FRACTIONS,
RATIOS, & DECIMALS ARE AMAZING!
NAMES:
Meghan
Powers, Annmarie McGonagle, Derrick LaBombard
CLASS/SEMESTER: EDR 524, Fall 2011
GRADE
LEVEL:
7^{th} Grade
NUMBER
OF STUDENTS
IN THE CLASS: Approximately
24
students
UNIT
TITLE:
Fractions, Ratios, & Decimals Are
Amazing!
RATIONALE:
Basic pre-requisite knowledge for higher
mathematical learning and thinking, as well as for day-to-day use.
INSTRUCTIONAL
GOAL(S): At the end of the unit, students will be able to
understand the relationships
between fractions, ratios and decimals. Students
should also be able to apply the
basic operations to rational numbers.
STUDENT
PERFORMANCE
INDICATORS/OUTCOMES:
Ratios
& Proportional
Relationships
7.RP
Analyze
proportional
relationships and use them to solve real-world and mathematical
problems.
1. Compute unit rates associated with ratios of
fractions,
including ratios of lengths, areas and other quantities measured in
like or
different units. For example, if a person walks 1/2 mile in
each 1/4 hour,
compute the unit rate as the complex fraction 1/2/1/4 miles per hour,
equivalently 2 miles per hour.
2. Recognize and represent proportional
relationships between
quantities.
a. Decide whether two quantities are in a
proportional
relationship, e.g., by testing for equivalent ratios in a table or
graphing on
a coordinate plane and observing whether the graph is a straight line
through
the origin.
b. Identify the constant of proportionality (unit
rate) in tables,
graphs, equations, diagrams, and verbal descriptions of proportional
relationships.
c. Represent proportional relationships by
equations. For
example, if total cost t is proportional to the number n of items
purchased at
a constant price p, the relationship between the total cost and the
number of
items can be expressed as t = pn.
The
Number System
7.NS
Apply
and extend previous
understandings of operations with fractions to add, subtract, multiply,
and
divide rational numbers.
1. Apply and extend previous understandings of
addition and
subtraction to add and subtract rational numbers; represent addition
and
subtraction on a horizontal or vertical number line diagram.
2. Apply and extend previous understandings of
multiplication
and division and of fractions to multiply and divide rational numbers.
c. Apply properties of operations as strategies to
multiply and
divide rational numbers.
d. Convert a rational number to a decimal using
long division;
know that the decimal form of a rational number terminates in 0s or
eventually
repeats.
3. Solve real-world and mathematical problems
involving the four
operations with rational numbers.1
_________________
1 Computations with rational numbers extend the
rules for
manipulating fractions to complex fractions.
Expressions
& Equations
7.EE
Use
properties of operations
to generate equivalent expressions.
Solve
real-life and
mathematical problems using numerical and algebraic expressions and
equations.
3. Solve multi-step real-life and mathematical
problems posed
with positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties
of
operations to calculate with numbers in any form; convert between forms
as
appropriate; and assess the reasonableness of answers using mental
computation
and estimation strategies. For example: If a woman making $25
an hour gets a
10% raise, she will make an additional 1/10 of her salary an hour, or
$2.50,
for a new salary of $27.50. If you want to place a towel bar 9 3/4
inches long
in the center of a door that is 27 1/2 inches wide, you will need to
place the
bar about 9 inches from each edge; this estimate can be used as a check
on the
exact computation.
IRA/NCTE Standards for the English Language Arts:
4. Students
adjust their use of spoken,
written, and visual language (e.g., conventions, style, vocabulary) to
communicate effectively with a variety of audiences and for different
purposes.
5. Students
employ a wide range of
strategies as they write and use different writing process elements
appropriately to communicate with different audiences for a variety of
purposes.
11. Students
participate as
knowledgeable, reflective, creative, and critical members of a variety
of
literacy communities.
Taken from the NCTE/IRA
Standards
(1996)
INTEGRATION/INTERDISCIPLINARY APPROACH/METHODS:
INSTRUCTIONAL PROCEDURES/STRATEGIES:
(a) Generalities of Lesson Plans
(b) Type(s) of Grouping Patterns (WC, SG and
type of SG, P, and I; include description of SG types)
· WC: The
whole class will go over the vocabulary words with the teacher.
· I:
Students will individually write their own short story about their
favorite
number, while incorporating the vocabulary words into it.
· No SG, or
P.
· P: Students
will then work with a partner and share their story, while the other
partner
draws their own picture representation of that story.
· I:
Students will post their pictures that they have created on the board. Students will finish class
with a review
worksheet (whatever is left to the worksheet will be assigned for
homework).
· WC: Students
will have the opportunity to share their story with the class on a
volunteer
basis.
· No SG.
· P:
Students will work with a partner(s) when going over the homework from
previous
class as well as when using technology in the computer lab.
· I: The
students will individually work on examples given by the teacher and
start
homework due the next class if time allows.
· WC: The
whole class will go over basic examples in class.
· No SG.
· P: Students
will work with a partner(s) when going over the homework from previous
class.
· I: The
students will individually work on examples given by the teacher and
start
homework due the next class if time allows.
· WC: The whole
class will go over basic examples in class.
· No SG.
· SG:
Students will work together in groups of 3 or 4 while determining which
fractions and proportions the food should be cut up into.
· I: Students
will individually work on examples given by the teacher and start
homework due
the next class if time allows.
· WC: The
whole class will go over homework together, as well as basic examples
in class.
· No P.
(c) Vocabulary Instruction:
· Direct: I
plan to lecture to the students about the
vocabulary. For
some of the words I will
simply read the definition and use them in sentences to solidify the
students’
understanding. Students
will discuss the
meanings of some vocabulary words in groups and then the class will
come
together to have a discussion. During
the discussion I will guide the students to help them with their
definitions.
· Indirect: The
students will be divided into groups so
that they can discuss the vocabulary terms and try to make sense of
them. These
learning stations will help students
work together to put the meanings of the terms into their own words.
(d) Meeting the Special Learning Needs of a
Student or Group of Students –
UNIT SCHEDULE –
· Thursday:
The Story Behind Your Favorite Number(s) (LP1).
· Friday:
Sharing Stories With Friends (LP2).
· Monday:
Fractions: Addition, Subtraction (LP3).
· Tuesday:
Fractions: Multiplication, Division (LP3).
· Wednesday:
Ratios (LP4).
· Thursday:
Decimals and Conversion (LP4).
· Friday:
Fractions Outside the Classroom (LP5).
· Monday:
Overview.
· Tuesday:
Long Quiz: Approximately 25 Questions.
INTRODUCTION/ MOTIVATION:
CULMINATION/CULMINATING ACTIVITY:
ASSESSMENT and EVALUATION PROCEDURES:
(a) Student Assessment (methods/techniques and
procedures):
1) Teacher’s
assessment of student: I will observe the students during class to make
sure
they are grasping concepts and skills.
There will also be weekly journal entries kept by the
students so that I
can read them and gather information.
I
will also interview each student individually throughout the unit to
determine
if they have any problems with material.
2)
Student self-assessment: During the
individual interviews, students will be asked to assess themselves on
how they
think they are progressing with the mathematical material.
(b)
Student Evaluation (methods/techniques and procedures): I will grade
worksheets, quizzes, a test at the end of the unit, journal entries
(pass/fail), math stories, and math pictures (pass/fail), etc.
(c)
Self-assessment/evaluation
(methods/techniques and procedures):
I
will assess my teaching and make adjustments accordingly based on class
discussions and student evaluations and assessments.
MATERIALS & RESOURCES:
(a) Types
of, Titles of, and Brief Descriptions of
Printed
Texts:
These trade books will
be
used throughout the unit to allow students to explore the stories and
pull out mathematical
ideas.
(b) Types of, Names of, and Brief Descriptions
of Audio-Visual
Materials:
(c) Types
of, Addresses of or Names of, and Brief Descriptions of at least three
Technology
Resources:
ADDITIONAL NOTES AND COMMENTS:
1. ADDITIONAL MATERIALS (Not
specifically included
in other sections):
(a) Quizzes and/or Tests; Rubrics for grading:
(b) Homework, newsletter, invitations:
(c) Guest speakers, details of field trips,
other out-of-class activities:
(d) Details of Introduction and Culmination of
the unit:
· The
students will now be able to do the "impossible" problem that was
presented to them at the beginning of this Unit.
It will be done individually and handed in to
the teacher; after which a confident volunteer will do the problem at
the
board, explaining each step as they solve it.
· Watch a
Mr. Duey video again; "Fractions," or another video related to the
next Unit the class will be learning.
· Play a
review game.
· For
homework one night, students will make/create at least 1 question
related to
this Unit (on fractions, decimals, and/or ratios), as well as giving
the
correct answer with their problem.
Little do they know that each of their problems will be
mixed into their
next quiz or test!
· Quiz or
test.
2. INFORMATION FOR SUPERVISOR
and/or READING
SPECIALIST and/or SUBSTITUTE TEACHER:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Rubric
Name:
Student Activity: Students are to create a short story about their favorite number (s) using mathematical vocabulary that is provided below. Students must use at least 7 vocabulary words and the rubric below must be followed.
Grammar/Spelling 4 3 2 1
Vocabulary use 4 3 2 1
At least 1 ½ pages 4 3 2 1
Creativity 4 3 2 1
Readability 4 3 2 1
Total: Score:
Vocabulary
list: circle, square, triangle, radius, rational, numerator,
linear, area, volume, diameter, perimeter, distance, cube, graph,
fraction,
denominator, ratios
(We created this rubric ourselves).
©
Prepared by:
Snowden,
P. L.
(1995). Department of Elementary and Special Education, Southeast
Missouri
State University, Spring Semester 1995 (revised Summer Semester 1996).
Additional
revisions:
Snowden,
P. L.
(1999). Center of Educational Studies and Services. Plattsburgh State
University of New York.
Snowden,
P. L.
(2005, 2006, 2007, 2009, 2011). Literacy Education. SUNY-Plattsburgh