Fractions for Seventh Grade

A FIVE DAY FRACTION UNIT USING FRACTION SQUARES, FRACTION
BARS, TANGRAMS, AND A GRAPHING CALCULATOR

Objectives of the Unit

NCTM Standards:
Number and Operation:

Understand numbers, ways of representing numbers, relationships among
numbers and number systems . Understand meanings of operations and how
they relate to one another. Compute frequently and make reasonable
estimates.

NYS Standards:
Number 3: Mathematics

Students will understand mathematics and become mathematically confident
by communicating and reasoning mathematically, by applying mathematics in
real world settings, and by solving problems through the integrated study of
number systems, geometry, algebra , data analysis. probability, and
trigonometry .

Number 7: Interdisciplinary Problem Solving

Students will apply the knowledge and thinking skills of mathematics,
science, and technology and make informed decisions.

Description of Resources

Textbook: Prentice Hall; Middle Grades Math: Tools for Success;
Course 2; Suzanne H. Chapin, Mark Illingworth, Marsha Landau,
Joanna Masingila, Leah McCracken; Chapter 5, p220-263; 2001

Everyday Learning Corporation; Everyday Mathematics: Grade
5; Max Bell, Jean Bell, John Bretzlauf, Amy Dillard, Robert Hartfield, Andy
Isaacs, Deborah Arron Leslie, James McBride, Kathleen Pitvorec, Peter
Saecker; Unit 5, p131 (student Math journal), p101, 102 (math masters);
2002

Longman; Elementary and Middle School Mathematics, Teaching
Developmentally: Fourth Edition; John A. Van de Walle; Chapter 12 & 13,
p209-232; 2001

Materials and Equipment

Textbook: Prentice Hall; Middle Grades Math: Tools for Success
Course 2
Partial Class set of graphing calculators TI-73
Overhead Projector
Calculator projector for the overhead
Overhead Tangrams
Overhead Fraction Bars
Overhead Fraction Squares
Overhead Fraction Circles
Scissors
Class set of wkst 131
Class set of wkst D-14
Class set of wkst 101
Class set of wkst 102
Class set of Fraction Models: Circles wkst
Class set of Fraction Models: Bars wkst
Class set of Divisibility Tests wkst
Fraction Spinners - 5 sets
Class set of Station packets
Class set of Adding Fractions worksheet

Outline

Day 1: Reducing Fractions and Equivalent Fractions
Students will look at fractions that are equivalent and prove that they
are equivalent when they reduce the fraction. Students will practice
reducing fractions

Day 2: Ordering Fractions and Comparing Them to 0, _, and 1
Students will focus on ordering fractions from least to greatest by
finding common denominators . Students will then be able to compare the
original fraction to 0, _, and 1 on a number line.

Day 3: Adding Fractions
Students will discover why fractions need a common denominator
before adding. They will review the process of addition of fractions.

Day 4: Subtracting Fractions
Students will discover why fractions need a common denominator
before subtracting. They will review the process of addition of fractions.

Day 5: Fraction Stations!
Each student will complete a station packet that involves four stations
so I can assess him or her on how well they understand the information.

Day 1

Number of students: 20
Time: 50 minutes

Objective:
Students will revisit fractions. They will determine equivalent
fractions using fraction squares. They will also explore the process of
reducing fraction.

Materials:

Anticipatory Set:

Students will answer in their notebooks the question of the day:
Shade 1/2 of a circle, then shade 2/4 of another circle.

Procedure:

Review what 1/2 of a shaded circle looks like on the overhead
compared to 2/4 of a shaded circle.

Make any connection between the fractions 1/2 and 2/4.

Demonstrate with fraction squares and fraction bars how 4/12 is
equivalent to 1/3 and 6/8 is equivalent to 3/4.

Introduce the procedure to finding equivalent fractions by multiplying
the numerator and the denominator by the same number.

Stress to the students that what they do to the top they must also
do to the bottom.

Go through the procedure to reduce fractions to simplest terms ,
divide the numerator and the denominator by the same number.

Remind students that what you do to the bottom, you must also do to
the top.

Give students the following fractions and allow them to work with
table partners to discover how else these fraction can be
written. Showing all of their work, students are encouraged to
find at least three equivalent fractions ( 1 smaller then the
original and 1 bigger than the original).

Allow students to use the fraction model worksheets and the
divisibility test table as guides.

Assessment:
As an exit pass, on 1/2 sheet of paper students must find an
equivalent fraction for 10/12 and 9/18.

Homework:
Line Up wkst p(D-14)

Reflection:

Day 2

Number of students: 20
Time: 50 minutes

Objective:
Students will continue practice with fractions by having a better
sense of where fractions belong on a number line.

Materials:

Anticipatory Set:
Students will answer in their notebooks the question of the day:
Order from least to greatest the following fractions:
1/3, 1/8, 1/5, 1/10 while homework is collected.

Procedure:

Go over the question of the day, focusing on the size of the pieces of
the wholes using fraction squares on the overhead.

Compare those pieces to 1/2.

On the overhead, create a number line where 0, 1/2, and 1 are the
prominent points labeled.

Ask students if they can put any more labels on the number line
between 0 and 1 (mainly looking for 1/4 and 3/4 as extra
guides).

Give students fractions such as 2/5, 6/7, 2/3, 5/8, 4/6, and 3/9.

Collectively we will add those fractions to our number line. Students
will create a copy in their notebooks.

Through out the activity give students the following tips:
When the denominator is 2 times the numerator , the fraction is close to or
equal to 1/2.
When the value of the numerator and the denominator is close to being
equal, the fraction is close to 1.
When the value of the numerator and the denominator are farther apart,
the fraction is closer to 0.

Distribute game pieces and give directions to the game “Build It Up.”

Students work with table partner using one deck of “Build It Up”
cards and two number lines to create a number line where
fractions are ordered from least to greatest.

One of the partners must record their number lines on a 1/2 sheet of
paper to be handed in.

Demonstrate on the overhead the calculator game, “Between a Rock
and a Hard Place.”
Students in the room will be split into two teams to play the game

Assessment:
As an exit pass, students will hand in their half sheet of paper from
the “Build It Up” activity.

Homework:
Comparing and Ordering Fractions wkst p (131)

Reflection: