- During this lesson, students will divide polygons into equal-sized parts and show how the area of each part compares to the total. Students are going to: 
- Divide polygons into equal segments. 
- Determine the unit fractions and use words and symbols to write their names.

- What relationships in mathematical contexts can patterns be used to describe? 
- How can identifying regularity or repetition help with problem-solving efficiency?
- In what ways can the characteristics of geometric shapes be applied to aid in mathematical reasoning and problem-solving?
- How can situations be modeled, described, and examined using geometric properties and theorems? 
- How are real-world situations or problems represented or sketched using spatial relationships, such as shape and dimension?

- Area: The measure of the surface enclosed in a geometric figure. 
- Denominator: The number or quantity below a fraction bar. Shows the number of parts into which a whole has been partitioned. 
- Fraction: A number expressible in the form a/b where a is a whole number and b is a positive whole number. 
- Numerator: The number or quantity above a fraction bar. Shows the number of parts out of the whole. 
- Patterns: Regularities in situations such as those in nature, events, shapes, designs and sets of numbers (e.g., spirals on a pineapple, geometric designs in quilts, the number sequence 3, 6, 9, 12, …) 
- Pentagon: A polygon with exactly five sides. 
- Polygon: A closed plane figure bounded by three or more line segments that only meet at their endpoints. 
- Quadrilateral: A polygon with exactly four sides. 
- Rhombus: A quadrilateral with sides of equal length.

- Pattern blocks. Note: If no pattern blocks are available, make copies of the Pattern Block Master (M-3-4-3_Pattern Block Master) and have students cut out the shapes to use.
- One copy of the Partitioning Polygons practice worksheet (M-3-4-3_Partitioning Polygons and KEY) per student
- One copy of the Polygons and Pattern Blocks practice worksheet (M-3-4-3_Polygons and Pattern Blocks and KEY) per student
- One copy of the Unit Fractions practice worksheet (M-3-4-3_Unit Fractions and KEY) per student
- One copy of the Lesson 3 Exit Ticket (M-3-4-3_Lesson 3 Exit Ticket and KEY) per student

- Students' ability to represent unit fractions with words and symbols can be assessed using the Unit Fractions practice worksheet (M-3-4-3_Unit Fractions and KEY). 
- The M-3-4-3_Partitioning Polygons and KEY practice worksheet on partitioning polygons can be utilized to assess students' proficiency in dividing polygons into smaller, equivalent pieces. 
- Utilize the Lesson 3 Exit Ticket (M-3-4-3_Lesson 3 Exit Ticket and KEY) to evaluate students' knowledge of unit fractions and their proficiency in writing them in both words and symbols quickly.

Clear instruction, active participation, and scaffolding 
W: Students will gain the ability to divide polygons into equal segments. Following that, the students will learn to identify these equal parts as unit fractions using both words and symbols. 
H: To introduce the idea of equal area, pattern blocks will be used to pique students' interest in helping them find blocks that will cover others. Students will also divide polygons into equal parts using pattern blocks and geoboards. 
E: By utilizing pattern blocks, students will comprehend the concept of equal areas better. Students will practice dividing polygons into equal sections using pattern blocks and geoboards. As a result, they will gain practical experiences that will reinforce their comprehension of unit fractions, such as one-half, one-third, one-fourth, and one-sixth. 
R: Students will practice dividing polygons into equal parts and labeling unit fractions with words and symbols using geoboards. We will use the Unit Fractions practice worksheet in class. 
E: The performance of the students on the Unit Fractions practice worksheet will be used to assess them. Lesson 3 Exit Ticket will also be used for student evaluation. 
T: You can use the ideas in the Extension section to modify the lesson so that it fits the needs of the students. Throughout the academic year, the Routine section offers ideas for reviewing the lessons' concepts. For students who might require extra assistance in order to learn how to identify fractions, the Small Group section offers targeted suggestions.
If a student is prepared to go beyond the requirements of the standard, there is an additional challenge in the Expansion section. 
O: Because the lesson is scaffolded, students utilize pattern blocks to grasp the idea of equal areas first. Then, using pattern blocks and geoboards, students divide polygons into equal parts. They also learn to label the equal parts as unit fractions by utilizing both words and symbols.

Divide polygons into equal-sized parts and show the area of each part as a percentage of the total in this lesson.

Polygons—Equal Areas

Give each group of three students a set of pattern blocks. Each group should have a minimum of 3 yellow hexagons, 6 red trapezoids, 9 blue rhombi, and 18 green triangles. (Neither the brown parallelograms nor the orange squares will be used.) If pattern blocks are unavailable, have students cut out the appropriate paper shapes by copying the Pattern Block Master (M-3-4-3_Pattern Block Master).

