What is a differentiated task?
A differentiated task is a question or activity that allows for multiple entry points as well as multiple ways to solve. One of the purposes of using differentiated tasks is to meet the needs of the varying ability levels of students that we often find in a single math class. Traditional worksheets often require students to focus on solving procedures and the questions are usually the same level of difficulty. See the example below:
In this example we have a worksheet for adding double-digit numbers. If a student doesn’t understand this concept yet, they will not even be able to get started on the worksheet, and those that do know how to add double-digit numbers will be working at a procedural level for the entire worksheet (and in this case, because they are stacked, will likely only be doing digit addition, rather than number addition).
Furthermore you will likely have students who are very quick in doing the procedure and so they will be done before you can even get around to helping those that don’t have a clue how to get started (and these students may not even need this much extra practice of something that they already know how to do well). I am sure many teachers can relate to this scenario; we are often rushing to help those they can’t even get started, and are trying to help the occasional student who ‘gets stuck’ on a certain question, and before we can even get through all of the students who need help there are many who have finished the worksheet and are needing direction on what to do next.
Why Should I Use Differentiated Tasks?
When I use differentiated tasks many of the problems I mentioned above disappear. An added bonus to using the differentiated tasks is that students are working not just on their procedural fluency but also are developing stronger conceptual understanding of the math concepts. Furthermore, they are actually doing number addition rather than simply digit addition, and so are developing stronger number sense. These tasks are open enough that even a student who is not working at grade level mathematics can still access the question and develop their math skills.
For example if we look at the differentiated task “two numbers have a sum of 82, what could those two numbers be?” a possible solution could be 81+1 = 82. Students who don’t yet understand how to add double-digit numbers can still solve this problem by adding a double-digit number to a single digit number. Although we are not yet working on the skill (double digit addition) we are aiming for, I would much rather my students be engaged in solving the problem and developing their math skills, rather than just sitting with their hands up waiting for help. Because we are working on the skill of adding double-digit numbers, I would encourage my students to try to seek out as many solutions as they can using double-digit numbers.
For those students who already have a solid understanding of how to add double-digit numbers, they can be looking for patterns or could be solving a parallel task such as “add two double-digit numbers that have a sum of 82 and one of the numbers has a seven in the one’s place value”. Using this type of tasks engages all the students in your class, regardless of their current the ability level, or skill set and is designed to challenge them at their level.
I also like using these types of tasks because students are actually required to think about the sizes of numbers that they will use rather than just following a procedure (which, by the way, many don’t really even understand why it works). When working with a differentiated task like this one students are also able to work at their own pace; those who are thinking deeply, or process more slowly, or write more slowly, are still learning and are not being penalized for not being as fast and those who work more quickly.
The goal is for students to understand and be able to apply the concept of adding double-digit numbers and this understanding does not happen at the same rate or in the same way for every student, therefore, it makes sense to allow for different approaches and different quantities of practice questions.
Can I justify spending a whole lesson on one question?
It might seem odd to spend 40 minutes working on one question, but I find that my students are doing a lot of important thinking, learning, and practicing while they search for the solutions. I also notice that my students come away with a better understanding of the concept when I do a differentiated task, rather than the traditional style worksheet. It is important to discuss how the students are solving as they tend to come up with many creative strategies for solving the problem and their peers can benefit from examining multiple approaches to the same problem.
I will often have students come up and write their solutions on the board. We then examine the solutions and ensure they are correct. This is very empowering for students, especially those who have traditionally not done well in math. Students love having unique solutions and it is a positive learning experience when there are many correct answers. It is also valuable for students to see and hear the different approaches that their peers took when solving the problem. These types of questions require more thinking rather than simply doing and as we know, mathematics should be a combination of both.
Differentiated tasks you can use in the classroom
You will find below some samples of differentiated tasks for some of the more basic whole number operations. With time and practice, you can create your own differentiated tasks based on the math concept that you are working on. A couple of tips that might help you get started are:
1. Give the students an answer and the operation and ask them to create the questions
2. Give a range of the numbers that can be used to salsa question (this way students can choose easier for more challenging numbers, based on their current skill level)
3. Create a worksheet by omitting part of the question and giving the answer. (See examples of questions below – note that the questions with an asterisk have more than one possible solution)
Whole Number Addition
Differentiated task: Two numbers have a sum of 873. What could the two numbers be?
