One of the Mathematical Practice standards is to "Use appropriate tools strategically." The word strategically incorporates estimating and knowing to gauge the answer by the their initial estimate and comparing. Through the CueThink phases, my students wrestled with creating and coming up with reasonable estimations. What I saw was a lot of guessing and not much thoughtful responses. I knew I wanted to select a problem helping them do just that, practice this skill.

If you haven't heard of Estimation 180, you need to. It's creator, Andrew Stadel (@mr_stadel) is a genius with ways, means, and methods to building students' estimation skills. CueThink has included some of Stadel's word count estimation problems within its bank. I really wanted to try the "What's the word count of the 8 mathematical practices?" problem because it looked quite challenging, but achievable, for my students.

If you haven't heard of Estimation 180, you need to. It's creator, Andrew Stadel (@mr_stadel) is a genius with ways, means, and methods to building students' estimation skills. CueThink has included some of Stadel's word count estimation problems within its bank. I really wanted to try the "What's the word count of the 8 mathematical practices?" problem because it looked quite challenging, but achievable, for my students.

I knew I wanted to take a step before this one to help scaffold students since I wanted to have it be a successful and exciting adventure. So I started with the MLK Jr word count problem I found on his website:

During a 25 minute session, I first started with the question, "What do you notice about the letters?" Students discussed with a partner first and then mentioned the shape of the letters, white spaces between words, how some letters were thinner/thicker, etc. The longer we went, the more they noticed, like how some letters within the word had additional spaces between them (Justified text). By the sheer number of "Oh, I didn't see that" emitted, I realized by taking time to do this step and drawing attention to these details, it helped gain awareness to factors ultimately contributing to a reasonable estimate.

When I pushed their thinking and asked how to solve this.....I got mixed responses indicating most really had no clue. So we started small with just the letter "M."

"How can we divide up letter "M" into a smaller parts to make a closer estimate?" Students worked with their partners to determine strategies to do so. We talked about breaking it apart into rectangles, counting one line, and then multiplying it to show an entire space (Think area of a shape). I was thinking they were on the right track...they were getting it.

So then, I showed them the Mathematical Practices problem and together we filled out the Understand phase of the problem. Having prepped and practiced with the MLK JR problem, it seemed to help the students scaffold the learning to the more difficult one for most students. We also focused on the "Estimate" area (On the bottom of the Understand Phase) and, in triads,worked to try to find a high and low estimate using his/her own strategy.

When I pushed their thinking and asked how to solve this.....I got mixed responses indicating most really had no clue. So we started small with just the letter "M."

"How can we divide up letter "M" into a smaller parts to make a closer estimate?" Students worked with their partners to determine strategies to do so. We talked about breaking it apart into rectangles, counting one line, and then multiplying it to show an entire space (Think area of a shape). I was thinking they were on the right track...they were getting it.

So then, I showed them the Mathematical Practices problem and together we filled out the Understand phase of the problem. Having prepped and practiced with the MLK JR problem, it seemed to help the students scaffold the learning to the more difficult one for most students. We also focused on the "Estimate" area (On the bottom of the Understand Phase) and, in triads,worked to try to find a high and low estimate using his/her own strategy.

I wanted to take time to really stress the importance of reasonable estimates and how to arrive an them before they dove into the problem. The Understand phase hold many keys for building a solid solution and estimation is one of them.

It wasn't all "Pie in the Sky" though....my more struggling students

I'd love to hear other ways teachers are building estimation skills within their problem solving practices. Feel free to share below:

It wasn't all "Pie in the Sky" though....my more struggling students

*really*needed an explicit strategy to help them. We walked through the estimates for high and low together.I'd love to hear other ways teachers are building estimation skills within their problem solving practices. Feel free to share below: