Now we are ready to learn more about designing math instruction for students with a significant intellectual disability. We have already reviewed how to make sure the skills we plan to teach are aligned to gradelevel standards. We have also spent some time talking about the research on teaching math, NCTM Focal Points, and the Common Core State Standards (CCSS).
For some students with a significant intellectual disability, it will be important to build early numeracy skills while linking instruction to grade level standards. For example, some student may not have mastered number identification or rote counting skills. While student still must gain access to grade level standards, it will also be important to build those early numeracy skills and concepts in order to provide students deeper conceptual understanding of those grade level standards.
Let’s review what early numeracy skills look like, and how elementary instruction can provide explicit instruction for students with significant intellectual disability to build these skills
Plan of the Day Slides Transcript
While it is important to continue to build students early numeracy skills, gradelevel aligned instruction is also necessary. We will now start to review a process you can use to build your own standardsbased math lessons. Based on the research of Browder, Jimenez, and Trela (2012) and Browder, Trela, Courtade, Jimenez, Knight, and Flowers (2012), the steps outlined below provide teachers with a researchbased approach to planning math instruction for students with significant intellectual disability.
First we are going to look at the 1st step, using stories to build context in mathematics.
Let us now look at a model for teaching gradealigned math instruction to students with significant cognitive disabilities. Listen to the slide presentation below to learn about the 1st step in math instruction Creating Storybased Math Problems.
Storybased Math Problems Transcript
In the slides you saw a sample math story and we have written one together to align to a 5th grade measurement standard, let’s watch a video clip (from Teaching to the Standards: Math by Attainment Company) of a teacher beginning her math lesson with a storybased math problem. Pay special attention to the different levels of adaptations and modifications the teachers makes to assure that all of her students are actively participating in the reading of the story.
Video Recap: In the video you just watched a high school teacher read a story about a class voting on what book has been their favorite in school. As you noticed, the teacher used the story to embed the data or facts. The teacher read the story while students read along with her. Students identified the facts in the story as the read, as well as the problem “What book was voted the favorite?” Did you notice the various different ways students participated in this portion of the math lesson? Some students read along with the teacher independently, others were prompted by the teacher to locate the important information in the story (e.g., Lord of the Rings), while other students had onetoone assistance (e.g., paraprofessional, peer) read with them. This video is a great example of group instruction designed to meet each student’s individual needs. 
Math instruction requires many new terms for students. It may be helpful to review common terminology that will be used in the lesson. It is important to make sure that students understand what is being asked in a lesson. An example would be the term “X” in algebra. Students will need to know that an X is used for unknown facts or numbers in algebra, in order to “solve for x”. Here is a short video clip (from Teaching to the Standards: Math by Attainment Company) in which the teacher is reviewing pictures and definitions of the new vocabulary that will be used in the upcoming lesson in geometry.
Video Recap: In the video you just watched, a middle school teacher reviews the vocabulary that will be used in the upcoming geometry lesson. Did you notice the format of the vocabulary words? They were all presented as written words and picture symbols. This increases the student’s comprehension of each word. Often students with severe disabilities are taught to identify sight words, while this is a timeworthy skill, it is also important to make sure that student gain understanding of those terms. One strategy is to teach students to match vocabulary words to pictures or definitions that represent the concept. For more information on how to use time delay to teach sight words and pictures, refer to the MAST module Systematic Instruction. 
Remember the story we created for the measurement skill. We will need that story to move onto the next step in teaching math. The use of graphic organizers is a great way to help students organize the facts of the problem. Think about the sample story we wrote to address the measurement standard. Does our story have a sequence of events?
Let’s review our story! We have written a story in which LaTia wants to hang a picture on the wall in her room. She wants to make sure that the picture is not too big to fit on a small wall in her room. She needs to measure the picture and measure the wall to decide if the picture will fit. First she decides to measure the picture, then will measure the wall. The picture is 12 inches wide and the wall is 18 inches wide. Will the picture fit on the wall?
