Multiplication Games for 4th Graders

Frequently Asked Questions:

Q1: What is distributive property of multiplication?

Ans: Distributive property of multiplication over addition simplifies multiplication of large numbers using the smaller known facts. One such example is: 40 x 105 which can be written as 40 x (100 + 5) = 40 x 100 + 40 x 5 which can be now solved mentally very quickly as 4000+200= 4200.

Q2: How do we multiply numbers by 1-digit numbers?

Ans: We can easily multiply 2, 3 or 4-digit numbers by 1-digit numbers using column method. We can write the digits in column as per their palce values and multiply them. We can also use area model or box model to multiply them.

Q3: How can we use area model for multiplication?

Ans: We can write both the numbers to be multiplied in expanded form and arrange them along length and the width of a rectangles. Then, we find the area of each rectangle using the formula: length x width. The sum of all the areas of rectangles is equal to the product of numbers.

Q4: How do we multiply 2-digit numbers by 2-digit numbers?

Ans: We can multiply 2-digit numbers by 2-digit numbers using column method, area model or lattice method. To practice multiplication, there are ample of games in SplashLearn website. You just need to find math games in the home page and find 'multiplication games' in the tab 'Math Games by Topic' to practice this concept.

Q5: How do we multiply numbers?

Ans: We can multiply numbers using column method, area model, or lattice method. To practice multiplication, there are ample of games in SplashLearn web page. To play fun games on multiplication, visit SplashLearn page and select your grade or find "multiplication games" in the tab "Math Games by Topics"; then your are ready to have fun while applying your knowledge.

Q6: How to multiply numbers by expanding them?

Ans: We can write both the numbers to be multiplied in expanded form and arrange them along length and the width of a rectangles. Then, we find the area of each rectangle using the formula: length x width. The sum of all the areas of rectangles is equal to the product of numbers.

 

Introduction

Multiplication and division should be introduced in its most basic form at the earliest opportunity so that children can begin to familiarize themselves with these key operations. According to a study, successive research has shown that: children as young as preschoolers solve many multiplication and division word problems by connecting modeling with counting and grouping skills and with various strategies involving addition and subtraction. Hence it is very important to grasp the concepts of multiplication well because multiplication forms the building block for other mathematical concepts. A lot of sums can be solved with confidence just by learning multiplication tables. For example, knowing that 3 x 3 = 9 will help children understand that 30 x 30 = 900, and 300 x 300 = 90000. Being versed with multiplication properties and multiplication facts too helps in calculations. Also, Multiplication definition can be the inverse function of the division. Multiplication knowledge can come handy in verifying the division sums using the inverse. For example, 28 ÷ 4 = 7 is correct because 7 x 4 = 28.

Mathematical Representations of Multiplication

First Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Then, multiply to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Let children begin by investigating the formulas for area and perimeter. They use their understanding of the area and perimeter formulas to solve multiplication problems including the language of times as much with a focus on math problems using area and perimeter as a context (e.g., “A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the field?”). Let kids create diagrams to represent these problems as well as write equations with symbols for the unknown quantities. For example, the width of a tent is 5ft and the length is twice the width. The rectangular air mattress measures 3ft by 6ft. If the mattress is put in the tent, how many squares feet of floor space will be available for the rest of the things?

In 4th grade math, the multiplicative comparison is crucial as it helps in understanding multiplication as scaling in Grade 5 and sets the stage for proportional reasoning in Grade 6. Introducing multiplication with area and perimeter allows for new and interesting multiplication word problems as children learn to calculate with larger numbers and interpret more complex problems.

First, let kids see perimeter as the sum of all four sides but a faster way is to double the sum of the length and width. Hence the formula as P = 2 × (l + w). Now let kids use the formula 2 × (l + w) to solve for perimeter and to find an unknown side length.

 

Kids can similarly find the area by counting the number of squares in the rectangle or counting number of squares in one row and then skip count that number for all the rows which are just multiplying the number of rows by the number in each row. Hence, a quicker way is to multiply the length times the width. Nine rows of 3 units each is like a multiplication array. We can just multiply 9 × 3. Total squares in the multiplication grid give the area of the rectangle.

This can be extended by exploring multiplication arrays to word problems. Let kids Solve multiplicative comparison mathematics problems by applying the area and perimeter formulas.

 

Multiplication by Single-Digit Numbers

Common core multiplication standards emphasize on reasoning, looking for and making use of multiplication table chart and various mathematical strategies that can help children understand better. Hence, for this purpose, SplashLearn has put together multiple strategies on how to teach multiplication that can be explored by parents to practice with their kids.

