Smaller Than One
Grade 6
Standard I Lesson
Summary:
Students will practice converting a fraction into a decimal and a percent.
Main Curriculum Tie:
Mathematics - 6th Grade
Standard 1 Objective 2
Identify relationships among whole numbers, fractions (rational numbers), decimals, and percents.
Materials:
For each group:
* White paper for books
* Base ten blocks
* Copy of shapes for extension
For each student:
* Scissors
* Glue
* Colored pencils/crayons
* Base 10 worksheet
Attachments
* base_10.pdf
* base_10_blocks.pdf
Background For Teachers:
The fifth grade core curriculum has students order and compare whole numbers, fractions (including mixed numbers), and decimals using a variety of methods and symbols.
Percent is a ratio comparing a part to a whole using the number 100. The percent is the number of hundredths that part is equal to.
Intended Learning Outcomes:
1. Demonstrate a positive learning attitude toward mathematics.
2. Become mathematical problem solvers.
3. Reason mathematically.
Instructional Procedures:
Invitation to Learn
1. Provide each student in the class with a card or paper with an assigned number (1-30, or the number of students in the class).
2. Have the student with 1 and the largest number stand on opposite sides of the room.
3. Instruct the rest of the class to place themselves in numerical order between the two numbers.
4. Repeat this process as needed by having the first two students hold 0 and 1. The other students should have numbers dealing with tenths, hundredths, or thousandths.
5. Repeat the game using fractions.
Instructional Procedures
1. Using the base ten blocks, show the 100 square. This equals 100/100 = 1/1 = 1.0 = 100%
2. Transfer information onto the Base 10 worksheet by coloring all 100 squares.
3. Using base ten blocks, show 50 out of 100, 1/2 = 0.50 = 50 %.
4. Transfer information onto Base Ten worksheet by coloring 50 of the 100 squares.
5. Continue making diagrams using:
10/100 = 1/10 = 0.1 = 10%
20/100 = 1/5 = 0.2 = 20%
25/100 = 1/4 = 0.25 = 25%
30/100 = 3/10 = 0.3 = 30%
40/100 = 4/10 = 0.4 = 40%
60/100 = 3/5 = 0.6 = 60%
70/100 = 7/10 = 0.7 = 70%
75/100 = 3/4 = 0.75 = 75%
80/100 = 4/5 = 0.8 = 80%
90/100 = 9/10 = 0.9 = 90%
6. Review how to convert a fraction into a decimal and then find the percent:
* To convert a fraction to a decimal, divide the numerator by the denominator.
* To convert a decimal to a fraction, write the place value of the decimal as the denominator. Write the digits of the decimal as the numerator.
* To convert a percent into a fraction or a decimal, rewrite the percent as a fraction over 100.
* To convert a fraction to a percent, use the following proportion:
part = percent value
whole 100
7. Construct a book to keep diagrams.
1. Fold a sheet of 8 1/2” x 11” paper in half, horizontally (paper A).
2. Measure and mark one inch from each side along the fold.
3. Cut one inch slits on either side of the mark. Unfold to full original size.
4. Take a new sheet of paper (paper B).
5. Fold in half, horizontally.
6. Measure and mark one inch from each side along the fold.
7. Cut between the inch marks to create a slit in the paper. Unfold to full size.
8. Take paper A and roll vertically.
9. Slide paper A through the slit in paper B.
10. Unroll paper A carefully and match slits.
11. Crease book again.
12. Add as many pages (like paper A) as needed. To complete book for above conversions, use 1 paper A and 3 paper B (on last page write the steps to conversion).
8. Have students glue in their diagrams, in numerical order, and label each page.
9. Title the book.
10. Use book as a quick reference for the remainder of the unit on decimals, percents, and fractions.
11. As extra credit or an extension, students find:
33 1/3 /100 = 1/3 = 0.3 =33 1/3%
66 2/3/ 100 = 2/3 = 0.6 = 66 2/3 %
15/100 = 3/20 = 0.15 = 15 %
35/100 = 7/20 = 0.35 = 35%
45/100 = 9/20 = 0.45 = 45%
55/100 = 11/20 = 0.55 = 55%
65/100 = 13/20 = 0.65 = 65%
85/100 = 17/20 = 0.85 = 85%
95/100 = 19/20 = 0.95 = 95%
Extensions:
* Using Number Cards, students could play War, Spoons, Memory, Gin, or Go Fish. (The cards equivalent to 1/3, 2/3, 1/8, 3/8, 5/8, and 7/8 are optional. 6/15 and 4/8 are also optional.)
* Create “percentage pictures” from geometric shapes.
1. Give each student two squares, two rectangles, two equilateral triangles and two circles.
2. Ask students to “using your scissors cut 50% (25%, 75%, etc...) off your square (rectangle, triangle, circle).”
3. When shapes have been cut use the shapes to create a picture.
4. Have students create a worksheet to accompany their picture. For example, if there is a picture of a sun one question on the worksheet could be, “What percentage of the circle made the sun?”
Materials
o Number Cards
o Geometric Shapes
Family Connections
* Students take their diagram book home and explain it to a family member.
* Students make their own set of game cards and play one of the games with a family member.
* Students have a family member complete his/her “percentage picture.”
* Students create their own answer key and test their family members.
Attachments
* number_cards.pdf
* geometric.pdf
Assessment Plan:
* Informal assessment includes observation of students, class discussion and discovery.
* Formal assessment includes completed diagram book with correct fractions and percents.
Bibliography:
Research Basis
Farivar, S. & Webb, N.M. (1994). Helping and Getting Help–Essential Skills for Effective Group Problem Solving. Arithmetic Teacher. 41, 521-525.
Using examples drawn from a program of peer learning in middle school mathematics, this paper identifies a set of helping behaviors that best aid learning in collaborative small groups. The paper describes conditions that must be satisfied for helping behavior to be effective and the responsibilities of students seeking help, students giving help, and teachers to make helping productive for learning.
Hatfield, M., Edwards, N., Bitter, G., & Morrow, J. (2000). Mathematics Methods for Elementary and Middle School Teachers. New York, NY. John Wiley & Sons Inc.
This resource included the NCTM Principles and Standards for School Mathematics 2000, as well as the newest NAEP data and findings from the TIMSS. The book emphasizes considerations regarding cultural diversity and includes a CD-ROM with vignettes of real classroom situations to help the reader study teaching practices as they occur naturally in the classroom.
Author: