More, Fewer, Same

Summary

Activities focus on number concepts, specifically more, fewer, and same.

Materials

Invitation to Learn

• Deck of cards
• Alligator puppet

Group Activity

• More or Less?

Center 1: Alligator More/Fewer

• Alligator More and Fewer
• Number cubes
• Pencil

Center 2: Counter Toss

• More/Fewer/Same
• Pencil
• Counters
• Cup

Center 3: More/Fewer/Same Spinner Game

• More/Fewer/Same Spinner
• Interlocking cubes

Center 4: Hoop Fun

• Three hoops
• Manipulatives
• Index cards
• Math journal
• Pencil

Center 5: Tower Power

• Number cubes
• Interlocking cubes
• More/Fewer/Same Spinner
• Pencil

Center 6: More/Fewer/Same Balance

• Simple balance
• Manipulatives
• More/Fewer/Same
• Pencils

Additional Resources

Books

Just Enough Carrots, by Stuart J. Murphy; ISBN 0-06-026778-X (Children's Book)
Moo-ving into Math Journals, by Margaret Allen, Ph.D.; ISBN 0-9722832-0-X (Professional Book)
More or Less?, by Judy Nayer; ISBN 1-56784-954-7 (Big Book)
More, Fewer, Less, by Tana Hoban; ISBN 0-688-15694-0 (Children's Book)

Organizations

National Council of Teachers of Mathematics, 1906 Association Drive, Reston, VA 20191- 1502 (703) 620-9840, www.nctm.org
National Association for the Education Of Young Children, 1509 16th St. N.W., Washington, DC 20036 (202) 232-8777 or (800) 424-2460, naeyc.org

Background for Teachers

Students that are successful in math have learned to link numbers to quantities. This is the first and most significant step in being a successful mathematician. Many students have an easy time counting but a difficult time when asked to put a number to that which was counted. They may also have a difficult time when the questions, "Which is fewer, 2 or 4?" or "Which is more, 2 or 4?" are asked. It is essential that students have opportunities to explore number combinations and that they are asked these important questions.

The vocabulary of more, fewer, and the same is an integral concept at the early stages of mathematical learning. At the beginning of the school year, most students understand the concept of more. Do not assume because they know which set has more that in turn they know which set has fewer. The vocabulary terms more, fewer and same have to be taught. The vocabulary of math is going to impact how students express their mathematical thinking and future math success. Quantity discrimination is extremely important because it is a key component in estimation and number representation.

Students will be entering your classroom this fall with a variety of informal or formal instruction on number concepts that they bring from home and pre-school. There is going to be a need to differentiate your instruction in number sense.

Intended Learning Outcomes

1. Demonstrate a positive learning attitude.
5. Understand and use basic concepts and skills.
6. Communicate clearly in oral, artistic, written, and nonverbal form.

Instructional Procedures

Invitation to Learn

Use a large deck of playing cards (remove the face cards) or multiple cards numbered from 1-10. Group Activity

1. Introduce the words more, same, and less. Talk about how the words less and fewer mean the same thing and that you will be using both of these math words.
2. Have the students look at the book cover and predict which group of flowers has more and which group has less.
3. Read the book More or Less to the class and have them predict the correct answers to the questions that are asked.
4. Go back through the book and have your students come up with their own more/less/same questions.
5. This book can be used over and over again. The photographs lend themselves to further exploration.

Center 1: Alligator More/Fewer

Part One:

1. Each student will need a copy of the Alligator More and Fewer recording sheet and two number cubes.
2. Explain that the alligator wants to eat the number that is more.
3. The student rolls the two numbered cubes.
4. The number that is more is written on the left side of the paper so that it visually looks like the alligator is going to eat it up!
5. The number that is less is written on the right side.
6. If the student rolls two numbers that are the same, he/she needs to roll again. The alligator cannot eat numbers that are the same.
7. The alligator's mouth looks like the symbol for more. Use this great introduction to teach students the symbols of greater than, less than, or equal.

Part Two:

1. A student rolls two number cubes and then arranges them to make the largest number and the smallest number (e.g., the roll 3 and 6 should be arranged as 63 for the largest number and 36 for the smallest number).
2. Students record this on the Alligator More and Fewer recording sheet. The number that is more should be written on the line so that it visually looks as if the alligator is going to eat it up!
3. The number that is the least should be written on the line behind the alligator's mouth.
4. If the student rolls two numbers that are the same, he/she needs to roll again. The alligator cannot eat numbers that are the same.

Center 2: Counter Toss

1. Students take a specific number of two-sided counters (e.g., 10, 20, 30 counters)
2. Put the counters in a cup.
3. Shake the cup and the counters
4. Dump the counters onto the table.
5. Sort the counters by color.
6. Record the toss on the More/ Fewer/ Same recording sheet.
7. Math Journal: This activity could be recorded in a journal and have the student draw the alligator on their paper.

