Math Background

Place Value to 100: Overview

Place value is a critical feature of our number system, which is a base-ten system. Familiarity with this system is the basis for children's future success in all areas of mathematics. Counting and writing numbers, adding and subtracting numbers, and multiplying and dividing numbers all require understanding of this base-ten system.

Your children have begun to develop an understanding of place-value concepts by adding ten and making ten to add earlier. While using counters and ten-frames to add ten, they had the opportunity to fill ten-frames with counters and connect the models to the digits in the tens and ones places of two-digit numbers. While making a ten to add, they had the chance to see how 10 ones may be exchanged for 1 ten and how 1 ten relates to the digit in the tens place of a two-digit number. They learned how the extra ones, or ones outside of the ten frame, relate to the digit in the ones place of a two-digit number. Building from this base of understanding, you can guide children to see how larger numbers are formed. Be sure to help children realize that the position of a digit represents its value. Help them understand that our system uses the digits 0 to 9 in different positions to write any number. Emphasize that zero represents a lack of ones in a number containing tens and ones. Take every opportunity to reinforce the concept that 10 is a benchmark number in our system and it is the number that determines new groups. Provide children with experiences that involve modeling larger numbers with manipulatives, taking care to help children connect the models and the symbols. Begin with proportional models, such as base-ten blocks, and progress to non-proportional models, such as colored counters and money.

By using manipulatives with children, you allow them to see the relationships among numbers, as they are added, regrouped, and modeled to 100. As they see a “ten” being built, they see that 10 ones equal 1 ten. Once 10 “tens” are formed, the children will see that 10 “tens” equal one hundred. Concrete models are the best to start your children in the right direction for understanding place value.

Another way that your children work to understand place value to 100 is by using a hundred chart. The hundred chart shows the numbers to 100 in a sequential pattern. By using this chart, children can see how numbers grow and the pattern that each group of ten follows.

The hundred chart: numbers one to one-hundred in rows of ten

Children can look at the hundred chart to see various patterns such as, all the numbers that have 5 ones; all the numbers that have zero ones; and the numbers you get if you add 10 to each, starting with 5. These, and any other patterns your children see, will continually reinforce place-value concepts.

As your children progress in their understanding of place value, they can begin to order and compare the numbers they see. By using a hundred chart, your children can see how the numbers are ordered as they follow the patterns on the chart. Once they see the ten and ones pattern, they should be able to start ordering numbers by comparing the numbers in the tens place and in the ones place. When you first ask your children to compare numbers, they can use cubes to model each number, to see which has more tens or more ones, and then decide which is greater or less. Once they have mastered this process, they can compare numbers without using models and can also start using the “greater than” and “less than” symbols (>, <) to show how the numbers compare. Comparing and ordering numbers is a skill that your children need as a basis for all future mathematics operations.


Houghton Mifflin Math Grade 2