4th Grade Math: Times Tables Games

One of the main agenda of grade 4 math curriculum is to develop the understanding and fluency with multi-digit multiplication. 3rd grade math deals with the two-digit multiplication of whole numbers. Before advancing to multi-digit multiplication, grade 4 focuses initially on understanding the concept in a deeper sense.

Math Manipulatives

Tape Diagrams or Bar Models/ Checkers, Coins: These can be used to show the grouping strategy for relatively smaller numbers.

Blocks: Buiding blocks can be used to show the factor pairs as shown:

Times Table Chart: The kids can identify the factor pairs using a times table chart. A 20 by 20 times table sheet would be helpful for finding the factor pairs of smaller numbers.

Area Models: Area models can be used to explain the factor pairs which would be discussed in detail, later in the lesson.

Math Games and Activities

The concepts taught using good math aids and reinforced using interesting kids educational games stays forever in kids’ minds.

Activity using times table charts: Kids can be grouped into 7 groups and printable multiplication charts up to 20 can be distributed among the kids.

Each group can be allotted a times table and a product from the table.

 

 

The group can use the multiplication chart to find one of the factor pairs of the product given.

Once they find the factor pair, use skip counting by each factor to identify the number of factors counted to reach the product. Teachers can help children to identify this number to be the factor pair of the considered factor.

Board Game with Primes and Composites: The game requires a 10 by 10 in which the numbers from 1 to 100 are written in order and a six-sided die. When the die is rolled, the players start moving on the condition that a player has to find a factor other than 1 and the number itself while standing on a number. If the player lands on a prime number, he/she has to go back to 1 and start fresh.

Apart from these, there are many online multiplication apps and learning games for kids that can be used for practice the concept learned.

 

Teaching Methodologies

Multiplication as Comparison using Verbal Statements

In grade 3, kids learned about the definition of multiplication as a repeated addition as well as using grouping strategy. Rectangular arrays were used to denote multiplication.

For example, the array below shows 20 dots arranged in 4 rows with 5 dots in each row.

That is, there are 5 ‘groups of’ 4s or 5 × 4 . The related multiplication equations are                5 × 4 = 20 and 4 × 5 =20 .

Here, the numbers 4 and 5 are called the factors and the number 20 is called the product.

In grade 3, they get familiar with the basic concept as well as they learn multiplication tables of one-digit numbers. In grade 4, kids learn to formulate verbal comparison statements from multiplication equations and vice versa. That is, consider the equation 3 × 4 = 12 .

This can be represented using a tape diagram or bar model as shown:

That is, 3 bars of 4s are topped one on the other two form the model. In other words, 12 is 3 times as many as 4.

Now, consider the related multiplication equation 4 ×v3 = 12 . Here, a similar bar model would of 4 groups of 3s topped on one another to form 12.

Thus, 12 is 4 times as many as 3.

This can also be represented using dots.

Comparing the representations of related equations, kids learn to evaluate which quantity forms a group and how many such groups exists. In other words, kids evaluate which one is the multiplicand and which one is the multiplier among the factors. Further, they can formulate the verbal comparison statements based on their evaluation.

Application in Real World Problems

Chang has 7 times as many as marbles as Sher in their marble collection. If Sher has 8 marbles, how many marbles does Change have?

In such real-world word, problems kid learn to formulate the equation by assigning a variable to the unknown factor. Since the number of marble that Chang has is unknown, we can give an arbitrary symbol, say x, to represent the same. Then, this can be written as an equation as:

7 × 8 = x

Knowing the multiplication tables, children can easily compute that 7 × 8 = 56 .

Thus, Chang has 56 marbles in his collection.

Further, kids can apply the similar knowledge in solving multi-step real-world word problems.

Sasha is looking for interior decorations for the annual day celebrations of her health club. A company called “All about Celebrations” rents chairs at the rate $7 for 10 chairs. Another company, “Posh Decors” gives them for $20 for 25 chairs. If Sasha is hiring 100 chairs, which one is more cost-effective? Justify the choice by the quoting the difference in money.

Let x be the cost for 100 chairs from All about Celebrations. There, 10 chairs cost $7, that is,  10 × 10 = 100 chairs would cost 10 × 7 = 70 . Thus, x = $70 .

Let y be the cost for 100 chairs from Posh decors. There, 25 chairs cost $20, that is,               4 × 25 = 100 chairs would cost 4 × 20 =80 . Thus, y = $80 .

Comparing x and y, it is more cost effective to hire the chairs from All about Celebrations. The difference in cost is $10.

