Assessment of Fractional Halves and Fourths

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SWBAT correctly use the terms halves and quarters. SWBAT partition a whole into equal parts and name each part with a fraction.

Big Idea

Students will work with the idea of 1/2 and 1/4 fractions through an assessment task and an activity that has them breaking squares, rectangles and circles into 1/2 and 1/4 pieces.

Warm Up

10 minutes

Advanced preparation:  You will need to print out both sets of number cards from the resource section.  Cut out the 31-60 cards and put them into one envelope and do the same with the 61-90 and put them in their own envelope.

I start this part of the lesson by asking the kids to sit in front of the classroom number line.  

"Today we are going to change up our Start At/Stop At routine.  We are going to add the numbers 61-90."  I will pull one card out of the 31-60 envelope and we will use that as our start at number.  I will then pull out a card from our 61-90 envelope and use that as our Stop At number.  We will then count as a class from our starting number to our ending number."

I will ask a student to point to each number as we count as a whole group.  I will continue this process as time allows.  I will also mix in counting backwards by starting at the higher number and counting to the lower number.  The Core Standards expect 1st graders to be able to count to 120, starting at any number, by the end of 1st grade.  This routine is the process in which I can assure that the students are continuously working toward that standard (CCSS.Math.Content.1.NBT.A.1).  

Discussion on Halves, Wholes, and Quarters

15 minutes

I start by gathering the students on the carpet.  I have a stack of 2 brown connecting cubes and a stack of 6 connecting cubes.  I am using the brown cubes to represent chocolate bars.  At this point, the cube stacks are kept out of the students' sight.  

"I want to total about chocolate, specifically a chocolate candy bar.  Let's pretend that it is the world's best chocolate and that it is your favorite sweet treat.  So, you want to get as much of it as you can.  Would you rather have half of a candy bar or a whole candy bar?"

I then go around the circle and take each student's response.  

"Why did each (or so many) of you choose the whole candy bar?"

You will get a variety of responses but focus in the conception that a whole is more than a half. Then take out the two cube stacks.  Point to the first one and say, "This is the size of full size candy bar.  It is like the ones that are by the register at the store.  The smaller stack if the size of a miniature bar, that you can buy in the bags.  Many of you said that having a whole would give you more chocolate. However, what if I offered you half of the big bar or a whole miniature bar. Which one would be more?"

I then break the bigger one in half and let them see the visual of the two bars.  

"Who could tell me why half of a big bar is larger than a full bar?"

There is a video of this discussion in the section resource (titled, Is Half More Than A Whole)?

I want to make sure that the students understand that not all halves or "wholes" are the same size, and that the starting size makes a difference. 

I then turn the discussion to the idea of fractional parts of one whole have to be equal. I take the stack of cubes representing the large candy bar and break it into four unequal pieces.  I talk to them about it being broken into four pieces but that it is not fourths because it is not four even pieces. There is another video in the section resource that captured this discussion.  

The students are portioning whole shapes into two and four equal shares and then describing the shares using words such as halves, fourths, and quarters.  They are also able to describe wholes as two of, or four of the shares and demonstrate an understanding  that decomposing into more equal shares creates smaller shares (CCSS.Math.Content.1.G.A.3).

This activity has students reasoning abstractly and quantitatively. 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).

Assessment Task

10 minutes

Before you start class, you will want to make enough copies of the assessment task (in the section resource) for your class.  

"I would like you to complete this task on halves and fourths.  It will allow me to see how you are doing with these fractional concepts."

This assessment has students dividing a square in half, coloring on fourth of a circle and determining if shapes have been divided into halves and fourths.

As students finish, they can go onto the activity in the next section.

Dividing Circles, Squares and Rectangles Into Fractional Parts

20 minutes

Advanced preparation:  You will need shape templates (that have squares, circles, and rectangles) or you can have pre-maid sheets with these shapes on them, blank paper, and colored pencils.

As students finish the previous task, you will show them how to complete this activity.  

"I want you to use the template to draw squares, rectangles, or circles on the blank sheet of paper. Then you will divide the shape into 1/2s or 1/4s. Then you will label each part and lightly shade in the parts with colored pencils." 

There is an example of a finished piece in the section resource and a movie clip of a student working on this activity.

The CCSS expect that first graders can compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) to create a composite shape, and compose new shapes from the composite shape (CCSS.Math.Content.1.G.A.2), and this activity helps support students in meeting this standard.

It is important that the students label their cake parts with the 1/2 notation.  Students need to understand that each equal part is one of two pieces that make a whole cake. This step is asking students to model with mathematics.  It is expected that mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace (CCSS.Math.Practice.MP4)

Lesson Wrap Up

10 minutes

The focus of this discussion is to review and reinforce the concept of partitioning a whole into equal parts and then naming them with fractions and exploring the idea that when you cut a whole into fractional pieces, the pieces are smaller.

"We have doen a lot of work with halves and fourths.  We are going to spend some time comparing halves and fourths."

I then show them the chart with the circles on them (I have included a pdf and notebook file for you to choose from).  

"These circles are the same size.  What is the first circle divided into (halves)?"  I then write in 1/2 on each piece and write the words "two pieces" under the circle.  I then do the same thing for the 2nd circle but with 1/4.  

"Which piece is bigger 1/2 or 1/4?  How can that be?  How can 2 be more than 4?  WHo can explain that? " Discuss their ideas and then move onto the 2nd poster (squares).  Again repeat the same process that you did with the circles.  

The Core expects that students can partition circles and rectangles into two and four equal shares, describe the shares using the words halvesfourths, and quarters, and use the phrases half of,fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares (CCSS.Math.Content.1.G.A.3).

Exit Ticket

5 minutes

As a final task, I ask each student to complete one last sheet on 1/2 and 1/4.  The task is in the section resource.  This task can be used as one final piece of informal assessment.