For teaching multiplication of multi-digit numbers by a single-digit kid should initiate by decomposing numbers into base ten units. Provide kids with sufficient multiplication practice of area models, the standard algorithm, and in the context of word problems, including multiplicative comparison problems, multiplication drills and multiplication and division worksheets. Multiplication charts and manipulatives like place value disks to represent multiplication also helps kids visualize the process. Once comfortable with the above methods kids can be progressed to the abstract level as they learn how to multiply three- and four-digit numbers by one-digit numbers. Finally, kids learn how to do double-digit multiplication by the partial products, the standard algorithm, and the area model via the distributive property of multiplication.

Place Value Disk Method

Let’s try to solve 2 digit multiplication with a single number using disks.

For example: 2 × 23

First, draw disks to represent 23 on the place value chart.

23 is: 2 tens 3 ones.

Draw 1 more group of 23 on the chart.

Now the value of the ones is 2 × 3 ones = 6 ones.

The value of the tens is 2 × 2 tens = 4 tens.

Add up the partial products. The final sum is 46.

Hence 2 X 23 = 46

Similarly, solve one digit by two digit multiplication of 4 × 54

First, draw disks to represent 54 on the place value chart. 54 is: 5 tens 4 ones.

Draw 3 more groups of 54 on the chart.

Now the value of the ones is 4 × 4 ones = 16 ones.

The value of the tens is 4 × 5 tens = 20 tens.

Add up the partial products. The final sum is 216.

Hence 4 X 54 = 216

Now extend the use of place value disks to represent one-digit by multi digit multiplication

Partial Products Drawing Method

Example: Solve 3 × 851 using a partial product drawing on the place value chart.

This time, rather than recording 3 groups of 851 to begin, record the partial products as we multiply each unit. Begin with ones place:  3 × 1 one is 3 ones.  Record that in the pace value chart.

In tens, we get: 3 times 5 tens which are 15 tens. Record this in the place value chart as 1 hundred 5 tens a bit lower than the ones so you can see the separate partial product.

Then do the hundreds. 3 times 8 hundreds is 24 hundreds. Record that in the place value chart as 2 thousands 4 hundreds. Now sum all the partial products to get the final answer. Hence, 3 x 851 = 2553

Standard Algorithm Method

Let us take a look at the sample problem in order to understand how to do multiplication through standard algorithm:

Problem: Solve 6 × 162.

First, represent 6 × 162 on the multiplication chart using the repeated addition way.

In this, we have, 6 hundreds, 36 tens, and 12 ones.

10 ones can be regrouped for 1 ten and 30 tens for 3 hundreds. The answer becomes 9 hundreds, 7 tens, and 2 ones. Standard algorithm is an efficient way of doing fast math.

Observe the ones column of the place value chart:

6 times 2 ones is equal to 12 ones.

Regrouping 10 ones for 1 ten leaves 2 ones.

Next record the number of regrouped tens on the line under the tens column. Record the number of ones in the ones place.

Now observe the tens column of the place value chart. 6 times 6 tens are same as 36 tens.

Exchange 30 tens for 3 hundreds leaving 6 tens. But 1 ten was regrouped from the ones, so 36 tens plus the 1 ten makes 37 tens. So, we have 3 hundreds and 7 tens after we regroup. Now record the number of hundreds on the line in the hundreds column.

Record the number of tens in the tens place.

Cross out the line in the tens place, as it has already been counted.

Now, observe the hundreds place. 6 × 1 hundred = 6 hundreds.

6 hundreds plus the 3 hundreds we regrouped equals 9 hundreds.

Write it at the hundreds place and cross out the 3 hundreds that have been used. Hence the answer becomes: 972

Connect Area Model and Partial Products Method

Let us look at 234 X 8 using the area model.

First, draw a rectangle with the length of 8 and the width of 200.

Multiply 8 times 200. That equals 1,600.

Draw two more rectangles both with the length of 8 and widths of 30 and 4 respectively. Multiply 8 times 30 (=240) and 8 times 4 (=32). Then combine all three rectangles and find the area of all three rectangles put together. Total Area = 1872

Comparing the partial products to the rectangular area model you will observe that the area inside each smaller rectangle is the same as each of the partial products. The distributive property allows breaking apart the large multiplication problem into three smaller ones. Add the areas individually which sums to 1872. Hence, the area model is another way to represent the partial products in multiplication.