Introduction to Fractions: A Concrete Experience

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Students will be able to identify wholes, halves, fourths, and eighths and label the total of each benchmark fraction of an artistic design.

Big Idea

Providing students ample opportunities to work with fractional parts and reason about equally partitioned shapes will help them develop a deep understanding of part-whole relationships.

Mini Lesson

15 minutes

To begin this lesson, and this unit, I assemble the students in our community center and place two same-size circles on the board.  (I have many of these circles, in various colors, on hand for the modeling.) I ask the students to tell their partners what they notice about the circles. (Same size, different colors.)

I then take one circle and fold it in half and demonstrate how that gives me a "line" to cut it.  Next, I cut the second circle into two pieces (not halves). Again, I have the students turn and discuss with their partner, what is the same and different about these two circles. It is important to provide some framework for the discussion (ups the rigor), and comparison is a critical skill that they are still learning. After a brief turn and talk, I ask them to explain and describe the pieces and I share a couple of the responses with the whole group.

Next, I follow the same folding and cutting demonstration with fourths and eighths, continuing to ask the students to notice the difference.  I am listening for my opportunity to explain that the parts that are equal are called fractions. Today's whole lesson is about gaining understanding that fractions are equal parts of a whole, so I directly teach this during the mini lesson.

Following this demonstration, I show the students the first pages of Ed Emberley's book Picture Pie. I explain that the artist uses halves, fourths and eighths, to create wonderful art. He never uses a whole circle, yet adds fractional pieces together to make a whole.

I use a few of the pictures to have the students figure out the total number of each fractional size. I withhold having the students find the proper total of the art for now, but will return to these pieces later to help explain the addition of fractions. 

Active Engagement

25 minutes

I explain to the students that they will now have a chance to create their own art, inspired by Ed Emberley. Their task will be to use halves, fourths and eighths to create a piece of art. I do not want them to use wholes, because the purpose of this lesson is to create concrete representations of how fractional parts add up to wholes. They will then write what sizes, and totals of each size, they use in order to create their image.

I model this with my own design, using the fractional pieces I have cut.  Next, I write the sentence: 

I used 2 halves, 7 eighths, and 3 fourths to create my flower. 

I give the students their baggies of circles and a piece of black construction paper to mount their one, and send them off to work.

While they are designing, I circulate to observe, confer, and prompt them to explain their thinking (using their precise mathematical vocabulary):

What are the fraction names of your pieces? How do you know this is true?

How many of each fractional size are you using?

Can you show me how to create a half or whole, using smaller fractional pieces?

Sharing as a Whole Group

10 minutes

After the mathematical artists are done creating and writing, I have the students set up their artwork at their desks with a piece of blank lined paper next to it.  

I've created discussion/feedback prompts on the board, as I've made a few changes to our usual talking moves to ensure students use the language of fractions.  The prompt was 

"I noticed that you used___  ________________in your artwork. They were asked to comment on how many and what type of fractional pieces were used. 

Using sentence starters not only requires students to use the mathematical vocabulary, it ups the rigor of their work. In order to create the accurate and comprehensible language that the starter sets up, the students have to dig into their own thinking, consider its accuracy, and find the words to express it.

I instruct the students to tour the artwork and leave comments using these talking/responding moves on the lined paper for the artist.  This allows for celebration, critiquing, and revision. Each of the students must think mathematically while observing the art. 

Wrap Up and Home Practice

5 minutes

As a wrap up, I review with the students by asking them to help me write a definition of the vocabulary word "fraction" for our math word wall.  

I will pass out a package of materials for them to take home and create a new design with their families.  They will bring it in tomorrow and we will use them to discuss creating a whole using the parts and renaming the totals.