##
* *Reflection: Rigor
Size Matters: A Journal Activity - Section 2: Active Engagement

Common language leads to common understanding. If we both use the same word, but understand its meaning differently, we cannot communicate. This is why I feel very strongly about students using the correct vocabulary when explaining themselves. In order to be mathematically precise, as well as insuring a common language (common understanding), the teaching of, modeling, and usage of important terms is critical.

The Mathematical Practices #3: Construct Viable Arguments and Critique the Reasoning of Others, and #6: Attend to Precision both require students to use accurate language. It is important for us, as role models, to use this vocabulary, explicitly teach it as well as support its use in the everyday classroom setting, and expect the students to communicate their thinking by using these terms in speaking and writing.

I also believe that the use of correct vocabulary terms can "demystify" mathematics for students. When children know, and can use, the mathematical terminology, asking for help or giving help becomes easier.

*Vocabulary*

*Rigor: Vocabulary*

# Size Matters: A Journal Activity

Lesson 10 of 13

## 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.

*50 minutes*

#### Mini Lesson

*10 min*

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!

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#### Active Engagement

*30 min*

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.

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#### Closing

*10 min*

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.

*expand content*

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- UNIT 1: Developing Mathematical Practices
- UNIT 2: Understanding Multiplication
- UNIT 3: Using Multiplication to Find Area
- UNIT 4: Understanding Division
- UNIT 5: Introduction To Fractions
- UNIT 6: Unit Fractions
- UNIT 7: Fractions: More Than A Whole
- UNIT 8: Comparing Fractions
- UNIT 9: Place Value
- UNIT 10: Fluency to Automoticity
- UNIT 11: Going Batty Over Measurement and Geometry
- UNIT 12: Review Activities

- LESSON 1: Making Meaning of Math Tools
- LESSON 2: Building Fractions Using Units
- LESSON 3: How to Create a Fraction Strip Poster: A Performance Assessment of Vocabulary
- LESSON 4: All Fractions Are Not Created Equal
- LESSON 5: That's Not Fair! Fractions of a Region Part 1
- LESSON 6: How Do I Share This? Fractions of a Region Part 2
- LESSON 7: And the Oscar Goes To….
- LESSON 8: Add 'Em Up
- LESSON 9: I Want Some Candy! A Journaling Assessment
- LESSON 10: Size Matters: A Journal Activity
- LESSON 11: What Is the Whole
- LESSON 12: Fractions of a Set
- LESSON 13: Find the Fraction of This Set "Smartie"