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This lesson plan is on Measuring, Graphing, and Cardinal Numbers




1, 2  

Title – Cardinal Numbers, Graphing Names
By – Scott Dan
Subject – Math
Grade Level – 1st – 2nd
Scott J. Dan

Concept: Cardinal Numbers
NCTM Curriculum Standards:
1. Mathematics as Problem Solving
2. Mathematics as Communication
3. Mathematics as Reasoning
4. Mathematical Connections
5. Number Sense and Numeration
6. Patterns and Relationships
7. Measurement
1. The students will develop one to one correspondence by writing the letters of their names in 1-inch square grids.
2. The students will develop one to one correspondence by using beans to count the number of letters in their name.
3. The students will develop visual discrimination and communication skills by comparing and contrasting various aspects of differing names in the classroom.
4. The students will begin to develop a basic concept of measuring by comparing various names in the classroom.
5. The students will explore the concept of a graph and make meaningful connections as to how they can use graphs in their daily life.
6. The students will explore the concept of patterns using the various names of children in the classroom by arranging and rearranging those names under specific criteria which will at first be set by the class and then by individual students.

Sorting and Categorizing:

The teacher will provide each student with precut squares of the patterns found at the end of this lesson labeled “worksheet A.” The student will be asked to put these into different piles, each pile being alike in some way. Allow time for all students to finish but do not exceed more than 5 minutes for this part of the activity. Ask for volunteers to demonstrate how they sorted their patterns on the overhead (see overhead sheet at back of this lesson). If many children decided to sort it differently than you had (based on size), give them the second set of precut squares, which contain more patterns, but with less distortion. Once again, discuss how the students sorted the patterns by asking for volunteers to demonstrate on the overhead (overhead sheet available at back of this lesson). The students will then be given six pieces of grid paper that is one inch squared. Below is an example of what the students would be receiving, except theirs will be as long as the longest first name in the class.

The students will begin by writing their names in the boxes, using one box for each letter of their names. They will repeat this six times. They will then count the number of squares used, and use a pile of beans (or any other counter) to double check their answer. They will then write that number on the back of their sheets to help them remember their answer. When a student has finished, he/she may walk around show their names to other students, asking them to try to find ways that their names are alike and different. Allow four to five minutes for exploration.
Reflection and Explaining:
The class will then meet back by the calendar area for a whole group discussion, where several children may share with the class how long their names are. They will only need to bring one of the grids back to this area, leaving the other five grids on their desks. The teacher may call two children up to the front and ask them to compare each other’s names, asking them how their names are alike, and how they are different. This may be done several times, each time encouraging the children to try to find different comparisons than the previous person. The teacher may also ask particular children if their name is either longer or shorter than another class member’s name. The teacher may also ask such questions as, “How much longer is your name compared to Sally’s name? Is your name closer in length (or size) to someone else’s name other than Sally’s name? Can you find anyone whose name is exactly the same size as your name?”
Since first grader’s attention span is shorter than an upper elementary grade level, the teacher may not be able to let everyone have a turn up at the front of the room. In order for every child to explore the questions that were asked earlier, an additional 5-10 minutes should be given to let the children walk around the room and once again compare their names to other children.
Generalizing and Articulating:
This section of the lesson is integrated into the previous section, reflecting and articulating. For example, when a student is explaining how long their name is, the teacher will be listening for some kind of label, letters, spaces, squares, etc. If a student would simply say my name is 10, the teacher may say that she doesn’t understand what the student means when they say “10,” could they please explain it a little more. This would most likely lead the students to say “10 spaces,” or something else similar. The teacher would then repeat what that student just said with some enthusiasm, “Oh, ten spaces,” emphasizing the word “spaces”.
The teacher would continue to follow this role during the rest of the activity, asking similar questions when the children are comparing their names.
Verifying and Refining: (may be done on another day)
The students will meet back by the calendar area where the teacher has already prepared a large piece of grid paper with each child’s name on the left hand side and numbers 1-30 on the bottom.


1 2 3 4 5 6 7 8 .
Ask the children if they know what this is and what we are going to do with it. Ask the children what do they see when they look at it (names, numbers, squares). Then have several children at one time come up to the large grid paper and color in (next to their name) squares for each letter in their name. This part of the lesson takes a while. In order to not let the children get bored, this would end today’s lesson. Children would continue to come up, one at a time, and color in by their name. The teacher could ask the students to have the person who just finished to stay up and help the next person. This would not only free up the teacher to continue with another lesson, but it would also lessen the possibility of a child not coloring in the correct number of squares for their name. When everyone has finished coloring in next to their name, ask the children what they see.
Day Two:
Explain that they have just created a graph. A graph is a way to organize information using a picture along with other information. “Does anyone see any patterns in our graph?” “Does anything on the graph really jump out at you?” “Is there one name on the graph that is longer than anyone else’s in the class?” “Are any names really short compared to others?” “Are there any names that are exactly the same length?” “Are there any names that are about the same length?” “Does anyone see anything on the graph that they think is interesting when they look at the it?”
The last question should be, “Is this graph easy to read?” If they answer yes, ask if they can think of any other way to organize the information. If they say no, then ask if they can think of another way to organize the information on the graph to make it easier to read. Break them up in small groups (groups of five) to explore this answer. Give the children about 5-10 minutes to discuss. Use the other five grids that the children made earlier and provide one to each of the other five groups. This is so that each group will have the names of everyone in class. Once a group has reached a final agreement on how they would like to organize the information, have them tape them down on large sheets of paper. If a group has more than one idea, they may explain it to the class when they present their other idea.
After everyone has finished presenting their ideas, compare the various ways children decided to organize their information. Then show a graph that you had made using the student’s grids that they had made earlier. Ask them if they can tell how you organized the information (from smallest to largest or vice versa).
If there is space available, hang the large graph of the names along with the student’s and teacher’s smaller graphs. Have the students name both the original graph and theirs.

Work Cited

1. Reys, Robert E. et. Al. (1998). Helping Children Learn Mathematics. Chapter 6, “Development of Number Sense and Counting.” (pp 96-97). Needham Heights, MA: Allyn and Bacon, A Viacom Company.

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