Grade 3
  1. Number Sense and Numeration  1.1. Understanding Numbers  1.1.1. Reading and Writing Numbers up to 10,000  1.1.2. Place Value up to Thousands  1.1.3. Comparing and Ordering Numbers  1.1.4. Rounding Numbers to the Nearest Ten and Hundred  1.1.5. Skip Counting by 2s, 5s, 10s, and 100s up to 1,000  1.2. Operations with Whole Numbers  1.2.1. Addition and Subtraction up to 1,000  1.2.2. Multiplication Facts (up to 10 x 10)  1.2.3. Division Facts (up to 100)  1.2.4. Multiplication as Repeated Addition  1.2.5. Division as Equal Sharing  1.2.6. Word Problems with Addition, Subtraction, Multiplication, and Division  1.3. Estimation  1.3.1. Estimating Sums and Differences  1.3.2. Estimating Products and Quotients  1.4. Understanding Even and Odd Numbers
  2. Fractions and Decimals  2.1. Understanding Fractions  2.1.1. Identifying and Representing Fractions  2.1.2. Fractions of a Whole and Part of a Set  2.1.3. Comparing and Ordering Fractions with Like Denominators  2.1.4. Equivalent Fractions  2.1.5. Simple Fraction Word Problems  2.2. Introduction to Decimals  2.2.1. Tenths and Hundredths as Decimals  2.2.2. Relationship between Fractions and Decimals
  3. Measurement  3.1. Length  3.1.1. Measuring in Centimeters and Meters  3.1.2. Comparing and Ordering Lengths  3.1.3. Estimating Lengths  3.1.4. Converting Between Centimeters and Meters  3.2. Mass  3.2.1. Measuring in Grams and Kilograms  3.2.2. Estimating and Comparing Mass  3.3. Capacity  3.3.1. Measuring in Milliliters and Liters  3.3.2. Estimating and Comparing Capacity  3.4. Time  3.4.1. Telling Time to the Nearest Minute  3.4.2. Calculating Elapsed Time  3.4.3. Using a Calendar  3.4.4. Understanding A.M. and P.M.  3.5. Area and Perimeter  3.5.1. Calculating Perimeter of Simple Shapes  3.5.2. Estimating and Measuring Area of Shapes  3.5.3. Finding Area by Counting Squares
  4. Geometry  4.1. Properties of Shapes  4.1.1. Identifying 2D Shapes (Triangles, Quadrilaterals, Circles, etc.)  4.1.2. Identifying 3D Shapes (Cubes, Spheres, Cylinders, etc.)  4.1.3. Describing Attributes of 2D and 3D Shapes  4.1.4. Recognizing Parallel and Perpendicular Lines  4.2. Symmetry and Transformations  4.2.1. Recognizing Lines of Symmetry  4.2.2. Identifying Flips, Slides, and Turns  4.3. Angles  4.3.1. Understanding Right Angles  4.3.2. Comparing Angles (Acute, Right, Obtuse)
  5. Data Management and Probability  5.1. Data Collection and Organization  5.1.1. Collecting Data using Surveys and Experiments  5.1.2. Organizing Data using Tally Charts and Tables  5.2.1. Creating and Interpreting Pictographs  5.2.2. Creating and Interpreting Bar Graphs  5.2.3. Reading Simple Line Graphs  5.3. Probability  5.3.1. Understanding Basic Probability Terms (Certain, Possible, Impossible)  5.3.2. Predicting Outcomes  5.3.3. Simple Probability Experiments
  6. Patterns and Algebra  6.1. Patterns  6.1.1. Identifying and Extending Numeric Patterns  6.1.2. Identifying and Extending Shape Patterns  6.1.3. Creating Patterns Using Rules  6.2. Introduction to Algebra  6.2.1. Understanding Variables as Unknowns  6.2.2. Solving Simple Addition and Subtraction Equations  6.2.3. Using Patterns to Solve Problems
  7. Problem-Solving Skills  7.1. Strategies for Problem-Solving  7.1.1. Using Pictures or Diagrams  7.1.2. Identifying Patterns in Problems  7.1.3. Making Organized Lists  7.1.4. Guessing and Checking  7.1.5. Using Logical Reasoning  7.1.6. Breaking Down Problems into Steps

