Numerators and Denominators

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Objective

Students will develop a conceptual understanding of what a numerator and denominator stand for in a fraction

Big Idea

Students always think of unit fractions (1/2, 1/3, 1/4), but the numerator can change. What happens when it changes? What does that mean for how much of the whole I have?

Warm Up

10 minutes

I begin today with a BrainPop Junior video on Fractions called "Basic Parts of a Whole." This video can be accessed by joining BrainPop Junior. This video is about 5 minutes long.

The video introduces what a fraction of a whole is and stresses the whole and its parts. It is a good video for students to reinforce their conceptual understanding of what a fraction really is.

We try the easy quiz that accompanies the video and then discuss questions and comments after the video is complete. 

The questions included such things as slicing an apple in 2 equal parts and eating one slice, what fraction of the apple did he eat? How do you write one third? What does the word divide mean if you divide a pizza into 6 equal parts (to split), Which fraction shows one out of 4 equal parts?

 

Parts of A Set

15 minutes

I bring the students to the rug. I have several boxes of school supplies (crayons, markers, colored pencils, etc.) I hold up the first box and say, this is a whole box or one box of crayons. I take out the crayons and ask how many pieces make a whole? (8) So if 8 pieces make a whole box, what fraction of the box would 1 be? (1/8). What about 3 crayons?  (3/8) 

Does anyone notice where I put the number for how many pieces in all? (on the bottom), yes and where do I put the number of pieces I am holding (on the top). Good. These places have special names. The bottom is the denominator (d for dungeon which is always at the bottom of the castle) and the top is the numerator (n for north which is at the top of a compass). 

I repeat this process with several other of the school supplies. I have students share the fraction of the whole and how many pieces make up the whole. I want students to be able to respond to these questions so I continue until everyone has responded at least once and I can see that students understand what I am doing.

I reinforce the terms numerator (to the north) and denominator (in the dungeon) as we share different fractions.

I tell students that now they will work on their own back at their seats.

Independent Time

20 minutes

During this section students work on their own to complete a practice packet that has them working with fractions of a set.

I want students to identify the unit fraction such as 12 crayons make up the set and 2 of the crayons is 2 out of 12 or 2/12 of the total unit of 12 crayons in the box. 

I circulate around the room to support students as needed.

Closing

10 minutes

I invite students to come to the rug. I ask them to bring their papers. Next I ask students to share some of the things they found when they did the work today. We share answers and how we arrived at these answers. 

Finally, I set a box of crayons in the center of the rug. I ask students if they remember what the words numerator and denominator mean? We talk about their meaning.

Now I ask students to look at their problems and to lightly in yellow color over the numerator in each fraction they wrote. 

I am looking to see if they remember the meaning of the term as we will use it in our next lesson.