Lesson 3: Operations with Fractions

When do we need to find a common denominator?
What is reciprocal and when do we use reciprocals?

1. Conceptual Understanding of Fractions Equivalence: Demonstrate that multiplying or dividing the numerator and denominator by the same non-zero number creates an equivalent fraction .Simplification: Identify the Greatest Common Factor (GCF) to reduce fractions to their "simplest" or "lowest" terms. Proper vs. Improper: Convert between mixed numbers and improper fractions, understanding their utility in different contexts (e.g., mixed numbers for measurement, improper fractions for algebraic calculation).2. Multiplicative Operations Multiplication: Apply the rule. Students are expected to simplify before multiplying to increase efficiency. Division & Reciprocals: Define the reciprocal of a fraction and apply the "Invert and Multiply" rule .3. Additive Operations Common Denominators: Recognize that addition and subtraction require a "common unit."Least Common Multiple (LCM): Determine the Least Common Denominator (LCD) for two or more fractions. Summation/Subtraction: Execute the process of converting fractions to a common denominator and combining the numerators while keeping the denominator constant.4. Application and Estimation Real-World Modeling: Solve word problems involving fractional parts of a whole (e.g., construction measurements or budgetary portions).Order of Operations with Fractions: Evaluate expressions that combine fractions with parentheses, exponents, and multiple operations (integrating Unit 1.1 standards).

Description: A review of prime factorization, simplifying fractions, and performing the four basic operations with rational numbers (including finding the Least Common Denominator).

Purpose: To demystify "scary" numbers. Algebra frequently results in fractional answers; students must be comfortable manipulating them without reaching for a calculator immediately.

DOK Level: 2 (Skill/Concept)

Some students will likely add both the numerator and denominator when adding fractions
Some students will likely convert both fractions to a common denominator when multiplying

Class and online work

Use practice problems 6 and 7 on pages 22 and 23 to assess students' understanding of the lesson concepts