##
* *Reflection: Developing a Conceptual Understanding
Units & Wholes (Days 1 - 3) - Section 2: Try It Yourself

This task allows the students to develop an understanding of the fractional parts with precision emphasized. The students were challenged to cut and fold, so that each part was exactly the same size. Many of the students tried to move quickly through this task, and then realized their pieces would need to be redone in order to be included on the class poster.

There were discussions among the students about why or why not the papers were folded correctly. One student was able to explain that if the fraction represented something real, everyone would want equal pieces (fair shares).

Although folding paper into fractions seems to be a simple task, the students were challenged to create evenly folded pieces as they began to understand the fractions. They were especially challenged by thirds and sixths. This was especially true if the students were working with circles.

Throughout the days of this lesson, students moved away from the challenge of using circles. They found the circles too difficult to fold into equal portions with precision. I want the students to begin looking at how the size of a fourth compares to a third or a sixth. It is important for them to realize when the size of the whole remains the same no matter which fractional piece is marked. I want my students to understand when the number of fractional pieces increases (denominator), the size of the fractional piece decreases because the whole amount remains the same.

*Understanding Fractions*

*Developing a Conceptual Understanding: Understanding Fractions*

# Units & Wholes (Days 1 - 3)

Lesson 3 of 18

## Objective: SWBAT to explain and reason that a shape shows equal fractions, creating models for halves, thirds, fourths, sixths, and eighths.

#### Introduce and Model

*10 min*

Over the course of five days, students create models of fractions for halves, thirds, fourths, sixths, and eighths. I demonstrate for students how to trace an object in the shape of a square, circle, or rectangle. Some of the items used in my classroom include a wooden block, a tissue box, a paper plate, pencil container, and even an iPad. The only restriction is that it must be smaller than a sheet of 8 ½ x 11 paper and larger than a glue stick. I chose these guidelines because a tracing smaller than a glue stick would be too difficult for students to fold.

Once an item is traced, the students cut on the pencil outline, and then precisely fold the shape into the given fraction. The order of the lessons is halves, fourths, and eighths. Objects being folded in sixths and thirds are more challenging. Because of the Common Core math practice of attending to precision, I demonstrate the correct and incorrect folding to show the difference between precise and sloppy.

The fractions folded by students will be displayed on a class poster to display each of the different fractions. I explain that only shapes folded precisely will be included on the poster. The shapes folded without precision will not be displayed, and will have to be redone. This precision also applies to cutting out the shapes.

All folded items are checked by myself or another adult in the classroom before they are collected for that day's poster.

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#### Try It Yourself

*20 min*

Students are provided with various sizes and colors of construction paper to begin tracing. I encourage students to look for different types of items to trace, and it's important to find symmetrical items. Some of the items the students found to trace include geoboards, books, whiteboard erasers, rulers, and notecards.

The students trace six items before beginning to cut and fold. When each item is folded, students trace the lines between the fractional parts, and then write the fraction inside of each section. Squares folded into fourths have ¼ written inside of each section, and squares or items traced into sixths, eighths, thirds, and halves have the matching fraction written into each piece.

Students create a poster to present to the class for each fraction unit.

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#### Wrap Up

*15 min*

This lesson ends with group and independent work - the creation of a class poster and drawing an example in personal math journals. Students glue their fractional piece onto the poster, and then draw a representation of the poster in their journal. The students are asked to describe in writing their process for folding for each fraction.

I want the students to be able to explain or write about the mathematical practice of precision in their journal writing and also address the consistency of the size of the whole while comparing the change in the fractional units of halves, thirds, fourths, sixths, and eighths. Addressing their successes and challenges in working on this project are included as a reflection for the students.

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- LESSON 1: Fraction Counting
- LESSON 2: Our Garden Problem
- LESSON 3: Units & Wholes (Days 1 - 3)
- LESSON 4: Fractions On A Number Line
- LESSON 5: Fraction Assessment
- LESSON 6: Ordering Fractions With Partners
- LESSON 7: Plant The Garden to 3/4
- LESSON 8: Creating Fraction Strips
- LESSON 9: Large Number Lines
- LESSON 10: Comparing Unit Fractions
- LESSON 11: Debate: Does This Shape Show Fourths? (Day 1 & Day 2)
- LESSON 12: Drawing Fraction Bars to Compare Fractions
- LESSON 13: Modeling Fractions Assessment
- LESSON 14: Unit Fraction Examples & Non-Examples
- LESSON 15: The Whole In Fractions
- LESSON 16: Ordering Fractions With Fraction Cards (Days 1 - 3)
- LESSON 17: Equal Unit Fractions?
- LESSON 18: Showing Halves