0. Blanche Jackson Glimps, Contributor
The Inclusive Classroom: Strategies for Effective Differentiated Instruction By
Margo A. Mastropieri
Thomas E. Scruggs
Blanche Jackson Glimps, Contributor
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

1. Mathematics
Chapter 15
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

2. Objectives
Describe, evaluate, and implement various strategies for teaching mathematics.
Provide instructional strategies for such concepts as counting, one-to-one correspondence, numeration, geometry, number lines, writing numbers, and understanding symbols.
Describe and implement strategies for remembering addition and subtraction facts.
List early addition and subtraction problem-solving strategies and multiplication and division concepts.
Identify teaching strategies for incorporating calculators and introducing new vocabulary for multiplication and division facts, and describe when these strategies are appropriate.
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

3. Objectives (cont.)
Understand and implement multiplication and division algorithms strategies.
Describe and implement strategies for mathematics for operations on money, time, and fractions.
Explain the use of manipulative materials and strategies for computation, solving quadratic equations, and problem-solving in algebra.
Describe and evaluate strategies for mathematical reasoning.
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

4. Mathematics and Students with Disabilities
Learning disabilities
May have difficulty with memory and strategy use
Processes and strategy use with math problems
Low motivation and affect
Intellectual disabilities
Acquisition of math concepts
Remembering and executing facts and procedures
Mathematical reasoning
Emotional or Behavioral disorders
Often score below average on mathematics achievement
Attention Problems
Difficulties organizing information
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

5. Mathematics and Students with Disabilities
Hearing impairments, communication disorders, ELLs
May have difficulty with the English language and communication aspects of mathematics
Visual impairments
Perform well on mathematics tasks with appropriate adaptations
Physical impairments
May need specific assistance if concrete manipulatives materials are used
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

6. Teaching Math in Inclusive Settings
Research-based principles for effective remediation in mathematics
Explicit instruction
Instructional design
A strong conceptual basis
Drill and practice
Cumulative review
Motivators
Progress monitoring
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

7. Development of Mathematical Understanding
Progress from concrete representations (beads and blocks) to
Semiconcrete representations (pictorial) to
Abstract representations (graphic)
Functioning also improves with direct instruction, reinforcement, mnemonics, and strategies training
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

8. Strategies for Beginning Math
Teach early number concepts
More, less, any, none, each
Teaching Counting
Best acquired with practice
Components of counting
Acoustic
Point counting
Resultative counting
Counting on
Skip counting
Subitizing
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

9. Strategies for Beginning Math
Teach one-to-one correspondence
Before later concepts can be mastered, students must understand the concept of numerical equivalence
Introduce geometry in early years
The concept of shapes
Present non-instances
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

10. Addition and Subtraction
Manipulatives
beads, buttons, dried beans, base 10 blocks
Number lines to promote operations
Promote number writing
Questioning to promote understanding of symbols
TOUCH MATH to promote computation
Materials represent quantity by dots on each of the numbers 1-9
Practice and specific strategies for facts
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

11. Teaching Addition and Subtraction
Practice and specific strategies for facts
Drill with flashcards
Practice with a partner
Subtraction facts
More difficult to learn than addition facts
Use of tutoring pairs, computer software, and homework can help promote mastery
Place value and regrouping
Use of base-10 blocks
Use of a self-monitoring checklist
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

12. Teaching Addition and Subtraction
Teaching early problem solving with addition and subtraction
Graduated word problem sequence strategy
RTI for early prevention and identification
Tier 1-high quality instructional procedures for the general education class
Small group tutoring as Tier 2 intervention
Students who failed to respond profitably from the Tier 2 instruction could be considered for special education
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

13. Teaching Multiplication Facts
Manipulatives
“Count-bys”
Count by 2, 3, 5, 10
Use strategies for facts
Drill and practice, flashcards, computers
Target essential facts
Bent Finger Strategy for x9
Pegword Strategy
Mnemonic strategies
Pegwords
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

14. Teaching Division Facts
Calculators when appropriate
Reinforce arithmetic vocabulary
Addend, sum, minuend, subtrahend, difference, product, divisor
Demonstration Plus Permanent Model
Demonstrate how to complete a particular type of problem with steps on someplace accessible
Modified long division
Construct the problem as usual but draw a line straight down vertically from the end of the problem
Use error analysis to inform instruction
Determine the type of error students make
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

15. Teaching Problem Solving
Promote use of word meaning
Reinforce arithmetic vocabulary
“Ask for one, tell for one” strategy for determining implied operations
Teach cognitive strategies
Solve It! (seven step strategy to solve word problems)
SAY, ASK, and Check “(self-instruction training)
Use Tier 2 problem-solving interventions
“Hot Math”
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

16. Cognitive Strategies for Problem Solving
Use of steps can help students remember how to solve word problems
Read the problem
Think about the problem
Decide the operation
Write the math sentence
Do the problem
Label the answer
Check every step
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

17. Money and Time
Practice coin recognition and counting money with appropriate materials
Use appropriate methods and materials for teaching about time
Use student clocks that can be set to specific times
Model times or specific features of a clock and ask students to repeat on their own clock model
Assign peer partners who are fluent in telling time
Some students may benefit from digital clocks and watches
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

18. Fractions and Decimals
Use appropriate methods and materials for teaching fractions
Involve students’ experiences as much as possible
Use appropriate methods and materials for teaching decimals
Decimals should not be an overwhelming challenge, if students have exhibited proficiency in aspects of arithmetic
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

19. Area and Volume Concepts
Provide visual and three-dimensional representations
Teach “big ideas”
Provide students with a more general idea of themes, rather than a large number of unrelated formulas and problem solutions
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

20. Strategies for Algebra
Use manipulatives for negative numbers
Teach problem-solving strategies
Number lines, financial debt example, algebra tiles
Teach algebraic representations early
Teach strategies for computation
Mnemonics like FOIL- First terms, Outer + Inner and Last
Teach strategies for solving quadratic equations
Self-questioning
Concrete, semiconcrete, or abstract presentations
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.

21. Teaching Functional Math
Functional math includes aspects of mathematics that serve people in their daily lives
Calendars
Checks
Calculating household expenses
Filling out income tax forms
Bill paying
The Inclusive Classroom: Strategies for Effective Differentiated Instruction, 5th ed., Margo A. Mastropieri, Thomas E. Scruggs, ISBN © 2014, 2010, 2007, 2004, Pearson Education, Inc. All rights reserved.