• Use observations in classroom discussions, workstations, and one-on-one conferences with students to aid in determining student level of fluency and understanding.
• The Random Reporter method may be used at any time during the lesson to ensure that students are on the right track and are mastering the skills of decomposition and composition.

“We are going to be in our workstations for most of the day today working with our secret numbers. We will practice joining and breaking apart numbers to become better mathematicians. Before we begin I have a special bag I want to show you.”

Guess What’s in My Bag Activity

Before you begin this activity, gather counters for students (farm animals if possible) or small animal picture cards, cups, Barn Story Board (M-K-1-4_Barn Story Board.doc), and Animal Spill Recording Sheets (M-K-1-4_Animal Spill Recording Sheet.doc).

Prepare a paper bag with 10 to 20 farm-animal counters inside and a Yes/No T-chart on the chart paper or board. Show students the bag and tell them they will need to ask you questions about what you have inside the bag. They have to ask questions that can be answered with a “Yes” or “No.” Once you answer each question, write the question on the T-chart under the Yes or No column.

Say, “I have something inside my bag. I want you to guess what I placed in the bag. You can figure it out by asking me questions that I can answer with a ‘Yes’ or a ‘No.’ For example: You could ask me a question like ‘Is it Red?’ I can answer that with a ‘Yes’ or a ‘No.’ Or ‘Can I use it to draw with?’ can be answered with a ‘Yes’ or a ‘No.’ I can’t answer this question with a ‘Yes’ or a ‘No’: ‘What color is it?’”

Go over additional questions that can be answered with “Yes” or “No.”

“As a class you can ask me ten questions today to try and figure out what is inside my bag. Remember, I will write down the questions in the T-chart.”

Continue with the activity until all ten questions have been asked. If students cannot guess what is in your bag, you can tell them or give them clues to figure it out.

“I’m going to show you a new workstation today using some farm animals that we had in the bag. It is called Animal Spill. You will use your secret number for Animal Spill, just as you are doing with all of the workstations.”

Each student should be given a secret number ranging from 4 to 12. The number is assigned to students based on their counting abilities and composing and decomposing skills. If necessary, you could have a chart with all the secret numbers hidden under a sticky note so students can check their secret number. Secret numbers should change as students learn better counting strategies and composing and decomposing skills.

“My secret number is seven. So I need to place seven farm animals in my cup. I think I will use pigs today. You can choose any of the animals you wish. See how I placed all of the pigs in my cup? Next you need to place your hand over the top of the cup like this and shake the cup three times.”

Show students how to cover the top of the cup so no animals spill out while you shake the cup.

“After you shake the cup three times, hold the cup about one foot above the Barn Story Board. Next you will gently spill the animals onto the Barn Story Board.”

Show students how high to hold the cup before spilling the animals out of the cup. The goal is to have some of the animals land on the barn and some off the barn, creating two parts: on the barn and off the barn. You can change how far above the board you want students to spill their cups.

“Let’s take a look where the animals landed on my story board.”

“Some of the pigs landed on the barn and some of the pigs landed off the barn. Let’s count how many pigs are on the barn.”

Count with students the pigs that landed on the board.

“We had seven pigs in our cup. We counted three pigs on the barn. Let’s find out how many pigs are off the barn by counting them.”

Some students will easily count the pigs where they landed. Others may need to gather all of the pigs that landed off the board and place them in an organized way before counting. Talk about good counting strategies if students are having difficulty keeping track of the pigs.

“We had seven pigs in our cup. We counted four pigs that landed off the barn. How can we use our numbers to describe what we see on our board?” Call randomly on several students to share their thinking.

A possible student response might be: I think we can say 4 and 3 make 7 because 4 pigs are off the barn and 3 pigs are on the barn. We had 7 pigs in our cup at the beginning. We didn’t add any more pigs so we still have 7 pigs.

“Talk with a neighbor to discuss what you think about our pigs and how we could use them to tell about the number 7.”

Give students time to talk with one or two neighbors. Randomly select a few students to share their thinking. Some student examples might include I see 3 pigs on the barn and 4 pigs off the barn. So 3 pigs and 4 pigs is the same as 7 pigs in our cup, or I know that if I have 4 pigs, I will need 3 more pigs to have 7 pigs.

Display a T-chart on the board or chart paper and record the number of pigs on and off the barn on the left and right sides of the chart. Model writing the numerals on the board in a number sentence such as “3 pigs on + 4 pigs off is the same as 7 pigs.”

“Let’s place the seven pigs back in the cup and spill them out again.”

Practice the Animal Spill workstation with students a few more times to make sure they understand what to do. Continue to record results in the same T-chart, and model writing the numerals in number sentences on the board for each example.

