Objective: 

Students will decompose the process of multiplying fractions by breaking down the problem into smaller, manageable tasks and using visual models to represent the area of a rectangle with fractional side lengths.

Materials Needed: 

• Grid paper

• Markers

• Rulers

• Fraction cards

• Problem decomposition template

Steps:

• Introduction: 

  • The teacher introduces the concept of breaking down complex math problems using decomposition, a key computational thinking skill.

  • Students learn they will solve fraction multiplication problems by decomposing the process into smaller steps, such as converting fractions, drawing models, and calculating areas. 

  • The teacher demonstrates how to decompose a fraction multiplication problem (e.g., 2/3 × 4/5) by first representing the fractions visually and then calculating the area of a rectangle.

• Activity: 

  • Working in pairs, students are given fraction cards (e.g., 3/4 × 2/5) and use grid paper to represent these fractions visually. 

  • They follow a problem decomposition template, which helps them break the multiplication process into steps: 1) Identify the fractions, 2) Represent each fraction on the grid, 3) Shade the unit squares to represent the product, and 4) Calculate the final area. 

  • Students use markers to color code the parts of the process, allowing them to track the smaller steps that lead to the final solution.

• Presentation and Discussion: 

  • After completing their grid models, students present their process to the groups of peers, explaining how they decomposed the problem into smaller steps and how each step contributed to solving the overall fraction multiplication. 

  • They reflect on how breaking down the task helped them understand the math concept more deeply.

Equity and Access: 

Provide pre-drawn grid templates and a scaffolded problem decomposition template for students needing extra support. Encourage mixed-ability pairings to foster collaboration.

Real-World Connection: 

• Relate the activity to how computer programmers break down complex tasks into simpler steps when designing algorithms for tasks like calculating areas or processing data.

CS Practice(s): 

• Recognizing and Defining Computational Problems: Students identify the individual steps required to solve complex fraction multiplication problems.
  
  

Standard(s): 

• CA Mathematics 4.NF.4b

• CA CS 3-5.AP.13

Objective: 

Students will use a block-based coding app to create interactive word problems involving addition and subtraction of fractions with unlike denominators.

Materials Needed: 

• Tablets or computers

• Fraction word problem worksheet

Steps:

• Introduction: 

  • The teacher introduces the concept of adding and subtracting fractions with unlike denominators and explains how students will use a coding app to create interactive word problems. 

  • Students view a sample word problem where the user needs to add 2/3 and 5/4, learning how to replace the fractions with equivalent fractions to solve the problem.

• Activity: 

  • Students work in pairs to design interactive fraction word problems using a coding app. They start by writing their word problem, such as "Add 1/2 and 3/5," and then code a solution where the app walks the user through converting the fractions to have like denominators, showing each step of the calculation. 

  • Students use coding blocks to animate the conversion process and display the correct answer. 

  • After creating their programs, they test them by solving their own and their classmates' problems.

• Presentation and Discussion: 

  • Each pair presents their coded word problem to the class, explaining how they used the app to guide the user through the steps of adding or subtracting fractions. 

  • They discuss the challenges they faced in ensuring the code correctly reflected the math process.

Equity and Access: 

Provide pre-built code templates for students needing extra help, and allow peer support in mixed-ability groups to encourage collaboration.

Real-World Connection: 

• Highlight how educational apps and games use coding to teach math concepts, similar to how the students are creating their own interactive fraction problems.

CS Practice(s): 

• Creating Computational Artifacts: Students design and code interactive fraction word problems. 

• Testing and Refining Computational Artifacts: Students test their programs to ensure the coding properly models fraction addition or subtraction.

Standard(s): 

• CA Mathematics 4.NF.1

• CA CS 3-5.AP.13

• CA CS 3-5.AP.17