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 → Operations with Whole Numbers ↓


Multiplication Facts (up to 10 x 10)


Understanding multiplication

Multiplication is one of the basic operations in mathematics. In simple terms, multiplication is a way of adding the same number over and over again. For example, if you have 3 groups of 4 apples, you can find out how many apples there are in total by multiplying 3 by 4.

When we multiply, we use the symbol * or sometimes just x. For example, 3 * 4 or 3 x 4 both mean 3 times 4.

Multiplication table

A multiplication table is a chart that shows the results of multiplying numbers from 1 to 10 by each other. It provides a quick reference that makes solving multiplication problems easier.

Part of the multiplication table looks like this:

* | 1  2  3  4  5  6  7  8  9  10
1 | 1  2  3  4  5  6  7  8  9  10
2 | 2  4  6  8  10 12 14 16 18 20
3 | 3  6  9  12 15 18 21 24 27 30
4 | 4  8  12 16 20 24 28 32 36 40
5 | 5  10 15 20 25 30 35 40 45 50
6 | 6  12 18 24 30 36 42 48 54 60
7 | 7  14 21 28 35 42 49 56 63 70
8 | 8  16 24 32 40 48 56 64 72 80
9 | 9  18 27 36 45 54 63 72 81 90
10| 10 20 30 40 50 60 70 80 90 100

Visualizing multiplication with rows and columns

One way to understand multiplication is to use an array. An array is a group of objects arranged in rows and columns. Each row contains the same number of objects, just as each column contains the same number of objects.

For example, let's imagine 3 x 4:

In the SVG above, the blue squares represent 3 rows of 4, which represents 3 groups of 4 in 3 x 4. The green squares represent an additional fourth column, making a total of 4 columns. In total, there are 12 squares, which is the product of 3 x 4. This is a simple way to see how multiplication works.

Text example

Now, let us discuss some textual examples of multiplication to understand it better:

  • Example 1: 5 x 6 means 5 groups of 6. If you have 5 bags, each containing 6 apples, you will have a total of 5 x 6 = 30 apples.
  • Example 2: 2 x 8 means 2 groups of 8. If you have 2 baskets and each basket has 8 oranges, in total you will have 2 x 8 = 16 oranges.
  • Example 3: 7 x 9 means 7 groups of 9. If you read 9 pages of a book every day for 7 days a week, you would have read 7 x 9 = 63 pages in a week.

Properties of multiplication

Exchangeable assets

The commutative property of multiplication says that changing the order of the numbers does not change the result. For example, 4 x 5 and 5 x 4 are equal. Both equal 20.

Associative property

According to the associative property of multiplication, when three or more numbers are multiplied, the way the numbers are grouped has no effect on the product. For example, (2 x 3) x 4 is the same as 2 x (3 x 4). In both cases, the result is 24.

Identity property

According to the identity property of multiplication, any number remains the same when multiplied by 1. For example, 9 x 1 = 9 and 1 x 9 = 9.

Zero assets

According to the zero property of multiplication, any number multiplied by 0 gives 0. For example, 8 x 0 = 0 and 0 x 8 = 0.

Practicing multiplication

Practice is key to mastering multiplication facts. Here are some strategies to help you practice multiplication:

  • Flash cards: Use flash cards with multiplication problems on one side and the answers on the other to test yourself.
  • Games: Play multiplication games like bingo or memory cards to make the process fun.
  • Worksheets: Complete worksheets with various multiplication problems.
  • Real-life applications: Look for everyday situations in which to apply multiplication, such as calculating total cost or quantity.
  • Repetition: Repeating the multiplication tables over and over, even for a few minutes a day, can help improve memory.

Conclusion

Understanding multiplication is very important in math. It relates to many real-world situations like shopping, cooking, and much more. Mastering the multiplication facts, especially 1 to 10, will form a strong foundation for more complex math concepts you will learn in the future.

In short, multiplication can be viewed as a way of repeated addition or grouping. Practice using tables, visual arrays, and real-life examples to strengthen your understanding. Remember, the fundamental properties of multiplication make it easier to work efficiently with numbers, and with consistent practice, you will become more confident with these math facts.

Develop a strong understanding and practice regularly to master the multiplication facts.


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Division Facts (up to 100)

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Multiplication Facts (up to 10 x 10)

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