Objective:

Students will compose and decompose numbers from 11 to 19 into "ten ones" and some extra ones using physical objects. Through this hands-on activity, students will visually represent number composition, break the problem down into smaller steps, and practice computational thinking skills such as problem decomposition and abstraction by writing out the steps and equations they followed.

Materials Needed:

• Counters, blocks, or small toys for counting

• Chart paper or whiteboard for recording drawings and equations

• Markers for writing

Steps:

• Introduction:

  • Begin by asking, "How can we break down a number like 14?" 

  • Use physical objects like counters to show that numbers from 11 to 19 are made up of a group of 10 and some extra ones.

  • For example, demonstrate that 14 can be composed of 10 counters and 4 more. 

  • Write the equation 14 = 10 + 4 on the board.

  • Explain that students will work with objects to explore how different numbers from 11 to 19 can be broken down.

  • Emphasize that this process mirrors how computers solve problems by breaking them into smaller, more manageable parts (problem decomposition).

• Group Activity:

  • Divide students into small groups and provide each group with counters or blocks. 

  • Assign a number between 11 and 19 to each group (e.g., 18). 

  • Students will count out a group of 10 objects and then count the additional ones (e.g., 8 more objects for 18). 

  • After composing the number with objects, they will draw a picture of their groupings and write an equation (e.g., 18 = 10 + 8).

  • Encourage students to think about the steps they followed, similar to how algorithms in computer science follow a sequence of instructions to solve problems.

• Arranging and Drawing:

  • After composing the number with physical objects, students will draw a picture of the objects, showing the group of 10 and the extra ones. 

  • Then they will write an equation to represent the number (e.g., 17 = 10 + 7). This process reflects how computers use data to generate outputs by following a structured approach, breaking larger problems into smaller parts.

• Testing and Refining:

  • Once students have completed their drawings and equations, ask them to recount their objects and verify that their drawings match the equation. 

  • Encourage them to "debug" their work, similar to how programmers refine their code, by making adjustments to their drawings or equations if necessary. 

  • Ask questions like, "Does your equation match what you see in your picture?" to reinforce the importance of accuracy in both math and computational thinking.

• Presentation and Discussion:

  • Each group will present their number decomposition to the class, sharing their drawings and explaining how they broke the number into 10 ones and the remaining ones. 

  • Lead a discussion on how breaking problems into smaller steps, like decomposing numbers, helps us understand math concepts better. 

  • Relate this to how computers follow sequences of instructions to solve complex problems, reinforcing the link between math and computational thinking.

Equity and Access:

Provide additional manipulatives for students who may need extra support. Encourage peer collaboration and scaffolded instruction to ensure all students can actively participate.

Real-World Application:

Connect the activity to everyday tasks, such as counting objects in groups of 10, like pencils, coins, or snacks. Discuss how understanding number composition helps in practical situations, such as organizing objects or solving real-world math problems, and how breaking tasks into steps is important in both math and computational thinking.

CS Practice(s):

• Developing and Using Abstractions: Students use physical objects to represent abstract mathematical concepts, connecting concrete manipulatives to written equations, similar to how data is abstracted in computational problems.

Standard(s):

• CA CCSS Mathematics K.NBT.1 

• CA CS K-2.AP.13

Objective:

Students will practice composing and decomposing numbers from 11 to 19 into ten ones and some additional ones using digital drawing tools or drag-and-drop features in an app. Through this digital activity, students will create visual representations of numbers, decompose them into parts, and record their steps, reinforcing computational thinking by breaking down problems into smaller tasks and sequencing actions.

Materials Needed:

• Tablets or computers

• Digital drawing tools

• Chart paper for reviewing number composition

Steps:

• Introduction:

  • Begin by discussing how numbers from 11 to 19 are composed. 

  • Ask the class, "How can we break down the number 15?" 

  • Explain that these numbers are made up of ten ones (a group of 10) and some more ones (e.g., 15 is 10 + 5). 

  • Show an example on the board, decomposing 13 into 10 ones and 3 ones. 

  • Explain that students will use digital drawing tools to visually represent the composition and decomposition of numbers.

  • Emphasize that today, students will use digital tools to visually represent the composition of numbers and break them down into smaller steps, similar to how computers process information step by step.

• Group Activity:

  • Divide students into pairs or small groups, each using a tablet. 

  • Assign each group a number between 11 and 19. 

  • Students will use digital drawing tools to create groups of ten ones (e.g., 10 circles) and some further ones (e.g., 5 additional circles for 15). 

  • After representing the number visually, they will write an equation (e.g., 15 = 10 + 5).

  • This mirrors how computational problems are broken into parts and represented visually.

• Creating and Sequencing:

  • Demonstrate how to use a digital app to draw groups of ten and then the extra ones. 

  • Encourage students to break down their process into steps: "First, draw 10 circles for the group of ten, then draw the extra ones, and finally write the equation." This reinforces problem-solving through decomposing numbers.

  • Have them document each step they took, reinforcing the computational thinking skill of sequencing, which is crucial in problem-solving and programming.

• Testing and Refining:

  • After students complete their drawings and equations, ask them to review their work by recounting the objects and checking if their equation matches the visual representation. 

  • Give students time to adjust their drawings or equations if necessary.

  • Explain that this step is similar to how computer scientists debug code to ensure the program works correctly.

• Presentation and Discussion:

  • Each group will present their digital work to the class, explaining how they represented their number and the steps they took to decompose it into tens and ones. 

  • Lead a discussion on how using technology helped them visualize the process and how breaking down numbers into parts is similar to how computers break down large problems into smaller, manageable pieces to solve them.

Equity and Access:

Offer templates or pre-drawn digital objects in for students who need additional support. Encourage peer collaboration to ensure all students can complete the task.

Real-World Application:

Connect the activity to everyday examples, such as counting items in groups of 10 (e.g., crayons or toys), and explain how understanding number composition helps in real-world tasks like grouping and organizing. Highlight how this process of breaking down numbers mirrors how computers solve larger tasks by breaking them into smaller steps.

CS Practice(s):

• Developing and Using Abstractions: Students use physical objects to represent the abstract concept of composing and decomposing numbers, connecting the concrete manipulatives to mathematical equations.

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

Standard(s):

• CA CCSS Mathematics K.NBT.1

• CA CS K-2.AP.13