• The Unit Fractions practice worksheet (M-3-4-3_Unit Fractions and KEY.docx) may be used to determine how well students can represent unit fractions using words and symbols.
• The Partitioning Polygons practice worksheet (M-3-4-3_Partitioning Polygons and KEY.docx) may be used to evaluate student mastery of breaking polygons into smaller equivalent parts.
• Use the Lesson 3 Exit Ticket (M-3-4-3_Lesson 3 Exit Ticket and KEY.docx) to quickly assess student understanding of unit fractions and their ability to write unit fractions in words and symbols.

This lesson focuses on partitioning polygons into parts with equal areas and representing the area of the parts as a fraction of the whole.

Polygons—Equal Areas

Distribute pattern blocks to each group of three students. Each group should have at least 3 yellow hexagons, 6 red trapezoids, 9 blue rhombi, and 18 green triangles. (The orange squares and brown parallelograms will not be used.) If pattern blocks are not available, make copies of the Pattern Block Master (M-3-4-3_Pattern Block Master.docx) and have students cut out the paper shapes to use.

Distribute Polygons and Pattern Blocks practice worksheet (M-3-4-3_Polygons and Pattern Blocks and KEY.docx) to each student.

The Polygons and Pattern Blocks practice worksheet has two purposes. First, it is important to allow students to explore any new manipulative. Second, students already have experience using the phrase equal to with numeric values. The Polygons and Pattern Blocks worksheet will help them understand the use of equal to in regard to equal areas.

Help students complete the first example. Place 1 red trapezoid on top of 1 yellow hexagon. Ask, “How many green triangles are needed to cover the rest of the hexagon?” Ask a student to volunteer to show how many green triangles are needed by placing them on top of the yellow hexagon to completely cover the hexagon. Ask, “What should be put in the blank to make the sentence true?” Enter 3 in the blank to model how to make the sentence true.

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

When they are finished, ask students to state their solutions and show the class how they solved each problem.

Partitioning Polygons

Distribute a Partitioning Polygons practice worksheet (M-3-4-3_Partitioning Polygons and KEY.docx) to each student. It uses pattern blocks to introduce the unit fractions one-half, one-third, one-fourth, and one-sixth.

The students should continue to work in groups of three, using the pattern blocks distributed for the previous Polygons and Pattern Blocks activity.

Lead the class in completing the first and third examples together. First, ask students to work in their groups to determine how many red trapezoids cover the yellow hexagon, as stated in the first example. When the groups have completed the task, ask a student to show the red trapezoids covering the yellow hexagon. [Use demonstration-sized pattern blocks or project the pattern blocks so the entire class can see.]

Pointing at one of the two red trapezoids, ask, “One red trapezoid is what fraction of the yellow hexagon?” Students are likely to say one-half, as they become quite familiar with this fraction at a very young age. Write one-half in the blank provided, and emphasize that you wrote the name of the fraction using words. Now, ask students, “How can we use symbols to write the fraction one-half?” Again, students are likely to be able to answer this as well. Regardless, show how to write one-half using symbols as . [Note: It is important to use a horizontal bar. Try to avoid using the slash to write 1/2. When students are writing, this slash often gets confused with a 1 and does not help students visually identify the numerator and denominator as clearly as the horizontal bar.]

Next, ask students to work in their groups to determine how many green triangles cover the red trapezoid, as stated in the third example. When the groups have completed the task, ask a student to show the green triangles covering the red trapezoid. Then help students write the fraction in words and symbols.

Pointing at one of the three green triangles, ask, “One green triangle is what fraction of the red trapezoid?” Students may suggest it is one-third. Write one-third in the blank provided, and emphasize that you wrote the name of the fraction using words. Now, ask students “How can we use symbols to write the fraction one-third?” Again, students may be able to answer this easily. Regardless, show how to write one third using symbols as  .

Ask students to work together in their groups to complete the remaining examples on the Partitioning Polygons practice worksheet.

When students are finished, ask students to state their solutions and show the class how they solved each problem. Be sure to help with the spelling of one-sixth if needed.

Extension:

The suggestions in the following sections may be used to tailor the lesson to meet the needs of the students. The Routine section provides ideas for reviewing the lesson concepts throughout the school year. The Small Group section is intended to allow additional practice opportunities for students who may benefit from it. The Expansion section includes a challenge for students who are ready to move beyond the requirements of the standard.

• Routine: As real-life situations arise during the school year, have students represent those using unit fractions, such as finding out how many students are eating school lunch, finding out how many students are wearing jeans, and so on. Then name one of those students as one-tenth of the students eating school lunch, for example, and so on depending on the counts. Emphasize that each student is one-tenth of the students eating school lunch as they all count equally. This emphasizes the idea of equal parts.
• Small Groups: Students who need additional practice may by pulled into small groups to work on partitioning polygons using pattern blocks and geoboards. Work on helping students understand the importance of having equal parts, making sure the denominator is the total number of equal parts, and having each part be a fraction of the whole.

Using the geoboard polygons, help students count the number of equal parts and understand that this is the denominator. Show that each equal part is one-fourth, one-fifth, and so on depending on the denominator. Students may play this game to practice identifying the appropriate unit fraction:

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

• Expansion: Students in need of a challenge should work in groups of 2 or 3 to play the following game focused on ordering unit fractions.

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

Students should be encouraged to draw pictures to order the unit fractions. Provide each student with grid paper.