Provide each student with a copy of the practice sheet for polygons and pattern blocks (M-3-4-3_Polygons and Pattern Blocks and KEY).

The Polygons and Pattern Blocks practice sheet has two purposes. First, it is important to let students explore any new manipulative. Second, when it comes to numerical values, students are already familiar with using the expression equal to. They will learn how to apply equality to equal areas by working through the worksheet on polygons and pattern blocks.

Help students in finishing the first example. Put one yellow hexagon and one red trapezoid on top of each other. "How many more green triangles are required to completely cover the hexagon?" Get a volunteer to cover the yellow hexagon entirely with green triangles to demonstrate the number of triangles that are required. "What should be put in the blank to make the sentence true?" is a question to ask. To demonstrate how to make the sentence true, type 3 in the blank.

Ask students to work in groups of three to finish the remaining examples on the Polygons and Pattern Blocks practice worksheet.

Ask students to present their solutions and walk the class through each step of their process when they're done.

Partitioning Polygons

Give each student a copy of the practice worksheet on partitioning polygons (M-3-4-3_Partitioning Polygons and KEY). It introduces the unit fractions one-half, one-third, one-fourth, and one-sixth using pattern blocks.

Using the pattern blocks that were distributed for the earlier Polygons and Pattern Blocks exercise, the students should keep working in groups of three.

Lead the class in completing the first and third examples together. As mentioned in the first example, first assign students to work in groups to count how many red trapezoids cover the yellow hexagon. After the groups finish the assignment, have a student demonstrate how the red trapezoids cover the yellow hexagon. [Use pattern blocks the size of demonstrations, or project the pattern blocks so the class can see them.]

Ask the question, "What fraction of the yellow hexagon is represented by one of the two red trapezoids?" Students are likely to answer with half because they are exposed to this fraction from a young age. Emphasize that you used words to write the fraction's name as you write one-half in the provided blank. Ask the class now, "How can we write the fraction one-half using symbols?" Once more, chances are good that students can respond to this as well. In any case, demonstrate how to represent one-half as 1/2 using symbols. [Note: Using a horizontal bar is crucial. Try not to write 1/2 with a slash. [In writing, this slash is frequently mistaken for a 1 and does not aid students in visually distinguishing the numerator and denominator as well as the horizontal bar does.]

After that, assign students to work in groups to count how many green triangles, as shown in the third example, cover the red trapezoid. Request that a student demonstrate the green triangles enclosing the red trapezoid after the groups have finished the assignment. After that, assist the students in writing the fraction using both words and symbols.

"What fraction of the red trapezoid is one green triangle?" points to one of the three green triangles. Students might argue that it is one-third. Write one-third in the blank space, and emphasize that you used words to write the fraction's name. Now, ask the class, "How can we write the fraction one-third using symbols?". Once more, students might have no trouble answering this. In any case, demonstrate how to write a third with symbols like ⅓.

Give students the Partitioning Polygons practice worksheet and instruct them to finish the remaining examples in their groups.

Ask students to present their solutions and demonstrate to the class how they handled each problem when they are done. Please make sure to correct any spelling errors related to one-sixth.

Extension:

You can modify the lesson to fit the needs of the students by using the ideas in the following sections. Throughout the academic year, the Routine section offers suggestions for going over the lesson topics again. The Small Group section is designed to give students who might benefit from it more practice opportunities. For those students who are prepared to go beyond the standard requirements, there is a challenge in the Expansion section.

Routine: During the school year, have students use unit fractions to represent real-life situations that arise. Examples include counting the number of students who are wearing jeans or eating school lunch. Subsequently, designate a student as one-tenth of the pupils consuming school lunch, and so forth, contingent upon the counts. Remind students that they all count equally and that they make up one-tenth of the students who eat school lunch. This highlights the concept of equal parts.

Small Groups: Students who require more practice can be divided into groups of two or three and given pattern blocks and geoboards to partition polygons. Assist students in realizing the significance of equal parts, ensuring that the denominator equals the total number of equal parts, and having each part represent a portion of the total.

Help students understand that the denominator is the number of equal parts by having them count the number of them using the Geoboard polygons. Demonstrate how, depending on the denominator, each equal part is one-fourth, one-fifth, and so forth. This game can be used by students to practice choosing the correct unit fraction.

http://www.topmarks.co.uk/Flash.aspx?f=EggFractions 

Expansion: Students looking for a challenge should play the following game in groups of two or three, which focuses on ordering unit fractions.

http://www.mathopolis.com/games/ordering-frac-unit.php 

It is advisable to encourage students to arrange unit fractions through drawings. Give a grid paper to every student.