Math Background

Lesson: Place Value to 100
Developing the Concept

By now your children should have a good understanding of place value for tens and ones. They should know that tens digits tell how many groups of ten there are, and the ones are the singles that are left over. Now that children have mastered this, they can start to compare and order two-digit numbers by comparing the tens digits and then the ones, to find which are greater or lesser. Then they can place the numbers in order from least to greatest.

Materials: connecting cubes

Preparation: none

Prerequisite Skills and Concepts: Children should understand the concept of tens and ones and number patterns through 100.

  • Say: We have been working hard to understand what tens and ones mean in two-digit numbers. You have learned that the tens digit tells us the number of groups of tens there are, and the ones digit tells us the number of ones that are left over. Today, we are going to use what we know about place value to compare and order the two-digit numbers we have been working with.
  • Say: Let's look at these two numbers. Write the numbers32 and48 on the board. If we want to compare these two numbers, we first have to look at the tens in each number. Make each number with your connecting cubes.
  • Ask: Who can tell me how many tens are in 32? (3)
    How many tens are in 48? (4)
    Which is more, 3 tens or 4 tens? (4 tens)
  • Say: We can now say that 48 is greater than 32, because 4 tens is more than 3 tens. There is a way we can write this, too. We can use the “greater than” sign. The “greater than” sign looks like this. Write > on the board. We can write that 48 is greater than 32 like this. Write48 > 32.
  • Say: Let's look at these two numbers: 53 and 59. Make these numbers with your connecting cubes. Let's look at the tens in each number.
  • Ask: How many tens are in 53? (5) How many tens are in 59? (5)
  • Say: We have the same number of tens, 5, in each number. Now we have to look at the number of ones in each number.
  • Ask: How many ones are in 53? (3) How many ones are in 59? (9) Which is greater, 3 or 9? (9) So which number is greater, 53 or 59? (59)
  • Say: To show this, we would write 59 > 53.

    Repeat this with many pairs of numbers and ask children to find which number is greater.

  • Say: We can use this same idea to put numbers in order from least to greatest. When we want to order numbers, we need to first look at the tens and then the ones. Look at these numbers: 28, 24, 27, 25, and 26.
  • Ask: What number is in the tens place in all of these numbers? (2)
  • Say: Since these all have 2 tens, we have to focus on the ones for each number.
  • Ask: Which number has the fewest ones? (24)
  • Say: We will start with 24. From here, we look for the number with the next fewest ones. This would be 25.
  • Ask: Who can tell me the next numbers in order? (26, 27, 28)
  • Ask: How did you know this was the right order? (Six is less than seven and seven is less than eight, so they had to go in this order.)

    Repeat for various number sequences.

Wrap-Up and Assessment Hints
Learning the terminology for place value may be difficult for some children. They need a lot of practice with and reinforcement of the terms as well as the concepts. Give your children as many chances as possible to practice using the terms and reading the numbers. The more place-value experiences they have, the better at understanding place value they will become. If children are having problems, allow them to use connecting cubes as often as they can, to model the numbers they are working with. This visual aid can help children see how the numbers compare or how they are built and what digits mean in different place-value positions.

Houghton Mifflin Math Grade 2