Fractions, Equivalent Fractions and Decimals.

GRADE LEVEL: 7-8

MATERIALS: Pen, Pencil, Paper, Calculator, Worksheet, Paper strips, charts on the blackboard, Thermometer, Micrometer and Gauge and overhead projector.

OBJECTIVE: The student, after a demonstration and explanation on number sense for fraction and decimals, will be able to relate fractions to decimals and find and compare equivalent fractions

MATHEMATICAL CONCEPTS:
-Revision on the definition of fractions and equivalent fractions.
-Concept of fraction, and decimals.
-Number sense for fractions and decimals.
-How to relate fractions to decimals to find equivalent fractions.

NCTM STANDARDS: STANDARD # 12: Fractions and decimals. -Develop concepts of fractions, mixed numbers, and decimals. -Use models to explore operations on fractions and decimals. -Apply fractions and decimals to problem situations.

PROCEDURE: The teacher will do a quick review on the concept of fractions: "What are numerator and denominator?"

The teacher will say that this is an exciting world we are living on and we want and we need to know exact information about things.

Things usually come out so many units and a little bit more, this little bit more is a fraction or a decimal part, fractions and decimals are the same thing. They both are an accurate measure for something that is smaller than one complete unit. Micrometers, Thermometers, and Gauges measure decimal and fractional parts. " The teacher will bring and show these three instruments to the class." (passing them around).

An example will be given to the class as to how we use the thermometer to calculate temperature. The teacher will take one student's temperature, the thermometer might register 97.5 oF and teacher will demonstrate in this way that normal average temperature is being expressed as a decimal on the real life.
The teacher will mention that in order to measure fractions and decimals we have to divide the unit of measurement into many equal parts. i.e.:


1/4    1/4     1/4    1/4    

3 out of 4 equal parts is equal to 3/4

So, in any fraction, the lower number "DENOMINATOR" shows the total number of parts in the unit. The top number "NUMERATOR" shows how many of these parts we are using.

Usually, we can choose the number of total parts into which a unit is divided. 32 PARTS TO ONE INCH, 16 PARTS TO ONE POUND.

We can expect to find fractions with any numbers of equal parts. Fractions written in this manner are called decimals: 0.5, 0.75, 0.25.

Fractions are easier to visualize: if we have a pizza divided into 8 equal slices and you remove two slices, what fraction of the pizza have you removed?. Answer: 2/8 or 1/4.

Decimals are easier to add, subtract, multiply and divide.

Fractions are changed to decimals by dividing the numerator by the denominator, students should be able to recognize that ½ is the same as 0.5, and that 0.4 and 0.45 are a little less than ½, also the teacher will explain that 0.6 and 0.57 are a little more than ½ by using a simple chart.

__________0.4____½______0.6_________

The teacher will show in the overhead projector two graphs as follows:

FIRST GRAPH


one fifth      two fifths      three fifths    four fifths     five fifths    

six fifths seven fifths eight fifths nine fifths ten fifths
SECOND GRAPH
 
one-fifth two-fifths three-fifths four-fifths one
one & one one & two one & three one & four two fifth fifths fifths fifths

The teacher will explain that five-fifths and one is the same, that six-fifths and one and one fifth is the same introducing in this way the concept of equivalent fractions and mixed numbers. Children will be given physical material to explore and compare equivalent fractions such as: PAPER STRIPS.


½ SAME AS 2/4


2/3 IS SMALLER THAN 3/4

As part of Closure, the teacher will also deliver a chart per group to sort the following fractions:

Each group will have to check the correct box and they will do this by drawing each fraction, or with paper strips divided in equal parts as required per fraction or by dividing numerator by denominator.

After the group activity has finished, the teacher will go over the results and correct them if wrong using the overhead projector.

ASSESSMENT: As part of the assessment, the students will watch 2 of their favorite TV programs and find out using a clock, how much time is devoted to commercials. Each student should time in minutes the whole program as well as each commercial from beginning to end. The student will compare number of minutes spent on commercials versus the time of the whole program and express the results in fraction and decimal form and compare the fraction and decimal to determine which program devotes more time to commercials.

REFERENCE: Ajose, S.A. (1994). "Problems, Patterns and Recreations", The Mathematics Teacher , 87(7), 516-19

Lola May, (May 1994). "Teaching Pre k-8". Teaching Math, 25(5), 24-25.

CONTRIBUTORS: Major: Maritza Simauchi.
Minor: Carol A. Marinas.


FRACTION           ABOUT 0            ABOUT ½             ABOUT 1                                                                                 

1/10                                                                         

4/7                                                                          

8/12                                                                         

1/3                                                                          

7/8                                                                          

2/5