Math for Quilters

By Dena Dale Crain

Most patchwork quilters follow published patterns and directions for their patchwork quilting projects. Math for Quilters empowers you with the mathematics to design patchwork quilts or change the size or proportions of a published project or pattern.

Many patchwork quilters are defeated in their efforts to use math by these problems:
—Making measurement conversions
—Fitting square blocks into rectangular quilt plans
—Planning an on-point setting
—Maximizing fabric and knowing whether they have enough fabric for a particular task
—Figuring how much their work might be worth and what price to ask for it

In Math for Quilters, find the easiest ways to overcome these and other obstacles as we revisit the math presented in primary and secondary school in a simplified and quilt-specific form.

Learn to plan and design quilts, including how to:

—Size a quilt for bed or wall
—Draw quilt designs and patterns to scale
—Understand ratios, proportions, and scale
—Analyze any quilt block so you can replicate it to any size
—Replicate compound block design
—Use arcs and curves in quilt block patterns
—Understand the importance of scale in block patterns
—Work with two measuring systems
—Master log cabin blocks
—Plan all elements of a quilt, including blocks, borders, sashing, cornerstones, and binding
—Review plane geometry, the foundation of all patchwork quilting
—Create original quilt design patterns
—Design patchwork quilts from the inside out and from the outside in
—Revisit high school algebra
—Master on-point quilt block settings (easier than you think!)
—Apply principles of symmetry to quilt and quilt block designs
—Use "square in a square" mathematics
—Discover "sacred geometry" in quilt design: the Sacred Triangle, the Sacred Rectangle, the Golden Mean, symmetry, tessellation, Fibonacci series, and fractal geometry
—Annotate quilt patterns
—Maximize fabric use by developing pattern lay-outs
—Build and use rotary cutting tables
—Handle a variety of complex pattern cutting situations, including fussy cutting, on-point appliqué patterns, and irregular shapes
—Lay out and cut sashing, cornerstones, borders, batts, and backings for quilts, as well as discovering three layouts for bindings: lengthwise, crosswise, and bias (each has its use!)
—Plan and execute patchwork borders
—Develop a total plan for making any quilt you can design
—Calculate the actual costs of making a quilt
—Price your work based on costs plus profit
—Sell your quilts

Math for Quilters includes 14 useful tables and instructions for drawing quilt designs on a computer without specialized, expensive software.

• Language: English
• Publisher: Dena Dale Crain
• Release date: Nov 25, 2019
• ISBN: 9780463560846

Dena Dale Crain

Dena Dale Crain relocated from the USA to Kenya in 1990, then returned to the USA in 2023. She spent most of her time in Kenya, living on the shore of Lake Baringo, two hundred miles and a five-hour drive north of Nairobi, with her partner Jonathan Leakey.Dena saw patchwork quilting as a way to employ local women, taught herself the basics, and began a small production quilting business in her home. With advanced degrees in design, anthropology, and textiles, she was uniquely positioned to help. As her experience and confidence increased, she began producing “one-off” works of art. Dena’s innovative art quilts were the subject of several solo art exhibitions and group quilt shows in Africa.Dena helped found the Kenya Quilt Guild and keeps a pulse on its activities. She helps educate members of the society at large about quilts as art. She has written magazine articles and lectured at quilting and non-quilting functions.Teaching in Cape Town, South Africa, for the Good Hope Quilters Guild National Quilt Festival in July 2002 moved Dena into the ranks of international quilting teachers. Since then, she taught art quilting at such prestigious venues as the Festival of Quilts in Birmingham, England; the European Patchwork Meeting in Val d'Argent, France; and the International Quilt Festivals in Houston and Chicago in the USA. In 2011, she earned South Africa National Quilt Guild Certification. In 2018 she became a Recommended Teacher for the same guild.In 2004 Dena joined the faculty of Quilt University, the first major online educational facility for patchwork quilters, later teaching for QuiltEd Online and the Academy of Quilting. An inventive and creative mind coupled with top-notch sewing skills makes Dena Dale Crain an educator of high merit in the world of patchwork quilting.Find links to Dena's patchwork quilt ebooks, live and virtual quilt classes, original pattern downloads, and more on her website.

