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Relating Fractions and Decimals

 


Author: David Riddick
Date Created: 1/5/2004 9:27:09 PM PST

 

Grade/Level:
4

Students:
29 Students. 16 boys and 13 girls. 3EO's; 6 IFEP's; 3 RFEP's; 14ELD2-4: GATE class - advanced learners

Subject Area(s):
Mathematics

Concept(s):
Students will learn to relate fractions and decimals through three different strategies; numbers written as a decimal, fraction notations, and drawing parts of a figure.

State Academic Content Standard(s):

CA- CCTC: Aligned CSTP's and TPE's

• Standard : CSTP: Standard for Understanding and Organizing Subject Matter for Student Learning
TPE: A. Making Subject Matter Comprehensible to Students
CSTP Description: Teachers exhibit strong working knowledge of subject matter and student development. Teachers organize curriculum to facilitate students’ understanding of the central themes, concepts, and skills in the subject area. Teachers interrelate ideas and information within and across curricular areas to extend students’ understanding. Teachers use their knowledge of student development, subject matter, instructional resources and teaching strategies to make subject matter accessible to all students.

• CSTP Key Element : Developing student understanding through instructional strategies that are appropriate to the subject matter.

 Question : develop and use a repertoire of instructional strategies well suited to teaching a particular subject matter?


CA- California K-12 Academic Content Standards

• Subject : Mathematics

• Grade : Grade Four
By the end of grade four, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare simple fractions and decimals. They understand the properties of, and the relationships between, plane geometric figures. They collect, represent, and analyze data to answer questions.

• Area : Number Sense

• Sub-Strand 1.0: Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers:

 Standard 1.6: Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1 ⁄2 = 0.5 or .50; 7 ⁄4 = 1 3 ⁄4 = 1.75).

 Standard 1.7: Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.

Objective(s):
Cognitive: Students will learn any fraction whose denominator is 10 or 100 can be written as a decimal.

Observable: Students will relate fractions and decimals by writing fractions as a decimal, notating fractions as a decimal, and drawing a model to illustrate fractions and decimals.

Criteria: Given a decimal or fraction whose denominator is 10 or 100, students will shade in a model that illustrates each decimal/fraction with 80% accuracy.

Prerequisite Background Skills/ Knowledge:
Students should have some experience in reading and writing fractions with a denominator of 10 or 100.

Students should be aware that the first place to the right of the decimal point is the tenths. The next place over to the right is the hundredths.

Vocabulary/Language Skills:
Listening: Students listen to verbal instructions given during directed lesson. ELD students are given help by peer tutors as teacher speaks.

Speaking: Students participate in directed lesson by raising hands and answering questions.

Writing: Students will take notes and write in their Math notebooks.

Reading: Students read from math textbook and Handout, "Relating Fractions and Decimals."

Vocabulary: decimals, fractions, tenths, hundredths, decimal point, equivalent decimals.

Materials:
1) Pencil & Paper
2) Transparencies
3) Transparency pen
4) Math Textbook p. 344-347
5) Handout "Relating Fractions and Decimals"
6) Transparency "Relating Fractions and Decimals"

Classroom Management:
When overhead is turned on, students are to remain quite and pay attention to direct instructions.

When overhead is turned off they are free to work cooperatively during independent practice.

Models of Instruction:
Learning Cycle

 

 

Procedure

 

 

 

 

Open:
As an attention getter, draw a rectangle on the board and split it into ten sections. Ask a child how we can label each section of the rectangle (i.e. 1/10). Write 1/10 in each section.

Color three of the rectangles.

Ask the children what fraction of the rectangle has been colored (1/10 + 1/10 + 1/10 = 3/10).

Explain that 3/10 can be written in another way - 0.3 (no units and three tenths)

Explain the features of the notation:
- The dot in between the 0 and the 3 is called the DECIMAL POINT and we use it to separate the units from the tenths.

- We always write in the 0 before the decimal point because it reminds us that the whole number is less than one.

- We say this number as "no and three tenths" or "zero and three tenths."

- Students should understand the decimal point reads "and." Model for them correct use of reading a decimal by using "and" instead of "point 3 tenths."

Input:
1st: Point out the standards we are working on (posted).

2nd: Inform students they will learn any fraction whose denominator is 10 or 100 can be written as a decimal. This is an essential concept that they will need to build from. In the comming lessons, they will learn how to convert fractions that don't end in 10 or 100 to the desired fraction.

Pass out handout, "Relating Fractions and Decimals."

3rd: Write this fraction on the board. "6/10" Ask students to read it.

Write this decimal on the board. ".6" Ask students to read it.

4th: Ask students if they see how 6/10 and .6 are the same value. Ask if students can make any connections between the two numbers.

5th: Write this fraction on the board. "37/100" Ask students to read it.

Write this decimal on the board. "37/100" Ask students to read it. Ask if students can make any connections between the two numbers.

6th: Explain how to read the shaded diagrams on pg. 344 and 345 in the textbook. Model for students how to shade in the two decimals/fractions.


7th: Read decimals and fractions to students. Students will record their responses in decimal, fraction, and by shading in their diagrams.

.08
.25
.3
.30
(ask if students see a connection between .3 and .30)

3/4
.9
.23
.07


8th: Students will work in cooperative groups to shade in the diagrams. High achieving students will work with lower achieving students.

9th: Once students have finished, have a student shade in the diagrams on the overhead and ask students if the responses are correct.

Guided Practice:
After direct, explicit instruction of each stage, allow students to work independently in cooperative groups.

Circulate among students to ensure they are on task and understanding the lesson.

Group students in diverse teams with consideration to gender, ethnicity, ability, and behavior.

Independent Practice:
Students will be given worksheet, "Relating Fractions and Decimals."

After direct, explicit instruction on each stage of the activity, students will relate fractions and decimals by writing fractions as a decimal, notating fractions as a decimal, and drawing a model to illustrate fractions and decimals.

High achieving students may use grid paper to plan a ten-row vegetable garden with two kinds of vegetables, similar to the one in Exercise 6 on page 346. Students may write two equivalent fractions and two equivalent decimals for the part of the garden planted in each vegetable.

Close:
Students will share their observations with the class and respond to how fractions and decimals relate to one another. Fractions with tenths and hundredths in the denominator can also be written as decimals.

In a grand conversation, students will reflect on what they learned and their surprises.

 

 

Assessment/ Reflection

 

 

 

 

Assessment:
Students will shade in a model that illustrates a decimal or fraction whose denominator is 10 or 100 with 80% accuracy.

Attachments:

 1. 

Relating Fractions Worksheet.xls

Reflection: