Objective:

Students will understand decimal place values by organizing and comparing decimals through an unplugged activity that contains computational thinking concepts like abstraction, debugging, and pattern recognition.

Materials Needed:

• Number cards (0-9)

• Place value chart papers

• Markers

• Pre-made decimal challenge cards

Steps:

• Introduction:

  • Begin by asking, "How do computers store and organize information? 

  • How does understanding numbers help with this?" 

  • Discuss how computers rely on systems to organize and process numbers, especially decimals, and how understanding place value helps us manage numbers efficiently in both math and computing. 

  • Introduce the activity as a way to simulate the steps that a computer might follow when comparing, rounding, or organizing decimals.

• Group Activity:

  • Divide students into small groups and provide each group with number cards and place value chart papers. 

  • Explain that their goal is to "program" a set of numbers by placing digits in specific decimal places on the chart. 

  • Using computational thinking, students will abstract the decimals by breaking them down into smaller units (e.g., tenths, hundredths, thousandths) and creating a visual representation of the decimal number.

• Creating and Organizing:

  • Students will draw decimal challenge cards, which require them to arrange their number cards to create a decimal number (e.g., 3.456). 

  • They will write out each decimal in expanded form, showing how the digits correspond to different place values. 

  • After this, they will use comparison symbols (> , =, <) to compare two decimals based on the placement and size of each digit. 

  • This process mirrors how computers use algorithms to sort and compare data.

• Testing and Debugging:

  • Once students complete their decimal charts, they will exchange their work with a partner group to check for accuracy. 

  • The partner group will check whether the decimal number is properly arranged and written in expanded form.

  •  If there are errors, the students will "debug" the issue by identifying mistakes in the digit placement and making corrections. 

  • This simulates how coders find and fix errors in their code.

• Pattern Recognition and Refining:

  • Ask students to look for patterns as they arrange different decimal numbers. 

  • For example, they might notice that moving a digit to the left increases its value by ten times, and moving it to the right decreases its value by one-tenth. 

  • This reinforces both mathematical concepts of place value and the computational thinking process of recognizing patterns in data.

• Presentation and Discussion:

  • Each group will present one of their decimal numbers to the class, explaining how they organized the digits using their place value knowledge and how they compared two decimals. 

  • During the discussion, emphasize how this process is similar to how computers handle and process numerical data. 

  • Connect the activity to real-world examples, such as how computers organize decimals in financial calculations or measurements.

Equity and Access:

For students who need extra support, provide pre-filled place value charts with some digits already arranged, allowing them to focus on comparing or expanding the decimals. Pair students with varying levels of comfort to ensure peer collaboration and support.

Real-World Application:

Explain how this activity relates to how computers use decimal numbers to manage financial transactions, such as calculating prices or interest rates, and how understanding place value is essential in coding algorithms that sort and compare data.

CS Practice(s):

• Developing and Using Abstractions: Students break down decimals into place value components, abstracting them into tenths, hundredths, and thousandths.

Standard(s):

• CA CCSS Mathematics 5.NBT.3

• CA CCSS Mathematics 5.NBT.4

• CA CS 3-5.AP.13

• CA CS 3-5.AP.17

Objective:

Students will use Scratch or another coding platform to create an interactive game that visualizes the place value of digits in multi-digit numbers. They will program animations to demonstrate how a digit's value changes by 10 times or 1/10 depending on its place in a number.

Materials Needed:

• Tablets or computers with Scratch installed

• Pre-made Scratch templates for place value games

• Whiteboard for explanation and visual representation of place value

Steps:

• Introduction:

  • Begin by asking, "How does the value of a digit change when it moves to the left or right in a number?" 

  • Discuss how the place value system works and how each digit is worth 10 times more when shifted one place to the left, and 1/10 less when shifted to the right.

• Group Activity:

  • In pairs, students will use a coding platform to create a place value game. 

  • The game will include an animation that asks users to select the value of a digit as it moves to different places in a multi-digit number. 

  • For example, students might program a game where a digit like "4" moves from the hundreds place to the tens place, and players have to guess the new value (e.g., 400 becomes 40).

• Creating and Coding:

  • Students will use blocks in Scratch to animate the movement of digits across the screen, changing their values as they shift places. 

  • They will also create interactive questions that prompt players to guess the new value based on its place. 

  • Encourage students to include clear labels and instructions, explaining the changes in place value through their code comments.

• Testing and Refining:

  • Once students have created their games, they will test them with their peers. 

  • They’ll look for any bugs in the animations, such as incorrect values or unclear instructions. 

  • Students will debug their code, refining it to ensure that the game accurately reflects how place value changes.

• Presentation and Discussion:

  • Pairs will present their place value games to other pairs or students. 

  • They will explain how their game demonstrates the concept of place value and how they used coding to represent the changes in digit values. 

  • The teacher will facilitate a discussion on the importance of understanding place value in math and how coding helps to visually explain these concepts.

Equity and Access:

Provide pre-built templates with basic animations for students who may need extra support, allowing them to focus on coding the place value changes rather than building the entire animation from scratch. Pair students with varying levels of experience to encourage collaboration.

Real-World Application:

Connect the activity to real-life scenarios, such as understanding place value when calculating money or measuring large distances. Explain how computers use similar concepts of place value when processing numbers in digital formats.

CS Practices:

• Creating Computational Artifacts: Students use a coding platform to create a game that demonstrates place value through animation.

• Testing and Refining Computational Artifacts: Students test their program and debug any issues related to place value changes.

Standard(s):

• CA CCSS Mathematics 5.NBT.1

• CA CCSS Mathematics 5.NBT.2

• CA CS 3-5.AP.13

• CA CS 3-5.AP.17

• CA CS 3-5.AP.19