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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
Expressions and Equations Explained

Expressions and Equations Explained

Key Concepts

Expressions and equations are fundamental in algebra. An expression is a combination of numbers, variables, and operators, while an equation sets two expressions equal to each other.

1. Expressions

An expression is a mathematical phrase that can include numbers, variables, and operations such as addition, subtraction, multiplication, and division. For example, \(3x + 5\) is an expression.

2. Equations

An equation is a statement that two expressions are equal. It contains an equals sign (\(=\)). For example, \(2x + 3 = 7\) is an equation.

Detailed Explanation

Expressions

Expressions can be simple or complex. They do not have an equals sign and cannot be solved for a single value. Instead, they can be evaluated for given values of the variables. For example, if \(x = 2\), then \(3x + 5 = 3(2) + 5 = 11\).

Equations

Equations, on the other hand, have an equals sign and can be solved to find the value of the variable that makes the equation true. For example, in the equation \(2x + 3 = 7\), solving for \(x\) gives \(x = 2\).

Examples and Analogies

Example 1: Expressions

Example: Evaluate the expression \(4y - 2\) when \(y = 3\).

Solution: Substitute \(y = 3\) into the expression: \(4(3) - 2 = 12 - 2 = 10\).

Explanation: The expression \(4y - 2\) is evaluated by substituting the given value of \(y\).

Example 2: Equations

Example: Solve the equation \(5x - 4 = 16\).

Solution: Add 4 to both sides: \(5x - 4 + 4 = 16 + 4\), which simplifies to \(5x = 20\). Divide both sides by 5: \(x = 4\).

Explanation: The equation is solved step-by-step to isolate the variable \(x\).

Analogy: Balancing Scales

Think of an equation as a balanced scale. Both sides of the equation represent the same weight. To solve the equation, you need to keep the scale balanced while isolating the variable, just like removing weights from both sides of a scale to find the unknown weight.

Practical Application

Understanding expressions and equations is crucial in various real-world scenarios:

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