4th Grade Unit 4: Equal Partitioning - Fraction Operations

Unit Driving Question

How does adding and subtracting fractions help you solve real world problems?

Essential Questions

1. How can non-unit fractions be decomposed?

2. What is the relationship between fraction operations and whole number operations?

3. How can we communicate a fraction sum which is greater than one?

Big Ideas

1. We can use a variety of manipulatives and pictorial models to decompose fractions and record the results with symbolic representations.
2. We can use models to add and subtract fractions with like denominators in real world and mathematical situations. 

Technology Resources 

Launch Task

1 Lesson

Planting a Garden - This hands-on task is designed to encourage students to think about the different ways a fraction can be decomposed.

Big Ideas for Development Lessons

2 Weeks (approximately 1 week per big idea)

Big Idea 1: We can use a variety of manipulatives and pictorial models to decompose fractions and record the results with symbolic representations.

Collaborative Engagement 

1. Decomposing a Submarine Sandwich - In this introductory task, students will focus on decomposing a whole into a sum of unit fractions in a variety of ways, using paper models of a submarine sandwich.  The lesson author explains her reasoning very thoroughly, and provides a wealth of resources, including pics of student work and videos of students explaining their thinking.  When presented as written, this lesson will take at least 2 class periods.  (source:  betterlesson.com)

Key Resources 

1. Decomposing and Composing Fractions- In this lesson, students identify real-world situations when it would be helpful to know how to decompose and compose with fractions, then gives discussion guidance and student practice opportunities.  (source:  betterlesson.com)
2. Teresa’s Pizza- This task-based lesson provides opportunities for students to demonstrate their understanding of fraction decomposition.  The task and exit ticket both involve decomposition fractions having a denominator of 4; depending on the degree of challenge desired, these fractions could be adjusted so that the students were working with larger-digit.  (source:  betterlesson.com)
3. Fraction Game -In this interactive app, students apply their knowledge of fraction decomposition and equivalence to compose various fractions equivalent to one.  (source:  NCTM Illuminations)

Big Idea Formative Assessment

1. Addition & Subtraction Assessment - This lesson includes an awesome review game for the entire class, as well as an assessment of fraction composition/decomposition understandings. (source: betterlesson.com)

Evidence of Understanding 

• Model the decomposition of a fraction in multiple ways, using models and pictures.

• Ex:  3/4 may be decomposed as 1/4, 1/4, 1/4, or 2/4 and 1/4.

• Record the results of decompositions using symbolic mathematical expressions (i.e., 3/4 = 1/4 + 1/4 + 1/4; 3/4 = 2/4 + 1/4)

• Explain why only the numerator changes in a decomposition equation, but the denominator remains the same.

• Ex:   in the decomposition equation, 3/4 = 2/4 + 1/4, why does the numerator change, but the denominator in each fraction is ‘4’?

Big Idea 2: We can use models to add and subtract fractions with like denominators in real world and mathematical situations.

Collaborative Engagement  

1. Introduction to Fractions Greater Than One - In this lesson from the Rational Number Project, students extend their understanding of fraction addition into the realm of fractions greater than one.  Students will use fraction circles (link here ) to compose and model fractions greater than one, using a variety of denominators.

Key Resources 

1. Composing/Decomposing Mixed Numbers - This lesson extends student understandings of fraction composition/decomposition into fractions greater than one.  Includes visuals, link to virtual fraction manipulatives, and student work samples. (source:  betterlesson.com)
2. Addition & Subtraction of Numbers Greater than One - In this hands-on lesson, students will use pattern blocks to model fractions.  The lesson is primarily focused on numbers greater than one (using the term ‘mixed numbers’), but the concepts would easily adapt to fractions less than one.  Includes student work samples, video explanation of student thinking, and remediation tips.  (source: betterlesson.com)
3. Adding & Subtracting Mixed Numbers: Word Problems - As a follow-up to the above modeling lesson, this gives students the opportunity to practice the addition/subtraction skills in real-world situations. (source:  betterlesson.com)

Big Idea Formative Assessment

1. This link will connect to several assessments appropriate for the concepts in this unit.  (source:  Howard County Public Schools)  Scoring rubrics are included with the assessment tasks.  Assessment Tasks 3, 10, 11, and 13 are designed to assess fraction decomposition.  Assessment Tasks 5, 9, and 15 would appropriately assess addition and subtraction of fractions.

Evidence of Understanding 

• Utilize a variety of representations to model scenarios involving the addition and subtraction of fractions.

• Use concrete manipulatives (i.e., fraction pieces, sets, pattern blocks).

• Illustrate addition and subtraction of  fractions, including fractions greater than one, using a number line or pictures.

• Justify results of fraction addition or subtraction symbolically, and be able to explain the model used.

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment)

Unit Re-Engagement

• Fraction Decomposition:  
• Peaches (source:  Illustrative Mathematics) 
•  Building Blocks (source:  Illustrative Mathematics) 
•  Pretzels (source: Howard County Public Schools) 
• Fraction Addition and Subtraction:  
• Fractions Decomposed (source:  Howard County Public Schools) 
• Pattern Block Fractions (source:  Howard County Public Schools)