Using Fraction Overlays
Purpose
This guide explains how to use the Math-U-See Fraction Overlays to model and teach key fraction concepts. Manipulatives like these help students visualize math problems and understand relationships between numbers in a hands-on, concrete way.
What are the Fraction Overlays?
The Fraction Overlays are physical, integrated manipulatives consisting of two key parts: colored vinyl pieces and clear, lined vinyl overlays that teach math operations with fractions. The colored vinyl pieces represent the numerator and correspond to the colors used in the Math-U-See Integer Blocks. The clear, lined vinyl overlays portray the denominator and show fractional parts that layer over the colored vinyl pieces, allowing students to see the relationship between wholes and parts.
Who Are the Fraction Overlays For?
Fraction Overlays are designed for students who are developing and strengthening their understanding of fraction concepts, particularly those working through Math-U-See’s Epsilon level. They are intended for use in instructor-led settings, where a parent or teacher guides students through fraction concepts using hands-on models.
The Fraction Overlays are also helpful for students who benefit from visual and tactile learning, need additional support with fraction relationships, or are reviewing fraction concepts introduced previously. Because the overlays model fractions concretely, they can support learners at different points in their math journey, regardless of age or grade level.
What Learning Experiences can I use with the Fraction Overlays?
Fraction Overlays are a key element in Math-U-See’s Epsilon level. They are relayed in lessons, videos, and activities to support hands-on learning with fractions.
In Epsilon Online Instruction with Video, instructors watch the lesson videos, then guide students in building fraction models using the Fraction Overlays during lessons, reinforcing understanding through hands-on interaction. This approach supports instruction across all major fraction topics in Epsilon, including comparing fractions, working with unlike denominators, performing operations with fractions, and connecting fractions to decimals and percentages.
Fraction Games and Activities are available as a supplemental online course. These focused activities are designed to reinforce specific fraction skills and concepts, providing targeted practice that can be used alongside Epsilon lessons or as stand-alone reinforcement when additional review is needed.
Because Fraction Overlays can visually and concretely convey universal fraction concepts, they can also be used to support instruction in other math programs outside Math-U-See, helping students better understand fractions regardless of the curriculum.
When Should I Use the Fraction Overlays?
Fraction Overlays are introduced once students are ready to begin formal work with fractions, after they have a basic understanding of whole numbers and part–whole relationships. If you are following the Math-U-See path, this will come after the Delta level. In Epsilon, the overlays are used to introduce and practice new fraction concepts through hands-on modeling. Instructors can also return to the Fraction Overlays anytime a student needs reinforcement, clarification, or review.
What’s in the Fraction Overlays Box?
Fraction Overlays, previously referred to as Fraction Overlay Kits, may vary slightly depending on when they were purchased. All versions include the core pieces needed to model and teach fraction concepts effectively.
Many versions include:
49 vinyl pieces matching the Math-U-See Integer Blocks
- 5 green pieces representing units
- 2 orange pieces and 2 clear overlays representing halves
- 3 pink pieces and 2 clear overlays representing thirds
- 4 yellow pieces and 2 clear overlays representing fourths
- 5 light blue pieces and 2 clear overlays representing fifths
- 6 purple pieces and 2 clear overlays representing sixths
- 8 brown pieces and 2 clear overlays representing eighths
- 2 clear overlays representing tenths
- 1 clear half-overlay representing eighths
- 1 clear half-overlay representing sixteenths
Our newer version includes additional pieces for expanded modeling, bringing the total to 79 pieces, which adds:
- 7 tan pieces and 2 clear overlays representing sevenths
- 9 mint pieces and 2 clear overlays representing ninths
- 10 blue pieces representing tenths
Where to Buy Fraction Overlays?
You can purchase the Math-U-See Fraction Overlays from our online store: store.demmelearning.com/products/fraction-overlay-kit
Why Use Manipulatives to Teach Math?
Math-U-See manipulatives are used to illustrate and teach new concepts in a way that is easy for students to visualize and understand. This provides a foundation for them to progress toward solving problems on their own.
While many math programs utilize manipulatives in early learning, Math-U-See continues using them into the high school levels to illustrate and attain mastery in the higher-level concepts present in algebra and geometry.
Research has shown that using manipulatives helps students:
- Engage multiple senses to transfer information to long-term memory
- Connect symbols to number concepts
- See abstract mathematical ideas in concrete form
- Understand the reasoning behind problem-solving methods
- Link mathematical concepts from early elementary through high school
- Develop a positive attitude toward learning
What Are a Few Concepts You Can Teach Using Fraction Overlays?
The Fraction Overlays can be used to demonstrate and practice the following concepts:
Fraction of one (part–whole relationships)
Taught in Epsilon Lesson 2
Adding and Subtracting Fractions with Common Denominators
Taught in Epsilon Lesson 3
Comparing Fractions
Taught in Epsilon Lesson 7
Adding and Subtracting Fractions with Unlike Denominators
Taught in Epsilon Lesson 5
Multiplying Fractions
Taught in Epsilon Lesson 9
Dividing Fractions
Taught in Epsilon Lesson 10
Simplifying Fractions
Taught in Epsilon Lessons 12–13
Mixed Numbers and Improper Fractions
Taught in Epsilon Lesson 15
Linear Measurement with Customary Units
Taught in Epsilon Lessons 14 and 16
Relating Fractions to Decimals
Taught in Epsilon Lesson 29
Percentages
Taught in Epsilon Lesson 29
The Rule of Four
Taught in Epsilon Lesson 7, The Rule of Four is a Math-U-See strategy to find common denominators for two fractions. It can be used to compare, add, subtract, or divide fractions with unlike denominators.
How the Rule of Four Works
- Make the first fraction.
- Steps 1 and 2: The thirds overlay is rotated 90° and placed over the first.
- Make the second fraction.
- Steps 3 and 4: The fifths overlay is rotated 90° and placed on top.
- Complete the indicated operation.
How Do I Use the Reference Materials?
The Fraction Overlays can reinforce key concepts taught in the Math-U-See curriculum. These materials provide visual examples and real-world connections to strengthen understanding.
Comparing Fractions
This shows how to compare fractional values by using the same green unit square as a visual baseline. It can be used alongside the overlays to demonstrate the relative size of fractions and support lessons on ordering or simplifying.
Customary Units of Length
This reference connects fraction overlays for halves, fourths, eighths, and sixteenths to the markings on a ruler. It helps students see how fractional measurements relate to real-world applications, such as inches and other customary units.
Related Articles & Blog Posts
Math Manipulatives Aren’t Just for “Little Kids”
How to Use the Math-U-See Manipulatives
From Math Manipulatives to Mastery
Addressing Hesitations About Manipulatives