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''Ten''ding the Herd: Counting Large Numbers by Tens and Ones

  • Lesson
Pre-K-2
1
Number and Operations
Laurie A. Penney
Acton, MA

In this lesson, students work at stations where they practice counting large numbers by grouping herds of cows into tens and leftover ones, developing a deeper understanding of place value. The activities involve the use of manipulatives, ten-frames, and the Illuminations online activity Grouping and Grazing. 

This lesson focuses on developing student understanding of how two-digit numbers are constructed of tens and ones and on the effectiveness of counting large numbers by tens and adding on the leftover ones. The student work is divided into 3 activities, all of which provide practice in a slightly different aspect of the concept. In Station 1, students practice carefully counting out groups of tens, and then counting up by tens and additional ones. Additionally, they begin to see the addition expressions that relate to the counting they have done. In Station 2, students fill ten frames to count large numbers. They solidify their familiarity of the makeup of tens and parts of tens, and recognize that frames that are not completely filled cannot be counted as a ten. Finally, the Station 3 activity helps students discover how to use place value to determine how many groups of ten a number has and how many ones are left over.

The teacher should give clear directions for all three stations at the beginning of the lesson, demonstrating the activities to the whole class and answering any questions. Stations are designed for independent work so the teacher can assist students where needed, and students should spend approximately 15 minutes at each one. However, the amount of time students spend at stations can be lengthened or shortened depending on teacher and student needs.

Station 1: Grouping and Grazing 

For this station, prepare the following:

Computers, opened to the Grouping and Grazing Illuminations activity. Familiarize yourself with this activity prior to the lesson.

appicon Grouping and Grazing 

At this station students will explore the Count by 10s section of the Grouping and Grazing Illuminations activity. As the teacher observes students at this station, it is easy to determine how many times a student has played this game by noticing how many barns are red at the bottom of the screen. If a student is struggling or very new to this concept, the “count with me” option can be helpful. In this option, the student must click first on each group of ten and then each one, and a voice says the numbers aloud. Most students will choose the “count alone” option, which asks them to input the total number of cows into a calculator on the screen and then  to check their work. Students who are ready to move ahead can choose the Count by 5s option, or even the Addition or Subtraction features of this activity.

Station 2: Counting Cows 

For this station, prepare the following:

  • Reproduce and cut apart the Cownters so that there are between 30-60 for each student at the station. Place them in a bowl or bag where the students can reach them.
  • Reproduce one Counting Cows Activity Sheet for each student.
  • Reproduce the Counting Cows Recording Sheet, making enough for each student in the class to have one, plus some extras.

pdficon Cownters 

pdficon Counting Cows Activity Sheet 

pdficon Counting Cows Recording Sheet 

pdficon Counting Cows Recording Sheet Answer Key 

At this station students also count by tens and ones, using ten frames to make groups. Students take handfuls of the Cownters, and count them by placing them in the ten frames on the activity sheet. Then, following the directions on the Counting Cows recording sheet, they determine the number of cows they have. The activity is repeated, taking new handfuls of cows each time. Before it is repeated, however, students should trade their completed recording sheets with a partner and each should check the other’s work. Have students discuss any mistakes and work together to rectify the mistake. If students are having difficulty grabbing a reasonable number of cows (too many or too few), another option is to separate the Cownters into bags or cups ahead of time. In this way, the teacher can guide students to numbers that provide an appropriate task (suggested range: 11-69). Before students begin on a new “herd,” each student should check his or her work by having a partner look it over and point out any errors. Students who are ready to move ahead can combine their ten frames with their partner’s to create and count much larger numbers.

Station 3: How Many Tens? How Many Ones? 

For this station, prepare the following:

  • Reproduce one copy of the How Many Tens? How Many Ones? Activity Sheet for each student.
  • Make spinners using the Spinners Activity Sheet, so that each student at the station has one.
  • Provide paper clips and pencils for spinning.

pdficon How Many Tens? How Many Ones? Activity Sheet 

pdficon How Many Tens? How Many Ones? Answer Key  

pdficon Spinners Activity Sheet 

At this station, students will start to solidify their understanding that the digit in the tens place of a number stands for the number of tens. Using the How Many Tens? How Many Ones? activity sheet, students will work with random numbers to determine the number of tens and ones. For the last page of the activity sheet, students spin a spinner to determine their number. A blank spinner has been provided for creating options with smaller or larger numbers to fit the diverse needs of the group. Students who are struggling with this concept should continue to draw representations of the numbers and circle groups of tens. Students who are ready to move ahead can try to determine the number of groups of tens in three-digit numbers.

After students have worked at all three stations, bring them together for a closing activity. Students should share what they have learned. Offer some two-digit numbers, and ask for volunteers to share how many tens and ones are in the numbers and how they know. Ask students to share their strategies for finding the tens and ones in a number, and discuss what they learned at each station.

Assessment Options 

  1. Have students count collections of other items by grouping tens and ones.
  2. Write a list of 2-digit numbers on the board, and have volunteers state how many groups of ten there are and how many remain.
  3. Encourage students to draw or use other strategies that would help them find their answers.

Extensions 

  1. Given pairs of two-digit numbers, have students determine how many more groups of ten one has than the other.
  2. How does the difference between groups of tens compare to the actual difference between the numbers? For example, how can 31 have one more group of ten than 29, yet the numbers are only two apart?
  3. Have students count objects by 20s. Can the student still determine how many tens are in the number?

Questions for Students  

1. Why do you think the spaceship picks up ten cows?

[Allows us to count by tens. Counting by tens is more efficient than counting by ones.]

2. What do the cow pens and the single cows represent?

[The cow pens are the tens, the single cows are the ones.]

3. How do you count the cows if they do not fill a whole ten frame?

[You count those cows by ones.]

4. What do you notice about the number of groups of tens and the digits in the tens place, and why is this so?

[They are the same. The digit in the tens place stands for the number of tens in a number.]

Teacher Reflection  

  • Was students’ level of enthusiasm/involvement high or low? Explain why.
  • How did the stations address auditory, tactile and visual learning styles?
  • How did the students demonstrate understanding of the materials presented?
  • How well did your students work independently?
  • How did the set-up of the stations affect the level of focus and engagement in the classroom?

 

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Learning Objectives

Students will:

  • Divide a large group of objects into groups of tens and remaining ones.
  • Count a large group by counting the tens and adding the remaining ones.
  • Extrapolate the number of groups of tens and remaining ones by looking at a number.

NCTM Standards and Expectations

  • Count with understanding and recognize "how many" in sets of objects.
  • Use multiple models to develop initial understandings of place value and the base-ten number system