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Dividing Fractions

Grade 5Math4 days

The 'Dividing Fractions' project is designed for 5th-grade students to explore and understand the division of fractions and whole numbers using visual models and story contexts. Students engage in activities such as creating fraction storybooks, remixing recipes, participating in a 'Fraction Quest', and connecting multiplication with division. These activities aim to reinforce comprehension of fraction division concepts through real-world scenarios and collaborative problem-solving, aligned with common core standards 5.NF.B.7.a, 5.NF.B.7.b, and 5.NF.B.7.c.

DivisionFractionsVisual ModelsStory ContextsProblem-SolvingGrade 5Real-World Scenarios

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we use visual models and story contexts to understand and solve real-world problems involving the division of fractions and whole numbers at Grade 5?

Essential Questions

Supporting questions that break down major concepts.

What does it mean to divide a unit fraction by a whole number?
How can visual fraction models help us understand division of fractions and whole numbers?
What real-world scenarios might require us to divide a whole number by a unit fraction?
In what ways does understanding multiplication help us comprehend division of fractions?
How can we create story contexts to make sense of dividing fractions?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Students will be able to interpret division of unit fractions by whole numbers using visual models and story contexts.
Students will be able to compute quotients of whole numbers divided by unit fractions in various real-world scenarios.
Students will demonstrate an understanding of the relationship between multiplication and division when working with fractions.
Learners will develop skills to create story contexts that model the division of fractions, enhancing problem-solving abilities.

Common Core Standards

5.NF.B.7.a

Primary

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.Reason: The project involves interpreting and computing quotients of unit fractions divided by whole numbers, which directly aligns with this standard.

5.NF.B.7.b

Primary

Interpret division of a whole number by a unit fraction, and compute such quotients.Reason: This standard is about division of whole numbers by unit fractions, a core component of the project.

5.NF.B.7.c

Primary

Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.Reason: Solving real-world problems using visual fraction models is a key focus of the project, aligning with this standard.

Entry Events

Events that will be used to introduce the project to students

Bake Sale Challenge

Kick off the project with a surprise bake sale where students must decide how to evenly divide amounts of ingredients when baking fractional quantities of their favorite treats for a class sale. This real-world scenario will require them to apply division of fractions to ensure every recipe turns out perfectly, sparking interest through relatable and tasty math problems.

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Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.

Activity 1

Fraction Storybook Creation

Students create a storybook illustrating scenarios where fractions are divided by whole numbers and vice versa. This activity helps students interpret both types of division in an engaging way while reinforcing comprehension through storytelling.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Choose or create a scenario that involves dividing a unit fraction by a whole number.

2. Sketch a visual fraction model that demonstrates the scenario, making sure it accurately reflects the division problem.

3. Write a short narrative that explains the situation and how the division is resolved, using the fraction model as a guide.

4. Repeat the process with a scenario involving the division of a whole number by a unit fraction.

Final Product

What students will submit as the final product of the activityA storybook containing illustrated division problems with accompanying narratives.

Alignment

How this activity aligns with the learning objectives & standardsAligns with 5.NF.B.7.a and 5.NF.B.7.b as students interpret and compute quotients through story contexts and visual models.

Activity 2

Recipe Remix

In this activity, students remix a simple recipe by dividing the ingredients using fractions. It challenges them to apply their understanding of dividing fractions to real-world situations, ensuring each recipe is suitable for a smaller or larger group.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Select a simple recipe and determine the fractional quantities of each ingredient needed.

2. Decide on a new group size that requires adjustment of the recipe, such as doubling or halving it.

3. Calculate the new quantity of each ingredient by dividing or multiplying the original fractions to suit the new group size.

4. Create a visual fraction model representing the old and new quantities of ingredients.

Final Product

What students will submit as the final product of the activityA remixed recipe with visual models showing the adjusted ingredient quantities.

Alignment

How this activity aligns with the learning objectives & standardsAligns with 5.NF.B.7.c as students solve real-world problems involving division of fractions through practical application in recipes.

Activity 3

Fraction Quest

A scavenger hunt-style activity where students search for and solve division problems involving fractions throughout the classroom, turning the solving of fraction problems into an adventure.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Hide problems around the classroom that involve dividing unit fractions by whole numbers and vice versa.

2. Organize students into teams and provide them with clues leading to each hidden problem.

3. Teams must use visual models and story contexts to solve each problem as they find it.

4. After solving a problem, teams receive a piece of a map leading to a treasure (could be a prize or a certificate).

Final Product

What students will submit as the final product of the activityCompleted treasure map showing mastery of division of fractions problems.