This task has so many different answers and could be done too simply for some students– because 872+ 1 would suffice. If you want them to work on the skill of adding multi-digit numbers together, then you could try some tasks like these:
1. ) Differentiated Task: Add 2 three-digit numbers that have a sum of 873. What can the two numbers be? Find as many solutions as you can.
2.) Differentiated Task: Add 2 multi-digit numbers that have a sum of 873. What can the two numbers be? Find as many solutions as you can.
3.) Parallel task: Add 2 three-digit numbers that have a sum of 873 and one of the numbers has a nine in the one’s place. What can the two numbers be? Find as many as you can. Do you see a pattern?
4.) Parallel task: Add 2 three digit numbers that have a sum of 873 and one of the numbers is about twice as big as the other. What can the two numbers be? How did you solve this?
Hint: Using Base 10 Blocks makes this activity far easier for most students. However, if the student chooses to solve the problems symbolically but then get stuck, you can ask them to use the Base 10 Blocks as a problem-solving tool, or as a way to get “unstuck”.
Task that shows you if your students understand contexts in which adding is the necessary operation to solve: Create a story problem that would be solved by calculating 345 + 143.
Whole Number Subtraction
1.) Differentiated task: 2 three-digit numbers have been subtracted and have a difference of 163, what could the two numbers be?
2.) Differentiated task: 2 multi-digit numbers have been subtracted and have a difference of 163, what could the two numbers be?
3.) Parallel task: 2 three-digit numbers have been subtracted and have a difference of 163, however one of the numbers has a nine in the one’s place. What’s could the two numbers be? Find at least five different solutions. Can you see a pattern amongst the solutions?
4.) Differentiated task: 2 three-digit numbers have been subtracted and have a difference of 27, what could the two numbers be? What strategy or strategies did you use to solve this? Find at least five different solutions.
Task that shows you if your students understand contexts in which subtracting is the necessary operation to solve: Create a story problem that will be solved by calculating 817-286.
Whole Number Multiplication
1.) Differentiated task: Two numbers have a product of 24, what could the two numbers be? Find all of the solutions you can using whole numbers.
2.) Differentiated task: A rectangle has an area of 36 what can the dimensions be? Find as many solutions as you can.
3.) Differentiated tasks: Two numbers have a product of 196, what could the two numbers be? Find as many solutions as you can. How did you solve this?
4.) Differentiated task: Two 2-digit numbers have a product between 400 and 600, what could the numbers be? Find as many solutions as you can. What was your strategy for finding your solutions?
5.) Parallel task: Two numbers have a product between 400 and 600, what could the numbers be? Find as many solutions as you can. What was your strategy for finding your solutions?
6.) Differentiated task: A number of friends are chipping in equal amounts of money to buy a gift for their teacher. The gift costs between $60 and $70, how many friends chipped in and how much money did they each chip in? Find as many different solutions as you can–which solutions are the easiest find? What strategy did you use?
Task that shows you if your students understand contexts in which multiplying is the necessary operation to solve: Create a story problem that would be solved by solving 4×6.
Whole Number Division:
1.) Differentiated task: David has between $400 and $600, he is going to divide it equally between his children, how much would each child get and how many kids could he have? Which numbers did you choose to make the work easier? Which numbers would you choose for more of a challenge?
2.) Parallel Task: David has between $400-$600 and is going to divide it equally between his 3 children. How much could each child get? Which numbers did you choose to make the work easier? Which numbers would you choose for more of a challenge?
3.) Parallel Task: David has $460 and is going to divide it equally between his 3 children. Show at least two different ways to do this division. (Hint: try breaking up $460 in many different ways that would help make it easier to divide by 3).
4.) Differentiated Task: Jamie has 75 toys and needs to share them equally with 6 kids. How many toys will each kid get? Will there be any toys leftover?
Task that shows you if your students understand contexts in which dividing is the necessary operation to solve: Create a story that would be solved by 45 ÷ 6 and include what any remainders mean in your story.
Give it a try!
I encourage you to try using some differentiated tasks and see, hear and feel how it is different from traditional worksheets and textbooks. Remember to tell your students that the goal is to deepen understanding, explore patterns and strategies and be creative! Please write in and share your experiences (good and bad) so we can all learn from each other. Have fun with it and see where it goes!
Educating Now was created due to teacher requests to have Nikki as their daily math coach. The site has lesson by lesson video tutorials for teachers to help them prep for their next math class and incorporate manipulatives, differentiated tasks, games and specific language into their class. Teachers who use the site can improve student engagement and understanding, in addition to saving prep time, by watching a 10 minute video tutorial and downloading a detailed lesson plan.
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