Center 3: More/Fewer/Same Spinner Game

1. This is a partner game that can be done in a center or as a group.
2. Each partner begins the game with ten interlocking cubes.
3. The first student spins the spinner that is marked More/Fewer/ Same.
4. If the spinner lands on more, the player takes one interlocking cube from his/her partner.
5. If the spinner lands on fewer, he/she has to give one interlocking cube to his/her partner.
6. If the spinner lands on same, they just stay the same.
7. The winner is decided when one player has all of the interlocking cubes.

Center 4: Hoop Fun

Part One:

1. Students take a small handful of two different manipulatives.
2. Put the manipulatives in two piles.
3. Count the number of manipulatives in each pile.
4. Use the sorting hoops on the floor.
5. Label index cards with the words More, Fewer, and Same.
6. Place the labeled index card above the sorting hoops.
7. Place the manipulatives inside the appropriate hoop. The manipulatives that have more go into the hoop labeled more. The manipulatives that have less go into the hoop labeled less. If the manipulative groups are the same, place all of them in the hoop labeled same.
8. Journal Activity- This activity could be recorded in a math journal. Students will need to draw three circles in their journals. Have the students label the three circles with More/ Fewer/Same. Have students draw a picture to represent the manipulatives in each circle.

Part Two:

1. Follow the same procedure but use only two circles.
2. Cross the circles to create a Venn diagram.
3. Journal Activity- Have the students draw a Venn diagram in their math journals. Have the students label the Venn diagram More/Same/Fewer. Have students draw a picture to represent the manipulatives in each space of the diagram.

Center 5: Tower Power

1. This game may be played as partners.
2. Each player rolls a number cube.
3. Players build their towers, using the interlocking cubes, according to the number that they rolled.
4. With the towers built, have one player spin the More/Fewer/ Same Spinner.
5. If the spinner lands on more, the student who has the most blocks takes all of the towers.
6. If the spinner lands on fewer, the student with the fewest blocks takes all of the towers.
7. If the spinner lands on same, the students do not exchange blocks.
8. The winner of each round will set aside the towers that they won.
9. The process is repeated with each player rolling the number cube and building a new tower.
10. Players take turns spinning the spinner.
11. The game ends when there are no more blocks to make towers.
12. Students could use a chart and keep track of wins by making tally marks.

Center 6: More/Fewer/Same Balance

1. Students are given a group of manipulatives.
2. One student puts a chosen number of manipulatives on one side of the balance and another student puts a chosen number of manipulatives on the opposite side of the balance.
3. Compare the manipulatives by looking at the balance to see which way it is leaning. (Students have been taught that the larger the number the more it weighs.)
4. The students then compare the number of manipulatives.
5. Which group has more?
6. Which group has less?
7. The manipulatives are taken off of the balance one side at a time and counted.
8. The students findings are recorded on the More/Fewer/Same recording sheet.
9. The number of manipulatives many be increased as students become number proficient.

Extensions

Curriculum Extensions/Adaptations/Integration

• Use the different stages of activities to meet the needs of your students.
• Ask mathematical questions during Language Arts and Content time.
• All students can use centers. Adaptations in quantity of numbers can be adjusted to meet the specific needs of each student.
• Center activities should be taught to the whole group and then placed in a center for students to practice and become proficient in the subject matter.

Family Connections

• Have the students take home a More and Fewer recording sheet. Have the students look around their houses. Tell them to draw/ write the name of something they have more of in their homes and something that they have less of in their homes (e.g., draw a picture of a chair in the more column and a picture of an oven in the less column).
• The alligator puppet could be sent home with a More and Fewer recording sheet. The students and their families could look around their homes for items that they have more/fewer of and record their findings on the recording sheet.
• Math Night- Parents would be invited to make the math activities for their homes.

Assessment Plan

• The math journal is an excellent way for you to evaluate a student's mathematical thinking.
• Observations: These can be recorded on small sticky notes or on an Observation Sheet. Make notes about students that need to be pulled into a small group for extra help.
• A Math Check list is kept to keep track of students' progress.
• Ask probing questions to focus students' thinking when using manipulatives.
• Have students share their thinking about the activity.
• Collect any recording sheets. This will give you time to make an in-depth assessment of a student's number sense.

Bibliography

Burns, M. & Silbey R. (April 2001). Math Journals Boost Real Learning. Instructor Magazine. p.18-20.

A math journal is one of the best ways to introduce writing into your math class. It helps students stretch their thinking and make sense of problems that can sometimes leave them confused or frustrated. When children write in journals, they examine, express, and keep track of their reasoning, which is especially useful when ideas are too complex to keep in their heads. By reading their journals, you can evaluate their progress and recognize their strengths and needs. The math journal thus becomes a great learning tool for your students- and you.

Ediger, M. (2006). Writing in the Mathematics Curriculum. Journal of Instructional Psychology. Vol. 33.

Criteria for Use in Mathematics Writing:

1. Learning needs to be meaningful. Students need to make sense out of what is being learned.
2. Interest is a powerful factor in learning. Mathematics teachers need to provide for the interests of the learner. A hands-on approach should also be stressed to add interest.
3. Students should perceive a purpose in the writing experience. Writing should not be done for the sake of doing so, but rather to achieve a definite goal.
4. Students should work individually as well as collectively in ongoing learning experiences.