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Math for Grade 5
1 Number Sense
1-1 Place Value
1-1 1 Understanding place value up to millions
1-1 2 Reading and writing numbers in standard and expanded form
1-1 3 Comparing and ordering numbers
1-2 Rounding
1-2 1 Rounding numbers to the nearest 10, 100, and 1000
1-2 2 Estimating sums and differences
1-3 Number Patterns
1-3 1 Identifying and extending number patterns
1-3 2 Using patterns to solve problems
2 Operations
2-1 Addition and Subtraction
2-1 1 Adding and subtracting multi-digit numbers
2-1 2 Solving word problems involving addition and subtraction
2-2 Multiplication
2-2 1 Multiplication facts up to 12x12
2-2 2 Multiplying multi-digit numbers by one-digit numbers
2-2 3 Multiplying multi-digit numbers by two-digit numbers
2-2 4 Solving word problems involving multiplication
2-3 Division
2-3 1 Division facts up to 12x12
2-3 2 Dividing multi-digit numbers by one-digit numbers
2-3 3 Dividing multi-digit numbers by two-digit numbers
2-3 4 Solving word problems involving division
2-4 Order of Operations
2-4 1 Understanding and applying the order of operations (PEMDAS)
2-4 2 Solving problems with multiple operations
3 Fractions
3-1 Understanding Fractions
3-1 1 Identifying parts of a whole and parts of a set
3-1 2 Equivalent fractions
3-1 3 Comparing and ordering fractions
3-2 Operations with Fractions
3-2 1 Adding and subtracting fractions with like denominators
3-2 2 Adding and subtracting fractions with unlike denominators
3-2 3 Multiplying fractions by whole numbers
3-2 4 Solving word problems involving fractions
4 Decimals
4-1 Understanding Decimals
4-1 1 Reading and writing decimals
4-1 2 Comparing and ordering decimals
4-1 3 Converting between fractions and decimals
4-2 Operations with Decimals
4-2 1 Adding and subtracting decimals
4-2 2 Multiplying decimals
4-2 3 Dividing decimals
4-2 4 Solving word problems involving decimals
5 Measurement
5-1 Units of Measurement
5-1 1 Understanding customary and metric units of length, weight, and capacity
5-1 2 Converting between units of measurement
5-2 Time
5-2 1 Telling time to the minute
5-2 2 Calculating elapsed time
5-2 3 Solving word problems involving time
5-3 Area and Perimeter
5-3 1 Finding the area and perimeter of rectangles and squares
5-3 2 Solving word problems involving area and perimeter
6 Geometry
6-1 Shapes
6-1 1 Identifying and classifying 2D shapes (triangles, quadrilaterals, etc )
6-1 2 Identifying and classifying 3D shapes (cubes, pyramids, etc )
6-2 Angles
6-2 1 Identifying and measuring angles
6-2 2 Classifying angles as acute, obtuse, right, or straight
6-3 Symmetry
6-3 1 Identifying lines of symmetry
6-3 2 Creating symmetrical shapes
7 Data and Probability
7-1 Data Representation
7-1 1 Reading and interpreting bar graphs, line graphs, and pie charts
7-1 2 Creating graphs to represent data
7-2 Probability
7-2 1 Understanding probability as a measure of likelihood
7-2 2 Predicting outcomes based on probability
7-2 3 Solving simple probability problems
Probability Explained

Probability Explained

Key Concepts

1. **Probability**: The likelihood or chance of an event occurring.

2. **Sample Space**: The set of all possible outcomes in a probability experiment.

3. **Event**: A specific outcome or set of outcomes in a probability experiment.

4. **Probability Formula**: The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

5. **Types of Probability**: Theoretical probability and experimental probability.

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 is certain to occur.

Sample Space

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

Event

An event is a specific outcome or set of outcomes in a probability experiment. For example, in rolling a die, the event "rolling an even number" includes the outcomes {2, 4, 6}.

Probability Formula

The probability of an event is calculated using the formula:

Probability (Event) = Number of favorable outcomes / Total number of possible outcomes

Types of Probability

**Theoretical Probability**: The probability calculated based on the possible outcomes and their likelihood. For example, the theoretical probability of rolling a 3 on a die is 1/6.

**Experimental Probability**: The probability calculated based on the results of an experiment. For example, if you roll a die 10 times and get a 3 three times, the experimental probability is 3/10.

Examples and Analogies

Example 1: Rolling a Die

When rolling a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. The probability of rolling a 3 is 1/6 because there is only one favorable outcome (3) out of six possible outcomes.

Example 2: Drawing a Card

When drawing a card from a standard deck of 52 cards, the sample space includes all 52 cards. The probability of drawing an ace is 4/52 (or 1/13) because there are 4 aces out of 52 cards.

Practical Application

Understanding probability is essential for various real-life tasks such as:

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