Who: The following lesson/activity is geared towards 3rd through 5th grade students. This is also a great lesson for tactile learners and those who like to bake!
Prior Knowledge: Students should already understand the concept of what a fraction is. Students should also be proficient at finding a fraction of a whole. Students should be familiar with what improper fractions and mixed numbers are, but they are not able to convert between the two.
Lesson Objective: By the end of this lesson you will be able to convert an improper fraction to a mixed number. I also hope that you will be able to describe this process to someone at home and explain its importance!
Ready to Bake!
To get started, I would like you to look at the recipe below and get out the following ingredients and baking tools that you will need, such as measuring cups, spoons, bowls, cooking sheets, etc.
Problem 1: The head baker for Fire Hook Bakery has a big problem! Her recipe for chocolate chip cookies got all messed up and she needs YOUR help! All of the measurements for the ingredients look really funny to her! She doesn't know what to do?!? I told her not to worry, that I had some really smart math students who could help her out!
So, let's check out this recipe and see if we can change it back to "normal" for her so she can bake her cookies!
11/4 cups all-purpose flour
4/3 teaspoon baking soda
3/2 teaspoon salt
1 cup (2 sticks) butter, softened
5/4 cup granulated sugar
5/4 teaspoon vanilla extract
2 large eggs
2 cups chocolate chips
7/4 cup chopped nuts
As you can see, this recipe is a little different looking than most recipes. If you are not sure what I mean, ask someone at home to show you a recipe for cookies. Compare these recipes, what do you notice is different? Do you notice that this recipe has NO mixed numbers and that they are all improper fractions? Well, in order for the baker to make these cookies, she needs these improper fractions to be converted to mixed numbers because right now she doesn't know how much of each ingredient to add and she can't make her cookies!
Please get out your flour and your measuring cups. How much flour do we need? That's right, 11/4. Now, why is this fraction an improper fraction? (Because the numerator is bigger than the denominator, right? And the fraction is then bigger than a whole!). So we need to change this improper fraction to a mixed number, so let's do some experimenting! What we need to do is figure out how many wholes we have and how much we have left over! So if we are talking about fourths, what measuring cup do we need? 1/4, good! I want you to see how many whole cups you can make with 11/4 and how many quarter cups you have left over. Hint: Scoop out 1/4 cups of flour and put this in your 1 cup measuring cup. Keep doing this until you have scooped out 11 quarter cups. Every time you fill up your 1 cup, record this on your paper, pour your flour into the bowl and then keep going until you have used 11/4 cups of flour.
How many whole cups did you make with your 11/4? 2 whole cups, right?
How many quarter cups were left over? 3, right? So that makes 3/4 of a cup, right?
So all together you have 2 wholes and 3/4 cups of flour or 2 3/4.
Great job! You just converted an improper fraction to a mixed number! Make sure you write this new amount down on your recipe!
The baker is going to be so happy! Now, I want you to do the same thing and change all of the improper fractions to mixed numbers! When you are finished, please submit the recipe to me and I will check your work! Have fun, be careful and enjoy your cookies!
Challenge Yourself!
If that was really fun and you want to challenge yourself, see if you can convert a mixed number to an improper fraction. Google any recipe that you would like to make and see if you can experiment with your ingredients to convert your mixed numbers to improper fractions!
Submit both recipes to me and I will check your work!
Thinking Behind the Lesson:
When I was in my first few years of teaching I always taught my students how to convert between improper and mixed numbers by using what I thought was a simple algorithm (because that is the way I was taught). Although some of my students caught on to this method, it was very frustrating for others and most of them did not understand the meaning behind it or what they were doing. They simply memorized a formula. I learned that I needed to make this concept much more visual and hands on for my students. I also learned that the more they figured things out for themselves, the better they would understand and retain the information. After reading about fraction concepts in John A. Van de Walle's book, I was even more convinced that I did not need to teach my students any conventional methods or rules for converting between the two. In his book, Van de Walle states that students should figure out how to convert between improper and mixed numbers by using any materials they wish or by drawing models. They should also be pushed to give an explanation and be able to justify how they arrived at their answer. He also goes on to state that there is no reason to provide a rule or algorithm, as students will develop their own rule AND it will be in their own words and with complete understanding (Van de Walle p. 260). Based on my experience and Van de Walle's methodology, I thought allowing students to figure out how to convert improper fractions to mixed numbers by experimenting with food would be a great way for them to gain an understanding of this concept and make learning more meaningful.
This activity is also very engaging for tactile students who like to bake or cook!
Reflections:
*While I recommend students have a good understanding of what improper fractions and mixed numbers are before taking part in this activity, as I reflect on this lesson, I think that this activity could also be a great way to introduce both of these concepts. For example, if students are given the fraction 11/4, they can use the flour and their measuring cups to figure out that once they use 4 quarter cups, they have reached a whole! This can then help them understand that 11/4 is more than a whole, and then they can be introduced to the vocabulary of improper fractions and mixed numbers.
*If your student is not a big fan of cooking, or if you do not want your student in the kitchen by themselves, you could always do this activity with non-edible ingredients such as dried beans, sand or other manipulatives.
References:
Van de Walle, J.A. (2006). Teaching student-centered mathematics: Grades k-3. Boston: Pearson.
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