Fractions of a Collection--Get Out Your Favorite Toys!

Who: The following lesson/activity is geared towards 3rd or 4th grade students who are not fluent with their multiplication facts. This is also a great lesson for tactile learners!

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.

Lesson Objective: By the end of this lesson you will be able to find a fraction of a collection. I also hope that you will be able to explain this process to someone at home and also apply this concept to a real life problem or situation!

Ready to Have Fun!

To get started, I would like you to get out some toys that you have a lot of. For example, you could get out Lego people or toy cars. You will need 12 of those toys.

Problem 1: Your best friend is coming over and you want to share some of your legos with him/her. Please find 1/2 of your collection. How many will you share with your friend? How many will you keep for yourself? Now I want you to think of what you just did to find 1/2 of your collection. Think it over, write down or discuss your strategy with someone at home. I want you to think about the following questions:

*Why did you make two seperate groups?
*Why did you give your friend 1 of those groups?

Now if you think you have a good understanding of what you did, try the next problem.

Problem 2: Your best friend is being kind of greedy and wants to play with more of the toys than you. He asks you for 2/3 of your toys. How many toys should you give him now? How many toys will you be left over with?

Think of the following questions:

*Think of what you did in the problem above.
*Think of what a fraction means or represents--(part of a whole, remember?)
*How many groups should you make?
*How many groups will you give your friend?
*How many toys are in those groups? (Can you skip count?)
*How many groups will you keep?
*How many toys will you play with? (Can you skip count?)

So, can we agree that 1/2 really means 1 out of 2 groups and 2/3 really means 2 out of 3 groups? If this is the case, can you figure out the following problem?

Problem 3: You really want to buy a new Lego set, however you don't have enough money! The lego set costs $30, but you only have 4/5 of that amount! How much money do you have? Hmmm, how can we solve this problem?

Think of the following questions:

*Can we use toys to represent the money?
*How many toys do you need to use?
*How many groups should you make with your toys?
*How many toys are in each group?
*How many groups represents the amount of money you have?
*How much money is that? Can you skip count by a certain number?
*How much MORE money do you need in order to buy the new Lego set?

Wow, you are doing awesome! Now here is your challenge! I need YOU to create a word problem and post in on the blog for me! I don't just want you to create it, but I want you to solve it and explain how you solved it too! Remember your complete sentences!

Thinking Behind the Lesson:

While there are many ways to teach a student how to find a fraction of a collection, including using multiplication, I like to make this lesson as engaging, applicable and hands on as I can! I find that teaching through Gardner's 9 intelligences

is a great way to teach any concept, but especially something tough like fractions. The more your student can touch and manipulate objects to understand the concept and make sense of the learning, the better! In this activity, your student is able to play with toys, understand why you would want to find a fraction of a collection, and physically figure it out for himself/herself. All of these components make the learning more meaningful for your student and allows fractions to come to life!

Reflections:

*While these problems above might be engaging and applicable for some students, they may be boring and unintersting to others. Pick a topic that is motivating for your student, and then rewrite the problems to suit his or her interests.

*While I did not reinforce this in the lesson, it is important to reinforce with your student when making groups they always need to be equal! For example, remind them that 1/2 of a collection means 1 collection divided into 2 EQUAL groups. This concept of equal groups will help them when finding fractions of a collection!

*These problems might move too fast for some students. You may want to stick with unit fractions for a while, until your student gets the concept down, such as 1/3, 1/4, 1/5 etc.

*When making groups, I also find that using mats are very useful. For example, you can fold a piece of paper into 4ths. If students are finding 2/3 of 12. They make 3 equal groups first with their chosen toy/manipulative. They can place the groups in 3 of the seperate boxes, this way they have a place for all of their manipulatives and groups, thus helping them organize better.