“For the next few days, we will be using workstations to practice number combinations. I will add Animal Spill to our workstations. While you are working, I will be coming around to each group to check on your work. If you have a question, quietly raise your hand and I’ll join your group soon. I may also be pulling a small group to work with me. If I am working with a small group, please continue with your work at the workstation and do not interrupt. Remember, everyone will have the opportunity to work with the Animal Spill workstation over the next few days.”

As students are working with Animal Spill or at other composing/decomposing workstations, visit with all students, correcting mistakes you see and allowing them to explain their thinking. You will be able to assess where students are in their learning based on the answers to questions you ask. You will be able to correct misconceptions. Sample questions to ask students while they are working may include:

• “Will you count how many animals you have on your story board?”
• “What are some of the ways you found to make the number ___?”
• “Do you think you found all of the ways to make ___? Why do you think that?”
• “Do you have more or fewer than five animals on your story board? How do you know?”
• “You have ___ animals on your board. If I gave you one more animal, how many animals would you have on your board?”
• “You have ___ animals on your board. If you gave me one animal, how many animals would you have on your board?”

After students have worked with the Animal Spill workstation several times, introduce the Animal Spill Recording Sheet.

“Today I’m going to show you how to record on the Animal Spill Recording Sheet. My secret number is seven. After I spill my animals onto my story board, I will need to record what is on my story board.”

Spill the animals onto the story board. We will use the example below to further explain the recording sheet (M-K-1-4_Animal Spill Recording Sheet.doc).

“My recording sheet has nine small barns on it. There are also some blanks and words under the barn. They say: ___ and ___ is the same as ___. I need to draw my animals on the recording sheet. Because I don’t want to take a lot of time drawing pigs, I will use circles to represent my pigs. I will draw one pig on the barn and six pigs off the barn. How many pigs did I have in my cup?” (seven) “That’s right. I had seven pigs in my cup. After I draw my pigs I need to fill in the ‘___ and ___ is the same as ___.’ statement. Who has an idea of how I could fill it in?”

Listen to student responses and highlight good thinking.

“____, you mentioned an idea. Could you explain what you were thinking?” (Possible explanation: We counted 6 pigs off the barn and 1 pig on the barn. So we had a 6 and a 1. I think we could write 6 and 1 is the same as 7. We had 7 pigs in the cup. If I have 6 pigs and count 1 more that is 7.)

Take this opportunity to discuss having 6 and 1 versus 1 and 6. Emphasize the commutative property as it applies to this circumstance and other number combinations students may encounter.

Model how to write the number sentences including the plus sign and equal sign. To reinforce the correct sentence form, have a student help you fill in the recording sheet. Read the number sentences aloud.

Remind students to draw circles or squares to represent the animals. Actual drawings of the animals would take too long. Have students complete their own Animal Spill Recording Sheet by “spilling” their own animals and recording their results a specific number of times (3–9 is sufficient, depending on the time available).

After students have had several opportunities to experience and get feedback on composing and decomposing numbers using the Animal Spill activity, you might want to evaluate their understanding on another animal spill or similar activity. A station rotation could also be set up so that students are challenged to correctly count the “spill” multiple times, thus eliminating the possibility that a student scores well by guessing.

Extension:

• Routine: Ask students to count objects and sets used or seen during activities and book reading. Point out situations where students can see a number in parts. Encourage students to notice examples they see at home of numbers that can be composed or decomposed and bring them to share during class. Emphasize the use of specific vocabulary words necessary to communicate number-sense concepts. Monitor student progress and responses, and allow students the opportunity to revise their work as their ideas are clarified.
• Expand: One way to tailor the farm animals activity is to change each student’s secret number. The larger the number, the more combinations a child must know.

Reduce the secret number for students who are having difficulty or are frustrated in their efforts, slowly increasing the number again as they gain confidence. Raise the number up to 20 or more for students who easily grasp the concepts.

Changing the manipulative and story board will also keep the activity fresh for students over time.

• Fine Motor Skills: Students having difficulty with fine motor skills should work with a partner during class activities or stations. Instruct the partner to do steps like spill the animals and record the results. Both students will contribute to the counting and verbal suggestions throughout the activity.
• Small Group: Teaching in small groups can benefit children who are having difficulty. Form one or more small groups based on student data from observation and other formative assessments. Review the Animal Spill game directions with the groups. Place three or four animals in a cup. Spill the animals and model your thinking while students record. Ask students to answer a few questions about what you are doing. After two or three turns, shift the emphasis to students describing their own thinking as they record.
• Expansion: Play the game Animal Spill but with an added twist. Instead of dumping all of the farm animals (counters) out of the cup, only dump some of them out. Then turn the cup over (with the remaining manipulatives still inside the cup). For a challenge, have students count how many counters have fallen out of the cup and estimate/calculate how many counters are left inside the cup.