For this warm up, I ask students to turn and talk with learning partner about the meaning of numerator and denominator. Some of my students are still wrestling with this idea and trying to make sense of fractions. Many of my students understand numerator and denominator. Allowing students to turn and talk with a partner about the meaning allows students to utilize math practice 3 and 6. This strategy gives students the opportunity to critique the reasoning of others as well as practice using precise language about explaining these concepts.
Most students responded with ideas similar to these:
The numerator tells you how many parts.
The denominator tells you how many to a whole.
The denominator tells you the size of the pieces.
All of these are acceptable answers for now, but I do want my students to become more precise in their language and communications about their ideas. Instead of students saying "to a whole", I want students to respond with, "how many parts MAKE a whole".
For this lesson, students will create a fraction person or a Fraction Me. I start by giving all students a piece of graph paper and explain that the objective is to make a mosaic person using colored squares, but that there are certain rules. ( I precut many 1 inch squares from various colors. In order to keep the size smaller, I have my students cut each one inch square into fourths for the actual mosaic squares they will use for their fraction me portrait.)
1. Use complete squares. You may cut your square into halves or fourths, but you must use all of those parts so you can count it as one square in your finished portrait.
2. Your person should look like you - not a robot or pretend fantasy creature
3. Calculate what fraction each color represents of your whole person
4. Use at least 3 different colors
5. Have fun!
I then show students this example of a finished Fraction Me!
Students create their fraction me first on graph paper using crayons. This is their rough draft. As student create their rough drafts I circulate the room and ask questions about the fraction me portraits. This gives me an opportunity to touch base with all students and ask questions about the meaning of numerator and denominator.
After students draw their rough drafts, and calculate their fractions, they then get colored squares and create their final fraction mosaics.
Note: One part of this lesson that could be changed is that students could also glue their colored squares onto graph paper to help with organization. Students could also create just the colored fraction me if time was an issue for lesson planning. I like the look of the finished products and I hang these up in the hallway as a Math and Art display.
The following photos are examples of what my students created. You can see the rough draft on the left and the final fraction me portrait on the right. They turned out really cute and each student's fraction me does resemble that student. They make me smile!
When you look at this last example, it's very easy to see how this student counted all of the squares to get her whole or denominator.
For this wrap up students participate in what I call a "See and Flee." This is similar to a gallery walk in the sense that each student has the opportunity to see peers work, however, this is much quicker than a gallery walk. During a gallery walk, students often answer questions posed at "stations" or particular projects. The See and Flee is more of an opportunity for students to take a quick glance at what other students created.
Towards the end, I ask questions like, "Which Fraction Me had the most squares used? Which fraction me looked the most like it's creator"?
I then use one example and list all the fractions on the board. I ask students what they notice about the numerators of the fractions. Most students are able to see or calculate that the numerators add up to the denominator. I then stress the language of part and whole to help students solidify the meaning of numerator and denominator.