Size Matters: A Journal Activity

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Objective

Students will be able to create, name, and write fractions by reasoning about the relationship between the whole and a unit fraction.

Big Idea

Understanding that a whole can be defined using different fractions is a complex task for students, unless they have great tools, like pattern blocks.

Mini Lesson

10 minutes

To begin the lesson, pass out bags or trays of pattern blocks.  Ask the students to put a trapezoid in front of them.  

This represents the whole.  Find the block that would represent 1/3 of the whole.  

The children should know that it is the green triangle, as it takes 3 of them to make the whole. Remind them that 1/3 is the unit fraction.

Ask them to show 2/3 of the trapezoid. Some may remove one of the green triangles to show 2/3, while others may use a blue rhombus.  Discuss this equivalency with the class if they are ready to explore this. 

Move through other models using various blocks as the whole, or by giving hints like:

If the green triangle is 1/4, what is the whole?  

The solution to this is not a pre-made block, so the students will need to use their knowledge of the numerator and denominator to solve. 

The student in this clip is sharing with the class how he figured out that a triangle is 1/6 of a hexagonal shape.  While explaining , he also realized the relationship between 3/6 and 1/2. BONUS!

Active Engagement

30 minutes

After several examples as a class, I have the students write down several situations in their math reflection journals.  Some examples are:

If a red trapezoid is 3/4, build the whole.

If a hexagon is 1/2, what is the whole?

What is the whole if the rhombus is 1/6?

The children have access to pattern blocks, shape templates, and each other.  As I walk around and confer, I listen for the use of vocabulary words, and observe/note the children's strategies.

In this video, you will notice that the mathematician was working through explaining how a trapezoid can be considered 3/4 to his partner.  She then better understands and as a result uses more appropriate vocabulary than he did to explain her new learning.

The girls in this video are explaining to me how they knew to use three triangles.  They understand what they are doing, but in speaking with them I prompt them to use the correct vocabulary for the task. This is one of your critical roles as teacher/facilitator for your students, as connecting them to the academic language provides a common language to use when explaining.  It is also what students will see on high stakes testing. 

Closing

10 minutes

To close the session, I explain to the students that tomorrow we will be using the information they learned today about unit fractions building a whole in order to respond to a journal prompt.  I then ask them to share with their partner something they learned today, or something they think helped them preserver through a tricky task.