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 ↓


Place Value up to Thousands


Understanding the concept of place value is crucial for elementary school students in developing strong foundational skills in math. Place value allows us to understand the numerical value of digits based on their position in a number. In grade 3 math, students are introduced to numbers up to the thousands, allowing them to work fluently and accurately with larger numbers.

What is local value?

Place value refers to the value of a digit in a number, determined by the digit's location within the number. Each digit has a different place value depending on its position. For example, in the number 5432, the digit 5 is in the thousands place, the digit 4 is in the hundreds place, the digit 3 is in the tens place, and the digit 2 is in the units place.

Visual representation of place value

thousands Hundreds Tens people 5 4 3 2

The above image shows the number 5432 broken down into its place values.

Division of number 5432 by place value

Let's break down the number 5432 by place value. Each digit of the number can be expanded to show how it contributes to the overall value:

5432 = 5000 + 400 + 30 + 2

Thousand: 5 → 5 × 1000 = 5000
Hundreds: 4 → 4 × 100 = 400
Tens: 3 → 3 × 10 = 30
Unit: 2 → 2 × 1 = 2

Each digit is multiplied by its place value, as shown. The sum of these values gives the original number.

Explore each place value

Thousands of places

In the thousands place, each digit represents a value multiplied by 1000. For example, if a number has a 6 in the thousands place, this means 6 × 1000 = 6000. This place allows us to work with numbers as large as 9999, which is the largest four-digit number before moving on to five digits.

Example: Consider the number 7468.

The digit 7 is in the thousandths place.

7 × 1000 = 7000

Thus, 7 contributes 7000 to the number.

The hundredth place

Each digit in the hundreds place represents a value multiplied by 100. For example, the digit in the hundreds place is 5, 5 × 100 = 500.

Example: Consider the number 8462.

The digit 4 is in the hundreds place.

4 × 100 = 400

Thus, 4 adds an extra 400 to the number.

The tens place

The digit in the tens place is multiplied by 10. For example, 2 in the tens place = 2 × 10 = 20. This helps to understand how numbers 'go up' to the tens as they move upwards.

Example: In the number 3264.

6 is in the tens place.

6 × 10 = 60

This means that 6 contributes 60 to the total number.

The ones place

The units place is the most straightforward, where the digit represents itself (the value of 1 is 1). Here a digit represents how many single units the number contains.

Example: Consider the number 1395.

5 is in the units place.

5 × 1 = 5

This shows that 5 represents 5 single units.

Comparing numbers using place value

Understanding place value helps us compare numbers effectively. We can determine which number is bigger or smaller by first looking at the digit with the highest place value.

Example: Compare 4823 and 4978.

Thousands: 4823 has 4, 4978 also has 4 (equal, see next place)
Hundreds: 8 in 4823, 9 in 4978 (4978 is bigger, close comparison)

Since 9 in hundreds place is greater than 8, hence 4978 is greater than 4823.

Writing numbers in expanded form

Writing numbers in their expanded form is another great application of place value. It involves breaking down a number into the place value contribution of each digit.

Example: Write 3056 in expanded form.

3000 + 0 + 50 + 6 = 3056

This shows the place value contribution of each digit.

Place value through addition and subtraction

When adding or subtracting, the concept of place value helps ensure that digits are grouped correctly. Align numbers to their last digit to properly manage place values in addition/subtraction.

Example: Add 2345 and 789.

   2345
+789

First add the smallest place (units), then add tens, hundreds and thousands.

Challenges in understanding place value

Common misconceptions regarding place value include misalignment of digits during calculations and difficulty understanding the value of each place.

Correction of misinterpretations

  • Make sure that numerical figures are aligned under their respective headings.
  • Use physical tools for a tangible learning experience.
  • Practice 'breaking down' the numbers regularly.

Conclusion

Understanding place value up to thousands is a transformational skill in numeracy, helping students understand the magnitude and construction of numbers. Through visualisation, decomposition and practical exercises, students can gain confidence and proficiency in handling numbers at this level. This foundational concept prepares young learners for more advanced mathematical challenges as they progress in their education.


Grade 3 → 1.1.2


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Reading and Writing Numbers up to 10,000
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Place Value up to Thousands

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