3rd Grade Math: Place Value Games

The kindergarten math curriculum has some basic everyday math like counting and shapes. In that age, any topic should be introduced using fun math games for kids. The learning process at that age can be enhanced using kids learning games. In first grade, kids learn what is place value with ones and tens. At this level, many math aids and math manipulatives can be introduced. Gradually, they learn to imagine multi-digit numbers with higher place values. Third graders gets familiar with what is place value in their lower grades. At this level, the place value definition is applied in rounding numbers, addition, subtraction and multiplication.

Rounding Whole Numbers to the nearest Ten and using Place Values

Rounding a number is finding a more ‘friendly’ number that the given number is close to. For example, if Reena has 97 crayons in her coloring set, she has about 100. The word ‘about’ points to some kind of an estimation.

How to do this estimation?

Consider a simple example of a small hillock and a stone on that.

Suppose a stone is taken from the point A to point B through the hillock. If the stone is left anywhere between the points A and C, it will slide down to A. Similarly, if it is left anywhere between C and B, it would slide down to the point B.

Rounding a number to the nearest 10 or 100 can be similar to this.

For example, round 58 to the nearest 10.

The first step is to identify the ‘tens’ before and after the number 58. The number 58 has 5 tens and 8 ones. That is, it comes between 5 tens and 6 tens, or 50 and 60.

Consider the part of a number line from 50 to 60 and plot the number 58.

The number 58 is closer to 60 than to 50. So, it rounds up to 60.

Here, the number similar to the point C on the hillock example, the number which is exactly at the middle is 55. So, any number less than 55 would round down to 50. As a custom, the number 55 also considered to round up. That is, any number greater than or equal to 55 rounds up to 60.

Another math manipulative to teach rounding off is hundreds chart.

Round 2136 to the nearest hundred.

Since the rounding is to the nearest 100, the first step is to identify the hundreds before and after the number. The number has 2 thousands, one hundred, 3 tens, and 6 ones. Talking in terms of hundreds, the number has 21 hundreds (2 thousands are equivalent to 20 hundreds.). Thus, the hundreds before and after 2136 are 2100 and 2200 respectively. Now, consider the number line containing the numbers from 2100 to 2200. Note that a number line does not count always by ones. Here each unit of a number line can count 10. That is, the part from 2100 to 2200 is divided equally into 10 parts each of size 10, adding up to 100.

Plot the number 2136.

Since 2136 is closer to 2100 than 2200, the number rounded to the nearest hundred is 2100.

The child basically follows the place value strategies than the standard algorithm for rounding here.

The child also applies the similar logic in rounding numbers before and after operations like addition, multiplication etc in math word problems. Many place value worksheets for rounding numbers to the nearest ten as well as nearest hundred are available at SplashLearn. These place value activities can help kids with a better computational fluency.

 

Addition of Two- and Three-digit Whole Numbers

Children get familiar with adding two digit numbers in grade 2 using a number line as well as place value strategies.

Place Value Strategies: Consider the addition of 54 and 35. There are 5 tens and 4 ones in 54, 3 tens and 5 ones in 35. Make sure to add the digits with the same place value together. That is, 5 tens and 3 tens have to be added together to get 8 tens. Similarly, 4 ones and 5 ones add up to 9 ones. Thus, the sum is 8 tens and 9 ones or 89.

 

This can also be shown using base 10 blocks. Each of the addends can be shown using the tens and ones blocks and can be counted together to find the sum.

Number line: This can be done using a number line with leaps of appropriate sizes. Start with the first number 54. Since the second addend has 3 tens and 5 ones, take 3 leaps of 10 and then a leap of 5.

The mathematics behind the addition of three-digit numbers is the same, just that the calculations get a bit more complicated.

For example, to find the sum 186 + 795.

Using Base 10 Blocks: 186 has 1 hundred, 8 tens and 6 ones. 795 has 7 hundreds, 9 tens, and 5 ones.

These numbers can be expressed using base 10 blocks.

