In this lesson students will be reviewing the meaning of mixed numbers by modeling with pattern blocks. They will then complete a length instructional task that requires them to add and subtract fractions with mixed numbers. And finally, we will be wrapping this unit up by creating a graph of post-it notes and fractions based on the graph.
To begin this lesson I provide each student with pattern blocks to include yellow octagons, blue rhombuses, green triangles, and red trapezoids. I display a mixed number on the board and ask the students to represent the number using their pattern blocks. I tell them that the octagon is equal to one.
The numbers I use are 5 1/2, 2 1/4, 1 1/6, 4 2/4.
For each number the students are quick to grab the yellow octagons to represent the whole numbers. The purpose however, of this activity is that students make a direct connection between mixed numbers and improper fractions.
I then ask the students if they can represent the same mixed number using only one color of blocks. For example, for 5 1/2, students could use 11 trapezoids to show 5 1/2. I further their thinking by asking if then there is another way to say the fraction 5 1/2. I want them to see it as 11/2 as well. Some students may even come up with using green triangles to represent 5 1/2. In that case they would have 33 triangles or 33/6.
The task for this lesson was derived from Angela Anderson’s lesson plan out of Coffee County Georgia. In the task students are required to look at three recipes for cookies. They pretend as though they are going to make a batch of each cookie so they begin the task by adding up the total amount of each supply needed. The second step is they have to determine how many containers they will need to purchase once they get to the store based on the given sizes of containers. The final step is that students must determine how much of each product is left over.
As you can see this is a definitely a multi-step task that requires the students to stay focused and on task(MP 1). It also incorporates all of the content that has been covered with this unit of fractions.
I provide students with a copy of the recipe task and allow them to work in small groups to solve the task. Each group must show all work for their calculations including modeling and using equations.
As students begin to work I circulate the room and assist if necessary.
To wrap up the length task we do a class vote to determine which type of cookie we would choose to eat if the cookies had been made. I provide each student with a sticky note and I draw a quick graph on the board.
Each student writes his or her name on the sticky note and places it on the graph in the column of the cookie they choose. Upon completion of the graph I ask students to make observations(MP 2).
The goal is to have students discuss the graph in terms of fractions. What fraction of the students chose the sugar cookie? What fraction chose the oatmeal cookie?