# 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:**

fraction squares | fraction models: bars (wkst) |

fraction bars | fraction models: circles (wkst) |

fraction circles | Divisibility Tests (wkst) |

overhead |

**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:**

fraction squares | TI-73 calculator |

overhead | calculator projector for overhead |

wkst 131 | “Build It Up” number line |

“Build It Up” cards | scissors |

**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:**

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