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


When we begin to understand numbers, we begin an exciting journey into the world of mathematics. In Grade 3, children learn to understand numbers by using different ways to look at them, think about them, and use them in everyday life. This deeper understanding builds on concepts familiar from previous grades and helps students advance in their math skills.

What are the numbers?

Numbers are symbols we use to count, measure, and label things. They are one of the most basic concepts in math and play a vital role in how we understand the world. Here are some basic number concepts:

Big ideas in number sense

Place value

Place value is one of the key components of understanding numbers. It refers to the value of a digit's position in a number. This includes understanding that in the number 345, the digit 5 is in the "units" place, 4 is in the "tens" place, and 3 is in the "hundreds" place.

Hundreds | Tens | Ones
3        | 4    | 5
300 + 40 + 5 = 345 3 hundreds + 4 tens + 5 ones

Counting and cardinality

Counting is a basic skill that is closely related to the concept of cardinality, which means understanding that the last number in a count represents the total number of items in a group. For example, if you count five apples, you understand that the number 5 represents the total number of apples.

1 apple + 1 apple + 1 apple + 1 apple + 1 apple = 5 apples

Comparing numbers

Another important skill is the ability to compare numbers. This means being able to tell which number is bigger or smaller. We use symbols such as > (greater than), < (less than), and = (equals) to compare numbers.

14 > 9 (14 is greater than 9)
8 < 12 (8 is less than 12)
7 = 7 (7 is equal to 7)

Even and odd numbers

It's also important to understand the difference between even and odd numbers. Even numbers are those that can be divided evenly into pairs, such as 2, 4, 6, 8 and 10. Odd numbers cannot be divided evenly into pairs, such as 1, 3, 5, 7 and 9.

2 ÷ 2 = 1 (even)
4 ÷ 2 = 2 (even)
7 ÷ 2 = 3.5 (odd)
9 ÷ 2 = 4.5 (odd)
2, 4, 6, 8, 10 (even) 1, 3, 5, 7, 9 (odd)

The role of zero

Zero is a special number that has a unique role in mathematics. It is the starting point for counting and represents "nothing" or "none" of something.

5 - 5 = 0
Zero means nothing

Number lines

A number line is a visual representation of numbers on a straight line. The numbers are arranged in order from left to right, with smaller numbers on the left and larger numbers on the right. Number lines are helpful tools for understanding the concept of numbers and the relationships between numbers.

0 1 2 3 4 5 6 7 8

Operations with numbers

Add

Addition is the process of combining two or more numbers to find their sum. It is one of the four basic math operations. The symbol used for addition is +.

3 + 5 = 8

Subtraction

In subtraction, the difference is found by subtracting one number from another. The symbol used for subtraction is -.

9 - 4 = 5

Multiplication

Multiplication is the process of repeated addition. It involves finding the product of two numbers. The symbol used for multiplication is x or *.

4 x 3 = 12

Division

Division is the division of a number into equal parts. It involves finding how many times one number is contained in another number. The symbol used for division is / or ÷.

12 ÷ 3 = 4

Building number sense

Developing number sense is about developing an intuition for numbers. This includes recognizing numbers, understanding their relationships, and making logical connections between them. Here are some effective strategies for developing strong number sense:

  • Play games: Math games and activities can be a fun way to become familiar with numbers.
  • Ask questions: Encourage thinking about numbers by asking questions like "How many more do we need?" or "If we add one more, how many will we have?"
  • Use real-life scenarios: Incorporate numbers into everyday activities, like cooking or shopping, to give a practical understanding of numbers.
  • Practice: Regular practice with problems and exercises helps to consolidate learning.
  • Estimation: Encourage guessing to make quick and logical guesses about quantities and numerical values.

Putting everything together

Understanding numbers is a foundation for all math. In Grade 3, students refine their skills with numbers and begin to see how math applies to their everyday lives. By mastering concepts such as place value, operations, and number lines, students develop confidence in their math abilities, which paves the way for more advanced topics in later grades.

Practice, play, and real-world connections are vital to internalizing these concepts. Encouraging curiosity and genuine interest in numbers will empower students as they continue to explore the rich world of mathematics.


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Understanding Numbers

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