Book preview

Math for Quilters

by

Dena Dale Crain

Copyright

Smashwords Edition

2019

Discover other titles by Dena Dale Crain at Smashwords.

Smashwords Edition, License Notes

This book is licensed for your personal enjoyment only. It may not be resold or given away to other people. If you would like to share this book with another person, please buy another copy for each reader. If you are reading this book and did not buy it, or if it was not bought for your use only, then please return it to Smashwords and buy another copy. Thank you for respecting the arduous work of this author.

Disclaimer and Terms of Use Agreement

The information contained in this book is solely the opinion of the author based on personal observations and experience. This material is for information and reference purposes only. The author does not warrant or guarantee the accuracy, completeness, timeliness, or usefulness of any information contained in this resource book and shall not be responsible or liable, directly or indirectly, in any way, for any loss or damage of any kind incurred as a result of, or because of the use of, or reliance on, any such content.

Information contained in this resource book is subject to change without notice. The author and publisher assume no liability whatsoever for the use of or inability to use any or all information contained in this publication. Use this information at your risk. If you wish to apply ideas contained in this book, you accept full responsibility for your actions.

This book may include links to World Wide Web sites and products. While supplying these links, the author does not guarantee, approve, or endorse the information available at these linked websites.

The author and publisher reserve the right to add to or to change the Disclaimer statement at any time.

Table of Contents

Preface

Acknowledgements

Testimonials

Frequently Asked Questions

List of Useful Calculations

Section 1: Preparation

---Chapter 1: Managing the Design Process

------Supply List

------Information Management: Labeling, Notes, Figures and Calculations

------Measurement Systems

------Conversions

------Rounding

---Chapter 2: Drawing Skills

------Draw by Hand

------Photocopier and Computer Assistance

------Computer Practicum

---Chapter 3: Sizing a Quilt

------Bed Cover Quilts

---------Pillows

---------Drop

------Sizing Other Kinds of Patchwork Quilts

Section 2: Quilt Elements

---Chapter 4: Block Structures

------Find the Grid

------Geometric Designs

---------Compound block designs

---------Variations on the grid

------Block Size and Complexity

------Symmetry

---Chapter 5: Block Scale

------Scale Up or Down

------Scale Log Cabin Blocks

------Scale Appliqué Blocks or Elements

------Scale and Measurement Systems

---Chapter 6: Other Quilt Elements

------Sashing

------Cornerstones

------Borders

------Binding

Section 3: Quilt Design

---Chapter 7: Quilt Planning

------Quilt Diagram

------What to Draw and What Not to Draw

---------Square quilts

---------Rectangular quilts

------Quilt Planning: Inside Out, Outside In

---------Planning from the inside out

---------Planning from the outside in

------Standard and Metric Block Dimensions Tables

------Technical Instructions

------Other Sizing Options

---Chapter 8: On-Point Settings

------Square in a Square: The On-Point Base Grid

------Standard and Metric On-Point Base Grid Tables

------On-Point Block Number Table

Section 4: Working with Cutting Layouts

---Chapter 9: Patchwork Fabric Layouts

------Shapes and Patterns for Patchwork

---------Seam allowances

---------Identical shapes

------Pattern Notations

------Specific Layouts to Maximize Fabric Use

------Straight-Sided Shapes

------Quilt Elements Cutting Table

---Chapter 10: Irregular Shapes and Special Layouts

------Shapes and Patterns for Patchwork

---------Seam allowances

---------Identical shapes

------Pattern Notations

------Specific Layouts to Maximize Fabric Use

------Straight-Sided Shapes

------Quilt Elements Cutting Table

---Chapter 11: Irregular Shapes and Special Layouts

------Pattern Materials

------Directional or Fussy Cutting

------On-Point Setting Half- and Quarter-Block Patterns

------Irregular Shape Pattern Layouts

---Chapter 12: Fabric Layouts for Other Quilt Elements

------Sashing without Cornerstones

------Sashing with Cornerstones

------Cornerstones

------Borders

---------Overlapped or butted borders

---------Mitered borders

---------Patchwork borders

------Batting

------Backing and Hanger Sleeve

------Label

---Chapter 13: Layouts for Quilt Bindings

------Quilt Dimensions

------Binding Width

------Area of Binding

------Binding Length

---------Bias binding

------------True Bias Table

---------Lengthwise binding

---------Crosswise binding

Section 5: Money

---Chapter 14: Cost a Quilt

------Price Versus Cost

------Costs of Materials

------Costs of Labor

------Costs of Overhead

------Quilt Costing Table

---Chapter 15: Price and Sell Your Quilts

------Why Sell Quilts?

