Objective:

Students will use base-ten blocks to model three-digit numbers and explicitly connect their understanding of place value to computational thinking by decomposing numbers and recognizing patterns in a structured way.

Materials Needed:

• Base-ten blocks (hundreds, tens, ones)

• Number cards with three-digit numbers

• Paper and pencils for recording

Steps:

• Introduction:

  • Introduce place value by explaining that numbers like 462 consist of 4 hundreds, 6 tens, and 2 ones. 

  • Explain that just like computer scientists break down problems into smaller tasks to solve them efficiently, we break down numbers into their hundreds, tens, and ones to understand them better.

• Group Activity:

  • In pairs, students will select a number card and use the base-ten blocks to represent the number. 

  • For example, for 562, students will use five blocks for hundreds, six blocks for tens, and two blocks for ones. 

  • Ask students to think of each block as a “unit of data” that they are organizing to make sense of the larger number, relating it to how computers process and organize information.

• Algorithmic Thinking:

  • Encourage students to follow a step-by-step process, or “algorithm,” to build their numbers. 

  • They will start with the hundreds, then move to the tens, and finally the ones. After building their number, they will write it in expanded form (e.g., 500 + 60 + 2) and identify patterns across numbers they build.

• Connecting to Computer Science:

  • Explain that just as they followed an algorithm to build their number, computers follow algorithms to solve problems. 

  • Decomposing numbers into smaller parts mirrors how programmers decompose complex problems into simpler tasks that are easier to solve. 

  • Ask students to discuss how breaking down a number made it easier to compare and understand.

• Discussion and Reflection:

  • Bring the class together to discuss how they approached building and comparing their numbers. 

  • Relate their experiences to how algorithms in computer science break down tasks and make problem-solving more efficient. 

  • Use this as an opportunity to emphasize that understanding place value is similar to organizing information or data in computer science.

Equity and Access:

Offer pre-grouped base-ten blocks for students who need additional support, and provide step-by-step instructions for decomposing numbers into hundreds, tens, and ones.

Real-World Application:

Connect place value to everyday activities like counting large quantities (e.g., in a store or in a classroom) or understanding numerical data such as populations or measurements. Highlight how computer scientists break down complex data sets into simpler units, just like students decompose numbers into hundreds, tens, and ones, to process information efficiently. This approach is also used in financial systems and digital communication to manage large amounts of data.

CS Practice(s):

• Recognizing and Defining Computational Problems: Students break down three-digit numbers into hundreds, tens, and ones, understanding the decomposition process like a computer breaks down tasks.

• Developing and Using Abstractions: Students use base-ten blocks to abstractly represent complex numbers and recognize patterns within the structure of numbers.

Standard(s): 

• CA CCSS for Mathematics 2.NBT.1

Objective:

Students will use Sphero, Ozobots, Beebots, or other robots to play a game that helps them understand place value. They will code the robot to represent different numbers by moving it to designated areas on a number grid, and then quiz each other on which number they are representing. This activity reinforces place value understanding and computational thinking by incorporating movement, coding, and problem-solving.

Materials Needed:

• Sphero, Beebot, or other robots (one per group)

• A large grid labeled with place values (Hundreds, Tens, Ones)

• Whiteboards or paper for keeping track of scores

Steps:

• Introduction:

  • Begin by reviewing the concept of place value and how digits in the hundreds, tens, and ones places represent different quantities. 

  • Explain that they will be playing a game where the robot will represent different numbers, and their classmates will guess what number the Sphero is representing based on its movement.

• Group Activity:

  • Set Up:

    • Divide students into small groups. 

    • Each group gets a robot and a tablet or laptop with the app. 

    • Lay out a large grid on the floor labeled with "Hundreds," "Tens," and "Ones."

  • Coding: 

    • Students will code their robot to move to different spots on the grid that represent the digits in a three-digit number (e.g., moving to the "6" in the hundreds column, the "4" in the tens column, and the "3" in the ones column to represent 643). 

    • They can use the app to create the sequence of movements.

  • Quizzing: 

    • Once the robot completes its movements, the group will call on another group to guess the number it represents. 

    • The guessing group writes down their answer based on where the robot moved on the grid (e.g., "643"). 

    • After the guess, the coding group reveals the correct number.

  • Scoring: 

    • For each correct guess, the guessing group earns a point. Rotate between groups so everyone has a chance to program and guess.

  • Testing and Refining:

    • If the robot does not move as planned, students can troubleshoot their code and try again. 

    • This step mimics the process of debugging in computer science, where errors are identified and corrected.

• Discussion and Reflection:

  • After playing the game, bring the class together to discuss what strategies worked best when coding the robot. 

  • Ask students how they made sure the robot moved to the correct place and how this activity helped them understand place value better.

Equity and Access:

Provide visual cues for programming steps and pre-written code for students who need extra assistance with the robot. Pair students with different levels of coding experience to foster peer learning.

Real-World Application:

Explain how place value understanding is used in real-world situations like budgeting money, handling large sets of data, or measuring distances. Highlight how programmers break down large tasks into smaller steps (just like they broke down numbers into hundreds, tens, and ones) to make complex problems manageable.

CS Practice(s):

• Creating Computational Artifacts: Students code the robot to represent numbers using place value.

• Testing and Refining Computational Artifacts: Students debug their robot’s movements to ensure the correct number is represented.

• Collaborating Around Computing: Students work together to program the robot and quiz each other on place value understanding.

Standard(s):

• CA CCSS for Mathematics 2.NBT.1

• CA CS K-2.AP.12