Students will be able to apply their place value strategies to the task of solving mystery number riddles.

Often, students are expected to solve standard equations while regrouping, but they are rarely asked to show strategies outside of the traditional algorithms. This lesson prompts the students to make sense of place value before finding a solution.

20 minutes

To begin our discussion of using place value knowledge to solve situations, I place a riddle on the board, which reads: I have 23 ones and 4 tens. Who am I?

I tell the students to solve this using any strategy that makes sense to them. As they work, I circulate, gathering evidence of knowledge and planning my next steps based on need and readiness.

These two students have different ways of approaching the situation and I can easily see that one student will need more practice in regrouping to tens, while the other student is ready to move on to larger number work.

Following enough time for most students to complete the task, I ask several students to share their solutions and strategies. During this type of sharing, I always ask the class to explain **why** another's work makes sense. This is an easy way to make sure your students are practicing critiquing other's work.

Following three different strategies, I try to make connections for the class in this video clip.

25 minutes

For practice, I give the students a page of "riddles" or situations to solve. As always, as students work I continue to meet with individuals and small groups to offer helpful suggestions and to listen to their understanding.

Prior to this clip, the student came across the room to get me, stating that he was totally confused. Naturally, I follow him to his desk and ask him to show me what he was working on. I quickly realize he only needs prompting in how to show his work. The content was not blurry for him at all.

You may consider allowing students to work in partnerships for this activity if you are not seeing the whole group having success. My class was ready for this, so they worked independently.

15 minutes

For our share out, I ask a student that I knew struggled with a certain problem to share what he finally figures out. It is really important to build an environment that is safe and where struggle is celebrated. Also, having struggling students share validates perseverance...because not only did it pay off in reaching a solution, it pays off in acquiring positive attention. This is the reason I choose mathematicians who struggle to share their success. It also helps cement their learning from that day.