Building Blocks: Fractions and Conversions
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we use building blocks to model fractions, convert between mixed and improper forms, and design structures that showcase our understanding of fraction simplification?Essential Questions
Supporting questions that break down major concepts.- How can we represent fractions using building blocks?
- How can we convert mixed numbers into improper fractions using building blocks?
- How can we simplify fractions using building blocks?
- How can different structures be designed using building blocks to represent fractions?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Students will be able to represent fractions using building blocks.
- Students will be able to convert mixed numbers into improper fractions using building blocks.
- Students will be able to simplify fractions using building blocks.
- Students will be able to design different structures using building blocks to represent fractions.
Entry Events
Events that will be used to introduce the project to studentsFraction Frenzy Challenge
Students are presented with a seemingly impossible building challenge using only specific ratios of building block sizes. This sparks curiosity and requires them to convert mixed numbers to improper fractions to determine if the challenge is possible, connecting math to a tangible problem.Mystery Blueprint
Students receive a blueprint for a fantastical structure (e.g., a castle, spaceship) where dimensions are given as both mixed numbers and improper fractions, but some are missing or incorrect. Students must correctly convert and simplify to identify the errors and complete the blueprint, leading to a collaborative building challenge.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Fraction Block Basics
Students will begin by understanding how individual building blocks can represent fractions. They will learn to assign fractional values to different block sizes and use these blocks to visually represent fractions.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA visual guide showing how different building blocks represent specific fractions, with labeled diagrams.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will be able to represent fractions using building blocks.Mixed Number Mania
Students will explore mixed numbers by combining whole blocks with fractional blocks. They will practice building and drawing mixed numbers.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA collection of diagrams showing building block representations of various mixed numbers, with each diagram labeled with the corresponding mixed number.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will be able to convert mixed numbers into improper fractions using building blocks.Fractional Blueprint Challenge
Students will design a structure using building blocks, where the dimensions of the structure are determined by fractions. They will then create a blueprint of their structure, labeling all dimensions with fractions and mixed numbers.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA detailed blueprint of a building block structure, with all dimensions labeled with fractions and mixed numbers. The blueprint includes calculations of the total dimensions of the structure.Alignment
How this activity aligns with the learning objectives & standardsLearning Goals: Students will be able to represent fractions using building blocks; Students will be able to convert mixed numbers into improper fractions using building blocks; Students will be able to simplify fractions using building blocks; Students will be able to design different structures using building blocks to represent fractions.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioBuilding Blocks: Fraction Mastery Rubric
Fraction Representation
Demonstrates the ability to accurately represent fractions using building blocks and diagrams.Accuracy of Fraction Representation
How accurately are fractions represented with blocks and diagrams?
Exemplary
4 PointsFractions are consistently and accurately represented with blocks and detailed diagrams. Demonstrates a sophisticated understanding of fractional parts.
Proficient
3 PointsFractions are accurately represented with blocks and diagrams. Demonstrates a thorough understanding of fractional parts.
Developing
2 PointsFractions are mostly accurately represented with blocks and diagrams, but there are some inconsistencies or minor errors. Demonstrates an emerging understanding of fractional parts.
Beginning
1 PointsFractions are inaccurately represented with blocks and/or diagrams. Demonstrates a limited understanding of fractional parts.
Clarity of Visual Representation
How clear and understandable are the diagrams representing the fractions?
Exemplary
4 PointsDiagrams are exceptionally clear, well-labeled, and easy to understand. Visual representations significantly enhance understanding of the fractions.
Proficient
3 PointsDiagrams are clear, well-labeled, and easy to understand. Visual representations effectively support understanding of the fractions.
Developing
2 PointsDiagrams are somewhat clear but may lack detail or have some labeling issues. Visual representations partially support understanding of the fractions.
Beginning
1 PointsDiagrams are unclear, poorly labeled, and difficult to understand. Visual representations do not effectively support understanding of the fractions.
Mixed Number Conversion
Demonstrates the ability to accurately convert between mixed numbers and improper fractions using building blocks.Accuracy of Conversion
How accurately are mixed numbers converted to improper fractions (and vice versa) using the blocks?
Exemplary
4 PointsConversions between mixed numbers and improper fractions are consistently accurate and clearly demonstrated using the blocks. Shows innovative application of block representations.
Proficient
3 PointsConversions between mixed numbers and improper fractions are accurate and clearly demonstrated using the blocks.
Developing
2 PointsConversions between mixed numbers and improper fractions are mostly accurate, but there may be some errors or inconsistencies in the block representations.
Beginning
1 PointsConversions between mixed numbers and improper fractions are inaccurate, and the block representations are unclear.
Explanation of Process
How well is the conversion process explained and justified?
Exemplary
4 PointsProvides a comprehensive and insightful explanation of the conversion process, clearly justifying each step with mathematical reasoning. Connects the block representation to the mathematical process fluently.
Proficient
3 PointsProvides a clear and logical explanation of the conversion process, justifying each step with mathematical reasoning.
Developing
2 PointsProvides a basic explanation of the conversion process, but the justification may be incomplete or unclear.
Beginning
1 PointsProvides a minimal or unclear explanation of the conversion process with little or no justification.
Fractional Blueprint Design
Demonstrates the ability to design a structure using building blocks and create a blueprint with accurate fractional dimensions.Accuracy of Blueprint Dimensions
How accurate are the fractional dimensions labeled on the blueprint?
Exemplary
4 PointsAll dimensions on the blueprint are accurately labeled with fractions and mixed numbers, demonstrating sophisticated understanding. Shows innovative design and complex use of fractional units.
Proficient
3 PointsAll dimensions on the blueprint are accurately labeled with fractions and mixed numbers.
Developing
2 PointsMost dimensions on the blueprint are accurately labeled, but there are some errors or omissions.
Beginning
1 PointsMany dimensions on the blueprint are inaccurately labeled or missing.
Clarity and Detail of Blueprint
How clear, detailed, and well-organized is the blueprint?
Exemplary
4 PointsThe blueprint is exceptionally clear, detailed, and well-organized, providing a comprehensive representation of the structure. The blueprint includes all necessary calculations and annotations in a professional manner.
Proficient
3 PointsThe blueprint is clear, detailed, and well-organized, providing a good representation of the structure. The blueprint includes all necessary calculations.
Developing
2 PointsThe blueprint is somewhat clear and detailed, but it may lack organization or have some missing information.
Beginning
1 PointsThe blueprint is unclear, lacks detail, and is poorly organized, making it difficult to understand the structure.
Accuracy of Total Dimension Calculations
How accurate are the calculations for the total height, width, and depth of the structure?
Exemplary
4 PointsThe total height, width, and depth calculations are perfectly accurate and demonstrate a sophisticated understanding of fraction operations and simplification. Shows advanced integration of skills.
Proficient
3 PointsThe total height, width, and depth calculations are accurate.
Developing
2 PointsThe total height, width, and depth calculations contain some errors, but the overall approach is correct.
Beginning
1 PointsThe total height, width, and depth calculations are largely inaccurate or missing.