## 1, 2, 3 Hooray for Number Equivalency!

### Liz West

#### Description

Students use concrete materials, number symbols, and number words to represent equivalent amounts.

#### Objectives

The student reads and writes numerals to 100 or more.

The student compares and orders whole numbers to 100 or more using concrete materials, drawings, number lines, and symbols (less than, =, greater than).

The student compares two or more sets (up to 100 objects in each set) and identifies which set is equal to, more than, or less than the other.

The student represents equivalent forms of the same number, up to 20 or more, through the use of concrete materials (including coins), diagrams, and number expressions (for example, 16 can be represented as 8+8, 10+6, 4+4+4+4, 20-4, 17-1).

#### Materials

-Markers
-18x24 sheet of construction paper for each child (see Teacher Preparation)
-Glue
-Assorted concrete materials, such as, wagon wheel pasta, beads, sequins, cotton balls, beans, split peas, small seashells, toothpicks, elbow macaroni, cotton swabs, stickers, and paper clips.
-Scissors for each student
-One plastic zip bag for each student

#### Preparations

The teacher will need to:
1. Fold construction paper into twelve equal parts, one for each child
2. Gather materials listed above, so there is enough for each group of students.

#### Procedures

Day 1
1. Ask students what they remember about the different ways that numbers can be represented. Write student responses on the overhead. (They should include symbols, number words and concrete materials.)

2. Tell students that today we are going to learn how these different number forms can be equivalent. Guide class to create a working definition of -equivalent.-

3. Using the overhead, show the students that the number 3 can be represented in several different ways. It can be shown symbolically (write the numeral -3-); it can be shown with the word (write the word -three-); or it can be represented by objects (place 3 manipulatives on the overhead.)

4. Ask students for other examples to demonstrate on the overhead. After several other examples, ask students, “Do we understand how numbers can be represented in different forms and still be equivalent?” As the class comes to agreement on equivalency, ask if there are any questions at this time.

5. Show students a sheet of construction paper that has already been divided into twelve equal parts.(See Teacher Preparation.)

6. Explain to the class that they will be using the paper to show the numbers 1-12 in three different ways, making a number collage.

7. In each part of the paper, have students label each section with a number from 1-12. Then, the students write the corresponding number word, choose one of the concrete materials and glue the appropriate number onto the paper, starting with the number one.

8. Have students continue in the same manner for each box on their paper. They should have a new number in each section and use a different concrete material to glue in each box.

9. As students work together to share manipulatives and work cooperatively, circulate and assist those who are having difficulty with the concept.

10. As students complete their projects, collect their work and review the material taught. Show class examples of student work that demonstrates understanding of equivalency and review the three ways to demonstrate numbers. (Symbols, words, and concrete materials.)

Day 2
1. Explain to the students that today they will cut apart their number collages and will practice ordering and comparing numbers.

2. Supply students with scissors and plastic zip bags.

3. Have students cut their number collages apart and place into the plastic bag.

4. Have students then take their numbers out of the bag and order from least to greatest. Have them compare their answers with a partner for accuracy as you circulate and observe.

5. On the overhead, display a number and have students select one of their own pieces that is -greater than- the one displayed. Have students suggest appropriate and nonappropriate answers. Complete the same process for -less than.- When students exhibit an understanding of these concepts, have pairs of students quiz each other. As students continue to work, circulate and check for accuracy. As you circulate among the students, ask individual students to compare numbers using appropriate vocabulary, such as, greater than, less than, and equal.

(Hint: a roster on a clipboard is helpful to record observations on each child as you gather formative assessment information.)

#### Assessments

During the lesson and the cooperative group project, use the following formative assessment criteria:

-Teacher observation of students’ number collage project: Circulate and assist students as they work. Check to make sure they have a strong understanding of number equivalency. Students should get 9 out of 12 correct. Verify that numerals are written correctly.

-During group work, assess students for their ability to share materials and work cooperatively using a criteria of
~Excellent, (shares all materials, works well with members of the group, helps others);
~Satisfactory, (shares some of the time, works with others occasionally, finishes their project);
~Needs Improvement, (does not share materials, works alone, does not finish project)

-On day two, as students order their numbers from least to greatest, circulate among the class to check for accuracy. Students should be able to order numbers with 100% accuracy. As you go to each child’s desk, take two of their number collage pieces and ask them to compare the two numbers using appropriate vocabulary. Give the child three opportunities to compare numbers and respond. Students should be able to get two out of three correct with appropriate vocabulary. Use the following performance criteria to assess the student:
~Excellent, (student is able to order numbers from least to greatest with 100% accuracy and is able to compare two numbers accurately, three out of three times)
~Satisfactory, (student is able to order numbers from least to greatest with 100% accuracy and is able to compare two numbers accurately, two out of three times)
~Needs Improvement, (student is unable to order numbers from least to greatest and is unable to compare numbers accurately)

#### Extensions

This lesson can be modified for students who are still at the concrete operational level by omitting the number word portion. It can also be modified for exceptional education students by changing the number of tasks assigned by either increasing or decreasing this.

As an added challenge or follow-up lesson, students can show equivalencies by selecting different number expresions that represent a given number.