What Is the Whole

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Objective

Students will be able to create, name, and write fractions to build wholes in different ways.

Big Idea

The Common Core defines understanding of fractions as a 3rd grade Critical Area, beginning with unit fractions. It's time to grow our understanding.

Warm Up

10 minutes

To engage the students, I put a trapezoid on the board and ask the children to use the pattern blocks to show their partner as many ways to make that shape as they can think of.

After a minute, I ask partnerships to share their strategies and models.

I then place a hexagon on the board and ask them to predict how many ways they could build it.  We also discuss the term "congruent" as meaning identical, as this word is about to be used in the prompt.

Active Engagement

20 minutes

I prompt the students to create "hexagons" using any pattern block other than the hexagon itself. They set about building a hexagon shape using various "same" blocks to represent the hexagon. Next, they are to label the fractional parts of their hexagon and write about their strategies of labeling and building.

The idea of this lesson is to have students work with fractional parts of a whole, moving on from and building upon the use of unit fractions. This may seem easy, but as you watch these videos, you will see that the students struggle with the naming of the fractional pieces.

This student is working to explain how she used 2/3 and 2/6 to create the whole.  She also needed some prompting in why that worked.

Notice this student.  He names the trapezoid 1/3 because he sees three shapes.  This is a huge misconception because a fraction's name only comes from its equal sized partitions.

This girl has been struggling with this unit and her explanation in this clip made me very happy, as she is now understanding the relationship between the unit fractions.

Sharing and Close

10 minutes

To close, several students share their favorite solution at the board.  Children are required to add any solution they did not already have to their journal pages.

As the children share, I ask them to explain how they decided to try a strategy and how they labeled the fractional amount of their pattern blocks.

The building of the hexagon was very easy for the children, but labeling each piece was pretty tricky and explaining it was even tougher.  This is an activity that will require more than one day of experience.