You may want students to recreate the picture out of red construction paper and the wall out of blue. They will need to actually practice the skills of measurement this way. Once they have measured the items, they can lay the picture on the wall to see if it will fit. In this sample lesson, the actual construction paper may be a form of graphic organizer. Watch the video clip (from Teaching to the Standards: Math by Attainment Company) below to see how a teacher directs her students to find the facts in an algebra story and place them on their graphic organizer.
Video Recap: In the video, you just saw a high school teacher teaching a lesson in algebra in which the students are solving for X to solve a problem about “how many gift certificates Irene needs to buy.” The three students in this video are being asked to locate the facts in the story. The teacher rereads the story to allow the students to locate the facts in the story. As the students locate each fact they record them into the algebra graphic organizer. This graphic organizer was created to allow students to organize the 1st fact, unknown fact, and last fact. Using another graphic organizer (number line) the students then were able to count up or down to solve the equation. The students did not need to answer verbally to find the facts and record their answer. Some students may be able to point to the facts in the story and record the answers using a pencil/paper format, other students may have Velcro numbers in the story they take off and place into their graphic organizer. It is important to think about the mode of communication students currently have (e.g., pointing, pulloff, use of augmentative communication device) and use that mode to allow students access to the skill being taught. 
In the video above you saw the students go through a process to start to solve the algebra equation. They had already read a story, identified what the problem of the story was, and they were beginning to identify the facts of the story and place them on their graphic organizer. They were following a task analysis to solve a math problem. A task analysis is created when you break down a chained skill. An example we are all familiar with would be teaching a student to tie their shoe. For more information about taskanalytic instruction refer to the MAST modules on Task Analysis and Systematic Instruction. See the example below:
Task analysis for Tying a Shoe:

Task Analytic Instructionin mathematics provides students with a process to solve any math problems. When you watch the next video, you will see a demonstration of the same teacher and students completing the final steps in the task analysis to solve the algebra math problem. Notice the teacher reviews the problem statement at the end of the lesson. It is essential that students have an opportunity to build math problem solving skills by answering the story question (e.g., 2+X=6; How many pieces of pizza did Jason need to buy for his party? 4. Jason had 2 pieces and he needed to buy 4 more.)
Video Recap: In the video, you just saw the final portion of the algebra lesson from the earlier videos. Did you notice how the students used the number line in the graphic organizer to solve for x? The students did not need to currently have counting skills or even number recognition skills to solve the equation. The students in this video did have some number recognition skills but needed the number line to help them solve the equation independently. Did you notice what the teacher did once the students solved for X? She went back to the question from the story. It is important to bring the students back to the main idea of the story. They were solving this algebra equation for a reason: to find out how many gift certificates Irene needed to buy. Students used the numbers and their answer to answer the “reallife” problem. 
Using the link below you can visit the UNC Charlotte’s General Curriculum Access grants website, where you will find an example math elementary school, middle school, and high school task analysis. http://education.uncc.edu/access/2009 Curriculum Summit.htm You may want to bookmark this site for exploration at a later date. The URL is also provided in the Resource list for this module.
You may have noticed different versions of the math task analysis. They are primarily the same steps; however, it is important to think about vertical differentiation across the school years. You can refer to the MAST module on Instructional Alignment for more information about what Vertical Alignment means for students with significant intellectual disabilities. In the high school task analysis you may have noticed an extra step in with students independently identify what graphic organizer needs to be used to solve the problem, rather than the teacher handing them a graph to sort data.
It may be unreasonable to expect all students to follow all steps of the taskanalysis independently. Teachers will need to prioritize which, if not all, steps on which specific students are working towards mastery. It is also important to recognize the opportunity for students to participate in more steps within the process as mastery occurs, as well as the need to consider strategies to allow students to participate in steps that may not follow a traditional method. Some questions and possible answers might include:
At this beginning of the Anchors Aweigh portion of this module early numeracy instruction was discussed. For many students with significant intellectual disability it will be important to embed opportunities to build early numeracy skills within the gradelevel aligned lessons. This can be done in multiple contexts (general education classroom, special education classroom, individualized or small group lessons). The slides below briefly outline research to support the effect early numeracy skills have on students’ ability to access gradelevel common core standards (Jimenez & Staples, 2013).