Same and different

Learning Objectives Identify when two mathematical expressions or quantities are the same (equal). Determine when two mathematical expressions or quantities are different (unequal). Compare and classify objects or data sets based on shared and distinct attributes. Apply comparison symbols ($=$, $ eq$, $<$, $>$) correctly to represent relationships between quantities. Analyze and explain why two ratios or percentages are either the same or different. Solve problems involving the comparison of numerical values, algebraic expressions, and geometric properties. Have you ever wondered how we decide if two things are exactly alike or completely distinct? 🤔 In math, understanding 'same' and 'different' is fundamental! This lesson will teach you how to ma...

TermDefinitionExample EqualityWhen two mathematical expressions or quantities have exactly the same value.$5 + 3$ and $8$ are equal because both simplify to $8$. InequalityWhen two mathematical expressions or quantities do not have the same value.$10 - 2$ and $7$ are unequal because $8 eq 7$. AttributesSpecific characteristics or properties used to describe and compare objects, numbers, or data.The attributes of a square include having four equal sides and four right angles. ComparisonThe process of examining two or more items to identify their similarities and differences.Comparing the heights of two students to see who is taller or if they are the same height. ClassificationGrouping items together based on shared attributes or separating them based on distinct attributes.Classifying nu...

Rule of Equality $A = B$ if and only if $A$ and $B$ represent the exact same numerical value or mathematical entity. Use the equals sign ($=$) to state that two quantities or expressions are identical in value. This is fundamental for solving equations and verifying statements. Rule of Inequality $A \neq B$ if $A$ and $B$ do not represent the same numerical value. Further, $A < B$ means $A$ is less than $B$, and $A > B$ means $A$ is greater than $B$. Use the not-equals sign ($\neq$) when values are different. Use less than ($<$) or greater than ($>$) to specify the relationship when values are different. Rule for Comparing Ratios/Fractions To compare two ratios $\frac{a}{b}$ and $\frac{c}{d}$, convert them to a common denominator or cross-multiply. If $ad =...