------Pricing from Costs plus a Factor

---------Sample quilt costs

------Pricing by Area

------Pricing by Quality and Demand

------Special Tips on Costing, Pricing and Selling

Appendices

---Appendix 1: Reviews

------1-1: Review of Fractions and Decimals

------1-2: Review of Ratios, Proportions and Scale

------1-3: Review of Easy Algebra

------1-4: Review of On-Point Settings

------1-5: Review of Plane Geometry

---Appendix 2: Sample Quilt Plan

------Line Drawings

---------Quilt block

---------Scale the block

---------Sample quilt diagram

---------Patch patternsAppendices

------Cutting Calculations

------Fabric Notes Tables

------Quilt Elements Cutting Table

------Fabric Layouts

---------Patch patterns

------Fabric Notes Table

---Appendix 3: Tables and Tools for Quilt Planning

------3-1: Blank Cutting and Quilt Elements Cutting Table

------3-2: Blank Fabric Notes Table

------3-3: Blank Quilt Costing Table

------3-4: Blank Time Sheet

------3-5: Metric Block Dimensions Table

------3-6: Metric On-Point Base Grid Table

------3-7: On-Point Block Number Table

------3-8: Sample Fabric Record

------3-9: Sample Quilt Block Pattern

------3-10: Sample Quilt Costing Table

------3-11: Sample Time Sheet

------3-12: Sample Yardage Table

------3-13: Standard Block Dimensions Table

------3-14: Standard On-Point Base Grid Table

---Appendix 4: Bonus Tutorial: Flying Geese in a Circle

---About the Author

---Other Books

---Online Quilt Classes

---Patchwork Quilt Patterns

---Feedback

Preface

Math for Quilters is for patchwork quilters who have difficulty with the mathematics of quilting. Problems often arise when a quilter tries to:

---alter an existing quilt design or pattern to fit a specific bed,

---create a quilted hanging to fill a certain wall space, or

---improve sewing quality through better measuring and cutting skills.

Teaching others how to understand a quilt's design, how to grasp its requirements, and how to maximize available are amongst the goals of this book.

To gain the most benefit from this book, follow a few simple guidelines as you read and study the information included:

1. Familiarize yourself with the math principles presented in the Reviews (see Appendices). The Reviews explain relevant math theory. Each Review has a brief set of practical exercises to assess strengths and weaknesses. Work the exercises and check your answers against the answer key. The reward for mastering the contents of the Reviews is better quilting!

2. Read each chapter quickly to get a general idea of what it holds. Then read it a second time more slowly. The second reading reveals unfamiliar information that needs extra attention from you. If some parts of the chapters seem too difficult, leave them for the moment. You can study more carefully after you work with the parts you can manage.

3. Use the information you find here soon! Mere reading is not enough; learning takes place through practice. Working through a quilt design helps cement the information into your memory.

4. Plan a quilt and figure its yardage requirements even if you never intend to make it. Work the calculations for costing and pricing a quilt even if you do not intend to sell—yet. These procedures cover most of the ways in which quilters use mathematics. Their logic can help in all your quilting efforts. The more you work with numbers today, the easier it will be to draw on that knowledge in future.

Acknowledgments

I am terrible at math!

As a quilter, I soon saw that I needed to find ways to work around my limitations. I also realized that if I had difficulty with mathematics and quilting, other quilters may have the same kinds of problems.

Teaching online for Quilt University, I had the idea of writing a class that addressed mathematics. Then Dean of Quilt University Carol Miller liked the concept. She also had such confidence in me as an online quilt teacher that she scheduled a date and began promoting the class. Only after this did she see my first draft of the lesson contents, and then—what a kerfuffle!!

