### Purpose

To construct understanding of the descriptive purposes of numbers by assigning numbers to objects.

### Context

This is a single lesson designed to help students understand and reinforce how numbers are assigned to objects, as well as think about more, less, or equal values. In this lesson, students are asked to describe, compare, and classify plants. Because plants are so similar, students must rely on very specific information such as number and shape of leaves, height, size relative to other plants, etc. to tell them apart. Students should be able to use numbers concretely and descriptively to count as they make specific observations about plants.

**Note:** Students' own meanings for number words determine to some extent their strategies for adding and subtracting and the complexities of the problems they can solve.(*Benchmarks for Science Literacy*, p. 350)

Students' beliefs and understanding of mathematical inquiry remain relatively unclear throughout their academic life. Some of the misconceptions that students carry are: there is only one correct way to solve any math problem; mathematics problems have only one correct answer; mathematics is done by individuals in isolation; mathematical problems can be solved quickly or not at all; and mathematical problems and their solutions do not have to make sense. (*Benchmarks for Science Literacy*, p. 334)

Because of this, students limit their mathematical behavior. It is important, therefore, that students be exposed to a wide array of concrete representations to help develop a foundation for the higher abstract ideas associated with mathematical inquiry. In this lesson, students will use concrete objects to construct understanding that numbers can be used to describe things in the world around them.

### Planning Ahead

You will need several plants of the same variety. The plants should be labeled in some way (other than numerically) so that you are able to identify them, but the students will not notice. A sticker or mark on the bottom of the container would be best.

In order to help students make detailed observations of their plants, you could provide tools such as hand lenses, rulers, cubes, or balances.

### Motivation

Say to students: *"Let's begin by looking at this plant. I want you to use as many different words that you can think of to tell about the plant. Who can think of some different features that we can use to describe the plant?"*

Allow students to generate a list of words to describe the plant. You may wish to post this list on the board as a cue to help direct the student observations.

### Development

Divide students into groups of two to four. Each group should be given a plant of the same variety. As described in the Planning Ahead section, you should have marked the bottom of the plants (with something other than numbers) so that you are able to keep track of them. Also, groups could be given hand lenses, rulers, cubes, or balances.

Tell students: *"You will be working in small groups to describe or tell about your own plant. It is okay to use some of the ideas that we came up with already, but you will have to tell us even more this time. We want to know exactly what your plant looks like so that we would be able to pick your plant out of a group." *

Give the groups 10 to 15 minutes to finish the description of their plants. Make sure that the students are reminded to write down their list of descriptions of the plants.

Allow students to post and share their descriptions. Take advantage of opportunities to ask questions such as:

- What did you notice about the color?
- What did you notice about the shape of the plant?
- Does any other group have a ___________ (tall, short, dark green, light green, fuzzy, shiny, etc.) plant?
- Who had a plant with ____ (2, 3, 4, etc.) leaves?
- Who had a plant that was _____ (2, 3, 4, etc.) inches/cm/cubes high?

Students should recognize that some descriptions or characteristics are more or less helpful for differentiating between the groups' plants. Ask students to decide which kinds of descriptions are common to all of their plants, and which are not. Have students star or underline those descriptions that were unique to only their plant.

Say to students: *"Let's look at the ways we used words to describe plants." *Discuss several examples.

Say to students: *"Now let's look at ways we described the plants using numbers. What sort of ways did you use numbers to describe your plant? Are their any other number descriptions you could have used? Look at your list to try to see if you could add numbers to any of the descriptions that you used."*

Allow the students another 5-10 minutes to write and share their numerical descriptions of their plants.

Ask students:

- Do the numbers help us describe something about the plant?
- How many leaves did your plant have?
- Did anyone measure the plant? How tall was the plant?
- Did anyone count stripes or spots?
- Do you think that numbers are important in describing the plant? Why or why not?
- What would happen if you had to find your plant in a group? Would you be able to find your plant based on your descriptions?

Collect the students' plants. As you collect each plant, check the marking to make sure that you know each group's plant. Move the plants all to the same table. Allow each group to go up one at a time to try to find its plant. Remind the students that they are to use their descriptions to find their plants.

Once each group has tried to find its plant, have all the groups go back to the table and select their plants. You may also wish to have students exchange their lists and see if they can find another group's plant.

Ask students:

- What information did you use to help you find the plant?
- What was the most useful word or information for finding your plant?
- Would it be possible to find your plant if there were 10 more plants on the table? How?
- What was one word that didn't help you at all in locating your plant? Why did you not need it?
- Are numbers useful in telling about your plants? Why or why not?
- What are some other ways that you use numbers to describe things around you?

Next, ask questions to encourage students to think about more, less, and equal values. For example:

- Did any plants have the same number of leaves?
- Whose plant has the most/fewest leaves?
- Whose plant is the tallest/shortest/heaviest/lightest?

If time allows, have the class attempt to develop a system for ordering and/or classifying the plants by number of leaves, height, leaf shape, etc.

Or, have students compare their group's plant to the class plant used in the beginning of the lesson. (This activity can be set up in a center, so students can rotate through in intervals of 5-10 minutes to complete the assessment over the course of a few days.) Students should compare the two plants by writing 2 to 3 sentences or words to describe the difference between the plants, such as My plant is ________ than the class plant. My plant has ________(2, 3, 4, 5) more/less leaves. This could also be done verbally for younger students.

These activities will allow students further opportunities to construct understanding of the descriptive purposes of numbers.

### Assessment

Give each student a piece of paper. Say to the students: *"We have been looking at numbers and how we use them everyday. I want you to take a few minutes using numbers to describe yourself. Write down all the descriptions about yourself that use numbers." *

Allow the students several minutes to write numerical descriptions of themselves. You may wish to have students draw a picture of themselves and label it using numbers.

Ask students: What were some of the descriptions about yourself that used numbers?

Allow the students to share their different numerical descriptions.

Ask students:

- Who had number values that were different?
- Who had number values that were the same?

### Extensions

Allow students to play the Let's Count!, Let's Count Animals! and Let's Count Again! activities found at the Fun Mathematics Lessons website.

This site gives students multiple representations that allow them to continue to practice their counting skills. Teachers can visit Cynthia Lanius' teacher page as a resource when using these activities.