Children also acquire a knowledge about estimation, where and how to estimate real-world problem-solving.

Factors and Multiples

In grade 3, kids learn about one-digit factors and their products. To revise it, if you have a multiplication equation 6 × 5 = 30 , the numbers 6 and 5 are called factors and 30 is called the product.

Here, 6 and 5 are called a factor pair of 30. A factor pair refers to a set of two numbers, which when multiplied result in a definite number, the product.

Consider the whole number 12.

Any number is a factor of itself as the number can be written as a product of 1 and the number itself. That is, 12 = 1 × 12 .

This can be represented using area model as:

Now, using these squares, the other factor pairs can be identified. There are 12 squares altogether that need to be re-arranged to form another rectangle.

Consider arranging them in two rows.

 

So, 2 and 6 are another factor pair.

Now, arrange the 12 squares in 3 rows.

Thus, 3 and 4 are also factor pairs of 12.

Now, it is not possible to arrange these 12 squares in 5 rows and maintain the rectangular array. So, 5 is not a factor of 12.

We have already listed 6 as a factor, thus completing the list of factor pairs.

 

Another method of finding the factor pairs is by listing them down.

Find the factor pairs of 30.

It is obvious that the number can be written as a product of 1 and the number itself. So,       1 × 30 = 30 . Thus, 1 and 30 are a factor pair of 30.

Since 30 is an even number 2 is a factor and 2 × 15 = 30 . So, 2 and 15 are also a factor pair.

In a similar way, 30 can be written as the product of the factor pairs in multiple ways.

3 × 10 = 30

5 × 6 = 30

So, (3, 10) and (5, 6) are also factor pairs.

Another manipulative that can be used to identify the factor pairs of a number is a multiplication chart.

Here, to find the factor pair for the number 24, look at the vertical and horizontal aligned numbers.

The practice multiplication sheets for factors in SplashLearn discusses identifying the factors of a given number as well as finding the number given the factors of the same.

Prime and Composite:

A number that has only two factors, 1 and the number itself, is called a prime number. A number that has more than two factors is called a composite number.

For example, 17 is a prime number as the only factors it has been 1 and 17.

35 is a composite number as the numbers, 1, 5, 7, and 35 are factors of it.

The number 1 is considered to be neither prime nor composite. The smallest prime number is 2 and it is the only even prime number.

Prime numbers have only two area models that represent the product of the number itself with 1. This is because a prime number of squares cannot be re-arranged maintaining the rectangular array alignment.

Multiples can be thought of as a result of skip counting by each of the factors.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Now, the skip counting by each factor will show that 36 is a multiple of the factor.

 

By the end of grade 4, children would be able to find the factors of any two-digit numbers. Certain multiplication facts that would be helpful for the process are listed below.

• Even numbers are multiples of 2.
• Any even number that can be halved twice to get a whole number is divisible by 4.
• Any number that ends with 0 is a multiple of 10.
• Any number ending with 0 or 5 is a multiple of 5.

Kids fluently deal with factors and multiples of two digit numbers. Further, how to multiply two digit numbers using place value strategies and long multiplication are discussed later.

The prime and composite numbers worksheet in SplashLearn gives a thorough practice for the topic by identifying the prime and composite numbers using a clear reasoning. The worksheets for multiples uses math manipulatives like multiplication cards for practice problems.

Analyzing Patterns

A pattern is a sequence that repeats following a particular rule. For example, the sequence 1, 3, 5, 7, 9, …. Starts with 1 and adds 2 to get the next term. This is an additive pattern.

Another pattern, 2, 4, 8, 16, 32,….. multiplies the previous term by two to get the next term. This is a multiplicative pattern. There are combined ones too.

St. Peters’s Public School has recurring and savings schemes for kids. The initial deposit for Kathy’s recurring account was $20 and she deposits $5 every week. What would be the account balance after 8 weeks?

Let x be the number of weeks that Kathy deposits the money for. She deposits $5 every week. So, in x weeks she deposits $5x. The initial deposit of the account is $20. Thus, at the end of x weeks, Kathy has $(5x + 20) in her account.

Once the child formulates the pattern in such a manner, it is easy to find the value in a particular week. To find the amount at the end of 8th week, substitute 8 for x.

5 × 8 + 20 = 40 + 20 = 60

Thus, at the end of the 8th week, the account balance would be $60.

Kids can get comfortable with identifying and forming patterns using the worksheets provided by SplashLearn. Further, the practice problems for analyzing the patterns encourages kids to identify the rules behind the patterns.