Students will use their sorting abilities to create questions and forecast outcomes. Students will be able to:
- collect, arrange, and present data.
- investigate object sorting with overlapping attributes (Venn diagrams).
- create questioning techniques to forecast events.

- How can information be presented and arranged to shed light on the relationship between different quantities? 
- How does the type of data affect display selection?
- What does it mean to evaluate or estimate a numerical quantity?
- What qualifies a tool or strategy as suitable for a particular task?

- Quantity: How much there is of something.

- chart paper and marker
- index cards
- paper tape
- Venn diagram sheet (M-K-5-3_Lesson 3 Sorting Circles)
- a collection of buttons
- Stuart J. Murphy. (2003). 3 Little Firefighters (MathStart). HarperCollins. 
- an assortment of colored paperclips, large and small
- Sorting Assessment sheet (M-K-5-3_Sorting Assessment)
- Venn Diagram Assessment sheet (M-K-5-3_Venn Diagram Assessment)

- To guide instruction, use a paper-and-pencil formative assessment (M-K-5-3_Sorting Assessment and M-K-5-3_Venn Diagram Assessment).

Scaffolding, Active Participation, Modeling, and Explicit Instruction 
W: Explain to students how sorting objects can help them make predictions and decisions. 
H: Create a list of styles, colors, and types of shoes that kindergarten students might wear so that a shoe store can better serve its customers. 
E: Allow students to create a floor chart based on their shoes, color, or some other distinguishing feature. Make educated guesses about what the results will reveal. 
R: To make the information appear more realistic, have the students stand on the chart or place one of their shoes on the chart. 
E: Discuss the results of the shoe color sorting. Try the exercise again with an alternative sorting rule, or use a second sorting rule to look for overlapping attributes. You can also try the exercise again on a different day and compare the outcomes. 
T: Give students small items, like paper clips or buttons, to sort according to two rules. Then, have them arrange the items into sorting circles to find items that satisfy both requirements and fit where the circles intersect. 
O: As they incorporate the abilities of forecasting and utilizing Venn diagrams to present the sorted results, students keep practicing sorting items. 

Students can relate to the need to sort and make predictions by using the real-world hook that opens the lesson. Students can verify their predictions and generate ideas for new sorting questions by organizing the sorting results into a Venn diagram format. The purpose of the lesson extension is to confirm that students have mastered the idea of independently organizing objects in a Venn diagram format and sorting by multiple attributes.

Explore Stephen R. Swinburne's book, Whose Shoes?: A Shoe for Every Job. Discuss the various types of shoes and their functions.

"We sorted a large number of objects using a variety of rules. You are pretty skilled at determining and inferring rules. We are going to come up with some sorting questions today to help us collect data."

"Consider the shoes you see most frequently worn by students your age. Which types of shoes do you think retailers order most frequently when they want to place an order? Which colors? Which color do you think we will list the most if we make a list of every shoe in this room right now? Will there be an equal amount of sandals and sneakers or more of one or the other?"

"Reflect on your guesses or predictions while I narrate you a story."

The narrative that follows will explain the rationale behind shoe sorting and test students' ability to devise suitable guidelines for compiling the necessary data.

"Kindergarten students' shoe preferences are of interest to a nearby shoe retailer. The store will use this information to determine what kids' shoes to order."

"What are the questions you believe the shoe store would like us to address regarding the shoes you are currently wearing?" While students brainstorm, write ideas on chart paper or the board. (Perhaps they want to know if we're going to tie them.)

“Okay, so they might ask, ‘Do you have shoelaces?'" (They might ask us what colors or designs we have.)

“That sounds like two questions: ‘What colors do you wear?’ and ‘Do you have pictures or art on your shoes?’” (What about if we have soft shoes or hard shoes? Or if our shoes are quiet or loud.)

“Does someone know the name of the bottom part of a shoe, the part that touches the floor when you walk?” (the sole) “That’s right. The store may ask, ‘What are the soles of your shoes like?’”

"How might we address some of these questions using the shoes you are wearing?" (For example, to determine how many people wear loud or white shoes, we could count them for each question.)

Counting shoes to find a quantity and provide an answer to a question is a good place to start. If we want to know how many people wear white shoes, should we also ask how many people wear other colors, such as black?" (Yes!)

"How would we easily count the colors of our shoes?" (Using a color rule, we could divide them into groups. We could even remove them and arrange them in piles!)