Grade 3 → Number Sense and Numeration → Understanding Numbers ↓


Comparing and Ordering Numbers


Understanding numbers is a fundamental part of learning math in grade 3. A key aspect is learning how to compare and order numbers. This skill helps us determine which numbers are bigger or smaller, and arrange them in order. It is an important step towards understanding mathematical operations, measurement, and data analysis. Let's dive deeper into the world of comparing and ordering numbers, exploring different methods and examples to fully understand this concept.

What does it mean to "compare numbers"?

Comparing numbers means looking at two or more numbers and deciding which is bigger, which is smaller, or whether they are equal. It's like looking at two apples and deciding which is bigger. In mathematical terms, we use symbols to make this comparison:

  • < means "less than"
  • > means "greater than"
  • = means "equals"

Examples of comparing numbers

Let's compare some numbers using these symbols. Consider two numbers 45 and 67.

45 < 67

The number 45 is smaller than 67 Therefore, we use the < sign. Let's try another example with 89 and 32.

89 > 32

Here, 89 is greater than 32, so we use > sign.

What about this: Compare 56 and 56.

56 = 56

Both numbers are equal, so we use = symbol.

Visual representation of comparing numbers

45 67 ,

In the visualization above, we have boxes for the numbers 45 and 67 The symbol < indicates that 45 is less than 67.

What does "serial numbering" mean?

Ordering numbers means arranging them in a sequence based on their value. Numbers can be arranged in increasing (also called ascending) order or decreasing (descending) order.

Increasing order

Arranging numbers from smallest to largest is called ascending order. For example, let's put the numbers 24, 76, 12 and 45 in ascending order.

12, 24, 45, 76

Here we start from the smallest number 12 and end with the largest number 76.

Decreasing order

Arranging numbers from largest to smallest is called decreasing order. Let us arrange the same numbers 24, 76, 12 and 45 in decreasing order.

76, 45, 24, 12

Here we start with the largest number 76 and end with the smallest number 12.

Visual representation of serial number

12 24 45 76

In this view, you can see how the numbers are arranged in ascending order from smallest to largest: 12, 24, 45, 76.

Practical steps for comparing and ordering numbers

A step-by-step guide to comparing numbers

  1. Look at the largest place value, usually starting from the left (e.g., hundreds, tens, then ones).
  2. If these digits are the same, go to the next smaller place value.
  3. Keep moving to the next local value until you find the difference.
  4. Based on these digits decide which number is bigger or smaller.

Example

Compare 458 and 436.

1. Compare the hundreds: Both have 4, so check the tens.
2. Compare tens: There are 5 in 458 and 3 in 436, so 458 is greater.
3. Conclusion: 458 > 436

A step-by-step guide to ordering numbers

  1. Identify the greatest place value for each number.
  2. Start arranging from smallest or largest number as per the desired order (ascending or descending).
  3. If two numbers have the same greatest place value, then compare the next place value to arrange them.
  4. Repeat the steps for all included numbers.

Example

Arrange the numbers 524, 389, 481, 294 in ascending order.

1. The smallest number is 294.
2. The next number is 389.
3. After this comes 481.
4. Finally, 524.
Result: 294, 389, 481, 524

Advanced concepts

As you become more confident comparing and ordering numbers, you can explore additional concepts such as:

  • Decimals: Compare and order numbers with decimal points, following the same principles as place value but extending to decimals, hundredths, and so on.
  • Negative Numbers: Understanding how to compare and order numbers below zero, where values farther from zero are considered smaller.

Conclusion

Becoming proficient at comparing and ordering numbers strengthens a student's arithmetic skills, which are important for everyday mathematical tasks and are foundational for further mathematical study.

Let's continue practicing these skills with many more examples. Remember, with practice and repetition you will become more comfortable comparing and ordering any numbers.


Grade 3 → 1.1.3


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Rounding Numbers to the Nearest Ten and Hundred

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Comparing and Ordering Numbers

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