2nd Grade Math: Place Value Games

Usually, preschool math curriculum is all about counting and shapes. Early childhood education should be started with the objects that the kids see around them using educational games and math activities for kids. Grade 1 students learn about what is place value using math manipulatives and place value activities. Place values play an important role in mathematics. In grade 1 they comfortably work with two-digit numbers and their place values. In grade 2, they graduate to the place values of three-digit numbers. For this groupable math aids like snap cubes as well as pre-grouped objects like base ten blocks can be used. Several math games for 2nd graders available online can reinforce the concepts learned.

Place Values of Three-Digit Numbers

First graders get familiar with place value definition using learning games for kids. They are introduced to the system using place value games and activities. The kids learn to unitize ten individual units to a single unit called “ten”.  Further, they use the place value strategies for addition and subtraction of two-digit numbers.

In grade 2, the kids further expand the place value system to the hundreds.

Children conceptualize a “hundred” as a bunch of ten “tens” using math manipulatives.

They already know place value definitions and have a clear concept about the connection between tens and ones. So, they do the counting initially by grouping the objects into groups of 10 and the left overs.

Consider the number 263. The children initially understand it as 26 groups of 10 and 3 left over and that makes it to 260 + 3 = 263. Gradually, they will mentally convert 26 tens into 10 + 10 + 6 tens, that is, 2 hundreds and 6 tens. Thus, the number 263 can be written as 2 hundreds 6 tens 3 ones.

After identifying the numbers of hundreds, tens and ones in a number, the kids are ready to analyze the value of each digit in a number. Using math manipulatives they can represent a three-digit with the correct place value.

Consider the number 135. Here, the child understands that there are one hundred, 3 tens and 5 ones in the number 135. The child uses a base ten cubic blocks, that is, 100 cubic blocks to represent the hundred, three cubic blocks of 10 each for 3 tens and 5 cubic blocks for 5 ones.

A place value chart can show things clearer.

Given a number, the child can understand the value of each digit as well as the digit at each place value.

For example, given a number 678, the child understands that there are 6 hundreds 7 tens and 8 ones. Further, the child can point to the value of the digit 6 as 600 because the place value of the digit is hundred. In a similar way, the value of the digit 7 is 70 and that of 8 is 8.

A mere Google search of “place value worksheets 2nd grade” can get you ample of math websites and math practice problems. SplashLearn’s the worksheets for representing three-digit numbers would reinforce the connection between the visual models, number form, and the standard forms of numbers as well as identifying the number of hundreds, tens, and ones in a number. Further, the math problems under the section understanding place value help children to expertise in identifying the value of each digit in a number and understand the concept deeper.

Bundles of Hundreds

Just the way children unitized ten ones into a ten, in grade 2 they learn to compose ten tens to form a hundred. They realize that in a ten there are zero ones. In a similar way, they conceptualize that there are zero tens and zero ones in a hundred.

For example, when the number 300 is modeled using base 10 blocks, there are 3 hundred blocks, zero ten blocks and zero unit blocks.

 

Similarly, 200, 400, 500, and 600 have 2, 4, 5, and 6 hundreds, zero tens, and zero ones in it.

 

Expanded Form

Grade 2 kids are familiar with various representations of two and three digits numbers as number form, standard form, split form(the number 135 as 1 hundred 3 tens 5 ones) and visual models. Also, the children are thorough with the concept of the value of a digit in a number. These act as a foundation for writing a three digit number in expanded form.

For example, the number 658 has 6 hundreds 5 tens and 8 ones. Consider the value of each digit, the number can be written in expanded form as 600 + 50 + 8.

On the other way, the number with the expanded form 300 + 8 has zero tens in it, so can be written in standard form as 308.

Comparing Three-digit Numbers

The students are familiar with counting up to 1000. So, like the comparison of two-digit numbers, the comparison can be done using the logic that the number that comes later in counting is of greater size. Probably this would be the logic used by kids of grade 1.

But let us look at the technical side of it too.

A second grader understands that one hundred is actually greater than any amount of tens and ones represented by a two-digit number. Thus, a three-digit number is greater than any two-digit number.

For comparing two three-digit numbers, the more the number of hundreds greater the value of the number. So, first, you need to compare the digit at the hundred’s place.

For example, consider the numbers 458 and 326. 458 has 4 hundreds in it and 326 has 3 hundreds. Thus, 458 is greater than 326.

Now when there are two numbers with the same number of hundreds, you need to consider the number at ten’s place next. Whichever number has the greater value at ten’s place, is a greater number in this case.

For example, consider the numbers 258 and 272. Both have 2 hundreds. So, consider the tens in each of them. 258 has 5 tens and 272 has 7 tens. Since 7 > 5, 272 is greater than 258.

When the digits at ten’s place are also the same, it is obvious that the decision should be made considering the ones.

Children need a numerous number of experiences verbally comparing two sets of objects using comparison vocabulary of less than (<), greater than (>) and equal to (=). This will help them connect the vocabulary to math symbols. SplashLearn has a good number of math worksheets for comparing the three-digit numbers.

Addition of Two 2-Digit Numbers

In grade 1 kids learned how to add a multiple of 10 to a two-digit number. In grade 2, they learn to add any two 2-digit numbers. But the standard algorithm of addition with carrying is not expected at this level. Rather, they use logical reasoning for adding two 2-digit numbers. The kids might adapt one of the below-described reasoning to find the sum.

