# Teacher Instructions: Fraction Book Cover

**Grade Level: **3 - 5

**Task: **Fraction Book Cover

**Standard:** Number Sense and Operations

Design a cover for a book about fractions using fraction pieces. Make the cover

attractive. Then find the total value of the pieces you used to create your
design.

Represent your solution numerically in the simplest terms possible, as well as
visually

by showing us what your cover would look like .

**Context – From the Task Author: **This task was assigned to students after
they had

considerable practice using fraction pieces, adding fractions , and changing
improper

fractions to mixed numbers. Students were encouraged to check their work using a

fraction calculator. Students could also be encouraged to change their fractions
to

decimals and to check their solutions this way as well.

**What the task accomplishes…**

This is an assessment of the concepts taught in addition of fractions,
equivalent

fractions, improper fractions, and mixed numbers.

This activity allows for student exploration
using various fractional pieces. It provides

a different way of adding fractions, and allows the student to develop a method
that

works best for him/her.

It also helps the student see relationships of equivalent fractions and to
make

connections.

**What students will do…**

The student will create and solve his/her own problem.

The student will demonstrate his/her proficiency in adding fractions, finding

equivalent fractions, writing fractions correctly, using and writing improper
fractions

and mixed numbers, converting improper fractions to mixed numbers, and
explaining

his/her work using the language of mathematics. Use of fraction calculators
affirms

the students' work.

**Time Required:** This task takes approximately one hour.

**Interdisciplinary Links:** Students could explore how different book covers are
made.

They could also create book covers for other subjects. Students could create
geography

book covers, and figure out the relative sizes of states or countries, or create
nutrition

pyramid book covers and figure out the fractional part of each layer of the food
pyramid.

**Teaching Tips…**

• In lessons prior to this assessment, the students can make various pictures
with

teacher direction. For example, make a mushroom that equals 5/8, a sailboat that

equals 5/6, a cat that equals 1 1/4, etc.

• Students will want to show what they can make on their own.

• It is helpful for each student to have their own set of fraction pieces with
which to

work.

• A great book to help students understand the idea of
using fraction pieces for

making pictures is Ed Emberly's Picture Pie 1 & 2. This book does not use all of
the

fraction pieces in a set, but it helps those students who need a point of
reference to

get started.

**Suggested Materials:**

Sets of fraction pieces (halves, thirds, fourths, sixths, eighths, etc.)

Drawing paper

Colored pencils, crayons, etc.

Fraction calculators, such as TI Explorer or the Casio Fraction Mate

**Possible Solution…**

The solutions are endless since students can create any figure they wish.

Students can demonstrate different solutions to determine the value of their
creation.

**Benchmark Descriptors:**

The benchmark descriptors and rubric are designed to help the teacher analyze

student thinking and understanding at each of the four performance levels.

The descriptors are generalizations of what student work could look like.

It is not possible to anticipate every answer a student can give, so in
scoring student

work the teacher must use these generalizations to come to their own conclusions

as to where a student is performing on the assessment.

It is recommended that teachers create their own task specific rubric by
listing the

specific math skills that would make up each section of the four performance
levels.

**Novice**

Although the student has created a fractional picture, s/he cannot add or
trade the

fraction pieces correctly, and cannot simplify and/or change an improper
fraction to a

mixed number.

**Apprentice**

The student has created a fraction picture and has added the pieces
correctly, but

cannot simplify and/or change an improper fraction to a mixed number.

The picture may also have been created to conveniently equal a whole number.

**Practitioner**

The student has created a fraction picture and added correctly. However, the

student has not been able to explain the process s/he went through to do this.

There may also be a minor mathematical error.

**Expert**

The student has exhibited mastery of all the mathematical processes required
and

shows an understanding of the concepts involved in his/her explanation.

