Cupcakes and Calculations

I love baking cupcakes.

Every person I know gets cupcakes on their birthday; a carefully crafted work of art and yumminess. The best part is not even the cupcake, but the frosting. I love taking the time to carefully decorate the tops of cupcakes, adding a sprinkle of color, or trying a new technique.

Today, I came across a new recipe for Perfect Cupcake Frosting. I’m dying to try it. However, I do not want to make a whole batch of cupcakes, just half a batch. This happens often. Sometimes, I want to make 4 cupcakes or get a little crazy and bake 24, and on some days, I just want 2, for myself.

So today, I’m making 12 cupcakes. I’ll need to half each ingredient in the frosting recipe in order to create half the amount of frosting.

2 packages of cream becomes 1 package of cream cheese because 2 x 1/2 = 2/2 or 1.

I can also perform conversions by thinking in terms of proportions. 4 cups of powdered sugar is to 24 cupcakes. How many cups of powdered sugar is to 12 cupcakes?

4/24=x/12

Using cross multiplication, 48=24x

Therefore, x=2

I’ll be needing 2 cups of powdered sugar.

Converting measurements doesn’t always give me nice, whole numbers. Sometimes, a little estimation is necessary, and that’s okay. The frosting (and cupcakes) will taste good.

Here are some proportion resources for students.

This website offers many ratio and proportion worksheets and allows students to understand real-life applications of proportions.

A flipchart that allows students to practice their proportion skills in real world settings.

Lesson plan: Fractions and Recipes. This lesson plan gives students opportunities to make conversions in order to adjust recipes based on the number of people eating.

Estimation: A Life Skill

How many miles do we have to go?
How much time until lunch? How much will the bill be? How many more items can I buy? How many people are in the room?

These questions are quickly answerable with a little estimation.

Life would be difficult without the ability to use estimation.

For students, estimation is an important skill in order to efficiently and accurately solve math problems. If students need not come up with an exact answer, estimation is the quickest way to get there. Additionally, estimation allows students to check the accuracy of their work. For instance, if a student is asked to solve 125 X 24 and comes up with a product of 250,000, they should recognize their answer can’t be correct. Using estimation to compute 120 X 20 = 2,400 quickly shows the student the place value is way off and they must re-commupute the answer. Estimation isn’t always an easy skill for children to learn. Here are come tips and tricks that may help.

Estimation teaches students that they don’t need to be glued to calculator in order to compute math problems. It allows them to solve problems both in, and out of, the classroom without the need of a calculator.  It allows children to solve real life problems by exploring their own curiosities such as, What is the circumference of the earth? It allows them to take a trip to the grocery store, form a budget, split a bill, and use time and distance with ease. Estimation keeps our minds sharp and active. It brings ease to situations that may otherwise cause difficulty.

There are many ways of bringing fun into lessons on estimation. One of my favorite ideas is having an estimation jar. Students can fill the jar with anything they choose (jellybeans, m&m’s, marbles, etc.) The class guesses how many items are in the jar. The idea is to be the closest to the actual number.

Here are a more ideas of incorporating fun activities into instruction on estimation.

Estimation Using Goldfish Crackers

Gummy Worm Measurement

Interactive Estimation Activities

Food and Fractions

As I sat, enjoying a pepperoni and onion pizza with two friends, we came to a dilemma: there were three hungry individuals and only two pieces of pizza left. This happens often, if you find yourself sharing food with other people. Luckily, we don’t have to think too hard when an 8-piece pizza cannot be evenly distributed between three people. We find a way to split up the remaining two pieces.

Maybe unknowingly, when we share food, we are displaying an understanding of fractions. When I split a cookie with my best friend, it is assumed that we break the cookie in half. Why? Because splitting one whole into two even parts leaves me with 1/2 of the cookie.

When teaching fractions to students, food is a good place to start. I mean, who doesn’t like food?

There are endless word problems involving food. Here are a few:

Daniel and his friends roasted 2/5 of a bag of marshmallows. Daniel’s sister and her friends roasted another 1/5 of the bag of marshmallows. In all, how much of the bag of marshmallows was roasted?

Harold’s family ordered an extra super deluxe supreme pizza. They ate 1/4 of the pizza in the parking lot and another 2/4 in the car on the way home. In all, how much pizza was eaten before they got home?

Abby used 1/5 of a mango in her fruit smoothie. Mac used 1/4 of a mango in his. Who used more mango?

Jesse put toppings on his salad. One fourth (1/4) of his toppings were cherry tomatoes and two eighths (2/8) of his toppings were olives. Did Jesse use more olives or more cherry tomatoes on his salad?

In addition to word problems, there are many hands on activities that can engage students in learning fractions.

Recipes are a great way for students to interact with fractions in a practical way. Students can use these recipes to encourage practicing fractions at home. And cooking is fun!

Pizza Fraction Fun is an activity that allows students to work together in groups to solve equivalent fraction problems with pizza.

You can always come up with your own activities involving your favorite food!

Are You “Set” for Fun?

We all know math is important. We have to do it. It’s part of education. We hope and trust that there is, in fact, a good reason that we are learning it. When you think of math, what words come to mind? Difficult, complex, frustrating, conceptual, concrete, computative, interesting? How about fun?

Math is fun…well, it certainly can be. Math is what we create it to be. Math is fun when it is incorporated into fun activities and games. It’s enjoyable when it’s applied to real life circumstances that matter to students. When we think about the words we associate with “math,” we think of what we have experienced based on how information has been conveyed and how concepts have been received. This exchange can create either positive or negative associations.

Take set theory, for instance. A set is a collection of objects. It may look like this: {1,3,5,7,9}. There are many ways to compare sets, as shown below.

We can compare sets; describe sets; find the intersection and union of sets, but if all we do is teach with numbers, how fun is that? How are students making connections to real life? Likely, they aren’t.

Let’s try comparing sets in a different way, allowing the students to be the subjects of the sets and working hands on with a problem.

1. Mark two overlapping circles using chalk or hula hoops.
2. Tell students that one circle is for individuals with brown hair and the other circle is for individuals with blue eyes.
3. Let them decide where they should stand.

Now there is meaning and the students are connecting with the lesson. Most importantly, they are having fun!

Here are a couple resources to gain ideas for teaching set theory in ways that are applicable to students.

Teaching Set Theory

Step-by-Step Introduction to Set Theory