Thin sliced problems were coined by Peter Liljedahl in his book Building Thinking Classrooms in Mathematics.

What are thin sliced problems & how can you use them to meet all the needs of your students? Be sure to listen to this episode so you can learn how to use thin sliced problems in your math classroom. 

In This Episode on Thin Sliced Problems:

• thin sliced problems naturally differentiate
• using thin sliced problems in your math classroom
• making sure every student is learning

So, What are Thin Sliced Problems?

The idea is that you create a series of problems for students to tackle that increase in challenge slightly with each problem . Students often have the choice between mild, medium, spicy problems to self-select the level of rigor. Also, thin sliced problems often offer the answer on the back so that students can self check and move onto the next problem.

Why Do Thin Sliced Problems Work in Student-Centered Classrooms?

1. Students have a choice. They can choose what types of problems they are ready for. In a student centered classroom we want the student to own their learning… to be in making decisions about what why need. We want the students to be in touch with their goals and progress toward their goals. That’s why reflection is such a huge part of a student centered classroom. Basically, students are doing the THINKING in a student centered classroom and that’s exactly what Building thinking classrooms equipped us with– moves that can help shift the thinking onto the students’ plates.

The choice that students have in thin sliced problems allows them to work toward their goals at their perceived level. They can choose mild problems if they are still learning or trying to understand, or maybe they are ready for spicy problems because they’re reading for a challenge.

2. Students can be independent. Thin sliced problems allow students to practice without teacher support. It truly allows them to explore the concept independently. If you choose they can find the answers independently and they are able to self check and self correct.

3. Problems increase in complexity as students complete problems, which builds students’ capacity. So therefore, thin sliced problems naturally differentiate.

Imagine This…

You’re practicing fraction multiplication with 5th graders. You offer 3 problems to the whole class that increase in complexity. Students work through those problems at their own pace (choice & independence) in their random groupings or even independently (depends on your routine).
The first problem is “The dog walker walked two dogs equally for 3 miles. How far did he walk each dog?” Draw a diagram and equation to match your work.

Most students finish that problem quickly, but you notice their diagrams are all over the place. Most groups are working on problem 2. However, you decide to stop the class and lead a quick debrief. I like to do this at a mid- way teaching point or a course correction. We gather around in a circle and examine the diagrams for the follow criteria 1. Accuracy 2. Precision 3. Clear. Students make suggestions for how the diagrams can be improved. Then, we always bring it back to the why… so I ask, “But why does that even matter? Why do the diagrams need to be accurate, clear, precise? They have the right answer, why is this important?”

Students respond with things like… 

• so others can understand your thinking 

• because communicating your ideas clearly is part of being a mathematician 

• when we look at each others’ work we can learn from it. 

• that’s how you prove your thinking

So, using thin sliced problems allow students to lead their learning, be independent, have choice, and work toward their goals at their own pace.

Differentiation & Thin Sliced Problems

Students will be at different levels… always. There will never be a point in which we have every student at the same level, everyday. That’s just not how learning works. Therefore, we have a student centered classroom that allows students to explore and show their current understanding. Then, once they’ve used what they know they can learn from others and from the discussion to learn.

So, when you have 3 different word problems that gradually get more difficult on a given learning target students will be able to deepen their math understanding through exploring and discussing.

How to Implement Thin Sliced Problems

Here’s how you can implement thin sliced problems in your classroom. This may vary slightly from the way Peter Liljedalh describes in his book. His description is that students may power through 20-30 problems… more practice problems, procedural practice. I’m suggesting here that students practice word problems… showing their reasoning on paper and problem solving. 

Here’s how you can use thin sliced word problems/ thinking tasks in your math class: 

1. Decide how students will work on problems (in random groups, in table groups, independently) 
2. Give everyone the first problem & ask them to record their thinking and reasoning. 
3. Move around the room and conference with students– this might be offering nudges and nuggets that help students continue to make progress. 
4. When it’s the right time (when you see everyone struggling and getting stuck in the same place or you see a common trend to address) stop the class and have a mini math discussion. 
5. Elicit (gather & show) a few examples from student work to examine. Discuss “What do you notice? Wonder?” Get students talking first and then start to focus their conversation on the teaching point you’d like to see them realize. 
6. Send students back to work on level 2 and 3 of the problems. Again focusing their attention on clearly showing their reasoning. So they are ready to discuss. 
7. As you confer with students and groups you’ll be gathering notes of what you want to share in the discussion to highlight the mathematical concepts and get students to discover and name a math conjecture or math truth. Once you’ve chosen the students you’ll want to consider the order you’ll share them. 
8. Bring students to the circle to share– ask the 2 to 3 students you selected to share their work and make it visual. This might be you projecting their paper or drawing up their solution or directing students to look at their whiteboard. 
9. Start the discussion with a broad question or prompt like notice/wonder and get all students talking. Then, start to move students toward the conjecture you’re hoping they come to.

NOTE:

This doesn’t always happen like this. This is the ideal flow. However, in a student centered classroom we follow students’ thinking. SO, even the best laid plans will end up turned on their head. Here’s the thing… you might give your students a set of leveled questions and they might freak out… and really get stuck on just representing fractions. Maybe you need to spend a lot more time building background knowledge about what a third is and how it compares. That’s okay, because even if you proceed with the “lesson” or intended learning target the students are TELLING and SHOWING you they aren’t ready for it. So, you can move forward… and sometimes we do, and not everyone will “get it”. It is best to stick with their thinking and continue to move them along starting from what they are showing you they understand through their representations & discussions.

Links Mentioned in This Episode:

🎙️Ep 93: Strategies for Consolidation with Peter Liljedahl

🎙️Ep 96: Building Thick Understanding in Consolidation with Peter Liljedahl

✏️ Thin Sliced Problems – If you don’t see the grade level you need, email me at hellomonamath@gmail.com! 

🔥 MY TEACHER HOT TAKE 🔥

• Teacher PD should match the TEACHER’S goals, not the schools goals.
• PD should be provided by teachers, that understand what it’s like to teach in this post-covid world.

That’s why I’m providing low cost PD series for you. (ONLY $11!!) 🤩

Each PD is designed with actionable strategies that I used in my own classroom and I know work with students who struggle.

📣 Register for PD HERE!


Have Questions? 📱 My DMs on IG are always open @hellomonamath