10 Tens

Est. Class Sessions: 1–2

Developing the Lesson

Compare the Number of Letters in Names. Ask students to count the letters in their first names. For example, Anna has four letters in her first name. Have volunteers share their numbers with the class.

Ask:

Do you think the total number of letters in the first names of everyone in this class is more than 100 or less than 100?
Why do you think so?

Assign students to groups of four and distribute 30 connecting cubes to each group. Ask each student to make a stack of connecting cubes to show the number of letters in his or her name. Have them compare the heights of their stacks within their groups. When everyone is ready, ask students to think of some sentences that describe the number of letters in the names in their group. Help them get started by giving examples such as the following:

The greatest number of letters is ________ .
The smallest number of letters is ________ .
________ names have six letters.
We all have the same number of letters. We each have ________ letters in our names.
Nicholas has more letters in his name than Grace.
Shannon's name has two more letters than Jacob's.

For small classes, it's possible that your total letters may not reach 100. If so, make your numbers larger by including your own first name and the first names of assistants or other adults such as the gym teacher, music teacher, recess monitors, etc., who work with the students.

Encourage students to think of their own sentences and then share them with the class.

Find Total Letters for Group. Now ask each group to combine the stacks for all their names into stacks of ten cubes and a stack of leftover ones. Give the students a few minutes to discuss among themselves how best to do this. It is important that they put away any extra cubes that were not used in building their name stacks so these cubes don't get mixed into the group totals. When they find their total, have them locate the total number of letters on the 100 Chart in the Student Activity Book Reference section.

Ask each group to report their total number of letters so you can record the results on the board. Have students set the stacks of ten cubes and leftover cubes on the tray of the board below the number as shown in Figure 1.

Count by Tens and Leftovers. When all the stacks from the groups have been displayed and the totals written on the board, step back and have the students look at them. Ask the students to think about the numbers they see.

Ask a few open-ended, reflective questions:

Describe what you see with all these numbers. (Possible responses: the numbers aren't very far from each other; there are only a few teens; they are not in order; only a few 30s; lots of stacks of tens and also smaller stacks)
Why do you think the numbers are close to each other?
How could we figure out the total number of letters for our whole class?
How can we use the cube stacks to figure out how many letters we have in all?
What would be the best way to add these together?

If no one suggests rearranging the stacks so that all the ten-stacks are together, start out counting from left to right. Have the class count along with you and start counting by tens. As soon as you come to a stack of ones, it should become apparent that it might be easier to put all the ten stacks together and count them first. Have some student volunteers rearrange the stacks so the tens come first and have others put the ones-stacks together to make stacks of ten. Make sure that the numbers written on the board for each group's totals are not erased.

Some students may suggest using a calculator to find the total. Tell them that using a calculator is also a good way and that the class will check its work at the end using their calculators.

When all the stacks have been rearranged, have the class count aloud with you, counting by tens. At 100, stop and ask:

How many stacks of 10 cubes make 100 cubes? (ten)
Is our total number of letters going to be more than or less than 100?

Continue counting until you have the total of all the letters. At this point, repeat counting the stacks of ten cubes and leftover ones and ask a student to point to the numbers on the classroom number line as the class says them. To check the results, have students use calculators to add the numbers gathered from each group, which should still be on the board.

When the counting reaches ten stacks of 10, some teachers put the ten stacks in a clear 1-gallon ziplock bag and label it "100." This segregates the first 100 and draws student attention to the fact that 10 tens make 100.

Collect Letters in More Names. Assign the How Many Letters Homework Master. After the students hand in their homework, tell the class how many students turned in data, and then ask them to predict the total number of letters in all the names collected on the homework pages.

Ask:

Would the number be about 100, 200, 300, 400?

Make this discussion a playful encounter with larger numbers.

Organize students into groups of four and have each group find the total number of letters in the names on the homework page.

Record the total from each group on the board and ask:

Look at the number of letters collected by each group. Do you think there are 100, 200, 300, or 400 letters in the names the class collected for homework? (Answers will vary.)

Conclude by having students use their calculators to find the total number of letters collected by the class.

Comparing Numbers. Refer students to the Comparing Names pages in the Student Activity Book. Tell pairs of students to use connecting cubes and their 100 Charts to answer the questions.

Use the Comparing Names pages in the Student Activity Book to assess students' abilities to represent and identify numbers to 100 using counters, 100 chart, and symbols [E1]; represent the partitions of two-digit numbers as tens and leftover ones [E2]; and compare the relationship of numbers using less than, greater than, between, and closer to [E3].