1st Grade Math: Place Value Games

Mathematics works on logical thinking. This makes it interesting for small kids. And with the basic concept of counting, different shapes around them, estimating the measurements of the things they use etc make them feel connected to the subject. At this stage, it is very important to use fun math games for kids. Any topic should be introduced using good manipulatives.

For counting, groupable math manipulatives like cubes, links, beans, and beads can be used. It is not suggested to use pre-group materials like base ten blocks or bean sticks as these do not give freedom for kids to manipulate and learn things by their own. Further, a lot of kids learning games should be included for reinforcing the concepts.

Counting as Grouping

In preschool math activities and preschool math games, children learn to count to tell the number of objects. They know how to count the number of toys, chocolate they have, understanding the one-to-one correspondence between the numbers and the object. They can count till hundred by ones and tens.

By grade 1, they understand the relation between ones and tens. This can be explained using groupable materials like cubes, links, beans, and beads.

Activity: The children can be divided into four groups and each group can be given 35 beads. They can be asked to make small groups of all 35 beads in their own ways. Some may group it as 5 groups of 7, others may group it as 4 groups of 8 and a group of 3 beads that are left over, another combination could be 3 groups of 9 and a group of 8.

 

There are many different ways of grouping them. In whatever ways the kids group the beads, it counts to 35. For a first grader, the equivalence between these groupings is not very obvious. They need to be explained repeatedly using good math aids and educational games.

Another important way of grouping is 3 groups of 10 and 5 left overs. This grouping lays the foundation for the place value definition in mathematics.

So, there are 3 tens and 5 ones in the number 35.

It takes time for kids to get used to this system of counting, but once they are comfortable with it, they can count with much ease. In a number, if there are 5 tens and 3 ones, the child can write the number as 53 easily.

 

Decomposing the teen numbers

In a kindergarten class, the counting was on the basis of individual units called “ones”. When the children graduate to grade 1, they learn to unitize ten individual units to one called “ten”. This makes the counting easier.

Suppose Saira has 10 chocolates with her and she wants to have 14. So, how many chocolates does she need to buy? The answer is 4. That is, she has 10 + 4 chocolates after buying 4 more.

 

That is, the number 14 is made of 1 ten and 4 ones. So, when the number 14 is written, the number 1 represents the ten and 4 represents the ones in the number. That is, 1 is the ten’s place and 4 is at the one’s place.

Similarly, all the teen numbers (numbers from 11 to 19) can be written as a combination of a ten and a few ones.

 

SplashLearn has a good number of math practice problems in decomposing teen numbers.

Once the children are comfortable with teen numbers, they are introduced with bundles of 10, such as 20, 30 etc.

If there are 5 packets of cookies each having 10, the children learn to see the cookies as 5 packets, not as 50 cookies. At the same time, the counting is easier as the child knows there are 10 cookies in each packet and so the total number of cookies is 10 + 10 + 10 + 10 + 10 = 50. This is much easier than counting in ones. Gradually kids learn that the number 20 has 2 tens, 30 has 3 tens etc.

Count groups of 10 is a topic that discusses counting by 10. This not only gives a better idea of the concept of place value system but also prepares children for the multiplication table of 10.

Counting of the numbers up to 100 using visual models is good place value worksheets for better mental math skills. SplashLearn deals with this in two sections, numbers up to 50 and numbers up to 100.

 

Comparing Two-digit Numbers

The students are familiar with counting up to 100. So, 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.

When there are more tens in a number definitely that number will be greater than the ones with a lesser number of tens. So, for comparing two-digit numbers, first, you need to compare the digit at ten’s place.

For example, consider the numbers 44 and 36. 44 has 4 tens in it and 36 has 3 tens. Thus, 44 is greater than 36.

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

For example, consider the numbers 32 and 37. Both have 3 tens. So, consider the ones in each of them. 32 has 2 ones and 37 has 7 ones. Since 7 > 2, 37 is greater than 32.

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 visual models and numbers.

Comparing 14 and 41: As the kids have just got introduced to the place value system, they might be confused with the number value placed at the two positions. The number 14 has 1 ten and 4 ones whereas the number 41 has 4 tens and 1 one. A place value chart below can explain it better.

           

So, only a thorough understanding about what is place value can help solve the issue.

Further, place value games and place value activities can reinforce the concepts learned.

Place Value in Addition

Children are already familiar with adding one digit numbers for solving word problems. For example, Simon has 4 marbles in his right hand and 3 in his left. How many marbles does he have altogether? By counting the marbles one by one, the child can find the sum 4 + 3 = 7.

In grade 1, children are introduced to the addition of a two digit number and a one-digit number.

Grade 1 in St. Peter’s Public School has 13 members in their Drama Club. If 5 new kids join the club, what would be the total number of members?

To find the total number 5 has to be added to 13. That is, 5 ones have to be added to 1 ten and 3 ones. For the addition, the ones have to add together. That is, 5 ones have to add to 3 ones. Thus, there are (5 + 3) ones or 8 ones. So, the total number is 1 ten and 8 ones or 18.

This can be done using counters or checkers as shown below:

 

Consider another addition 26 + 4. That is, 2 tens and 6 ones have to be added to 4 ones. Adding the ones together, (6 + 4) ones or 10 ones. Thus, adding 2 tens and 6 ones to 4 ones, you get 2 tens and 1 ten, that is, 3 tens or 30.

24 + 6 = 30

Thus, when there are as many ones as ten, the child needs to compose a ten in the resultant sum.

Another example, 37 + 5. There are 3 tens and 7 ones in 37. This needs to be added to 5. Adding the ones together, (7 + 5) ones or 12 ones. But 12 ones is same as 1 ten and 2 ones. So, the sum of the numbers is 3 tens, 1 ten and 2 ones. That is 4 tens and 2 ones or 42.

Children need a lot of practice for splitting and adding the tens and ones this way.

Further, adding multiples of ten would give a base for adding two-digit numbers and multiples of ten.

Rhea has 44 candies in a pouch. If she adds 30 more to the pouch, how many candies does she have in her pouch?

Using counters, it is easier as there is an addition of 3 tens to 44.

There are 4 tens and 4 ones in 44. To add 30, 3 tens need to be added. Note that the tens have to be added together. Thus, the sum would have (3 + 4) tens and 4 ones. That is 7 tens and 4 ones or 74.

Therefore, 44 + 30 = 74.

Another way of looking at it is using a number line.

Start at 44 and make 3 leaps of 10 each.

Thus, 44 + 30 = 74.

A hundred chart or a numbered ten by ten grid also can be used for the same.

In a hundred chart the consecutive numbers in each column are a difference of 10.

To add 44 and 30, first, locate 44 in the chart. To add 10 moves one row down in the same column. To add 30, that is, 3 tens repeat the process twice more.

Thus, 44 + 30 = 74.

 

Subtraction

The kindergarten kids are familiar with subtracting one digit numbers. In grade 1, they get introduced to subtraction of two digit numbers. Initially, they conceptualize the addition and subtraction of ten with/from a two digit number.

Using counters it is very easy to imagine the subtraction by cutting off one set of tens.

32 – 10 = 22

Just like addition, subtraction can also be shown using a number line with a backward leap of 10.

Once the concept is clear to the kids and with repeated practice, they can do it as a mental math.

In a similar way, when there is more number of tens to subtract, repeat the same process.

Consider 70 – 40.

Talking in terms of place value, to subtract 40 from 70, you need to subtract 4 tens from 7 tens. Thus, the difference is (7 – 4) tens or 3 tens. Therefore, 70 – 40 = 30.

SplashLearn provides worksheets for subtracting multiples of 10.