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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
Calculating Simple Probabilities

Calculating Simple Probabilities

Key Concepts

1. **Probability**: The likelihood of an event occurring, expressed as a number between 0 and 1.

2. **Sample Space**: The set of all possible outcomes of an experiment.

3. **Favorable Outcomes**: The outcomes that meet a specified condition.

4. **Formula**: The probability of an event \( P(E) \) is given by \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \).

Detailed Explanation

Probability

Probability is a measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means the event will definitely occur. For example, the probability of rolling a 6 on a standard die is 1/6.

Sample Space

The sample space is the set of all possible outcomes of an experiment. For example, when rolling a die, the sample space is {1, 2, 3, 4, 5, 6}.

Favorable Outcomes

Favorable outcomes are the outcomes that meet a specified condition. For example, if the condition is rolling an even number on a die, the favorable outcomes are {2, 4, 6}.

Formula

The probability of an event \( P(E) \) is calculated using the formula:

\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]

Examples

Example 1: Calculate the probability of drawing a red card from a standard deck of 52 cards.

Solution: There are 26 red cards in a deck of 52. The probability is:

\[ P(\text{Red card}) = \frac{26}{52} = \frac{1}{2} \]

Example 2: Calculate the probability of rolling a 3 or a 4 on a standard die.

Solution: The favorable outcomes are {3, 4}. The probability is:

\[ P(\text{3 or 4}) = \frac{2}{6} = \frac{1}{3} \]

Analogies

Think of probability as the chance of picking a specific color from a bag of marbles. The sample space is all the marbles in the bag, and the favorable outcomes are the marbles of the specific color you are looking for. The formula helps you calculate the exact chance of picking that color.

Practical Application

Understanding simple probabilities is essential in various fields such as statistics, economics, and science. It helps in making informed decisions, predicting outcomes, and analyzing data effectively.

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