Halves of Cakes and Clocks
Lesson 1 of 5
Objective: SWBAT use the terms fractions, halves, and half. SWBAT divide a whole into equal parts and name each part with a fraction. SWBAT tell time to the half hour.
Using the Quick Flash Cards (see section resource), I flash the 1st image using my document camera. I display the image for 3 seconds and then I cover it up. The students then draw the describe the shape. I then flash the shape again for another 2 seconds to allow them o check their work. I finally, leave the image showing as students describe the shape they drew. I repeat this for the 2nd and 3rd shapes.
"I am going to flash a few different shapes. I will flash it once for about 3 seconds. Your job will be to draw and describe the shape. I will then flash it again so that you can check your work. When you are finished, I will ask people to describe what they saw and drew."
Cutting Into Halves
"We are going to spend the next few days talking about fractions and what it means to break things up into equal parts. During our measuring unit, some of you were using the term 1/2. This is an example of a fraction and it is called one half. What else do people know about halves?"
As you talk about the ideas shared (2 halves of a game, favorite show is a half hour long, etc), you want to make sure that you point out that each example represents a whole divided into 2 equal parts.
"Let's pretend that I want to share a cake with my best friend. In order to do this, I will have to cut it in half. I want to make sure that we both get an equal share. Let's take a look at this first cake/circle (I show a full circle from the Cutting Circles resource). I want you to think about where I would draw a line to cut this cake in half?" There is a video in there resource section called Are the Circles Cut in Half? that models this part of the lesson.
Then I draw a line through the circle that clearly doesn't cut it into two equal parts.
"Is this cake cut in half? How do you know? How would you fix it?" To see this part of the lesson, watch the clip Making the Correct Cut.
I then show them more of the circles from the resource asking the same questions as above. If finish by asking for one student to come up and draw a line through the last blank circle.
"Who could come up and cut this cake in half? Did he/she do it correctly? How do you know? Now that we have a cake that is cut in half, I want to show you how to label each half."
I then model the 1/2 recording. It is important that the fraction be written 1 over 2 and not with a slanted line (like I used in this narrative). Using a slanted line is not an accurate recording because it indicates a ratio rather than a fraction.
"My kids and I love cakes. We have cake every Saturday. We need one cake to feed our family dessert."
I show them the recording sheet labeled Making Cakes in the section resource. You should make enough copies for you whole class.
"Sometimes we disagree because my wife and I want chocolate frosting and my kids want vanilla. However, our baker is very kind and will frost half the cake with chocolate and half with vanilla."
I then show them the example that is at the top of the paper.
"You will now be the bakers and create your own half and half cakes. Half of your cake will be frosted one way and the other half will be frosted another. You can use any flavors you like. I will put out crayons and colored pencils for you to use to color each half. You will need to make sure that you label each half."
"Before you start, I want to look at a few ways that a cake can be cut in half. Let's look at the easel (see picture in section resource titled, Ways of Cutting a Cake)."
I then fold a paper circle in half and show them what it looks like with the line going through the middle and draw that line through the center of one of the circles on the easel. I then turn the paper circle and model (on the easel) where the line is cutting the circle now. Again, I model it on the easel. I want to make sure that the students see that even though the line is in different places, there are still two equal parts.
There is an example of a completed recording sheet. To meet the standard,s students must be able to not only divide a whole into equal parts but also label each of these equal parts. This particular student didn't label each half with the fraction notation. You should make sure that the students are doing this with their work, otherwise they are not yet meeting the standard CCSS.Math.Content.1.G.A.3 fully.
There is also a video of a student working on the activity in the section resource.
This activity has students reasoning abstractly and quantitatively. The students are demonstrating an understanding that each cake will have two equal parts. The choice of frosting doesn't matter and each circle will be divided into two equal parts. They are making sense of quantities and their relationships in problem situations. They are bringing two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents (CCSS.Math.Practice.MP2).
Looking At Half Hour Times
I gather the students in a circle and hand out small demonstration clocks to each of them. I want to make sure that they start making the connection between half and half hour early to solidify their understanding of the concept of half in both the geometry standard (CCSS.Math.Content.1.G.A.3) and the measurement standard CCSS.Math.Content.1.MD.B.3.
"Over the past few weeks, we have been talking about "on the hour" or "o'clock" times. Let's practice a few together. Please set your clock to 10:00. When you have it please hold it up so I can see it. Now, let's try this (I write 11:00 not he board). Please set your clock to this time. Again, hold it up once your clock is set."
"I want you to watch my clock as I move from two to three o'clock. You will see that the minute hand goes all the way around and the hour hands moves from the 10 to the 11. What would my clock look like if the big hand only went halfway around the clock?"
"Let's think about the half circle activity we just did with cakes. If I was frosting this clock and started at the 12 and moved around the clock this way (moving my hand clockwise), how far would I frost. yes, I would stop at the 30."
"Does anyone know what time this is? This clock shows 10:30. From 10:00 to 11:00 is one hour, so from 10:00-10:30 is a half an hour. What do you notice about the hands on the clock now?"
You want to make sure that the students see the minute hand is at the 30 minute mark and the hour hand is exactly between the two hour numbers.
"When you read this clock you say 10:30. Some people will say half past 10 o'clock."
"Now I want you to try setting your clocks to some half hour times. I will call out a time and you set your clock. If you are not sure, you should set it for the hour time and then move to the half hour time."
There is a video in the section resource that models this part of the activity.
Lesson Wrap Up
For reinforcement of today's fractional concept, I have included this exit ticket. There is a blank copy and an example of a finished exit ticket. This will allow me to informally assess how students are doing with the half concept.