with Jinfa. As with all learning, the more things I try, the longer my list of questions for him grows! After last week’s lessons, I was left with two questions that I can’t wait to discuss:

1. How do we honor all of the posed problems within the timing of a lesson?
2. How do we infuse opportunities to reason about the problems that can and cannot be answered with the information in the situation?

The lesson focused on addition of fractions with like denominators. As an adaptation to the curriculum materials, I only showed students the bolded part of the task and asked them to share things they noticed and wondered. Because their ideas were all falling into the ‘wonder’ column, I quickly pivoted to the problem posing work.

## Problem-posing launch

In their journals, I asked students to take a couple of minutes to write mathematical problems they could pose about this situation. They shared their problems as a whole class and I recorded.

It was so interesting, yet not surprising, that they asked the exact same problem the curriculum task was posing! I had them work as a group to solve that problem and told them that if they finished before we came back together as a group, to re-read the other problems on the board to see if they could answer them as well.

## Problem solutions

Students represented their solutions in many different ways as they leveraged their understanding of fractions, addition, and multiplication. It was particularly interesting that you could see in their work how they used one expression to derive subsequent ones. Here are a couple of examples:

As a whole group, we compared and connected student work like in the 2 examples above. Discussing questions such as:

• Where are the ¼ cups in the expression?
• Where are the ¾ cups in the expression?
• Where is one expression in the other?