## Description

**Perceptions: Changing the Way You Look at Math**

Perceptions Blue is a 16-week Intensive Math Intervention focused on the** Operations of Multiplication, Division, and Fractions which includes Multiple-Digit Multiplication with Regrouping, Long Division with Remainders, and Addition, Subtraction, Multiplication, Division of Fractions, Mixed Numbers, and Improper Fractions, plus much more! **

This Instruction Manual is part of the Perceptions Blue Program and is designed to be used in combination with the Lesson-by-Lesson Video Instruction, Perceptions Blue Student Book, MasterPieces, and MasterFractions.

Using the Construct, Express, & Apply methodology, students and instructors learn how to construct and express concepts and operations, and then apply to reason into real-world scenarios creating a powerful learning environment.

Scope & Sequence

Unit 1 - Understanding Multiplication and Division

Lesson 1: Multiplication: Repeated Addition Making Rectangles and Squares

Lesson 2: Factors and Products

Lesson 3: Beginning Factoring

Lesson 4: Factoring and Prime & Composite Numbers

Lesson 5: Beginning Division

Lesson 6: Solving for Unknowns

Unit 2 - Multi-Digit Multiplication and Division

Lesson 7: Distributive Property and Place-Value Notation (Expanded Form)

Lesson 8: Two-Digit Multiplication

Lesson 9: Two-Digit Multiplication with Regrouping

Lesson 10: Long Division

Lesson 11: Division with Remainders

Lesson 12: Multi-Digit Multiplication

Lesson 13: Multi-Digit Division

Unit 3 - Introduction to Fractions

Lesson 14: Interrelationships: Combine & Compare

Lesson 15: Rational Numbers: Ratios & Fractions

Lesson 16: Parts of a Fraction and Fraction of a Number

Lesson 17: Types of Fractions and Comparing/Combining Fractions

Lesson 18: Add & Subtract Fractions with Same Denominators & Decomposing Fractions

Lesson 19: Equivalent Fractions

Lesson 20: Finding Equivalencies, Simplifying, and GCF

Unit 4 – Operations with Fractions Part 1

Lesson 21: Adding and Subtracting Fractions

Lesson 22: Cross-Multiplication (Concrete)

Lesson 23: Cross-Multiplication (Abstract)

Lesson 24: Changing Improper Fractions & Mixed Numbers

Lesson 25: Addition with Improper Fractions & Mixed Numbers

Lesson 26: Subtraction with Improper Fractions & Mixed Numbers

Lesson 27: Adding Multiple Fractions

Unit 5 – Operations with Fractions Part 2

Lesson 28: Multiplication with Fractions

Lesson 29: Division with Fractions

Lesson 30: Division with Fractions Using the Reciprocal

Lesson 31: Canceling (Pre-simplifying) when Multiplying Fractions

Lesson 32: Solving for Unknowns in Fractions

Lesson 33: Solving for Unknowns (Optional)

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