In this lesson students will be building upon their prior knowledge of fractions by examining pattern blocks and benchmark fractions.
Students begin the lesson by working with a partner to draw pictures of food items that they would be able to share with a group. The students will first draw a few food items and then create scenarios in which they would be sharing the food. After giving the partnerships about ten minutes to work I call upon a few groups to present their drawing and scenario.
The purpose of this is activity is to get students to reason abstractly and quantitatively(Mathematical Practice Standard 2). Students will be contextualizing the concept of sharing or a fraction of the whole.
In order to deepen students’ understanding of a whole in terms of fractions, I will guide them through an investigation with pattern blocks in which the value of the whole may change. I want to students to start to see patterns of fractional units within a whole.
I provide all students with pattern blocks(yellow octagons, red trapezoids, green triangles, and blue rhombuses) and begin guiding them through the investigation. My goal is to make the investigation hands on and also interactive.
How many green triangles are in one blue rhombus?
How many green triangles are in one red trapezoid?
How many green triangles are in one yellow octagon?
How many blue rhombuses are in one yellow octagon?
How many red trapezoids are in one yellow octagon?
Now let’s switch our brains into fraction mode. If we look at one blue rhombus and two green triangles, which are the parts and which is the whole? If we were to look at just one green triangle, what could we say about its relationship to the blue rhombus?
Now let’s look at the red trapezoid and three green triangles. What can you tell me about the relationship between these blocks? What if just had two green triangles, what part of the red trapezoid would that be?
Can anyone come up with another part whole relationship using the blocks?
I began this investigation with some very targeted questions to the students. As I move further into this investigation I put more of thinking on students and have them generate relationships and questions to ask their peers. I would like students to focus on constructing meaningful contributions to the discussion and be able to explain their thinking(MP 3).
I close this lesson by having some students share an example of a part whole relationship to the class on the document camera. I tell the students they may present an example of a fractional relationship or pose a question to the class centered around fractional relationships. This activity is an extension of using MP 3 in the practice portion of the lesson.