Students will arrange different object collections according to one or more criteria, and then present the outcomes. Students are going to: 
- determine the qualities that could be applied to groupings of objects. 
- determine the rules governing the sorted objects. 
- examine the probability of basic events when sorting objects.

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

- Length: How far from end to end. 
- Quantity: How much there is of something.

- mystery bag filled with items from the classroom (such as crayons, glue sticks, pencils, small blocks and toys, clothespins, etc.)
- Stuart J. Murphy. (2003). 3 Little Firefighters (MathStart). HarperCollins.
- Jayne Harvey. (2003). Cat Show (All Aboard Math Reader) Vol. 1. Harcourt/Rigby.
- Stuart J. Murphy. (2000). Dave’s Down-to-Earth Rock Shop (MathStart). HarperCollins.
- David Bauer.. (2002). Let’s Sort. Coughlan.
- Roger Priddy. (2004). Turn the Wheel Shapes and Sorting. St. Martin’s Press.
- string, yarn, or hoops to make large sorting circles
- Backyard Bugs counters or other set of classroom manipulatives that can be sorted by two or more attributes
- Sorting Observation Checklist (M-K-5-2_Sorting Observation Checklist)

- If students need more challenges or assistance, teachers will be able to assess it through observations during small-group discussions, workstations, and one-on-one conferences with students. 
- To monitor a student's progress, utilize the Sorting Observation Checklist (M-K-5-2_Sorting Observation Checklist).

Explicit instruction, modeling, scaffolding, and active engagement 
W: Start the lesson by going over the ideas of similar and different by contrasting the resources in the classroom. Don't forget to include elements like shapes, purposes, and colors. 
H: Choose a book from the list and talk about how the characters arranged the items in the narrative. 
E: Assign students to compare their objects with those of the students who presented before them in small groups using the classroom materials you gathered. Ask the students to arrange their belongings based on a chosen attribute.
R: Conduct a guessing game where you come up with a particular mystery attribute, help the students divide the items into two groups according to the attribute, and then ask them to guess what the attribute is. Next, the pupil can select the next mystery attribute if their initial guess is correct. 
E: Evaluate students while they discuss the sorting process and make their guesses. When sorting, ask particular students to defend their decisions about what to include or not include. If students show that they are ready, add another attribute to the game. 
T: Classifying students according to rules and asking them to guess what the rules are are regular exercises that can be implemented all year long. You could also go back to the assortment of previously gathered classroom items and ask students to determine whether a particular attribute is possible, unlikely, certain, or unlikely based on a random selection of one of the items. 
O: Organizing objects according to one or more attributes is the main goal of this lesson. The objectives of the learning process are to identify similarities and differences between objects and to provide evidence for the groupings that the sorted objects belong in. 

First, the class hears a story about sorting buttons and discusses the different sorting features. Next, they investigate the ideas of similarities and distinctions through object comparisons. Lastly, students create groups using the sorting rules and then name the rules based on group observations. Extending the lesson allows students to investigate how the outcomes of events can be applied to sorting objects.

Recap the ideas of "similar" and "different" before beginning this lesson. Stuff a bag with a variety of school supplies, including crayons, pens, pencils, blocks, and tiny toys. Ask, "How are these two objects similar? How do they differ from one another?" Encourage different kinds of answers. Take away another object and inquire about the similarities and differences between it and one of the earlier objects. Assign students to remove objects from the bag in turns, and then describe how each new object differs from or is similar to one or more of the previously removed objects.

Assign students to read Stuart J. Murphy's book 3 Little Firefighters after the discussion.

"I want to tell you a story. The story concerns a few firefighters who require buttons for their jackets. When I'm done reading, I'd like you to tell me how similar or different the buttons they selected were."

Other storybooks, such as Cat Show by Jayne Harvey, Dave's Down to Earth Rock Shop by Stuart J. Murphy, Let's Sort by David Bauer, and Turn the Wheel Shapes and Sorting by Roger Priddy, could be used to introduce sorting and demonstrate sorting by attributes.

After reading the narrative, have the students discuss what they observed about the firefighters' button choices and how they organized them into sets. (Note: If you use one of the other sorting-related storybooks, have students identify one method used to sort the objects in the story.)

Make an attribute anchor chart or class poster showing the various ways the characters are arranged. Throughout the unit, keep adding to this poster. (Students may say, unable to find enough buttons for their coats, they attempted to sort the buttons by color. They tried sorting by shape, but that didn't work, so they had to sort by size instead, and that did the trick!)

"You were concentrating quite well. The firefighters used three different rules to sort a collection of buttons. They had to continue arranging the buttons until they discovered a sufficient number that shared a common characteristic. Let's now take another look at the assortment of items in our bag and consider possible classifications."

Extract a pair of scissors and a roll of tape, or two contrasting items, from the bag. For some students, starting to describe the objects based on their differences will be easier. (Though the tape holds things together, the scissors cut things apart. The tape is a different color and shape from the scissors.)

Encourage students to keep looking for similarities between the objects. (The tape has a central hole, similar to the holes in the handles of scissors.)

"Well observed. These two objects have punctures in them."

