Students with visual impairments may face challenges when working on the Mathematics standards in the Common Core State Standards (CCSS). As a response to this, Perkins School for the Blind convened a panel of experts to identify specific standards that would be a potential challenge to students who are blind or visually impaired, and then proposed ideas for materials, foundational skills, tips and strategies, and lesson ideas to help to address these challenges.

This post is part of a series about different parts of the Mathematical standards.

### What is a student likely to be working on in the area of Number Systems:

- A number system is a way to represent number.
- Base ten or the decimal system is one common number system.
- Other number systems are Binary (base 2), Hexadecimal (base 16), and Octal (base 8).
- Early elementary grades study numbers and operations in base ten usually in whole numbers and some.
- By the time a student reaches 3rd grade fractions are included in the study of numbers.
- Once in middle school students work with the Number System includes the study of positive and negative number, and rational number and irrational numbers.
- In high school students learning is extended from rational and irrational numbers to imaginary numbers to form complex numbers.
- As students advance through the grades they apply and extend their understanding of the number system.
- Studying the number system enables the student to do mathematics; calculate, solve equations and represent measurements.

### What are the particular challenges for a student who have a visual impairment?

The number system can become abstract particularly as the student advances from grade to grade. It is recommended concrete, along with tactile, examples be used when working with students. The use of real world examples of uses of the number system

### Foundational Skills:

- Addition
- Subtraction
- Multiplication
- Division
- Decimals, terminal and repeating
- Fractions
- Rational Numbers
- Irrational Numbers
- Understand the relationship between fractional integers and rational numbers
- Imaginary numbers
- Complex numbers

### Materials

- Braille/Large Print Number Line
- APH Mathbuilders Unit 1 (Braille/Large Print)
- Magnetic Fraction squares, circles, or tiles
- Focus in Mathematics Kit
- APH Mathbuilders Unit 7 Fractions, Mixed Numbers and Decimals (Braille/Large Print)
- Fractional parts of whole Sets
- Talking Calculator
- Talking Scientific Calculator
- Braille Notetaker
- Perkins Brailler
- Electronic Notepad with Scientific Calculator
- Adapted Practice Checkbook and Register
- Abacus
- APH Fraction kits
- Nemeth Code
- Math Window
- Tactile Stickers or markers

### Tips and Strategies

- When using large print or braille number lines, tactile markers or stickers may be useful.
- When using APH Mathbuilders Unit 1, student will need a divided board with one side positive and one side negative.
- When using Nemeth, students need to understand the special rules for superscript.

### Lesson Ideas

- Lessons on pluses and minuses
- Use one item to represent a positive and one item to represent a negative.
- Use one side of a board to add and one side to subtract.
- Discuss how credits can be positive and debits can be negative and what happens when we add and subtract each.
- Use same positive and negative tokens to discuss multiplication and division.
- Use double negatives in language to discuss multiplying 2 negative numbers.
- Subtract fractions with like denominators (halves, thirds, fourths, and tenths) with minuends less than or equal to one.
- Relate to measuring cups in cooking and how many halves, thirds, or fourths are left.
- Express a fraction with a denominator of 100 as a decimal.
- Compare quantities represented as decimals in real world examples to hundredths.
- Relate hundredths to pennies and make comparisons on a number line to where an amount of money would lie.