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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
4 Decimals Explained

4 Decimals Explained

Decimals are an essential part of mathematics, representing numbers that are not whole. Understanding decimals is crucial for performing accurate calculations and solving real-life problems. This webpage will explain the key concepts related to decimals and provide examples to help you master them.

Key Concepts

1. **Understanding Decimals**: Decimals represent parts of a whole number, similar to fractions. They are written with a decimal point, separating the whole number from the fractional part.

2. **Place Value in Decimals**: Each digit in a decimal number has a specific place value, which determines its value in the number.

3. **Comparing Decimals**: To compare decimals, you need to look at the digits in each place value starting from the left.

4. **Rounding Decimals**: Rounding decimals involves approximating a decimal number to a specified number of decimal places.

Detailed Explanation

Understanding Decimals

A decimal number is a number that includes a decimal point. The part to the left of the decimal point is the whole number, and the part to the right is the fractional part. For example, in the number 3.75, 3 is the whole number and 0.75 is the fractional part.

Example: Decimal Representation

The number 4.25 represents 4 whole units and 25 hundredths of a unit.

Place Value in Decimals

Each digit in a decimal number has a specific place value. Starting from the decimal point, the place values are tenths, hundredths, thousandths, and so on. For example, in the number 12.345, the digit 3 is in the tenths place, 4 is in the hundredths place, and 5 is in the thousandths place.

Example: Place Value

In the number 7.89, 7 is in the ones place, 8 is in the tenths place, and 9 is in the hundredths place.

Comparing Decimals

To compare decimals, start by comparing the digits in the highest place value. If they are the same, move to the next place value to the right. For example, to compare 0.34 and 0.36, start with the tenths place (both are 3), then move to the hundredths place (4 is less than 6), so 0.34 is less than 0.36.

Example: Comparing Decimals

Compare 0.123 and 0.124.

Step 1: Compare tenths place (both are 1).

Step 2: Compare hundredths place (both are 2).

Step 3: Compare thousandths place (3 is less than 4).

Conclusion: 0.123 is less than 0.124.

Rounding Decimals

Rounding decimals involves approximating a decimal number to a specified number of decimal places. To round a decimal, look at the digit in the place value immediately to the right of the place you are rounding to. If it is 5 or more, round up; if it is less than 5, round down. For example, rounding 4.789 to two decimal places results in 4.79.

Example: Rounding Decimals

Round 3.14159 to three decimal places.

Step 1: Look at the fourth decimal place (5).

Step 2: Since 5 is 5 or more, round up the third decimal place (1 becomes 2).

Conclusion: 3.14159 rounded to three decimal places is 3.142.

Examples and Analogies

**Example 1**: Think of decimals as money. For instance, $3.75 represents 3 dollars and 75 cents. The decimal point separates the dollars from the cents.

**Example 2**: Comparing decimals can be likened to comparing heights. If two people are 1.5 meters and 1.55 meters tall, you compare the centimeters (hundredths place) to determine who is taller.

By mastering the concepts of decimals, you will be better equipped to handle more complex mathematical problems and real-life situations involving precise measurements and calculations.

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