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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
Angles Explained

Angles Explained

Key Concepts

1. **Definition of an Angle**: An angle is formed by two rays that share a common endpoint called the vertex.

2. **Types of Angles**: Angles can be classified into different types based on their measure: acute, right, obtuse, and straight.

3. **Measuring Angles**: Angles are measured in degrees, denoted by the symbol °. A full circle is 360°.

4. **Complementary and Supplementary Angles**: Complementary angles add up to 90°, and supplementary angles add up to 180°.

5. **Adjacent and Vertical Angles**: Adjacent angles share a common vertex and one side, while vertical angles are formed by the intersection of two lines and are equal in measure.

Detailed Explanation

Definition of an Angle

An angle is formed when two rays (or lines) meet at a common endpoint called the vertex. The two rays are called the sides of the angle.

Types of Angles

Angles can be classified into four main types:

Measuring Angles

Angles are measured using a protractor. The protractor is a semi-circular tool with degree markings from 0° to 180°. To measure an angle, place the center of the protractor on the vertex of the angle and align the baseline with one of the sides of the angle.

Complementary and Supplementary Angles

Complementary angles are two angles that add up to 90°. For example, a 30° angle and a 60° angle are complementary because 30° + 60° = 90°.

Supplementary angles are two angles that add up to 180°. For example, a 120° angle and a 60° angle are supplementary because 120° + 60° = 180°.

Adjacent and Vertical Angles

Adjacent angles share a common vertex and one side. They are next to each other and do not overlap.

Vertical angles are formed when two lines intersect. They are opposite each other and are equal in measure. For example, if two lines intersect and form a 45° angle, the angle opposite it will also be 45°.

Examples and Analogies

Think of an angle as a slice of a pizza. Each slice represents a different type of angle. A small slice would be an acute angle, a slice that is exactly half of the pizza would be a right angle, a larger slice would be an obtuse angle, and a slice that is a straight line across the pizza would be a straight angle.

Practical Application

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

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