"Let's attempt the color sorting method. I'll write each color you see on one of these cards if you name the colors you see." Ask students to extend their feet in front of them. Take note of the colors on each person's shoe and write them down on cards (pick the primary colors, not the accents).

"All right, the colors for our rule are here. To help us arrange our shoe colors, let's create a floor graph." Using strips of paper tape, create a large floor graph. You should have at least four columns. Next, put a colored card at the base of every column.

Assign students to stand in the floor graph column corresponding with the color of their shoes. After identifying the dominant color, the students should choose the matching group. For any shoes that don't fit into one of the specified color columns, you could add a column marked "Other." If there isn't enough room in the classroom, you could ask each student to remove one shoe and place it on the graph instead of having them stand there. If so, label any comparable shoes with paper tape with the students' names to ensure they can locate their shoes after the activity.

"What information can we learn by looking at our groups?" (The majority of people are wearing white shoes. Nobody else is wearing red shoes. Black is the second most common. We wear black shoes a lot.)

"Therefore, we can conclude that the majority of people wear black and white today. I'll include that in our inquiry under the heading, "What colors do you wear? In our class today, the majority of people wear black and white. Take a moment to reflect on the color guesses you made earlier. Are the majority of our shoes black or white, as you might have predicted?"

"Let us consider another question and come up with a sorting rule that will assist us in obtaining a response. Next, let us forecast the most prominent feature on the graph."

Proceed with an additional sorting rule. Students may select a rule (shoelaces, no shoelaces, etc.) that best represents having the attribute or not having it. Students can also propose extensions for a rule (shoelaces, Velcro, zippers, slip-ons, etc.).

If there is a lot of student interest, this activity may be moved to another day. Using a Venn diagram with one circle labeled "White Shoes" and the other labeled "Velcro" could also increase the difficulty of the task. White shoes with Velcro would be where the circles intersect. Students' ability to identify the overlapping circles as a Venn diagram is not crucial at this stage. Instead, the objective is for them to gain an understanding of what occurs when an object is classified into multiple groups. Utilize the Lesson 3 Sorting Circles worksheet (located in the Resources folder under M-K-5-3_Lesson 3 Sorting Circles).

"Is it possible for everyone to fit a shoe into one of these groups?" (No. I don't have Velcro on my blue shoes.)

"Let's see how many shoes we can sort together." Assign students who wear white shoes or those with Velcro to place a shoe in the relevant area of the Venn diagram. Invite students to talk about what they've noticed.

Extension:

To modify the lesson to your student's needs, use the following strategies and activities.

- Small Group Reteaching: Cut out paper buttons similar to those in Stuart J. Murphy's 3 Little Firefighters, or use an assortment of buttons for sorting. Utilize the M-K-5-3_Lesson 3 Sorting Circle as well. Start by having students read the book again, and then ask them to recommend a sorting guideline for the button collection.

"Does anyone have a rule for organizing the buttons?" Take a few recommendations and decide which to try. Label the circles with "gray" and "four holes." Talk about a name for the intersection of the circles, such as "gray with four holes."

Help students who are struggling to arrange the buttons into a single circle first.

"First, let's locate every gray button and arrange them in this circle." Allow time to work. "Now, locate the buttons with four holes by examining the ones that are not gray. Place them in the opposing circle. " Allow time to work.

"Let's just focus on the gray buttons and put away all the extras. Of these, which has four holes? Since those are gray and have four holes, move them to the center so they will be in both circles." Once students are satisfied with their selections, go over their work and offer comments.

"How satisfied are you with your groups? Examine your groups now. Gray buttons were the norm in this circle. Can we see every gray button? " (Yes) "Do we notice that every button in this circle has four holes?" "(yes)" What is the guideline for these central buttons then?" (They must have four holes and be gray. I understand now! No buttons can be moved.)

Extra small-group instruction using various sorting collections might be beneficial for some students.

- Extension: Assign students to sort a different collection, like big and small colored paperclips (or marbles and erasers), if they can work independently. Ask students to choose a sorting rule that encompasses items that belong in both categories, like big or red paperclips. Make sure students understand that they are not required to use every paperclip in the set. On the Lesson 3 Sorting Circles worksheet (M-K-5-3_Lesson 3 Sorting Circles), students might need assistance writing the group names. However, they should be encouraged to finish the sorting on their own and discuss the validity of the findings.