All students are individuals able to know, use, and enjoy mathematics. The IM curriculum empowers students, with activities that capitalize on their existing strengths and abilities, to ensure that all learners participate meaningfully in rigorous mathematical content. Lessons support a flexible approach to instruction and provide options for additional support to address the needs of a diverse group of students, positioning all learners as competent, valued contributors.

Curriculum features that support access

Each lesson is carefully designed to maximize engagement and accessibility for all students. Purposeful design elements support access for all learners but are especially helpful for students with disabilities, include:

Lesson Structures Are Consistent

The structure of every lesson is the same: Warm-up, activities, Lesson Synthesis, Cool-down. By keeping the components of each lesson consistent from day to day, the flow of work in class becomes predictable for students. This reduces cognitive demand and enables students to focus on the mathematics at hand rather than the mechanics of the lesson.

Concepts Develop from Concrete to Abstract

Mathematical concepts are introduced simply, concretely, and repeatedly, with complexity and abstraction developing over time. Students begin with concrete examples, and transition to diagrams and tables before relying exclusively on symbols to represent the mathematics that they encounter.

Individual to Partner, or Small-Group to Whole-Class Progression

Providing them with time to think through a situation or a question independently before engaging with others allows students to carry the weight of learning, with support arriving just in time from the community of learners. This progression allows students to first activate what they already know, and to continue to build from this base with others.

Opportunities to Apply Mathematics to Real-World Contexts

Giving students opportunities to apply the mathematics they learn clarifies and deepens their understanding of core math concepts and skills, and provides motivation and support. Mathematical modeling is a powerful activity for all students, but especially students with disabilities. Each unit has a culminating activity designed to explore, integrate, and apply all the big ideas of the unit. Centering instruction on these contextual situations can provide students with disabilities an anchor on which to base their mathematical understandings.

Instructional strategies that support access

Use the following general instructional strategies to enhance access to rigorous, grade-level content, for all students: 

Eliminate Barriers

Eliminate any unnecessary barriers that students may encounter that prevent them from engaging with the important mathematical work of a lesson. This requires flexibility and attention to areas such as the physical environment of the classroom, access to tools, organization of lesson activities, and means of communication.

Processing Time

Increased time engaged in thinking and learning leads to mastery of grade-level content for all students, including those with disabilities. Frequent switching between topics creates confusion and does not allow for content to deeply embed in the mind of the learner. Mathematical ideas and representations are carefully introduced in the materials in a gradual, purposeful way to establish a base of conceptual understanding. Allow students  additional time, as needed.

Assistive Technology

Assistive technology is a vital tool for students with learning disabilities, visual-spatial needs, sensory integration, and students with autism. Assistive technology supports, suggested in the materials, are designed to either enhance or support learning, or to bypass unnecessary barriers.

Manipulatives

Physical manipulatives help students make connections between concrete ideas and abstract representations. Often, students with disabilities benefit from hands-on activities, which allow them to make sense of the problem at hand and communicate their own mathematical ideas and solutions.

Visual Aids

Visual aids, such as images, diagrams, vocabulary anchor charts, color coding, or physical demonstrations, are suggested throughout the materials to support conceptual processing and language development. Keeping relevant visual aids posted in the classroom supports independence by allowing students to access them as needed, and is especially beneficial for students with challenges related to working or short-term memory.

Graphic Organizers

Word webs, Venn diagrams, tables, and other metacognitive visual supports provide structures that illustrate relationships between mathematical facts, concepts, words, or ideas. Students use graphic organizers to collect and manage their thoughts and ideas, planning problem-solving approaches, visualizing ideas, sequencing information, and comparing and contrasting ideas.

Brain Breaks

Brain breaks are short, structured, 2–3-minute movement breaks taken between activities, or used to chunk a longer activity (approximately every 20–30 minutes during a class period). Brain breaks are a quick, effective way of refocusing and re-energizing the physical and mental states of students during a lesson. Brain breaks also have been shown to positively impact students’ concentration and stress levels, resulting in more time spent engaged in mathematical problem-solving. This universal support is beneficial for all students, especially those with attention challenges.

Access for Students with Disabilities

Supplemental instructional strategies, labeled Access for Students with Disabilities, are included in each lesson. They are designed to help meet the individual needs of a diverse group of learners. Each support is aligned to one of the three principles of Universal Design for Learning, to provide multiple means of engagement, representation, or action and expression, and includes a suggested strategy to increase access and eliminate barriers. Use these lesson-specific supports, as needed, to help students succeed with a specific activity, without reducing the mathematical demands of the task. Phase them out as students gain understanding and fluency. 

The following areas of cognitive functioning are integral to learning mathematics (Brodesky et al., 2002), and are indicated in each access support so that teachers can leverage students’ strengths to address potential barriers or challenges that exist in the learning environment.

• Conceptual Processing includes perceptual reasoning, problem-solving, and metacognition.
• Language includes auditory and visual processing and expression of language.
• Visual-Spatial Processing includes processing visual information and understanding relation in space of visual mathematical representations and geometric concepts.
• Organization includes organizational skills, attention, and focus.
• Memory includes working memory and short-term memory.
• Attention includes paying attention to details, maintaining focus, and filtering out extraneous information.
• Social-Emotional Functioning includes interpersonal skills and the cognitive comfort and safety required in order to take risks and make mistakes.
• Fine-Motor Skills include tasks that require small-muscle movement and coordination, such as manipulating objects (graphing, cutting with scissors, writing).