Consider the addition 46 + 35.

1. Place Value Strategy: Kids know that there are 4 tens 6 ones in 46 and 3 tens 5 ones in 35. So, adding the tens together they have (4 + 3) tens or 7 tens. Adding the ones together, (6 + 5) ones or 11 ones. Thus the sum has 7 tens 11 ones or 81.
2. Decomposing into tens: 46 is 4 less than 50, so break off 4 from 35 and add to 46 to make it 50. Now the addition is 50 + 31. Adding 5 tens and 3 tens the child has 80 and there is 1 left over to make the sum 81.
3. Expanded Form with Commutative Property: The numbers can be written in expanded form as 40 + 6 and 30 + 5. Though kids do not know about commutative property, by changing the order in which they are adding the addition becomes easier. Using Commutative Property, the sum can be re-written as:

40 + 6 + 30 + 5 = 40 + 30 + 6 + 5 = 70 + 6 + 5 = 76 + 5 = 81

By using reasonings like these children learn to add any two 2-digit numbers.

 

Addition of Four 2-Digit Numbers

Children continue to use similar reasoning techniques instead of standard algorithm even when there are four numbers.

Place value strategies of adding tens together and ones together is the main technique used here. To find 23 + 62 + 54 + 48,  first add the tens.

20 + 60 + 50 + 40 = 170

Now add the ones: 3 + 2 + 4 + 8 = 17

170 + 17 = 187

Thus, 23 + 62 + 54 + 48 = 187.

Another technique that can be used is to add the numbers in the convenient order.

Two numbers have 2 and 8 at ones place which will add up to 10. So, add those two numbers first.

62 + 48 = 110

Now, add the next number.

110 + 23 = 133

133 + 54 = 130 + 3 + 50 + 4 = 180 + 7 = 187

Addition of 3-Digit Numbers

Children are already familiar with techniques of the addition of two-digit numbers. They use the similar techniques for adding a three-digit number and a one digit number. The ones in the one-digit number should be added to the ones of the three digit number. SplashLearn has quite a number of practice problems for the addition.

When a 3-digit number is added to a 2-digit number, the tens are added together and the ones are added together. Children visualize this using base ten blocks.

The first number shown in the diagram below is 311 and to that, the number 10 needs to be added. The number 10 needs to be added to the tens in 311.

When the addition is between two 3-digit numbers similar techniques can be applied.

Using base 10 blocks, an addition of 153 and 172 can be shown as below:

 

The similar blocks need to be added together. There are 5 tens in the first number and 7 tens in the second, adding up to 12. But 12 tens is equivalent to 1 hundred and 2 tens. So, there are three hundreds altogether, 2 tens and 5 ones. Thus, the sum is 325.

Using the place value strategies this can be done algebraically by writing the number in the expanded form adding the similar place values together.

For example, to find the sum 654 + 235, rewrite the sum as 600 + 50 + 4 + 200 + 30 + 5.

Add the hundreds:  

Add the tens:

Add the ones:  

Combine them:  

Another way of finding the sum is using a number line. Starting from the first number of the sum on the number line, first, take leaps of hundreds as many times as the number of hundreds in the second number. Then, take the tens and at last ones leap depending upon the number of tens and ones in the second number. You can practice addition of 3 digit number with 3 digit number

Further, math word problems involving addition can reinforce the concepts and techniques learned.

 

Subtraction

For subtracting a two-digit number from another one, again they can be decomposed into tens and ones, and the corresponding place values can be subtracted. For example, consider 35 – 14. There are 3 tens in the first number and 1 ten in the second. Subtracting you have, 2 tens. Similarly subtracting the ones, you have 1 left over. Thus, the difference is 2 tens and 1 left over or 21.

When it comes to subtracting three-digit numbers, using base ten blocks might help students to visualize the concept of taking away as well as decomposing.

Consider the difference .

Start with the base ten block for the minuend 526.

Now the subtraction can be performed by taking away blocks equivalent to the subtrahend 389. There are 3 hundreds in 389, so first take away 3 hundreds.

Now, there is 226 in the minuend and 89 in the subtrahend. The number of tens in 226 is two, there aren’t enough to take away 8 tens. So, the solution to this problem is to decompose one of the hundreds into 10 tens. Here, the child needs to trade 6 tens out of the new 10 tens as there are already 2 tens available. So, in the minuend, there are 1 hundred 4 tens and 6 ones are available from where the child needs to take away 9 ones.

Again, one of the tens needs to be decomposed to ten ones to take away 9 ones. Here, the child needs to trade 3 ones out of the new 10 ones as there are already 6 ones available. So, in the minuend left are 1 hundred 3 tens and 7 ones which are the difference.

Thus, .

Further, after quite a number of practices of place value strategies and pre-grouped manipulatives like base ten blocks, children learn to calculate the addition and subtraction of 10 or 100 as mental math. That is the questions like, “what do you get if you add 10 to 358”, the child realizes that 10 needs to be added to the tens in 358 and thus the answer is 368. In a similar way, they learn to add or subtract 100 too. That is, . The child concludes that when one adds or subtracts 10 or 100 that only the tens place or the digit at the hundreds place changes by 1.