For each unit, when working with individuals or groups of students, I like to make sure I am giving them every opportunity to thoroughly learn the subject matter for every single lesson: my aim is to provide multiple entry points through differentiated learning opportunities. I make use of several different kinds of worksheet but not only that; I also am careful to ensure each student receives the correct level of sheet and so I make use of a tiered system, where there are three versions of each kind of worksheet, with increasing complexity from one to the next: for example, worksheet 1 might have hints and smaller numbers to ensure the task is understood and the skill is grasped by a student in need of additional support, while worksheet 3 is aimed at challenging accelerated learners.
With this in mind, I created each of the following kinds of worksheet or task for each lesson.
1. Skill Practice (3 Tiers)
These worksheets cover the basic skills of the topic, while addressing each kind of problem that might arise is the common core curriculum. Both numerical and basic word problems are included.
2. Spot the Error(s) (3 Tiers)
Fully comprehending a lesson means that the student is able to identify the mistakes of others. In this activity, four problems with solutions are provided and the student must identify where a mistake was made and then correct it.
3. Error Analysis (3 Tiers)
As with the above task, the purpose here is to encourage the student to check the given work, with the idea of highlighting the benefits of double-checking their own work.
4. Four Problems (Assessment)
It is extremely important that the student is given the opportunity to express their own creative problem solving skills, while it is also beneficial for them to feel as though they have a choice in their mathematical learning experience. So, in this case, I ask students to complete any two of four word problems, where they are asked to solve the problem, showing all work, and then justify their work.
5. Agree or Disagree? (Partner/Group Activity – 2 Versions)
For this activity, individual students are asked to solve the given problem, justify their solution, and then switch with their partner to see whether or not they agree with their work and or if they have another method of solution.
6. Post-it! (Group Activity – 3 versions)
A problem is provided to each group and then each member of the group is given about 3 minutes or so to independently solve the problem, showing their work on a post-it note. As soon as all of the students have solved the problem, they place their post-it note on the activity sheet and then take turns comparing and sharing their solutions. The group then works to decide upon a perfect solution, which one group member will then write on the sheet.
7. Solve & Justify (Assessment – 3 Versions)
This is another independent assessment opportunity, where each student is asked to solve a word problem and then justify their work by explaining what they did and why they did it. Having three versions of this assessment allow you to provide each student with the right kind and level of problem.
8. Create a Problem (3 Versions)
When a student fully grasps a lesson, they should be able to anticipate the kinds of problem associated with the skills involved. By creating problems, students are also asked to consider the solution process, thus refining their own problem solving skills.
9. Pop Quiz (Versions A and B)
Another assessment to provide students with the opportunity to demonstrate the skills they have accumulated up to this point. Here, I like to give students a chance to choose which version they would like to complete, therefore giving them greater ownership in the results that they produce.
10. Culminating Task
This is a four part themed problem, where students are asked to demonstrate all of the skills they have learned and worked on over the lesson’s entirety.
11. Lesson Test (Versions A and B)
Having two versions of final test allows me to discourage wondering eyes, while also enabling the opportunity for students to re-take a test that they may perform poorly on.
12. Bonus Problems
These are always great to have around, as motivation for the early finisher and any student wishing to gain a few extra points (yes, I don’t mind giving extra credit!).