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


Number sense and arithmetic is a fundamental part of mathematics that helps us understand the meaning of numbers and their relationship to one another. In Class 3, students are introduced to various aspects of number sense, including understanding place value, comparing numbers, recognizing patterns, and performing basic arithmetic operations. This explanation will explore these concepts in depth and use visual examples to illustrate the ideas.

Understanding place value

Place value is the basis of our number system and it helps us understand the value of each digit in a number. In our base-10 number system, each place represents a power of ten. Let's take a look at the number 345:

  Hundreds (10^2) Tens (10^1) Ones (10^0)
        3 4 5

In this number, the digit '3' is in the hundreds place, that is, it represents 3 hundreds or 300. '4' is in the tens place, which represents 40, and '5' is in the units place, which represents 5. Together, these two make the number three hundred and forty-five.

3 4 5 Hundreds Tens people

Understanding place value helps students understand the size of numbers and perform arithmetic operations such as addition and subtraction.

Comparing and ordering numbers

Comparing numbers involves determining which of two numbers is larger, which is smaller, or whether they are equal. By using the greater than, less than, and equal symbols, students can compare numbers effectively. Here are some examples:

  •  45 < 50
    (45 is less than 50)
  •  78 > 66
    (78 is greater than 66)
  •  32 = 32
    (32 = 32)

To order numbers it is necessary to arrange them either from smallest to largest (ascending order) or from largest to smallest (descending order). For example, the numbers 12, 7 and 20 are given:

  • ascending order:
     7, 12, 20
  • descending order:
     20, 12, 7

Recognizing patterns

Recognizing patterns is an important skill in math because it helps students predict future events and understand the world around them. Patterns can be found in numbers, shapes, and objects. Let's explore a simple number pattern:

Consider the sequence: 2, 4, 6, 8, ...

  • Rule: Add 2 to the previous number.
  • Next points:
     10, 12, 14, ...

In this pattern, each number increases by 2. Recognizing this pattern helps determine subsequent positions, which is an essential part of building problem-solving skills.

Basic arithmetic operations

In Class 3, students strengthen their understanding of the basic arithmetic operations: addition, subtraction, multiplication, and division. Let's understand each with examples.

Add

Addition is the process of combining two or more numbers to find the total or sum. For example:

  47
+ 35
,
  82

To add 47 and 35, start by adding the ones place (7 + 5 = 12), write down the 2, and carry forward the 1. Then add the tens place (4 + 3 = 7) and add the carried forward 1, giving a total of 8 tens.

Subtraction

Subtraction is the process of finding the difference between numbers. Here's an example:

  62
- 29
,
  33

To subtract 29 from 62, start by subtracting the ones place (2 - 9 is not possible, so take 1 from the tens place). Thus, 12 - 9 = 3, and then in the tens place, 5 - 2 = 3.

Multiplication

Multiplication is the process of combining equal groups to find the total number. Consider:

  4 x 3 = 12

This means that 4 groups of 3 make 12. Multiplication is also repeated addition (4 + 4 + 4 = 12).

Division

Division is dividing a number into equal parts. Suppose we divide 12 apples among 4 friends:

  12 ÷ 4 = 3

Each friend gets 3 apples. Division is the inverse of multiplication.

Different

Fractions introduce the concept of parts of a whole. The numerator tells us how many parts we have, and the denominator tells us how many equal parts the whole has.

Consider a pizza cut into four equal pieces:

  1/4

If one piece is eaten then 3 pieces, or

 3/4
There is half of the pizza left.

1/4

Conclusion

Number sense and arithmetic allow students to understand and work with numbers in a meaningful way. From place value to arithmetic operations, recognizing patterns, and exploring fractions, these skills are crucial for developing mathematical literacy and problem-solving abilities. As students continue to explore these concepts, they build a strong foundation for more advanced mathematical learning.


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Number Sense and Numeration

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