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Math for Grade 4
1 Number Sense and Operations
1-1 Place Value
1-1 1 Understanding place value through millions
1-1 2 Reading and writing numbers in standard, word, and expanded form
1-1 3 Comparing and ordering numbers
1-2 Rounding and Estimating
1-2 1 Rounding numbers to the nearest 10, 100, and 1000
1-2 2 Estimating sums, differences, products, and quotients
1-3 Addition and Subtraction
1-3 1 Adding and subtracting multi-digit numbers
1-3 2 Solving word problems involving addition and subtraction
1-4 Multiplication and Division
1-4 1 Multiplication tables up to 12
1-4 2 Multiplying multi-digit numbers by one-digit numbers
1-4 3 Dividing multi-digit numbers by one-digit numbers
1-4 4 Solving word problems involving multiplication and division
1-5 Factors and Multiples
1-5 1 Identifying factors and multiples of a number
1-5 2 Finding the greatest common factor (GCF)
1-5 3 Finding the least common multiple (LCM)
2 Fractions and Decimals
2-1 Understanding Fractions
2-1 1 Identifying and naming fractions
2-1 2 Comparing and ordering fractions with like and unlike denominators
2-1 3 Equivalent fractions
2-2 Operations with Fractions
2-2 1 Adding and subtracting fractions with like denominators
2-2 2 Solving word problems involving fractions
2-3 Understanding Decimals
2-3 1 Reading and writing decimals to the hundredths place
2-3 2 Comparing and ordering decimals
2-4 Operations with Decimals
2-4 1 Adding and subtracting decimals
2-4 2 Solving word problems involving decimals
3 Geometry and Measurement
3-1 Basic Shapes and Properties
3-1 1 Identifying and classifying 2D shapes (triangles, quadrilaterals, etc )
3-1 2 Identifying and classifying 3D shapes (cubes, pyramids, etc )
3-2 Perimeter and Area
3-2 1 Finding the perimeter of polygons
3-2 2 Finding the area of rectangles and squares
3-3 Lines and Angles
3-3 1 Identifying and measuring angles using a protractor
3-3 2 Classifying angles (acute, obtuse, right, straight)
3-4 Time and Measurement
3-4 1 Telling time to the nearest minute
3-4 2 Solving word problems involving time
3-4 3 Measuring length, weight, and capacity using standard units
4 Data Handling and Probability
4-1 Collecting and Organizing Data
4-1 1 Creating and interpreting bar graphs, line plots, and pictographs
4-1 2 Collecting and organizing data in tables
4-2 Analyzing Data
4-2 1 Finding the mode, median, and range of a set of data
4-2 2 Interpreting data from graphs and tables
4-3 Introduction to Probability
4-3 1 Understanding the concept of probability
4-3 2 Predicting outcomes based on data
5 Problem Solving and Critical Thinking
5-1 Strategies for Problem Solving
5-1 1 Using logical reasoning to solve problems
5-1 2 Applying the four operations to solve multi-step problems
5-2 Patterns and Relationships
5-2 1 Identifying and extending number patterns
5-2 2 Understanding and using simple algebraic expressions
5-3 Critical Thinking and Reasoning
5-3 1 Evaluating and justifying solutions to problems
5-3 2 Making connections between different mathematical concepts
Understanding Fractions

Understanding Fractions

Key Concepts

Fractions represent parts of a whole. They are written as a numerator (the top number) over a denominator (the bottom number). The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.

Types of Fractions

1. Proper Fractions: The numerator is less than the denominator. For example, 3/4.

2. Improper Fractions: The numerator is greater than or equal to the denominator. For example, 5/4.

3. Mixed Numbers: A whole number and a proper fraction combined. For example, 1-1/2.

Equivalent Fractions

Equivalent fractions are fractions that represent the same value. They can be created by multiplying or dividing both the numerator and the denominator by the same number. For example, 1/2 and 2/4 are equivalent fractions.

Examples

Example 1: Identify the type of fraction: 7/8.

Since the numerator (7) is less than the denominator (8), this is a proper fraction.

Example 2: Find an equivalent fraction for 3/5.

Multiply both the numerator and the denominator by 2: (3 × 2) / (5 × 2) = 6/10.

So, 6/10 is equivalent to 3/5.

Analogies to Make Concepts Clearer

Think of a fraction as a slice of pizza. If you have a whole pizza divided into 8 slices and you eat 3 slices, you have eaten 3/8 of the pizza. The denominator (8) tells you how many slices the pizza was cut into, and the numerator (3) tells you how many slices you ate.

Practical Application

Understanding fractions is essential for everyday tasks such as cooking, where recipes often use fractions to measure ingredients. It also helps in understanding money, time, and other aspects of daily life where parts of a whole are involved.

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