So, 186 can be represented using one hundred block, 8 ten blocks and 6 one blocks. The number 795 can be shown using 7 hundred blocks, 9 ten blocks and 5 one blocks. The addition can be performed by combining the similar blocks. There are 6 + 5 =11 ones blocks. But 10 ones would add up to a ten and would form a tens block. There are already 8 + 9 =17 tens block, adding the new one, there is 18 tens block altogether. But 10 tens blocks add up to form a hundred block, thus with 18 tens blocks, you have a hundred block and 8 tens blocks. Thus there are 7 + 1 + 1 = 9 hundred blocks. Therefore, the sum is 981.

Standard Algorithm: Algebraic calculation of this is similar to that of the two-digit ones.

The most important thing is to line up the digits that have the same place value. That is, here 6 and 5 have the same place value, hence they need to be lined up.

So, the correct alignment would be:

 

Now, the corresponding place values can be added to find the sum. There are 6 ones in the first number and 5 ones in the second, adding them together there are 11 ones. But, 10 ones will add up to one ten and would be moved to the next place value on the left, tens leaving only 1 one at the one’s place. Thus, the one’s place in the sum has 1 and one ten need to be added with the tens of the addends.

Continuing the process by adding the tens, there are 1 + 8 + 9 = 18 tens in the sum. Again, 10 tens make a hundred and it gets carried to the next place value, hundreds.

Adding the digits at the hundred’s place, there are  hundreds in the sum.

Thus,  .

Place Value Charts / Expanded Form: The addends can be written in expanded as, 100 + 80 + 6 and 700 + 90 + 5 respectively. For adding them, the corresponding place values can be added together.

 

Using place value chart, this can be shown as:

Addition of two- and three-digit numbers is explained in different sections in SplashMath. These math practice problems start with easy ones and slowly, in a very structured manner, move to difficult math problems. 

Subtraction of 2- and 3-digit Whole Numbers

Saira is collecting money for donating to a flood relief camp. Her target is $350. She has already collected $124. How much money is required more to achieve the target?

The question is to find the amount of money that has to be added to $124 to reach $350.

Consider these numbers on a number line. The difference between 124 and 350 is the distance between the two numbers.

The child should take appropriate leaps reach from 124 to 350, using reaching friendly numbers.

Now, the leaps can be added to find the difference.

.

Thus, Saira has to collect $226 more to reach her target.

Subtraction by taking away the base ten blocks from the minuend is something that kids are familiar with. In grade 2 the kids have done the decomposing of tens blocks to one's blocks to perform the subtraction of two-digit numbers. The similar logic applies for 3-digit numbers as well.

Another method for doing subtraction is using place value charts. For example, find the difference 452 – 278.

Using the place value and expanded form, the two numbers can be shown as:

Note that the subtraction should be started from the right most or lowest place value, one.

Here, 8 ones cannot be taken away or subtracted from 2 ones. So, decompose one of the 5 tens from the left that leaves 4 tens in the number with 12 ones. Subtracting 8 ones from 12, the difference has 4 ones.

Now, subtract in the tens place. Since 7 tens cannot be subtracted from 4, decompose one of the hundreds.

Now, subtracting 200 from 300, the number of hundreds in the difference is 1.

Thus,  .

This is exactly the same procedure followed for standard algorithm.

Like addition, SplashLearn deals with the subtraction of two- and three-digit whole numbers in different sections of education worksheets.

 

Multiplication using Place Value Strategies

The product of One-digit and 10: Multiplication is a repeated addition. So, when there is a product , it is as good as adding 10, three times. That is .

In a similar way, one can write:

 

This is easier to imagine using base 10 blocks.

The number of ten blocks equal to the multiplicand can be combined together to show the product.

On a number line, the leaps of 10 equivalent to the multiplicand will result in the product.

The numbers 10, 20, 30, etc are called multiples of 10.

The product of One-Digit and a Multiple of 10: Just like in the case of multiple of ten, a number line can be used to find the product.

For example, 330 can be shown using taking 3 leaps of 30 on a number line.

Thus, 3 30 = 90 .

The product of a one-digit number and a multiple of 10 can be simplified by taking the multiple of 10 as a product of a one-digit number and 10. That is,   can be written as    . The product of 20 and 10 is same as adding 10, twenty times. That results in 20 tens or 200.

Another example, .

Now, this twelve can be split into .

These are easier products.

Simplify.

 

A good amount of math worksheets for multiplying a multiple of 10 by a one-digit whole number are available on SplashLearn.