**APS Mathematical Standards…
The math standards stated for this task are aligned to the APS Draft
Standards 2000.**

**Strand – Number Sense and Operations:**

Students will demonstrate number sense through experiences with meaningful

mathematical problems that focus on number meaning, number relationships, place

value concepts, relative effects of operations, and multiple representations to

communicate sound mathematical thinking.

**Benchmark (K – 5):**The student will understand place value of whole numbers,

compose and decompose whole numbers, understand the operations and their effects

on numbers and solve problems with fluency and a variety of methods.

Performance Standards:

Performance Standards:

Third Grade:

•

**Reads, writes, and uses**conventional fraction words and notation and links them

to their pictorial representations.

•

**Explains**that when all fractional parts are included, such as four-fourths, the result

is equal to the whole and to one.

•

**Adds and subtracts**unit fractions that have the same denominator, using

manipulatives.

•

**Explains**common equivalents, especially relationships among wholes, halves,

fourths, and eighths, as well as wholes, thirds and sixths.

•

**Uses**fractions to solve everyday problem situations.

Fourth Grade:

•

**Explains**that equal fractions of a whole have the same area but are not necessarily

congruent.

•

**Explains**how the "size of the whole" affects the size of the fraction (e.g. Is ½ of $1

better than ¼ of $100?).

•

**Explains**the meaning of the numerator and denominator in fractional notation.

• Identifies and constructs models to represent equivalent fractions, mixed numbers,

and improper fractions.

•

**Adds**and

**subtracts**fractions with common and uncommon denominators using a

variety of strategies (e.g. manipulatives, numbers, and pictures).

•

**Compares**proper, improper, and mixed fractions to fractions and whole numbers

using a variety of strategies (e.g., manipulatives, numbers, pictures, and a number

line).

•

**Uses**fractions to solve everyday problem situations.

Fifth Grade:

•

**Uses**addition and subtraction of mixed numbers with common denominators in

problem solving situations.

•

**Uses**fractions and decimals to help solve everyday problem.

•

**Explains**that the size of a fraction is based on the relationship between the

numerator and the denominator and is dependent on the size of the whole.

•

**Estimates and solves**problems involving addition and subtraction of fractions, and

justifies the reasonableness of the solution.

**Strand - Global Mathematical Processes:**

Students will understand and use mathematical process.

**Benchmark (K - 12):**The student will use problem solving, reasoning and proof,

communication, connections, and representation as appropriate in all mathematical

experiences.

**Performance Standards:**

Grades Kindergarten through twelve:

•** Develop** resourcefulness and perseverance in problem solving in mathematics and

other disciplines.

• **Recognize** when to use previously learned strategies to solve new problems.

•** Develop and use** strategies for solving given problems.

•** Monitor and reflect** on the process of mathematical problem solving.

• **Make and investigate** mathematical conjectures and use them successfully in

developing and evaluating mathematical arguments and proofs.

• **Use** the concept of counterexample to test the legitimacy of an argument.

•** Develop** a logical sequence of arguments leading to a valid conclusion or
solution to

a problem (statement/reasons, proof, informal proof, and algebraic steps ).

• **Work** in teams to share ideas, to develop and coordinate group approaches to

problems, and to share from each other in communicating findings.

• **Relate** applications to mathematical language in various modalities.

• **Communicate** mathematical thinking coherently and clearly to others.

• **Analyze and evaluate** mathematical thinking and strategies of others.

• **Identify** and **connect** functions with real-world applications.

• **Identify** how seemingly different mathematical situations may be essentially
the

same (e.g. the intersection of two lines is the same as the solution to a system
of

linear equations ).

• **Investigate** and **explain** the mathematics required for various careers.

• **Recognize** and **apply** mathematics in contexts outside the mathematics course.

• **Develop** a repertoire of mathematical representation that can be used
purposefully,

and appropriately interchangeably (e.g. pictures, written symbols , oral
language,

real -world situations, and manipulative models).

• **Select, apply,** and **translate** among mathematical representations to solve

problems.

•** Use** representations to model and interpret physical, social, and mathematical

phenomena.

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