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Math for Grade 7
1 Number Sense and Operations
1-1 Integers
1-1 1 Understanding positive and negative numbers
1-1 2 Comparing and ordering integers
1-1 3 Absolute value
1-1 4 Adding and subtracting integers
1-1 5 Multiplying and dividing integers
1-2 Rational Numbers
1-2 1 Understanding fractions, decimals, and mixed numbers
1-2 2 Comparing and ordering rational numbers
1-2 3 Converting between fractions, decimals, and percents
1-2 4 Adding and subtracting fractions and mixed numbers
1-2 5 Multiplying and dividing fractions and mixed numbers
1-3 Exponents and Roots
1-3 1 Understanding exponents
1-3 2 Laws of exponents
1-3 3 Square roots and cube roots
2 Algebra
2-1 Expressions and Equations
2-1 1 Writing algebraic expressions
2-1 2 Evaluating algebraic expressions
2-1 3 Solving one-step and two-step equations
2-1 4 Solving inequalities
2-2 Patterns and Functions
2-2 1 Identifying and extending patterns
2-2 2 Representing patterns with tables, graphs, and equations
2-2 3 Understanding functions and function notation
3 Geometry
3-1 Shapes and Angles
3-1 1 Classifying polygons
3-1 2 Measuring and drawing angles
3-1 3 Understanding complementary and supplementary angles
3-2 Transformations
3-2 1 Understanding translations, reflections, and rotations
3-2 2 Identifying congruent and similar figures
3-3 Perimeter, Area, and Volume
3-3 1 Calculating perimeter and area of polygons
3-3 2 Understanding and calculating the area of circles
3-3 3 Calculating the volume of rectangular prisms
4 Data and Probability
4-1 Data Representation
4-1 1 Collecting and organizing data
4-1 2 Creating and interpreting bar graphs, line graphs, and pie charts
4-1 3 Understanding mean, median, mode, and range
4-2 Probability
4-2 1 Understanding probability as a ratio
4-2 2 Calculating simple probabilities
4-2 3 Understanding experimental versus theoretical probability
5 Problem Solving and Critical Thinking
5-1 Strategies for Problem Solving
5-1 1 Using logical reasoning and critical thinking
5-1 2 Applying the problem-solving process
5-1 3 Using estimation and approximation
5-2 Real-World Applications
5-2 1 Applying mathematical concepts to real-world scenarios
5-2 2 Understanding the relevance of mathematics in daily life
Evaluating Algebraic Expressions

Evaluating Algebraic Expressions

Key Concepts

1. **Algebraic Expression**: A mathematical phrase that includes variables, constants, and operations (like addition, subtraction, multiplication, and division).

2. **Substitution**: Replacing variables in an algebraic expression with specific values.

3. **Simplification**: Performing the operations in the expression to find the value.

Detailed Explanation

Algebraic Expression

An algebraic expression is a combination of numbers, variables, and operations. For example, \(3x + 5\) is an algebraic expression where \(x\) is a variable, 3 and 5 are constants, and the operations are multiplication and addition.

Substitution

Substitution involves replacing the variables in an algebraic expression with specific values. For example, if \(x = 2\) in the expression \(3x + 5\), you replace \(x\) with 2: \(3(2) + 5\).

Simplification

Simplification involves performing the operations in the expression after substitution. For example, after substituting \(x = 2\) in \(3x + 5\), you get \(3(2) + 5 = 6 + 5 = 11\).

Examples

Example 1: Evaluate \(4y - 7\) when \(y = 3\).

Solution: Substitute \(y = 3\): \(4(3) - 7 = 12 - 7 = 5\).

Explanation: Replace \(y\) with 3, then perform the multiplication and subtraction.

Example 2: Evaluate \(2a^2 + 3a - 1\) when \(a = 4\).

Solution: Substitute \(a = 4\): \(2(4^2) + 3(4) - 1 = 2(16) + 12 - 1 = 32 + 12 - 1 = 43\).

Explanation: Replace \(a\) with 4, then perform the exponentiation, multiplication, and addition/subtraction.

Analogies

Think of evaluating algebraic expressions as following a recipe. The variables are like ingredients, and the operations are like the steps to cook the dish. Substitution is like adding the exact amount of each ingredient, and simplification is like following the steps to complete the dish.

Practical Application

Understanding how to evaluate algebraic expressions is crucial in various fields such as science, engineering, and finance. It helps in solving real-world problems by translating them into mathematical expressions and finding their values.

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