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Everyone Means All: Differentiation in a Math Lesson for Students with Intellectual Disabilities

Melissa Ainsworth, M.A., M.Ed. and Elizabeth Obester, M.Ed.

Guest authors Melissa Ainsworth and Elizabeth Obester are educators in Fairfax County (Virginia) Public Schools - Melissa as a classroom teacher at the secondary level and  Elizabeth as an Assistant Principal  at the elementary level.   Each has a considerable history of special education classroom experience and continues to work with students with significant intellectual disabilities.   They collaborate often to present successful and practical  instructional strategies from their own experience around the state of Virginia.   This article is a follow-up to a recent presentation, ASOLs Everyday: Planning Your Math Instruction, given in two regions of the state.

Classes in Virginia public schools can be quite diverse. For example, in one classroom for students with intellectual disabilities in which math ASOLs were taught, there were seven students. Of the seven, four spoke a language other than English at home, three of the seven were non-verbal, and two had significant physical disabilities. Additionally, their academic abilities ranged from emergent to early first grade skills. Despite this diversity, the students worked well together and many group lessons, where everyone participated and learned, were able to be conducted.

A favorite math activity was bowling. By using Universal Design and differentiation, students were able not only to bowl, but to work on their own individual math goals while building class spirit and team work. "When the content, materials, and teaching strategies are developed to consider the needs of all students, including those with disabilities and other learning needs, educators are using what is known as 'universal design'(Snell & Brown, 2006, p. 493). In Universal Design, there will be many different ways for information to be presented, for students to engage with the material, and for students to express what they have learned (Snell & Brown, 2006). Differentiation is an overlapping concept that involves many of the same aspects as Universal Design with the addition of "varying the complexity and nature of content presented during the course of a unit of study" (Browder & Spooner, 2006, p. 25). This is a key concept because it allows for all students to participate in one lesson while each one is working on a potentially different goal. In the following math lesson, students are working on various goals, including communication and group skills, as well as the designated math concept of more than.

The lesson is structured in the LEARN lesson format, developed by Fairfax County Public Schools, which breaks the lesson into the following segments: Link (connect what students are about to learn to something they already know), Engage and Educate (this is the teaching portion of the lesson where new information is explicitly taught), Active Learning (this is largest portion of your lesson, where the students participate with hands-on activities), Reflect (the students review what they have learned; this section is student centered, not teacher directed), and Now and Then (bridge what the students just learned to other subjects, other areas of practice or to something that is coming up).

Lesson: Bowling Math

Objective: Students will demonstrate an understanding of the concept of more than through a variety of measures as listed individually for each student.

Related ASOL: M-NS 1
The student, given two sets containing 10 or fewer concrete items, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.


  1. Plastic bowling set, easy to find at a dollar store or yard sale, with numerals written in permanent marker on one side of them (letters can be written on the other for literacy activities)
  2. Individual containers, such as pie tins, one for each student
  3. Pompoms, colored chips, or other fillers
  4. Calculators
  5. Pencils and paper


Remind students of the bowling trip taken recently. Tell them that today we are going to do math bowling. (If you have not taken a bowling trip, you can link the activity to the concept of more that will be covered, or to a book you read where bowling was a part of it, etc.)

Engage and Educate:

  1. Teacher says, "When we bowl, we knock down pins. When we bowl, we try to knock down lots of pins because whoever knocks down the most wins. In order to know how many pins we knocked down we need to see who knocked down more pins."
  2. Show them a PowerPoint activity that is designed to teach the concept of more. Other options include using a software program, such as Early Learning: Math Skills, as a teaching tool, or you can use manipulatives or a book. The important aspect of this portion of the lesson is that the teacher is presenting and teaching the concept.

Active Learning:

Here are the basics:
Each student has several opportunities to roll the ball and knock down pins. Each student will get a colored pompom in their personal container for each pin they knock down.

Here is how the lesson is differentiated for each student:

Tier 1 (2 students): The students who fall into this tier have the most significant needs. Both of these students are non-verbal. One has very severe physical disabilities. For both of these students, use of their communication devices is a major focus of their IEPs, so each of these students will need to indicate "my turn" before they bowl. After they have had the opportunity to knock down pins, they will have help to pick up the pins they knocked down. As they are picked up, the adult working with them tells each of them to be counting in their heads while the adult counts aloud. Once the pins have been counted, a pompom is placed in their individual containers, right in front of the students, and the expectation is that the students count again while the adult counts aloud. They will then indicate which of the two of them has more than the other with adult support.

Tier 2 (2 students): The students who fall into this tier are both verbal and have limited number identification skills. After they have bowled and knocked down the pins, they have the opportunity to identify the numbers written on the pins — however, this is not the focus of this lesson, this is more incidental learning. The students will then help count the pompoms as they are put into their individual containers, noting the quantity of pins they have knocked down and who has more of the two of them.

Tier 3 (3 students): The students who fall into this tier have some higher math skills than the students in the other two tiers. So in order to maximize their experience they will approach the bowling a little differently. After these students have had the opportunity to bowl, they will write down the numbers on the pins they knocked down. Then, with a calculator, they will add up the numbers and get a total for each turn. At the end of the lesson they will use the calculators to add up the totals for each turn to get a final number. These students will also get to put pompoms in their individual containers for each pin they knocked down. These students can compare between the students who've just bowled to see who has more, as well as, comparing their own scores between turns.

In this section of the lesson, the students will review and again apply their learning. The students in Tiers 1 and 2 will look at a range of individual containers and determine which container has more than the others. Tier 1 students will have a range of two containers with obvious differences in amounts to look at in order to determine more than.
Tier 2 students will have three or four containers to look at in order to determine which one has more than. Students in Tier 3 will compare their final calculations to determine who has the biggest number and therefore more than the others. Also, they may look at the individual containers for each student and determine who has more than their classmates.

Now and Then:

Remind students that they can see more than all around them. Give them some examples such as: Who got more fries in their lunch? Which bus has more students on it? Tell them to be on the lookout for more!

Through Universal Design and differentiating lessons, it is entirely possible for all students, despite individual skills, goals and needs, to participate meaningfully in a group lesson that will build team work and class unity, as well as, group dynamic skills.


Browder, D.M., & Spooner, F. (2006). Teaching Language Arts, Math, & Science to Students with Significant Cognitive Disabilities. Baltimore: Paul H Brookes.

Early Math Skills software

Snell, M.E., & Brown, F. (2006). Instruction of studemts with severe disabilities (6th ed.). Upper Saddle River, New Jersey: Merrill Prentice Hall.

Universal Design for Learning