Thin-Slicing with Manipulatives
I discussed using manipulatives in larger thinking tasks in the last post. If you missed that make sure to take a look. The design of thin-sliced tasks versus larger thinking tasks, allows teachers to give students access to new content in a more linear fashion. These slices/questions are designed to be done in order versus giving a task that may appear more open in its starting point. They also work within the idea of Variation Theory: “The principle that underpins the theory is that new learning occurs when learners understand how a critical aspect of a new concept changes (varies) against something that does not change (invariance).”
One of the things I love about designing sliced tasks is the opportunity to give students practice with Standard for Math Practice number 7: Look for and make use of structure. When working on creating or looking for these tasks I ask myself “How does this problem connect and use the one before to help with sense-making?” I find that number strings are a great place to start. However, if I want to give all kids access and a starting point I often begin with a pictorial representation of a manipulative. When recording their thinking I might push them into another representation.
So how do you know when to design a thin or thick sliced task?
Here are some things I keep in mind when I am designing tasks:
Thinner slices
- Reduces frustration from task to task
- Help keep students in flow
- Students see success faster, more buy-in
Thicker slices
- Good for students with significant prior knowledge of topic
- Challenges students to think while still giving structure and allowing students to make connections between the slices.
- Something to work towards as students get familiar with thin-slicing.
I generally use manipulatives when designing thinner-sliced tasks. This allows me to start with a manipulative and move to an abstract problem representation. However, they can be used for all tasks when a variation is introduced.
I include two examples here:
When you are looking at these examples, think about the variation from one slice to another. What is changing? Are there places where you could skip a step? Or add one?