Mathematically proficient students need to be able to construct arguments, explain their thinking, and critique the ideas of others. (MP3). First Graders become more mathematically proficient when they are able to have these rich mathematical discussions with their peers. Today's lesson is introducing the idea of fractions and how to divide pieces into equal/not equal pieces. I know from past experience that my students will disagree about how to divide some shapes in particular and how to divide shapes equally in general. This disagreement will force them into providing explanations for their thoughts and having to consider their friends' point of view. I need my students to learn how shapes and quantities can be divided into equal shares and be able to distinguish what is equal and not equal. This requires them to discuss with others what they are seeing and how they think it fits into one category or another. (1.G.A.3). Today's lesson will allow my students an opportunity to discuss with their fellow classmates about how to divide a shape into equal parts and whether a shape is divided equally or not. This will be a rich learning opportunity by allowing them the chance to discuss their math thinking using verbal and concrete representations.
I will pre-fold construction paper shapes and have students cut exactly on the creases. Some of these folds will provide shapes that divide into equal pieces and some into unequal pieces. I will use the following instructions:
Students I am giving everyone a piece of construction paper that has been folded. Please use your scissors to cut right on the crease that I made when I folded it. Don't add any new folds and make sure you cut each crease I put in it. When you are done lay your pieces on your desk and try to put your "puzzle" back together by moving your pieces around until they fit into their original shape.
I will use butcher paper to create a large anchor chart and pre-label it "Equal" and "Not Equal" with a line drawn down the middle. I will hang the anchor chart on the chalkboard and begin a discussion with my students for them to help me decide if their shapes divided into equal or not equal parts. I will encourage my class to discuss with each other and me;
As the students decide where their shapes belong I will glue them on our chart in the proper category.
I will read the totally engaging children's book If You Give A Mouse A Cookie by Laura Numeroff. My students just had an experience during our previous lesson section learning how shapes can be divided into equal pieces. I got this great idea from Adventures in First Grade blog. I am conducting a read aloud with this book to create a hook to the "cookie." When I am finished with the read aloud I will ask them:
Now I want to plant a seed of knowledge with my students that fractions represent quantities, not just parts of shapes. I just want to give a small amount of time to this idea because it is actually a concept that does not come to fruition until 3-4th grade. To introduce the idea, I use quantities of cookies rather than the shape of the cookie:
We are going to build our little friend the "Mouse" and I am going to give you two of his paper cookies. I want you to imagine that you are sharing one cookie with one friend and the other with three friends. Cut the cookies to show me how you would divide them. You will be gluing the parts on your paper with you mouse. Remember we are not robots and cannot do things exactly perfect. Try your best to divide your cookie with your friends equally.
I will fold a brown sheet of construction paper in half (hamburger fold) and cut a large half heart out of it. I will provide my students black strips for whiskers, googly eyes, pink pom pom for a nose, and little brown hands. Please look at the example in the resource section. My students will build their mouse and then come get their cookies. One cookie they cut to show me they are sharing it with one friend. The other cookie they will cut to show me they are sharing it with three friends.
I want to check my class to see what they understood from today's lesson on equal and non-equal parts. I will ask students to answer questions pertaining to whether two shapes were divided equally or not. They must tell me why or why not they say it is equal. Print the exit ticket from the resource section. This exit ticket will allow me to know who understood the concept of equal and whether I need to reteach the topic.
When I am short on time, but still need to conduct a quick discussion, I ask verbal questions and let the hands shoot in the air. Then I tell my class I am going to pick 3 students to answer. This allows everyone to think about the question and listen to their classmates share ideas. I hate it when I do not have time to call on everyone, but even if they just get to listen to their classmates share, it allows them an opportunity to process and compare that information to what they already know. Today, I am going to have students respond on paper. This is still a fast method to complete a closure activity and students will answer a particular question or describe their new ideas on it.
After all this hard work on cookies and enticing them with the great children's literature, I cannot end today's lesson without bringing out some real cookies. When they turn in their response I am going to give each student a soft chewable Chips Ahoy! cookie. I will ask them to try and divide into 2 equal shares and allow them to eat both. Don't forget to check for allergies in your room.