My class has developed a strong foundation in dividing objects and shapes into equal pieces, but I want to work with them on dividing quantities into these same fractional pieces. In later grades, students will have to make the connection between fractions and the fact that they are numerical quantities (not just shapes), so I am laying the groundwork here. I have learned from past experience that if I approach this topic with food, First Graders seem to grasp the idea faster because they definitely want treats and food divided equally.
Students, if I have 6 Skittles and want to share them equally with one friend, how many will we each get? (You will get 3 each) What if I have 7 Skittles and want to share them with a friend? (You will get 3 each and 1 left)
If you have students who do not understand how to divide the quantities equally, follow these steps. Use unifix cubes as the pretend Skittles, pick a helper, place the 7 cubes between you and proceed to give one to the helper, one to yourself until they are all gone with one left.
Ask: If I give this last one to my helper, will we have equal amounts? (No, he/she will have 4 and you will have 3)
Today is a review lesson on fractions, this includes equal parts, whole, halves, fourths, and quarters. Before I let my students begin a worksheet or activity to review the material, I like to have a discussion with them. This discussion will provide me with an opportunity to see what my students remember, identify any misconceptions, and focus their minds on the concept of the day. I will begin with the following questions;
I will open up the shapes document on my smart board and pick one shape to divide in halves, but I will purposely divide it unequally.
I will ask: Is this shape divided into halves?
I show something the wrong way because it provides me an opportunity to ask and forces them to answer the question "why not?" I get to hear their explanations of how the shape should be divided "because it has to be equal." I will do the same for fourths and quarters.
Next, I will ask for volunteers to come up and divide shapes alternating fourths, quarters, and halves. I will leave the division lines on the board. My students discovered 3 ways to divide into fourths equally. The last task I will have them do is call on volunteers to come up and color in 1/2 or 1/4 of certain shapes. Common Core does not expect First Graders to master the notations 1/2 and 1/4 because it is not age appropriate, but I will use this opportunity to review the symbols meanings and present examples.
I will show them the fraction symbols on the board and share: (Write 1/2 on the board.) Students this means 1 out of 2 pieces is colored.
I will do the same for 1/4, but I will not expect my students to write it and memorize it. My goal is for them to know this is a symbol for halves, fourths and quarters. Just like the minus sign means subtract. I want to at least introduce these symbols to them because they will be seeing them on practice sheets towards the end of the year in First Grade and at the beginning of Second Grade. Also, this helps my students see that fractions are numerical quantities. Second Grade Common Core skills will dive deeper into fractions and focus more rigorously on using the symbols.
I like these worksheets because they are not just plane shapes. The practice includes objects that students must think abstractly to make their division lines and they use the CCSS terminology of halves, fourths, and quarters. As my students are practicing this skill I will be monitoring their work and participating in mini-conferences with my students. When they are working, this provides me a great opportunity to ask questions and gain knowledge about what they know and understand. If I find several students who are struggling in similar areas, I will gather them together and have a small intervention session.
I will place 8 crayons out on the table and ask my students to draw a picture showing me how to divide them by fourths and halves. I can help my students make the numerical connection behind fractions by helping them to further label those drawings with 1/4 and 1/2. For example, when my students draw 4 crayons and 4 crayons, I can have them draw next to those two sets 1/2 and 1/2. We can discuss that if we put the two sets of 4 back together, we will have a whole.