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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 Decimals

Operations with Decimals

Key Concepts

Operations with decimals involve adding, subtracting, multiplying, and dividing decimal numbers. Each operation requires a specific approach to ensure accuracy and understanding.

Adding Decimals

To add decimals, align the decimal points of the numbers you are adding. Add the numbers as you would with whole numbers, and place the decimal point in the result directly below the decimal points in the original numbers.

Example: Add 2.34 and 1.57.

Step 1: Align the decimal points: 2.34 + 1.57.

Step 2: Add the numbers: 2.34 + 1.57 = 3.91.

Result: 2.34 + 1.57 = 3.91.

Subtracting Decimals

To subtract decimals, align the decimal points of the numbers you are subtracting. Subtract the numbers as you would with whole numbers, and place the decimal point in the result directly below the decimal points in the original numbers.

Example: Subtract 4.68 from 7.25.

Step 1: Align the decimal points: 7.25 - 4.68.

Step 2: Subtract the numbers: 7.25 - 4.68 = 2.57.

Result: 7.25 - 4.68 = 2.57.

Multiplying Decimals

To multiply decimals, multiply the numbers as you would with whole numbers. Count the total number of decimal places in both numbers, and place the decimal point in the product so that the number of decimal places in the product matches the total number of decimal places in the factors.

Example: Multiply 2.3 by 1.4.

Step 1: Multiply the numbers as whole numbers: 23 × 14 = 322.

Step 2: Count the decimal places: 2.3 has 1 decimal place, and 1.4 has 1 decimal place, so the product will have 2 decimal places.

Step 3: Place the decimal point: 322 becomes 3.22.

Result: 2.3 × 1.4 = 3.22.

Dividing Decimals

To divide decimals, move the decimal point in the divisor to the right until it becomes a whole number. Move the decimal point in the dividend the same number of places to the right. Divide as you would with whole numbers, and place the decimal point in the quotient directly above the decimal point in the dividend.

Example: Divide 4.5 by 0.3.

Step 1: Move the decimal point in the divisor (0.3) to the right to make it a whole number: 0.3 becomes 3.

Step 2: Move the decimal point in the dividend (4.5) the same number of places to the right: 4.5 becomes 45.

Step 3: Divide 45 by 3: 45 ÷ 3 = 15.

Result: 4.5 ÷ 0.3 = 15.

Examples and Analogies

Think of adding and subtracting decimals as combining or separating parts of a whole. For example, if you have 2.34 meters of rope and add 1.57 meters, you are combining lengths of rope. Multiplying decimals can be thought of as scaling up or down. For instance, if you have 2.3 liters of juice and you want to double the amount, you are multiplying by 2. Dividing decimals is like sharing equally. If you have 4.5 kilograms of flour and you want to divide it equally among 0.3 kilograms per person, you are dividing the total amount by the amount each person gets.

Practical Application

Understanding how to perform operations with decimals is essential for everyday tasks such as shopping, where prices are often given in decimals, or in cooking, where measurements are frequently in decimals. These skills also help in understanding money, time, and other aspects of daily life where parts of a whole are involved.

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