Using the number line on the white board to practice counting fractions, I write the numbers 0, 1, 2, and 6 on the number line. I have tick marks for the other whole numbers and a tick mark between the 0 and 1 for the fraction 1/2. Because the students have been practicing counting unit fractions between zero and one, this counting task may initially be a little confusing for them. It is necessary for them to show flexibility in moving from counting tasks between fractions to whole numbers.
After the students count, I have them write the same number line on their own whiteboards, and include the half fractions between each whole number.
This lesson is addressing 3.NF.3c - expressing whole numbers as fractions and recognizing equivalent fractions that are equal to whole numbers and 3.NF.3d - comparing fractions with the same denominator and recognizing the size of the whole is critical in comparing fractions. To begin the lesson, I show the students separate pieces of a puzzle. I ask, "What is this? Why is it important? Is there anything this makes?" I pass out puzzle pieces to each student and ask the students to describe their own puzzle piece.
The students easily recognize that these puzzle pieces only create a picture if they are put together. I ask the students to think of a number that represents the pieces of the puzzle. Some of their responses may include 25 pieces or 1/25 as they develop an understanding of unit fractions.
Next, I show the students one apple. You could use anything that can be divided into pieces - relatively equal pieces.
I ask the students the same questions as I did with the puzzle pieces to give me a number to represent the apple. The students respond quickly with one apple. Then I show them two apples and, finally, three apples, and the students provide the numerical representation each time.
Next, I display a number line, representing 0 - 1, marked by thirds. We count the third aloud 1/3, 2/3, 3/3 as I point to/and then label them. I then write in the number below 3/3 as one. I explain the numerator and denominators are the same, so it equals one. I also draw models of fractions to demonstrate the three pieces are the whole amount.
I repeat the number line and the picture model with other unit fractions so that students see this as the whole amount including fourths 1/4, 2/4, 3/4, and 4/4 also written as one.
Returning to the puzzle pieces, I ask how many puzzles will the 25 pieces create. I want to know if students can connect the number of pieces of a fraction to create a whole amount.
The context I set for independent practice is one geared to appeal to my students. We think of a few "things" that they like to have "alot of", such as M&Ms, brownies, legos. Now students compare the sizes of the whole items to determine which is preferred. It is important for students to see that as the size the whole amount changes, influences its appeal.
Students will compile lists of whole amounts for things they would want in a whole amount, and things they would want in a half amount. The students create the lists on white copy paper.
Give One, Get One: After they come up with a list of ten items for each side, they then work with partners to give one idea to a partner, and then get one from a partner. The students goal is to have the most ideas which helps the students to move quickly to other students and continue gathering ideas. This rich discussion between students comparing fractions to whole amounts with real life tasks, items, and applications is an essential component of the Common Core Standards.
To end the lesson, the students record in their journals five of the best examples, in their opinion, of things you would want in a whole amount and things they would want in half amounts. I choose to have the students record in their journals this information because we are working with real life connections, and I feel it is important that the students have the opportunity to reflect on their own needs and wants. Their lists are not published, but we do have an informal discussion about interesting ideas that the students thought of while making their lists at the end of the lesson.