The additional supports for students with disabilities were designed, using the Universal Design for Learning Guidelines (http://udlguidelines.cast.org). Each support aligns to one of the three principles of UDL: engagement, representation, or action and expression.

Engagement:

Students’ attitudes, interests, and values help to determine the ways in which they are most engaged and motivated to learn. Supports that provide multiple means of engagement include suggestions for motivating students to engage with content, develop effort and persistence, and internalize self-regulation.

Provide Access by Recruiting Interest	Offer choice. Invite students to select a subset of problems to complete, and to decide which problem to start, which strategy to use, the order in which to complete the task. Provide access to a variety of tools or materials. Leverage curiosity and students’ existing interests. Invite students to name connections to their own lived experiences. Use visible timers and alerts to prepare for transitions.
Develop Effort and Persistence	Chunk this task into more manageable parts. Check in with students to offer feedback and encouragement after each chunk. Differentiate the degree of difficulty or complexity by starting with accessible values. Periodically revisit math-community norms, and provide group feedback that encourages collaboration and community.
Internalize  Self-Regulation	Offer on-going feedback that helps students maintain sustained effort and persistence during a task. Encourage self-reflection and identification of personal goals. Provide access to tools and strategies designed to help students self-motivate and become more independent.

Representation:

Reduce barriers and leverage students’ individual strengths by inviting students to engage with the same content in different ways. Supports that provide multiple means of representation include suggestions for offering alternatives to the ways information is presented or displayed, for developing students’ understanding and use of mathematical language and symbols, and for describing organizational methods and approaches designed to help students internalize learning.

Provide Access for Perception	Present content, using multiple modalities: act it out, think aloud, use gestures, use a picture, show a video, demonstrate with objects or manipulatives. Annotate displays with specific language, different colors, shading, arrows, labels, notes, diagrams, or drawings. Provide appropriate reading accommodations.
Develop Language and Symbols	Support use of vocabulary, mathematical notation, and symbols, with charts, pictures, diagrams, and tables. Highlight connections between representations to make patterns and properties explicit. Present problems or contexts in multiple ways, with diagrams, drawings, pictures, media, tables, graphs, or other mathematical representations. Use translations, descriptions, movements, and images to support unfamiliar words or phrases.
Internalize Comprehension	Activate or supply background knowledge to build connections to prior understandings and experiences. Provide access to blank or partially completed outlines, graphic organizers, or representations, to emphasize key ideas and relationships. Maximize transfer and generalization by naming connections to previous examples and inviting students to identify important details or features to remember.

Action and Expression:

Throughout the curriculum, invite students to share both their understanding and their reasoning about mathematical ideas with others. Supports that provide multiple means of action and expression include suggestions for empowering students with: access to appropriate tools, templates, and assistive technologies, options for the ways they communicate their learning, and resources that facilitate executive functioning.

Provide Access for Physical Action	Provide independent think time before students engage with others or responses are discussed. Ensure students have enough time to complete tasks. Offer extra time if needed. Provide access to pre-cut materials, assistive tools, devices, or software.
Develop Expression and Communication	Offer flexibility and choice with the ways students demonstrate and communicate their understanding. Invite students to explain their thinking, verbally or nonverbally, with manipulatives, drawings, and diagrams. Support fluency with graduated levels of support or practice. Apply and gradually release scaffolds to support independent learning. Support discourse with sentence frames or visible language displays.
Internalize Executive Functions	Support the development of organizational skills in problem-solving, with access to templates, rubrics, and checklists. Post visible goals, objectives, and schedules. Offer opportunities for self-assessment. Enable students to monitor their own progress.

For additional information about the Universal Design for Learning framework, or to learn more about supporting students with disabilities, visit the Center for Applied Special Technology (CAST) at udlguidelines.cast.org.

Accessibility for Students with Visual Impairments

For students with visual impairments, accessibility features are built into the materials:

1. A palette of colors distinguishable to people with the most common types of color blindness.
2. Tasks and problems designed so that success does not depend on the ability to distinguish between colors.
3. Mathematical diagrams, presented in scalable vector graphic (SVG) format, can be magnified, without loss of resolution, and rendered in Braille.
4. Where possible, text associated with images is not part of the image file, but rather included as an image caption accessible to screen readers.
5. Alt text on all images makes interpretation easier for users accessing the materials with a screen reader.

If students with visual impairments are accessing the materials, using a screen reader, it is important to understand:

• All images in the curriculum have alt text: a very short indication of the image’s contents, so that the screen reader doesn’t skip over as if nothing is there.
• Some images have a longer description to help a student with a visual impairment recreate the image in their mind.

Understand that students with visual impairments likely will need help accessing images in lesson activities and assessments. Prepare appropriate accommodations. Accessibility experts, who reviewed this curriculum, recommended that eligible students have access to a Braille version of the curriculum materials, because a verbal description of many of the complex mathematical diagrams is inadequate for supporting their learning.