After passing the bag to each student individually, ask them to remove an object to continue the activity. Allow enough time for each student to explain the object and discuss how it differs from or is similar to the one that came before it. Assume the following pupil pulls out a glue stick. (It's sticky on my glue stick. Furthermore, the tape is sticky. But there's no hole in my glue stick.)

"That's accurate. Because both of your objects are sticky, they are similar. Unlike the tape and scissors, the glue stick is not punctured."

Encourage students to search for flat sides, shared colors (they are both red), shared purposes (they write), whether the objects will roll, whether they have words, and other similar characteristics if they are having trouble identifying similarities. Assist them in observing the various characteristics of every item. They will benefit from this in the ensuing sorting tasks.

Allow students to keep the object for the following sorting activity after they have taken turns pulling an item out of the bag and drawing comparisons.

Sort the class's objects into two groups based on whether they have the suggested likeness or not. Choose one of the likenesses provided by the students. To identify the groups (those who write and those who don't), draw two sizable circles on the ground using string or hoops.

Say, "I'm going to pick a rule that will enable us to arrange our items in a novel way. Once more, we will divide into two groups. This circle is for writing instruments, and this one is for non-writing instruments."

Give each student a turn to place their item in the appropriate group and explain the reasoning behind the group selection. (Students may state, My pencil writes, so it belongs in this group. This block goes here because it doesn't write.)

After all of the items have been sorted, put them back in the mystery bag and engage in the Sort My Rule sorting activity. Create a rule that covers a portion of the items in the bag, but not all of them. Don't share your guidelines.

"I can't help but notice how some of these items are similar to one another. You will take something out when we pass the bag again. Once I see your item, I will let you know if it complies with my rule. You'll place it in this circle if it does. If not, you'll include it in this one. I want you all to take a moment to quietly consider what you believe my rule to be. Hold off on saying it aloud until I ask you to estimate."

Once more, pass the bag and allow a few students to take turns pulling out an object. Once several objects have been distributed among the groups, pause the activity and invite the students to guess the rule. Sort the objects again if the guesses are off.

After a student correctly guesses the rule, return the objects to the bag and let them choose the sorting rule for the following game. Assist students in selecting clear and precise rules. When using objects in the classroom that aren't big or small, it would be challenging to enforce a rule about object sizes.

To give more students a chance to pull an item out of the bag, replay the game as long as time allows.

Utilize a checklist (M-K-5-2_Sorting Observation Checklist) to assess students' progress.

Ask students to identify the characteristics of a few objects in each group that either fit the rule or do not fit the rule after each time the class correctly guesses a rule. Check if students can name characteristics and provide evidence for why an object belongs in a particular group.

Two sorting rules—separating objects that roll and objects with flat sides, for example—could be used to expand this exercise. Students can come up with fresh suggestions for groupings when they learn that some objects, like crayons, have flat sides in addition to rolling. If students are ready to move up to more complex sorting rules, an overlapping Venn diagram may be introduced.

Extension:

You can modify the lesson to fit the needs of your students throughout the year by using the strategies and activities listed below.

Routine: If you have a few extra minutes before lunch or recess, this activity would be a great way to pass the time during the day. It could also be completed frequently at a set time, like before math class.

Construct a rule that divides students into two groups, but keep the sorting rule a secret. You could pick students with long sleeves and students with short sleeves, for instance. Assign each student to one of the two groups and have them stand in front of the class one at a time. Ask other students in the class to guess your rule when you see multiple students standing. The activity comes to an end if they are right. If they are incorrect, divide the class up into new groups until everyone has guessed the rule correctly. Assess which students may require remediation to reinforce the fundamental concepts of sorting and classifying by keeping an eye on student participation and how quickly each student picks up the material.

Choose a secret rule and limit the number of students standing in each of the two groups to two to increase the difficulty of the exercise. Select a volunteer and ask them to explain why they chose to represent that particular group. Ask the volunteer to select a different student who belongs to the same group if they selected the right one based on your code of silence. Ask another student to select a group and guess the rule if the volunteer's guess is incorrect. Keep going until the rule is understood.

Extension: Reuse the mystery bag for this task. Tell the students that the items were gathered from the classroom and arranged in various ways. Inform students that you will identify a quality this time, and they will have to determine if it is possible to pull something with that quality out of the bag, which includes whether it is likely, unlikely, certain, or impossible.

"What is the probability that I will take out a classroom item if I reach into the bag without looking?"(That's for sure. All of the items in the bag are from the classroom.)

"What is the likelihood that I will take out a steam iron?" (This is illogical.)

"What makes you think that?" (Because when you put things in the bag in the classroom, we didn't have an iron.)

"Is it possible that I will use something from the bag in an art class, or is it unlikely?" (That's probably because the majority of the items in the bag are tools used in our artistic endeavors.)

Ask students to come up with questions they would like to ask about items that are likely, unlikely, certain, or impossible to pull out of the bag as they get more comfortable with this exercise.

To facilitate group work, assign students a small set of manipulatives that can be sorted based on two or more attributes, such as Backyard Bugs counters. Sort the bugs into two groups by asking students to choose a rule. While the students work, watch to see if they are sorting based on one or two attributes. Does their rule group bugs into two separate categories (spiders and dragonflies) or do they have sets of bugs that overlap (red caterpillars, red bugs, and red caterpillars)? Is there a clear sorting rule for compliance in their sets? Are classmates able to guess the rule?