Worksheets and Differentiation – Not Always Mutually Exclusive!

I hate worksheets.

Is there anything worse than a math classroom where the pace and expectation are dictated by the almighty worksheet?  OK class, continue working on the blue worksheet, and homework will be on the pink worksheet.  Tomorrow, we will do test review with the aqua worksheet.  And then we will have a whole new chapter packet to work on….blah….

Don’t get me wrong…I’m not anti-practice.  Much of math is like learning to play the piano, you need to expend some sweat in order to master skills.  But, like playing the piano, all students will master the skills differently, with different timelines.  And, like piano players, some students will handle rigor and improvisation quicker than their peers.

So, how do we provide students with appropriate practice, while at the same time allowing students to have some say in their learning, assess their own progress, and provide for differentiation? Here are two strategies for you to try:


In this strategy, students are not required to complete all assigned problems (unless they choose to). Instead, problems are assigned individual point values, and students complete enough problems to earn the assigned number of points. Easier problems have smaller point values, while more challenging ones are worth more.

Here’s an example, which use the Linear Functions Review given here (pdf): Linear Functions Review

This review has 18 problems, increasing in difficulty.  One way to assign point values would be:

  • Problems 1-7, 1 point each: these problems can be done mostly by looking at the linear pattern and providing a quick answer.
  • Problems 8-14, 2 points each: these problems mostly ask students to match function rule to situations.
  • Problems 15-18, 3 points each:  open-ended, and all require students to develop a function rule.

For this assignment, I would ask students to complete 12 points worth of problems.  This would require students to reflect upon their understanding, and provide differentiation.  How could students complete the assignment?

  • Students at a basic level could complete all 1-point problems, but would then also need to complete at least 3 of the 2-point problems (of their choice).
  • Students comfortable with the material could complete a mix of 1, 2 and perhaps 3-point problems.
  • Students at the advanced level could complete only all 4 of the 3-point problems.

The worksheet provided here was created uses the fantastic site Problem Attic, developed by EducAide software.  The site has a large bank of problems from various state, national and international assessments, and allows users to create their own customized assessments.  Definitely worth checking out!


Many textbooks (particularly high-school texts) will arrange their problems sets into A, B and C levels.  Do I need to see students complete all problems from a set?  If a student demonstrates mastery of a C-level problem, do I really need to see them complete many A and B level problems?  This strategy allows students to choose the best path for completing an assignment, using this template:

Choose a Path

In this assignment, all students start with a B problem, then choose their own path for completing the assignment, by selecting one of 3 colored paths.   This could mean completing a few A problems, with a few B problems.  Other students many choose the series of B problems, with a few A’s sprinkled in.  Ambitious students may choose the challenging C problem to complete.

With both strategies, students are challenged to reflect upon their own learning, make appropriate choices, and take responsibility for their progress.  Classroom expectations don’t change at the drop of a hat, and may take a few conversations and failed attempts before working the way you like.  But they payoff, increasing student responsibility and reflection, are worth the pain.


By Bob Lochel

HS Math Teacher. Hatboro-Horsham School District, Horsham, PA.

9 replies on “Worksheets and Differentiation – Not Always Mutually Exclusive!”

Thank you. This is a great tool. Do you show your students the circle with points? If so, what do you do if they have to get say 20 points instead of 12?

Anne, the circle is easily made and adapted using Geometer’s Sketchpad. I used color on the blog, but I might use a combination of dotted lines and/or old lines if I am making Xerox copies. The points can definitely vary; usually, the point goal will require a “basic” students to complete all A problems, and a number of B problems, while at the same time allowing an advanced student to complete all (or many) of the C problems only. It really depends on the nature of the assignment.

Thanks for a wonderful idea. I do have a few questions on the grading end of your homework when you differentiate. How do you grade the actual homework in the classroom when you have kids doing so many different problems? What are some of the challenges you had with grading? How do you keep track of what type/level problem each kid did? How do you deal with a student who did only challenging problems but got them wrong? Thanks in advance !

Sue, differentiating homework can certainly become a logistical problem. But I found that as I taught for more and more years, I was less interested in playing the HW grading game. Rather than worrying about which student completed what tasks, I would rather have students reflect upon their progress. If I did need to have a grade, I would ensure that it was a common problem or two I was checking. I rarely ran into students who completed only challenging problems, and would have a one-on-one conference with students who did, where we talk through a best course of action.

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