Using Parallel Tasks to Differentiate Whole Group Math Instruction
This post is part of a blog series about differentiating whole group instruction. You can read about WHY whole group instruction should be part of our math classrooms by reading Four Ways to Differentiate Whole Group Instruction.
Parallel tasks are a pair of questions that are very similar but a modification is made to one of the questions so that it is opened up to students at a variety of levels. Students have a choice as to which problem they solve allowing them to solve the problem that is most appropriate for their level of understanding. The two problems are similar enough that you can discuss the problems at the same time after students have had time to work on them.
The modifications that you make to one of the problems can be as simple as changing the numbers to make them more or less challenging to work with (changing the number of digits, working with whole numbers or fractions/decimals, etc.). You could modify the problem by changing the concept just a bit (decimals to fractions, or square to circle, etc.). It’s these small modifications that make the problem more appropriate for a larger group of students. Here are two examples of parallel tasks:
Example #1: Create a parallel task by changing the numbers.
Problem A: Aldo multiplies a whole number by 3/2. What do you know about the product?
Problem B: Aldo multiplies a whole number by 2/3. What do you know about the product?
The modification I made to this problem was simply changing from a fraction less than one to an improper fraction. This small change in numbers opens this problem up to discussions later on about what happens to numbers when we multiply by fractions greater than one and less than one. This is an important concept for students to understand because it breaks the “rule” students believe about multiplication, which is that “multiplication always makes things bigger.” This task proves that this rule is not always true by giving an example and non-example.
This problem is differentiated for students because some students may have different comfortability levels with improper fractions. For some, improper fractions may be more intimidating than a fraction because they aren’t exposed to improper fractions as often. Some students may realize that 3/2 is 1 1/2 which may be easier for them to model or visualize 1 1/2 groups of a number. By making small changes to the problems, students are able to choose a problem that best fits them, and afterwards the class as a whole can have a really meaningful discussion to make new and exciting math connections!
Example #2: Create a parallel task by changing the concept.
Problem A: The perimeter of a rectangle is 24 units. What could the dimensions of the rectangle be?
Problem B: The area of a rectangle is 24 square units. What could the dimensions of the rectangle be?
Both of these problems are similar, but they require different types of thinking. Some students may start out with the perimeter problem and as they are solving the perimeter problem they might come up with an idea for the area problem. Some students may feel really comfortable with area because of the strategy they’ve chosen to use and may not quite understand how to come up with a solution for the perimeter problem yet.
With parallel tasks, it isn’t always about one problem being hard and the other problem being easy. It can be about which concept is most appropriate for your students going into the task and then discussing both tasks together to bridge the gap between the two problems.
It is the discussion that happens afterwards that really pushes students’ learning even further! With parallel tasks you have the added bonus of being able to discuss how the thing that is different (the modification you made) about the two problems impacts the answers of each problem. How’s that for critical thinking?!
For teachers who are required to teach a specific curriculum, this strategy can be an extremely valuable tool for differentiating whole group instruction. Take one of the problems from your math program, make the necessary modifications to the question to open it up to different levels of understanding, and present both problems to the class.
Parallel tasks, along with other fantastic differentiated questions, can be found in the book Good Questions, as well as tips for creating your own parallel tasks. This book is GOLD! It is something you can refer to every day if you are looking for tasks to differentiate your math instruction! This book was one of the texts I used during my master’s program and it is one I share with so many teachers. I HIGHLY recommend it!
If you are looking for more strategies to differentiate whole group instruction, head back to the first post in this series to be linked to the three other strategies we’ve discussed!