Units & Wholes (Days 1 - 3)

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

Big Idea

It is important for students to learn to compare the size of the same fraction units as the size of the whole amount changes.

Introduce and Model

10 minutes

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.  

Try It Yourself

20 minutes

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.


Wrap Up

15 minutes

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.