Multiplication Games for 3rd Graders

The development of basic math skills such as counting numbers up to tens, hundreds and thousands in takes place progressively in the preschool years. The analogous skills are the “place-value” system, number-sense, comparison and ordering with counting. With the ability to count numbers, math prowess continues to upskill with operations such as addition and subtraction (as skip counting on a line plot, backward and forward and using base-10 blocks).

The grade-3 math curriculum initiates the advanced math operations. These operations are multiplication and division. The two operations are referred as repeated addition and subtraction respectively. Next section reviews the basics of multiplication.

What is Multiplication?

The elementary math operation “multiplication” is similar to the addition of a certain number to itself and evaluating the aggregated sum as a multiple. The technique of multiplication is construed by the different methods of “addition”.

Akin to other math operations, a multiplication equation is framed using math symbols and numbers. These symbols or math operators are:

The elements of a multiplication equation are identified by the terms; multiplicand, multiplier, and product.

Some examples of a multiplication equation are as follows:

Math Games for 3rd Grade Multiplication

The math operation “multiplication” is the elementary skill to grasp advanced mathematics post learning addition and subtraction. The multiplication is used to comprehend the concepts of geometry such as area, “division” of numbers, number-sense for fractions as well as proficiently using the units of measurement for physical quantities.

The upcoming section illustrates the projected learning outcomes and prerequisites for understanding multiplication.

1. Learning & outcome: 

The iterative addition of objects based on random examples is the fundamental approach to introduce kids to multiplication. With the knowledge of multiplication and math symbols, kids learn to proficiently write multiplication tables, writing math-expressions for single-step problems and divide two numbers by framing an equation. 

The visual interaction of a multiplication problem using array models and area models are instrumental in grasping the procedure and the utility of “multiplication” operation.

The expected learning outcomes for multiplication in grade-3 are listed as follows:

2. Required Math Skills

The prerequisites for learning multiplication include firm counting skills in hundreds and more. With fluency in performing addition of numbers; visualizing the objects in equal size groups or sets as an array enables to comprehend the multiplication of two factors.

3. Engagement:

The interactive educational games for SplashLearn envision math learning as a playful routine. The inquisitively designed content for homeschooling nurtures the concept fundamentally to use in the later grades. Aligned to the common core math standards, the comprehensive word-problems and riddle worksheets stimulate the math reasoning in kids to excel in math. Also, the enthralling theme-based games are highly engaging and propel confidence to learn math.

Distinct models of Multiplication

The different models of multiplication are discussed as follows:

a. Array Model

The array model for multiplication visualizes the arrangement of objects in a uniform order. An array has an equal number of objects in each row. For example, the arrangement of chairs in a classroom or a tray containing eggs.

Using the visuals for the array, the elements of the multiplication sentence are identified. In the stated example, the elements are:

• Multiplicand = 5, Multiplier = 3 and product is evaluated using the following sentence:
• 5 x 3 = (5 + 5 + 5) = 15

  b. Area Model

The “area” model for multiplication is widely used in evaluating the area of a square or rectangle. By configuring the length and width of the figure as factors, the product of the two quantities determines the area.

For example:

• A sample of “paper-card” measures 3 inches in length and 2 inches in width. What is the total area of the card?

• The area of the card is evaluated as:
• 3 x 2 = 6 square inches
• 1 + 1+ 1+ 1+ 1+ 1 = 6 units

  c. Line-plot

The operation of  “multiplication” is analogous to counting numbers on a line plot for adding two numbers. The counting starts from the number “0”. The number of places for each jump is determined by the multiplicand. The factor “multiplier” evaluates the number of jumps. The number recorded after the total number of jumps is the product of the two factors.

For example:

Manipulatives used for Multiplication

To use the manipulatives such as base-10 blocks and counters for multiplication, the comprehension of few basic properties of multiplication is required.

