Objective:

Students will decompose numbers up to 10 into pairs using physical objects, focusing on breaking down the process into smaller steps. This hands-on activity will develop computational thinking skills such as problem decomposition and abstraction by having students explain their step-by-step approach to solving math problems.

Materials Needed:

• Counters, blocks, or small toys for counting

• Chart paper or whiteboard for recording steps and equations

• Markers for writing and drawing

Steps:

• Introduction:

  • Begin by asking, "How can we break down numbers into smaller parts?" 

  • Using blocks or counters, demonstrate how the number 6 can be split into different groups, such as 4 and 2 or 5 and 1. 

  • Explain that today, students will not only decompose numbers into smaller parts but will also practice explaining the steps they follow. This process mirrors how computers break down large problems into smaller, manageable steps.

• Group Activity:

  • Divide students into small groups and give each group a number between 1 and 10. 

  • Provide physical objects like counters or blocks, and ask them to decompose their number into different pairs. For example, if their number is 8, they might split it into 3 and 5, then 4 and 4. 

  • After each decomposition, prompt students to describe the steps they took, such as, "First, we counted out 8 counters, then we split them into 3 and 5." This mirrors how computers follow sequential steps (an algorithm) to solve problems.

• Arranging and Sequencing:

  • Once students have decomposed the number in several ways, ask them to draw pictures representing their groupings and write the steps they followed. For instance, if they split 6 into 4 and 2, they might draw four circles and two squares and write, "We counted out 6 counters, then made a group of 4 and a group of 2." This process helps students visualize the problem and develop a structured approach to problem-solving, similar to how programmers develop a plan to solve coding challenges.

• Testing and Refining:

  • After students have drawn their decompositions and written their steps, have them check their work by reviewing the sequence they followed. 

  • Ask questions like, "Do the steps match what you did with the counters?" 

  • Allow time for students to make adjustments to their drawings or sequences if needed. This step encourages them to think critically about their process and refine it, similar to how programmers test and debug their code.

• Presentation and Discussion:

  • Each group will present their decompositions to the class, explaining both how they split the number and the steps they followed. 

  • Lead a discussion on how breaking down the problem into smaller steps helps solve the math problem, linking this to everyday tasks that require sequencing, like following a recipe. 

  • Emphasize how problem decomposition is a critical part of computational thinking.

Equity and Access:

Offer additional manipulatives or visual aids for students who need extra support. Encourage peer collaboration to ensure all students can actively participate in decomposing numbers and writing sequences.

Real-World Application:

Relate the activity to real-world experiences, such as dividing snacks among friends or organizing school supplies into different categories. Discuss how breaking tasks into steps is essential in daily life, from completing chores to following instructions, and how computers break down large tasks in similar ways.

CS Practice(s):

• Developing and Using Abstractions: Students break down the concept of decomposing numbers into steps, representing them with physical objects and equations.

• Decomposing Problems: Students decompose the steps of solving a math problem into a clear sequence, describing how they arrived at the solution.

Content Standard(s):

• CA CCSS Mathematics K.OA.3

• CA CS K-2.AP.13

Objective:

Students will decompose numbers up to 10 into pairs using a digital app with drag-and-drop features, such as Seesaw or Google Slides. Through this activity, students will visually represent number decomposition, sequence their steps to solve the problem, and connect these actions to computational thinking skills such as problem decomposition and abstraction.

Materials Needed:

• Tablets or computers 

• Chart paper for reviewing decomposition and sequencing

• Digital images or drawing tools (e.g., shapes, counters)

• Seesaw

Steps:

• Introduction:

  • Begin by asking, "How can we break numbers into smaller parts?" 

  • Using physical objects, demonstrate how a number like 6 can be decomposed into 4 and 2, or 5 and 1. Then explain that students will use an app like Seesaw to digitally decompose numbers, and they will write out the steps they take to perform the decomposition. 

  • This process is similar to how computers solve problems by breaking them into smaller, manageable parts (decomposition).

• Group Activity:

  • Divide students into pairs or small groups. 

  • Have students choose a number less than or equal to 10 and use a digital app to visually decompose that number. 

  • For example, students might draw 5 circles and 2 squares to show that 7 = 5 + 2. 

  • Next, guide them in writing out the steps they followed to decompose the number (e.g., "First, I drew 5 circles, then I drew 2 squares, then I wrote the equation 7 = 5 + 2"). 

  • This reinforces the computational thinking skill of sequencing instructions.

• Creating and Sequencing:

  • Demonstrate how to use digital drawing and text tools to represent the decomposition of numbers. 

  • Have students first create their visual representations (e.g., 6 as 3 + 3 or 4 + 2) and then write step-by-step instructions for how they decomposed the number, making sure to include each action they took.

  • After they create their visual representation, have them write a sequence of instructions explaining each step, just as programmers follow a series of steps to solve problems with code.

• Testing and Refining:

  • After completing the decompositions and sequences, have students revisit their steps to check if the process accurately decomposes the number. 

  • Ask, "Does your drawing match your equation? Do the steps match the actions you took?" 

  • Allow time for students to refine their sequences and make adjustments to their visual representations and written instructions if necessary.

  • Allow students to refine their digital representation and written instructions if necessary, just as coders debug their code to ensure accuracy.

• Presentation and Discussion:

  • Each group will present their work on Seesaw, explaining both how they decomposed the number and the sequence of steps they followed to create their visual representation and equation. 

  • Lead a discussion on how decomposing a problem into smaller steps helps in both math and coding, emphasizing the parallels between solving math problems and creating algorithms.

Equity and Access:

Provide additional support by offering templates or pre-drawn shapes in Seesaw for students who need extra guidance. Encourage peer collaboration and pairing to ensure all students can engage with the activity.

Real-World Application:

Connect the concept of decomposition to everyday tasks, such as sharing snacks or organizing tasks. Explain how breaking tasks into smaller steps can help us solve real-life problems, similar to how we split numbers in math or break down problems in coding.

CS Practice(s):

• Developing and Using Abstractions: Students break down the concept of decomposing numbers into steps, representing them with physical objects and equations.

• Creating Computational Artifacts: Students create digital representations of number decompositions using digital drawing and text tools.

• Decomposing Problems: Students decompose the task of splitting a number into smaller steps, breaking down the problem and explaining each step of the process in a digital app.

Content Standard(s):

• CA CCSS Mathematics K.OA.3

• CA CS K-2.AP.13