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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
Operations with Fractions

Operations with Fractions

Key Concepts

Operations with fractions involve adding, subtracting, multiplying, and dividing fractions. Each operation requires a different approach to ensure the fractions are in the correct form and the result is simplified.

Adding and Subtracting Fractions

To add or subtract fractions, they must have the same denominator. If the denominators are different, find a common denominator by finding the Least Common Multiple (LCM) of the denominators.

Example: Add 1/4 and 1/3.

Step 1: Find the LCM of 4 and 3, which is 12.

Step 2: Convert each fraction to have the denominator 12: 1/4 = 3/12 and 1/3 = 4/12.

Step 3: Add the fractions: 3/12 + 4/12 = 7/12.

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together. Simplify the result if possible.

Example: Multiply 2/3 by 3/5.

Step 1: Multiply the numerators: 2 × 3 = 6.

Step 2: Multiply the denominators: 3 × 5 = 15.

Step 3: The result is 6/15, which simplifies to 2/5.

Dividing Fractions

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal is found by switching the numerator and the denominator of the second fraction.

Example: Divide 2/3 by 4/5.

Step 1: Find the reciprocal of 4/5, which is 5/4.

Step 2: Multiply 2/3 by 5/4: (2 × 5) / (3 × 4) = 10/12.

Step 3: Simplify the result: 10/12 = 5/6.

Examples and Analogies

Think of adding fractions as combining slices of pizza. If you have 1/4 of a pizza and add 1/3 of a pizza, you need to cut both pizzas into the same number of slices (common denominator) to combine them.

Multiplying fractions can be thought of as finding a part of a part. For example, if you have 2/3 of a cake and you want to give away 3/5 of that portion, you are finding 3/5 of 2/3.

Dividing fractions is like sharing a part of a whole. If you have 2/3 of a pizza and you want to divide it equally among 4/5 of your friends, you are dividing 2/3 by 4/5.

Practical Application

Understanding how to perform operations with 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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