Alignment

How this activity aligns with the learning objectives & standardsReinforces 5.NF.B.7.a, 5.NF.B.7.b, and 5.NF.B.7.c by requiring application of all aspects to hunt and solve problems.

Activity 4

Multiplication-Division Connection Workshop

This activity focuses on the relationship between multiplication and division with fractions, reinforcing the understanding that multiplying by the reciprocal is how division with fractions is achieved.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Review the concept of multiplying by the reciprocal to perform division with fractions.

2. Provide practice problems that require students to switch division problems into multiplication problems using reciprocals.

3. Use visual fraction models to illustrate each conversion and solution.

4. Discuss how this understanding helps solve real-world problems.

Final Product

What students will submit as the final product of the activityA worksheet with examples of converted and solved multiplication-divison problems using reciprocals.

Alignment

How this activity aligns with the learning objectives & standardsSupports understanding of 5.NF.B as it highlights the multiplication-division relationship crucial to division of fractions.

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Fraction Division Mastery Rubric

Category 1

Conceptual Understanding

Assesses students' grasp of division concepts related to fractions and whole numbers, as demonstrated through visual models and narratives.

Criterion 1

Division of Unit Fractions by Whole Numbers

Ability to interpret and compute quotients of unit fractions divided by whole numbers using visual models.

Exemplary

4 Points

Shows sophisticated understanding by accurately creating and explaining visual fraction models that demonstrate division of unit fractions by whole numbers, often relating it to real-world contexts.

Proficient

3 Points

Consistently applies knowledge to create correct visual models for dividing unit fractions by whole numbers, with clear explanations linked to contexts.

Developing

2 Points

Shows basic understanding by creating simple visual models that demonstrate division of unit fractions, although with some inaccuracies or incomplete explanations.

Beginning

1 Points

Struggles to create visual models for division scenarios, often inaccurate or incomplete, indicating minimal understanding.

Criterion 2

Division of Whole Numbers by Unit Fractions

Ability to interpret and compute quotients of whole numbers divided by unit fractions using visual models.

Exemplary

4 Points

Consistently demonstrates advanced understanding by creating accurate, detailed visual models to represent division of whole numbers by unit fractions, linked to story contexts.

Proficient

3 Points

Regularly creates correct visual models linked to narratives for dividing whole numbers by unit fractions, with complete explanations.

Developing

2 Points

Creates basic visual models for division problems with some errors or missing details in explanations, indicating partial understanding.

Beginning

1 Points

Difficulty in creating models for division of whole numbers by unit fractions; often contains mistakes or lacks context, suggesting limited understanding.

Category 2

Application and Problem Solving

Evaluates students' ability to apply fractional division knowledge in real-world scenarios and through collaborative problem solving.

Criterion 1

Real-World Application

Use of fractional division concepts in practical, story-based situations.

Exemplary

4 Points

Consistently applies division concepts to solve real-world problems involving fractions, creating detailed scenarios with effective use of models to support conclusions.

Proficient

3 Points

Regularly applies knowledge to successfully solve practical problems, with mostly accurate scenarios and supporting models.

Developing

2 Points

Applies some concepts to real-world problems, but scenarios or models may be incomplete or occasionally incorrect.

Beginning

1 Points

Struggles with applying concepts to real-world scenarios; solutions often inaccurate or incomplete.

Criterion 2

Collaboration and Communication

Ability to work effectively in teams and communicate mathematical ideas clearly.

Exemplary

4 Points

Exhibits leadership in group activities, effectively orchestrating discussions and clearly explaining ideas to peers using mathematical language.

Proficient

3 Points

Contributes valuably to teamwork, frequently explaining ideas and engaging in discussions using appropriate mathematical language.

Developing

2 Points

Participates in group work with some contributions to ideas or discussions, but explanations may be limited or unclear.

Beginning

1 Points

Limited participation in group work; rarely explains ideas or engages with peers, affecting group dynamics and understanding.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning

Question 1

Reflect on how your ability to solve real-world problems involving fractions has improved through these activities.

Text

Required

Question 2

On a scale from 1 to 5, how well do you understand the relationship between multiplication and division when working with fractions?

Scale

Required

Question 3

Which activity helped you most in understanding division of fractions, and why?

Text

Required

Question 4

In what ways can visual fraction models enhance your understanding of division?

Text

Optional

Question 5

How confident do you feel in creating and using story contexts to solve fraction division problems?

Scale

Required