Objective:

Students will explore equivalent fractions using visual models, applying computational thinking by breaking down the concept of fractions into smaller parts and using abstraction to represent fractions visually. They will compare fractions, such as 1/2 and 2/4, using patterns and reasoning to identify equivalencies.

Materials Needed:

• Fraction strips or fraction circles

• Large chart paper

• Markers or colored pencils

Steps:

• Introduction:

  • Begin by explaining the concept of equivalent fractions and how computational thinking can help us understand this. 

  • Discuss how breaking fractions down into smaller parts is like breaking down complex problems in computer science. 

  • Explain that equivalent fractions, like 1/2 and 2/4, represent the same amount even though they look different.

• Group Activity:

  • Divide students into small groups. 

  • Each group receives fraction strips or fraction circles and large chart paper. 

  • Students will use abstraction to simplify and represent fractions visually by coloring the fraction models. 

  • For example, they will color 1/2 and 2/4 to show that these fractions represent the same amount.

• Using Computational Thinking:

  • Guide students in using decomposition to break the fractions into smaller, manageable parts (such as dividing a whole into fourths or halves). 

  • They will recognize patterns by identifying relationships between fractions, using reasoning to determine why two fractions are equivalent.

• Testing and Refining:

  • After visually representing equivalent fractions, students will test their understanding by explaining their findings to their group members and class. 

  • They will refine their explanations based on peer feedback, similar to debugging code in computer science, where students refine their work to improve clarity and accuracy.

• Presentation and Discussion:

  • Each group presents their visual fraction models to another group, demonstrating how they used decomposition to break down the fractions and abstraction to represent them. 

  • Lead a discussion on how computational thinking helped them understand equivalence, much like how coders break down and abstract problems to find solutions.

Equity and Access:

Provide pre-labeled fraction strips and additional guidance for students who need support in understanding the concept of equivalent fractions. Encourage collaborative problem-solving where students with different skill levels can work together.

Real-World Application:

• Understanding equivalent fractions is crucial in real-world tasks, such as dividing a pizza into equal slices or sharing resources. Computational thinking, such as decomposition and abstraction, also applies in everyday decision-making, helping students solve complex problems efficiently.

CS Practice(s):

• Developing and Using Abstractions: Students abstract the concept of fractions by visually representing them and recognizing patterns in their equivalence.

Standard(s):

• CA CCSS.Mathematics.3.NF.3.a

• CA CS K-2.AP.13

Objective:

Students will use Sphero, Ozobot, or other robots to model fractions on a number line by programming the robots to move to different fraction points. This hands-on activity will help students visualize fractions as parts of a whole and understand how fractions are represented on a number line.

Materials Needed:

• Sphero robots

• Large chart paper with a number line from 0 to 1 drawn on it

• Tablets or devices with the robot app installed

• Markers or tape to indicate fraction points on the number line (e.g., 1/2, 1/3, 3/4)

Steps:

• Introduction:

  • Begin by explaining that fractions represent parts of a whole. 

  • Today, students will program Sphero robots to move to different fractions on a number line. 

  • Demonstrate how the interval between 0 and 1 can be split into equal parts, and how the Sphero will travel to specific fraction points on the number line (e.g., stopping at 1/2 or 3/4).

• Group Activity:

  • Divide students into pairs. Each pair will receive a robot and chart paper with a number line from 0 to 1. 

  • Students will mark key fraction points like 1/2, 1/3, and 3/4 on the number line using markers or tape. 

  • They will program the robot to move to these fraction points, adjusting the speed and distance the robot travels to match the fraction's position.

• Creating and Coding:

  • Students will program the robot to move from 0 to specific fractions (e.g., 1/2, 1/3, or 3/4) by adjusting the robot’s travel distance to match each fraction point. 

  • As they program the robot, they will test its movement and refine their code to ensure it stops at the correct fractions on the number line.

• Testing and Refining:

  • After creating their programs, students will test the robot’s movement on the number line, ensuring it stops at each marked fraction. 

  • They will make any necessary adjustments to their code to accurately reflect the distance between fraction points. 

  • Encourage students to refine their programs until the robot moves smoothly to each fraction.

• Presentation and Discussion:

  • Each group will present their number line and demonstrate the robot moving to each fraction point. 

  • They will explain how they calculated the distance for each fraction and how they programmed the robot to stop at the correct locations. 

  • Lead a class discussion on how fractions represent parts of a whole and how they are used in everyday life.

Equity and Access:

Provide pre-programmed code templates for students who need additional support. Use visual aids, such as fraction diagrams, to help students understand the concept of fractions before programming.

Real-World Application:

• Understanding fractions is essential for everyday tasks like measuring ingredients in cooking or dividing objects equally. Programming the Sphero to navigate a number line gives students a hands-on way to connect math concepts to real-world applications.

CS Practice(s):

• Creating Computational Artifacts: Students program a robot to visually represent fractions on a number line.

• Testing and Refining Computational Artifacts: Students test and refine their robot programs to ensure accuracy in navigating to fraction points.

Standard(s):

• CA Math 3.NF.1

• CA CS K-2.AP.12

• CA CS K-2.AP.13

• CA CS K-2.AP.17