1. Math Teaching Strategies for the Blind, Grades 3-5, Ideas to Survive
IESBVI
Iowa Educational Services
for the Blind & Visually Impaired
Math Teaching Strategies for the Blind, Grades 3-5, Ideas to Survive
Sara Larkin
Summer Institute August 2-3, 2017

2. Terms TVI – Teacher of the Visually Impaired
Nemeth Code – Braille code for math and science
Notetakers – Braille computer with word processor, spreadsheet, , internet, calculator, stopwatch, etc.
Perkins braillewriter – Braille typewriter for multiple lines and showing work
Braille on Demand – a way to get last minute materials, 10 page max, can’t have an ISBN number (Heartland AEA has their own person so BOD is not available there)
IDB – Iowa Department for the Blind, brailles materials with ISBN numbers and others with more advance notice
APH – American Printing House for the Blind (quota funds)

3. Nemeth The braille code for math and science APH Nemeth Tutorial
Iowa Braille School Nemeth Lessons and Handouts
The Nemeth Braille Code for Mathematics and Science Notation 1972 Revision
Math Window (tiles with both print and braille)
Maryland Common Core State Curriculum Frameworks for Braille
See Nemeth Code Template

4. Access Think about Materials Textbook Reading Writing Notes Homework
Technology – Hardware and software

5. Operations and Algebraic Thinking
Interpret products as groups of ___ objects each
Interpret quotients as objects partitioned equally into ___ shares, or as objects partitioned into equal shares of ___ objects each
Interpret multiplication as a comparison where one set is ___ times as many as another set
x, ÷ to solve word problems involving equal groups/arrays or multiplicative comparison by using drawings/equations with a symbol for the unknown. Assess reasonableness of answers using mental computation/estimation/rounding strategies

6. Operations and Algebraic Thinking Cont’d
Determine the unknown number in a multiplication/division equation
Apply properties of operations as strategies to multiply/divide
Understand division as an unknown-factor problem
Fluently multiply/divide
Identify patterns (including in the addition/multiplication table), and explain them using properties of operations
Factors, multiples, prime, and composite
Generate a number/shape pattern that follows a given rule

7. Operations and Algebraic Thinking – Expressions/Graphs
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane

8. Number and Operations in Base Ten
Use place value understanding to round whole numbers
Fluently add/subtract using strategies/algorithms based on place value, properties, and/or the relationship between +, - or use the standard algorithm
Explain patterns in the # of zeros of the product when multiplying by powers of 10 and in placement of the decimal point when a decimal is x, ÷ by powers of 10
Recognize a digit in one place represents 10 times what it represents in the place to its right and 1/10 of what it represents in the place to its left
Read/write numbers using numerals/number names/ expanded form. Compare numbers based on meanings of the digits, using >, =, and < symbols to record results

9. Number and Operations in Base Ten Cont’d
Multiply two numbers, using strategies based on place value and properties of operations. Illustrate/explain the calculation by using equations/rectangular arrays/area models or use the standard algorithm
Divide two numbers, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division. Illustrate/explain the calculation by using equations/rectangular arrays/area models
Read, write, and compare decimals
+, -, x, and ÷ decimals, using concrete models/drawings and strategies based on place value, properties of operations, and/or the relationship between addition/subtraction; relate strategy to a written method and explain the reasoning used

10. Number and Operations—Fractions
Understand the fraction 1/b as 1 of b parts and a/b as a multiple of 1/b
Understand/represent fractions on the number line diagram
Recognize/generate simple equivalent fractions. Explain why fractions are equivalent by using a visual model
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers
Compare fractions w/ same numerator/denominator by reasoning about their size or w/ different numerators/ denominators by creating common denominators/comparing to 1/2. Record w/ >, =, or <, and justify using visual model

11. More Number and Operations—Fractions
Decompose a fraction into a sum of fractions w/ same denominator, record w/ equation. Justify using visual model
+, - fractions and mixed numbers
Solve word problems involving +, -, x of fractions and mixed numbers by using visual fraction models/equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers
Use decimal notation for fractions with denominators 10/100
Compare two decimals by reasoning about their size. Record w/ >, =, or <, and justify by using visual model

12. Even More Number and Operations—Fractions
Interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to fractions or mixed numbers by using visual fraction models or equations to represent the problem
Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas
Explain why multiplying a given number by a fraction > 1 results in a product larger than the given number; explaining why multiplying a given number by a fraction < 1 results in a product smaller than the given number
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions

13. Measurement and Data Tell/write/measure time.
Know relative sizes of km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Convert among units within a measurement system. Record measurement equivalents in a two-column table. Use conversions in solving real world problems.
Measure/estimate liquid volumes/masses using grams/kilograms/liters.
Use +, -, x, and ÷ to solve word problems involving distances, intervals of time, liquid volumes, masses, and money, including problems w/ fractions/decimals, and problems that require expressing larger units in terms of smaller units. Represent measurement quantities using drawings/diagrams such as number line diagrams

14. Measurement and Data - Graphs
Draw a scaled picture/bar graph to represent a data set w/ several categories. Solve "how many more" and "how many less" problems using info presented in scaled bar graphs
Generate measurement data by measuring lengths using rulers. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving operations on fractions by using information presented in line plots

15. Measurement and Data – Perimeter/Area/Volume
Recognize area as an attribute of plane figures. Understand concepts of area measurement. Measure areas by counting square units. Relate area to operations of multiplication (rectangles) and addition (figures divided into multiple rectangles). Apply area/perimeter formulas for rectangles
Solve problems involving perimeters of polygons, including finding perimeter, finding an unknown side length, and exhibiting rectangles w/ the same perimeter and different areas or w/ the same area and different perimeters
Recognize volume as an attribute of solid figures. Understand concepts of volume measurement. Measure volumes by counting unit cubes. Relate volume to operations of multiplication and addition. Solve problems involving volume.

16. Measurement and Data - Angles
Recognize angles as geometric shapes that are formed by two rays w/ a common endpoint. Measure angles using a protractor. Sketch angles of specified measure
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure

17. Geometry - Shapes
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole
Classify two-dimensional figures into categories based on their properties

18. Geometry – Lines/Angles
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry

19. Geometry – Coordinate Plane
Graph points on the coordinate plane
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation

20. Resources Iowa Braille School (Math section)
Perkins School for the Blind Math
Paths to Literacy
Texas School for the Blind and Visually Impaired Math
APH Products aligned to the Common Core State Standards