LESSON FIVE
HALVING AND DOUBLING FRACTIONS WITH FRACTION TOWERS
OBJECTIVE :
The student will demonstrate an understanding of the relationship between the value of a whole unit and its parts.
The student will compare and order fractions using a concrete model.
The student will explain and record observations using objects, words, pictures, numbers and technology.
TEKS:
7.14 (A) – The student is expected to communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.
7.15 (B) – The student is expected to validate his/her conclusions using mathematical properties and relationships.
TOOLS AND MATERIALS :
Fraction tower for each student
ENGAGE :
- Distribute fraction towers to students.
- Have students work in pairs.
- Have one partner represent 1 on the fraction tower and the other partner represent 1/2 on the fraction tower.

EXPLORE:
Lesson Sequence and Facilitation Questions:
- Ask students: o How does the fraction 1/2 compare to 1? 1/2 is half of the size of 1.
o How many 1/2s are in 1? Two.
- Have students show the value of half of 1/2 and then ask: o What value does that amount represent? 1/4.
o How many 1/4s are there in 1? There are four equal parts in one fraction tower.
- Have students demonstrate half of the 1/4 value of the fraction towers and ask students: o What value does that amount represent? 1/8 How many 1/8 parts are there in one whole tower?
8
- Have students represent two of the 1/8 parts on the fraction tower. Ask students: o How does this value compare to the whole fraction tower? It is equal to 1/4 of the whole tower.
o How many 1/4 parts are there on the whole tower? 4
- Have students represent two of the 1/4 parts of the fraction tower. Ask students: o How does this value compare to the whole fraction tower? It is equal to 1/2 of the fraction tower.
- Have students show the value of 2/2 on the fraction tower. Ask students: o How does the value of 2/2 compare to the whole tower? 2/2 is equal to 1 whole fraction tower.
- Have students show the value of 1/3 and then ask students: o How many 1/3 parts are there in a whole fraction tower? 3
- Have students show the value of half of 1/3 and then ask: o What value does this represent? 1/6 o What does this mean? It means that there are 6 equal parts on the fraction tower and this value represents 1 out of 6 parts.

- Have students represent two 1/6 parts on the fraction tower and then ask: o How does this value compare to the whole fraction tower? It is equal to 2/6 or 1/3 of the whole tower.
- Have students show two 1/3 parts on the fraction tower and then ask: o How does this value compare to the whole fraction tower? It is equal to 2 out of 3 parts or 2/3 of the whole tower.
- Have students double the value of 2/3 of the tower and then ask: o How does this combined value compare to the whole tower? It is equal to one whole tower plus 1/3 more or 4/3 of the tower.
o What value would you have if the value of 1/3 is removed? One whole tower.

PRACTICE:
- Working in pairs, have students practice different combinations by completing the worksheet along with demonstrating values on their fraction towers.
- Have students complete Halving and Doubling worksheet.
DISCUSSION:
As a group, have students discuss their responses to the work sheet. Have students arrange the fractions according to their values.
1/1
6/6
1/2
2/4
3/6
4/8
1/3
2/6
1/4
2/8
2/3
4/6
EVALUATION:
Have students record their observations and reflect on the lesson in their journals. (See journal writing rubric on LESSON FOUR.)

HALVING AND DOUBLING WORKSHEET
Directions: Shade the portion of each fraction tower to represent the value of the fraction shown below each tower.
1/1 1/2 1/4 2/4
2/3 1/3 2/6 4/6
6/6 3/6 4/8 2/8

HALVING AND DOUBLING WORKSHEET KEY
1/1 1/2 1/4 2/4
2/3 1/3 2/6 4/6
6/6 3/6 4/8 2/8