## Many Sets of Buttons

Students classify buttons and make disjoint and overlapping Venn diagrams. In an extension, they make and record linear patterns.

Teach the students the song, "If You’re Happy and You Know It" using the available Song Lyrics.

Give each student a small plastic bag containing about fifteen buttons. Ask the students to dump their buttons onto their table or desk and tell them to find buttons in their set of buttons that fit each description that you will give.

First name an attribute such as “red.” Now lead the students in singing the song, substituting, “If you found a red button, hold it high” for “If you’re happy and you know it, clap your hands.” Sing several verses with other attributes, for example, big, square, broken, and four-holed-button.

Now hold up one button and ask the students to describe it in as many ways as they can. Record the descriptive words on the board.

Choose two descriptive words that are mutually exclusive (such as blue and white) and write them on separate index cards. Next form two circles with yarn and put one index card face up in each yarn circle. Tell the children the figure is called a Venn diagram.

Now hold up a button and ask where it should be put. [If the button is neither blue nor white, place it outside the circles.] Repeat with several more buttons, then remove both cards and all the buttons and repeat with other attributes.

Next, on separate index cards, write words that might describe a single button (for example, big and red). This time, overlap the yarn circles and place one index card in each circle. Place a button in the correct position and elicit reasons why it goes in that place.Place a button in the correct position and elicit reasons why it belongs in that place. Now hold a button and ask where it should be placed in this new Venn diagram. Then call on volunteers to place other buttons on the diagram. [Buttons that have both attributes should be placed in the overlapping section.]

Next remove the buttons and the cards from the circles, and place two different index cards upside down, one in each yarn circle. Without revealing the sorting rule, place several buttons in the circles, then ask for volunteers to try to place additional buttons. If a student places a button incorrectly, move it to the proper position without explaining why.

When several buttons have been correctly placed, ask a volunteer to tell how he or she figured out what was written on the index cards. Then display the cards right side up so the students’ hypotheses can be verified. Repeat the activity with other attributes, using a different pair each time. To record the activity, ask each student to draw two overlapping circles, label them, and draw buttons in the circles.

- Song Lyrics
- Plastic bag containing 15 buttons for each student
- Index cards
- Yarn

**Assessment Option**

At this stage of the unit, it is important for students to know how to:

- classify buttons according to given attributes
- identify the attributes by which objects were sorted
Because identifying attributes and classification are the foundations for understanding number, the abilities to classify and identify are prerequisite to success in combining and removing sets. Therefore, students who are not able to demonstrate competency in both of them should receive additional instruction before continuing with the lessons in this unit.

Extensions

- Display a Venn diagram into which buttons have been placed. Do not label the circles. Remove the buttons one at a time and create a linear pattern by repeating a pattern core (for example, green, and yellow) three times. [The pattern will be easier to detect if you use non-overlapping circles. To provide a special challenge, you may wish to use overlapping circles.]
Ask the students to watch as you remove the items from the Venn diagram and to discover the rule you are using to place them in a straight line. Ask for a volunteer to place the next button in the pattern. If the student placed a button correctly, say so and call for another volunteer to place the next button. If the button was placed incorrectly, ask the student to hold on to it and try again later.

After the students have placed several buttons, call on a volunteer to read the pattern aloud. Then help the students who placed their buttons incorrectly to add them to the pattern. Repeat with other patterns, using a different core pattern each time. [Appropriate cores include

*AB*(shown in this example),*ABB*,*ABC*and*AAB*.] - Next ask the students to make a pattern with their buttons. [They may prefer to sort them first, although this is not necessary.] Call on a volunteer to read his or her pattern and ask whether anyone else has a pattern that is like that one in some way.
Encourage several students to read their button patterns. [You may wish to put the students into pairs and have each student make a pattern with three repeats, then try to add a repeat to his or her partner’s pattern.]

**Questions for Students**

- Can you find two buttons that are alike in some way? How are they alike? How are they different?
- How did you know where to place a button when you could not see the labels?
- Look at these buttons. What labels could you use to describe them?
- Choose two ways to describe this button. If you made a Venn diagram with these attributes, would the circles overlap?
- How would you tell another student how to place buttons?

**Teacher Reflection**

- Can most of the students recognize the attributes used in sorting? Which students still find this challenging?
- Can most of the students sort independently? What activities are appropriate for those who cannot do this yet?
- What activities are appropriate for those who can do this?
- Which student pairs worked well together? Which student pairings need to be changed?
- What parts of the lesson went smoothly? Which parts should be modified the next time that I teach this lesson?

### Button Trains

*before*,

*after*, and

*between*. They also review and use both cardinal and ordinal numbers.

### How Many Buttons?

### More and More Buttons

### Numbers Many Ways

*fact families*. (A fact family is a set of three [or two] numbers that can be related by addition and subtraction, for example: 7 = 4 + 3, 7 = 3 + 4, 7 - 4 = 3, and 7 - 3 = 4. When the number is a double, there are only two members of the fact family. An example would be 10 - 5 = 5, and 5 + 5 = 10.)

### Lost Buttons

### Shirts Full of Buttons

### Looking Back and Moving Forward

### Learning Objectives

- Classify buttons according to given attributes.
- Identify the attributes by which objects were sorted.

### NCTM Standards and Expectations

- Count with understanding and recognize "how many" in sets of objects.

- Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

- Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.

- Use multiple models to develop initial understandings of place value and the base-ten number system

- Develop and use strategies for whole-number computations, with a focus on addition and subtraction.

- Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

### Common Core State Standards – Mathematics

-Kindergarten, Measurement & Data

- CCSS.Math.Content.K.MD.B.3

Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Grade 1, Geometry

- CCSS.Math.Content.1.G.A.1

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP3

Construct viable arguments and critique the reasoning of others.