Open problems are probably my most used strategy to help meet each student where they are.  Problems that offer a low floor and high ceiling are great because all students engage in the learning, then can participate and learn from each other.  However, some teachers also like to offer Parallel Tasks as a way to differentiate instruction.  The idea here is that students can be given a choice of a task/problem, some being more difficult than others, yet all of the tasks/problems deal with the same standard (curriculum expectation).  Let’s take a look at an example of how a quality parallel task can work:

Take a look at the problem below.  What is it asking us to do?

I’d love some actual responses here.  Build it using actual manipulatives (ideally) or using virtual manipulatives (This Illuminations Applet might help).

Notice that each choice allows students to do the same expectation related to proportional thinking, however, students are given choice about what numbers they want to think about.

Think about what the answers would look like?  When we discuss designs afterward, we should be able to discuss the solutions to each problem and compare the similarities and differences.

Here are some designs students made.  Can you tell which option each student chose?

Actually try to match the designs to each of the tasks/problems.  Take a moment to think this through.  What do you notice about the 4 images above?

This task was designed very cleverly to help make a point… to help us bring ALL of our students together to have a conversation  (Even when we ask our students to do different things from each other, we still need to make sure we come together and have shared experiences).

Did you notice anything about the 3 options?  Did you try decimals or fractions to solve any of the students’ designs?  If you did, you would notice that all 3 options used the same proportions.

A great parallel task helps us to learn things together…  It helps us see others’ thinking…  It allows every student to start to think where they are comfortable, yet be able to learn and grow from the ideas of others.

If you were to offer a parallel problem/task for your students would you:

• Choose which students get each choice, or allow students to pick themselves? (Does this matter?)
• Expect all students to create the design using blocks or digitally?  (Does this matter?)
• Ask students to work independently or in a small group?  (Does this matter?)
• Offer calculators or not?  (Does this matter?)
• Engage in 3 different conversations – 1 per group – or 1 conversation all together?  (Does this matter?)

The small decisions we make tell a lot about what we value!    Personally, IF I want to offer Parallel tasks/problems, I want to make sure that all of my students feel successful, that everyone realize their ideas are valued, that there isn’t a hierarchy of ability in the room… and of course, that the mathematics we are engaged is important.