The upcoming section describes the multiplication properties within the scope of grade-3.

  a. Base-10 blocks

The use of base-10 blocks for multiplication is a simple and versatile approach to comprehend a problem. As the elements of a multiplication sentence are identified, place the unit “ones” as shows in the grid.

Using the multiplicative identity property, each unit “ones” is multiplied to corresponding unit ones will yield 1. The grid of unit “ones” is filled accordingly and the sum of “ones” from each row/column is added to evaluate the product.

In later grades, while multiplying two-digit numbers, ten unit “ones” are replaced by one “tens” block.

b. Counters

Counters are used to instigate counting skills in kids in an order. To multiply two numbers using counters, arrange the counters in an array model to evaluate the product.

• For example:
• Multiply 7 and 2
• The seven counters are arranged in two distinct rows to calculate the product of the given numbers

Using counters to learn basic math operations is one of the most effective methods. However, when the factors (multiplicand and multiplier) are large numbers, the visual modeling is difficult. Hence, the technique is useful only in the case of single-digit numbers and to write multiplication tables of numbers 1-to-9.

Multiplication of two numbers

  a. As Doubles (2s facts), doubling twice (4s) and doubling three times (8s)

The multiplication of any number with two can be understood as the addition of the number with itself. For example:

Similarly, multiplication of any number with 4 can be comprehended as multiplication with “2” twice.  Rephrasing the expression will foster mental computation skills to quickly multiply the numbers without error. For example:

Using the facts of multiplication stated above, multiplication with “8” is comprehended as multiplication with “2” thrice. For example:

  b. As tens facts and five facts (half of 10)

As a number is multiplied by 5, the number obtained in the product always ends with either 0 or 5. Using the “division” operation, mental computation can be applied while multiplying by 5 and 10.

Any number multiplied by 10 yields the product which is the number itself, appended by 0 at the end; multiplication with “5” is an easy step.

  c. Skip counting

The method of skip counting is instrumental in nurturing the comprehension of multiplication tables. For each single digit number (1-to-9), multiplication table can be written by skip counting. Starting from 0, each skip/jump by the factor (multiplier) results in the product of the multiplicand and the number of the jump.

Using skip counting, multiplication tables for the numbers are written to multiply and divide two numbers.

  d. Squares

The “square” of a number refers to the product of the number by itself. The math expression for squares is:

• a x a = square of (a) or a2

The squares of numbers are primarily used in finding the area of shapes and representing geometric figures using algebraic expressions.

  e. Multiplication with nine (as tens fact and reduced by the “multiplier”)

As the multiplication of a number with “10” is a quick process, kids can easily multiply a number by 9 using mental computation.

The math equation to multiply a number (a) by 9 can be framed as:

  f. Decomposition into known facts

The word-problems based on multiplication can be solved easily by decomposing the expressions into known facts using simple factors.

For example, consider the following word problem:

Similarly, facts such as multiples of 10, 5 and 2 can be applied to quickly solve an expression using mental computation.

  g. Applying properties

The multiplication properties such as associative, commutative, distributive and multiplication identity properties can be applied to solve the word problems and multiplication sentences. With math reasoning and abstract thinking, elements of a multiplication equation such as multiplicand and the multiplier are identified.

Followed by identification, the technique of decomposition into known facts simplifies the process. Apply the properties as illustrated in the previous section to solve the math expressions.  

Relate Multiplication and Division

The math operations “addition” and “subtraction” ( as a case of reverse addition); multiplication and division are inverse operations. Any of these two operations between the two or more numbers are interchangeable by interchanging the operators and configuring the places of the numbers.

For example:

• 4 x 9 = ?
• ? / 4 = 9

To solve the expression, decompose the equation to a known fact (such as multiple of 10) or use the multiplication table of 4 or 9 (using commutative property).

Application

The math operations multiplication and division are the extension of the multi-step addition and subtraction. The operations are closely associated and form the basis of learning other math concepts in the later grades pertaining to measurement, data interpretation, and geometry.

Next section delineates the terms to remember for multiplication.

Terms to remember

List of Multiplication Games for Third Graders