## Fraction and Decimal Ordering

### Lois ChristensenColleges and Universities - Florida

#### Description

Students learn to order numbers in fraction and decimal form, in a critical thinking and kinesthetic fashion.

#### Objectives

The student compares and orders commonly used fractions, percents, and decimals to thousandths using concrete materials, number lines, drawings, and numerals.

#### Materials

- Mathematics textbook with chapters on fractions and decimals
- Cards (about 8.5 X 11) on which are printed various numbers in fraction and decimal form to the thousandths (some will need to be equivilent) - one per card
- Graph paper (either as a design on the board or on an overhead transparency) for use in explaining decimals

#### Preparations

1. Prepare cards using large type/font. These could be prepared on a PC. The cards should have a wide variety of quantities represented from basic fractions to four or five-place decimals. Some of the quantities should be equivalent. Mixed numbers could also be used.

#### Procedures

NOTE: This lesson only addresses the portion of the standard that pertains to decimals and fractions.

1. Gain student attention by asking them to line up according to their birthdays with January 1 at one end of the line and December 31 at the other end.

2. Discuss ordering – putting items in a sequential order either ascending or descending.

3. Using the textbook, review what the students know about fractions and decimals.

4. Practice expressing various quantities in equivalent fraction and decimal forms.

5. Compare the ratio of numerator to denominator in various fractions and what that means as far as quantity is concerned.

6. Compare decimals in terms of the number of integers used, the placement of integers around the decimal , and what that means as far as quantity is concerned. The use of graph paper with one integer per square often helps students understand this concept.

7. Give each of several students (6 to 10) a card on which is printed, in large numerals, a fraction and ask them to line themselves up in the same way they did with their birthdays. Students should stand in a line with the card displayed in front of them. Students who have cards expressing equivalent quantities should stand one behind the other. Repeat several times with different students and different cards. After each array, discuss/debrief how the students arrived at their conclusion (critical thinking).

8. Do the same activity with numbers expressed in decimal form. Repeat several times with different students and different cards. Discuss/debrief as above.

9. Do the activity a third time with a mixture of fractions and decimals. It works well to randomly select cards from the stack, place them face down on a table, and let the students self-select. Discuss/debrief as above.

10. Discuss how this knowledge is used in the real world (sports statistics, pharmaceuticals, mechanics and tool making for such things as drill bits, cylinders, etc.)

11. Have students each write five or six groups of numbers in fraction and decimal forms to the thousandths (6 – 10 each) and trade them with a partner who works out the order. Have them then correct each other’s work and discuss the cognitive strategies they used.

#### Assessments

Because of the kinesthetic nature of this activity, the teacher can easily assess the students as they work out the order in front of the class. Further, the discussion of the methods and strategies that the students share aloud will help the teacher assess the degree of mastery of the students. The final activity, in which students work in pairs, may be handed in at the end of the class period for a final check by the teacher. This activity should be considered a formative assessment.

#### Extensions

Students need prior knowledge of basic fractions and numbers written in decimal form. Encourage students to help each other by explaining aloud their strategy in figuring out their position in the ordering line. This permits the sharing of critical thinking. Knowledge may be extended to time lines or any other area in which sequence is a factor. Because the activity is kinesthetic, it permits many students to work out the problem more effectively than on paper.

If applicable, students could use calculators to support their decisions, particularly when converting fractions to decimal fractions.