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This lesson is on Grouping and Place Value using various objects




1, 2  

Title – Place Value
By – Scott Dan
Subject – Math
Grade Level – 1st – 2nd
N343 sec 02

Format: Guided Discovery

Concept: Grouping and Place Value

1. Place Value Mat
2. Beans
3. Cards with numbers on them (enough for everyone to have at least 10)
4. Overhead transparencies of tens units (made out of peppers)
5. Overhead transparency of the place value mat
6. 12 small Bowls (enough for every group of two to have one)
7. Base Ten Units made out of tongue depressors and ten beans
8. Overhead Projector

NCTM Curriculum Standards for School Mathematics:
1. Mathematics as Problem Solving
2. Mathematics as Communication
3. Mathematics as Reasoning
4. Mathematics as Connections
5. Estimation
6. Number Sense and Numeration
7. Concepts of Whole-Number Operations

1. The students will expand their awareness of numbers and knowledge of number sense by expressing a symbolic number in various ways.
2. Through the process of counting and manipulation of beans, children will discover various ways to group numbers so that they may become easier to recognize and count.
3. The students will begin to explore the concept of place value through the grouping of beans into sets of tens and their appropriate placement on a place value mat.

1. Make place value mats for the tens units and ones units.
2. On a separate day (before this lesson), have children make base ten bean sticks (thumb depressors with ten beans glued on). Each child should make ten of these sticks. Have them write their names on the back of each depressor

1. Have the students clear off their desks so that they may have a good working surface.
2. Place one pepper on the overhead and turn it on for about 4 seconds. Turn off the machine and ask anyone if they can tell how many peppers were placed on the overhead. Take a child’s answer and then turn on the machine to see if they were right. Do the same for 3 peppers and 5 peppers.
3. Then, randomly place 8 peppers on the overhead and ask the same question. If the children have trouble answering this question, turn on the machine and count how many peppers there are. Repeat the number 8 one more time, but this time place the peppers into one group of five and one group of three.

If the children have an easier time answering this time, ask what helped them.
4. Place ten peppers on the overhead in no particular order. Have the children guess
the number and then repeat with one stick of ten peppers.
5. Reinforce this concept of grouping with the following numbers: 11, 15, 20, 25, 30 and 39. Turn on the machine with the numbers already organized into groups. For every ten, use a base ten pepper rod. Ask the children to guess the number of peppers every time, and then turn on the machine to check their answers.
6. Ask the children, “How am I grouping the numbers?” Ask them, “Do you always have to group by tens?” Ask them, “Can someone come up and show me another way to group the number 20.” Take several volunteers until no one else has a new way. Do this with a couple of numbers, but be aware of the children’s attention span and interest level in the activity. Also discuss which way is easier when counting large numbers. Is it counting by two’s? By fives? Or by tens?
7. Give every child a pile of beans (peppers will burn their eyes) and their 10 bean sticks that they made the previous day. (*Note: To save time, the teacher should put every child’s bean sticks and a pile of beans into a zip lock bag with their name on it. The teacher can then pass out the bags when it is time for the activity.)
8. Guide the children through a few more examples by writing a number on the overhead and allowing the children time to work on grouping that number so that it is easiest for them to read. After every example, allow a couple of children to come up to the overhead to explain how they decided to group their numbers. Discuss any use of bean sticks if it is brought up by one of the children.
9. If no one brings up the use of bean sticks for grouping in sets of ten, then ask the children to do a fairly large number, such as fifty. Allow time for them to work, ask for volunteers to share how they solved the problem and then share how you had divided them up; five sticks of ten (if no one brings up the idea first).
10. Pass out the number cards to the children and ask them to continue grouping the numbers so that they are able to read and recognize that number quickly. Allow this part of the lesson to continue for about 10-15 minutes. Stop and visit each child in the room to see how they are doing.
This would be the end of this today’s lesson.
The following is what would be done on the next day.
The same materials and objectives apply, as it is a continuation of the previous day’s lesson.

1. Have the children separate into groups of two.
2. Pass out the place value mats and discuss what they see. Ask if anyone can guess what we are going to use the mats for today.
3. Pass out the bowls, each bowl containing no more than 99 beans. Also pass out the children’s zip lock bags containing their base ten rods that they made.
4. Explain to the children (as you demonstrate on the overhead with a transparency of the place value mat) that they may take turns in grabbing a handful of beans and laying them on them on their place value mat. Tell the children that sometimes they may grad big handfuls or small handfuls of beans, so long as they don’t keep getting the same number over and over. Explain that they are to count the number of beans that they grabbed and then are to group them using the place value mat that is in front of them. Remind them of the activity that they did yesterday, and ask them what they did every time that they had ten of something (they used a stick). Ask them to place their sticks under the tens column on their place value mats. Ask the children to explain why they think we are putting the groups of ten under this column.
5. Demonstrate a couple of numbers for the children. For each completed example ask the following three questions: “What was my number?” “How many tens did I have?” “How many ones did I have?” “If I count by tens and add the ones do I get the number of beans I grabbed?” Demonstrate that last part out loud so the children can hear how you think it through. Then ask for a few volunteers to come up to the overhead to complete one. Ask them the same questions as you asked before. Ask if they have any questions and then let them work in their groups for about 20-25 minutes.
6. The teacher should use this time to walk around the room and talk to the children about how they are doing. He/She should also encourage them to ask those three questions that were stated earlier.
7. At the end of the lesson, ask the children if they want to share anything that they found out while they were using the beans. Some children might point out that there were only 99 beans in the tray. Other children might point other various interesting points that they enjoyed about the lesson.

Connections to the Students’ Lives:
1. Everyday continue to use the overhead to show both scrambled numbers and organized numbers to increase the students’ abilities in number recognition.
2. Continue this process both inside and outside the classroom by:
a. Using everyday materials (pencils, keys, misc. non-messy food) and spilling them on the floor. Challenge the students to count the materials by grouping them in their heads.
b. Taking trips outside and counting objects in nature (trees, bugs, shoes).
c. Ask children to count as many things as they can at home by grouping them into easy to recognize sets.

Work Cited

1. Reys, Robert E. et. Al. (1998). Helping Children Learn Mathematics. Chapter 6, “Development of Number Sense and Counting.” (pp 88-89). Needham Heights, MA: Allyn and Bacon, A Viacom Company.
2. Reys, Robert E. et. Al. (1998). Helping Children Learn Mathematics. Chapter 7, “Developing Number Sense with Numeration and Place Value.” (pp 115-123). Needham Heights, MA: Allyn and Bacon, A Viacom Company.

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