In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a fullblown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission comes from my former student Kristin Ambrose. Her topic, from PreAlgebra: adding and subtracting fractions with unequal denominators.
What interesting (i.e., uncontrived) word problems using this topic can your students do now?
Cooking is a great example of where you frequently add and subtract fractions with unequal denominators. For example, here is a realworld word problem I came up with for adding and subtracting fractions in cooking:
You are making dinner tonight and you’re having Lemon Chicken with Scalloped Potatoes. The recipes for these can be found below (and yes they are real recipes that you can use in real life).
Lemon Chicken: ½ lb. boneless chicken breasts 1/8 cup flour ¼ tsp. salt 1 tbsp. butter ½ tsp. lemon pepper seasoning ½ cup of asparagus 1 lemon Instructions:

You only have a half a cup of flour left in your pantry. Looking at the recipes above, do you have enough flour to make dinner? Or do you need to go to the grocery store to buy more flour?
In order to solve this problem students would first have to add the different amounts of flour for each recipe (1/4 + 1/8 = 3/8). Then students would have to subtract this amount from the amount of flour they had to see if they would have enough (1/2 – 3/8 = 1/8). Since 1/8 cup of flour would be left, they have enough flour to make dinner.
How can this topic be used in your students’ future courses in mathematics or science?
It would be difficult to do mathematics without knowing how to add and subtract fractions with unequal denominators. In mathematics when adding or subtracting fractions, it doesn’t always work out nicely where the denominators are the same, so it’s important to be able to solve problems even when the denominators are different. One example of this is summations. Take ; what this equation really means is to add 1/2+1/4+1/6+1/8=25/24 or 1 1/24. Therefore adding fractions with unequal denominators could arise in summations. Also, in Algebra students will study quadratic functions and the factors of quadratic functions often take a form similar to something like (x+a)(xb), with a and b being numbers. Students will have to know how to multiply these factors out and simplify the expressions. For example, a set of factors could be . When multiplied out students will have . Students will have to know how to subtract 2/3 from 1/2 in order to simplify the expression.
How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?
YouTube can be a good source for finding videos to engage students in a topic. In particular, I found a short, funny video that reminds students of the significance of fractions. Here is the link to the video: https://www.youtube.com/watch?v=CBy8QbZyzy4. It makes a difference when a superhero only saves half of your stuff and not all of it. Just like you wouldn’t want only half your things saved, you wouldn’t want to add 2/3 of a cup of flour to a recipe that only calls for 1/4 a cup, or you wouldn’t want to fill up 2/3 of your tank of gas if it was already 1/2 of a tank full. Understanding fractions and how to add and subtract them is an important part of daily life.
I also found another video that demonstrates where fractions can come into play in science. Here is the link to the video: https://www.youtube.com/watch?v=hLGDJFGAmic. The YouTube channel ‘Numberphile’ in particular has many interesting videos involving numbers and mathematics, and would be a great resource for finding interesting videos to engage students.