Summary
Students will practice converting a fraction into a decimal and a percent.
Materials
For each group:
For each student:
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
- 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).
- Have the
student with 1 and the largest number stand on opposite
sides of the room.
- Instruct the rest of the class to place themselves in
numerical
order between the two numbers.
- 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.
- Repeat the game using fractions.
Instructional Procedures
- Using the base ten blocks,
show the 100 square. This equals
100/100 = 1/1 = 1.0 = 100%
- Transfer information onto the Base 10 worksheet by coloring
all 100 squares.
- Using base ten blocks, show 50 out of 100, 1/2 = 0.50
= 50 %.
- Transfer information onto Base Ten worksheet by coloring 50
of the 100 squares.
- 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%
- 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
- Construct
a book to keep diagrams.
- Fold a sheet of 8 1/2" x 11" paper in half, horizontally
(paper
A).
- Measure and mark one inch from each side along the fold.
- Cut one
inch slits on either side of the mark. Unfold to full
original size.
- Take a new sheet of paper (paper B).
- Fold in half, horizontally.
- Measure and mark one inch from each
side along the fold.
- Cut between the inch marks to create a slit
in the paper.
Unfold to full size.
- Take paper A and roll vertically.
- Slide paper A through the slit
in paper B.
- Unroll paper A carefully and match slits.
- Crease book again.
- 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).
- Have students glue in their
diagrams, in numerical order, and
label each page.
- Title the book.
- Use book as a quick reference for the remainder of the
unit on
decimals, percents, and fractions.
- 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.
- Give each student two squares, two rectangles, two
equilateral triangles and two circles.
- Ask students to "using your
scissors cut 50% (25%, 75%,
etc...) off your square (rectangle, triangle, circle)."
- When shapes
have been cut use the shapes to create a picture.
- 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
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.
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.
Created: 02/27/2006
Updated: 02/03/2018
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