Trained as a designer, I approached the material from a direction that was the opposite of what Carol, a traditional patchwork quilter, expected. Already committed to a deadline, we quickly had to iron out our difficulties. Manuscripts flew back and forth daily. We had less than a month to complete the work and publish the class lessons. We had to develop a class that would satisfy us both, and we had to do it in a terrific hurry!

In the end, of course, we met the deadline and the class opened on time. Most of the credit for that accomplishment was due to Carol Miller's patience and tenacity.

Indeed, I owe much of what I am today to Carol Miller and Quilt University. Ahead of its time, Quilt University offered top quality specialized education to patchwork quilters the world over. My deepest thanks go to Carol Miller; sadly, posthumously.

However, I also thank all those quilters who enrolled in Math for Quilters when Quilt University offered the class. Their experiences with the class materials fed back into the content and helped me make this version of the information the best yet!

Testimonials

What a class! The lessons were absolutely excellent. I would sign up for any class Dena teaches. The depth is there that is required to understand and/or just review what one has learned in high school and college. This is the type of class that the material provides both the curious and the serious quilter with an excellent resource package to keep forever!

I was a math major in college and, boy, did this bring it all back! I have done some quilt design work, and the information included in this book affirmed what I had been doing was correct. I was able to use information on setting blocks on-point and determining changes in quilt size, fabric requirements, etc., on a quilt currently in progress - great timing!

Material was very well laid out. Not until it was all presented, did I realize just how much math is involved in quilting! I will be able to refer to the information going forward.

Enjoyable? Yes! Actually, more detailed than I expected. I learned a few new things but mostly appreciate how the review of math topics took the scary out of doing geometry to figure out how my quilts should go together. I may never design my own quilt, but I understand how they are developed and how to plan and organize my fabric choices, which will help in a lot of ways.

The material was so well presented I didn't really have any questions, just read carefully and the information is there.

Exactly what I had wished for years!

I certainly enjoyed the class and definitely learned new skills, as well as a new way of approaching my work.

Definitely would take another class with Dena. She responded promptly and gave me lots of good information above and beyond what was required by the class!

Frequently Asked Questions

What is the difference between arithmetic and mathematics?

According to the Cambridge International Dictionary of English, arithmetic is the process of making calculations such as adding, multiplying, etc., using numbers. Mathematics is the study of numbers, shapes, and space using reason and usually a special system of symbols and rules for organizing them. Algebra, arithmetic, and geometry are all mathematics, but not all mathematics is arithmetic.

Who needs to use math?

Quilters! Everything we do as quilters has to do with mathematics and numbers, whether we are aware of it or not.

How do you use math?

Our traditional block patterns are exercises in geometry. We often estimate blindly how much fabric we need to complete a project. We compare the dimensions of our quilt tops with those of our batting and backing. We buy fabric by a given measurement. We classify fabric by thread counts, the number of threads per square inch. We measure the lengths and widths of our machine stitches and count the number of stitches per inch. We sew with measured seam allowances, cut with rulers, and measure the size of needles by numbers. We live in a world of numbers!

Why do I need math?

Mathematics plays a large part in our everyday lives. We perform many mathematical activities at the subconscious level of our minds. We often rely on others to provide you with measurements and calculations of quantities, such as letting the shop clerk figure out how many yards of backing material we need. By working unconsciously and depending on others, we sacrifice our control over the work we do.

Knowledge of math empowers us to plan and design quilts, as we want them, instead of always being dependent on others for quilting projects. Can you imagine how much more efficiently you would work if your understanding of mathematics was better than it is now? With what greater accuracy? Better control? More flexibility? More creativity? These are the reasons you need math.

What can I do with math?

With improved math skills, you can:

---Use any patterns available in your language by comparing and demystifying measurement systems

---Plan bed quilts or wall hangings to fit any bed or wall space

---Design and draft quilt blocks

---Design quilts

---Change the setting of a design from straight to on-point

---Make correct patterns and templates with accurately drawn seam allowances

---Develop pattern layouts and rotary cutting plans

---Calculate precisely how much fabric a project requires

---Figure how much binding to cut

---Learn how much it costs to make a quilt

---Set a fair price for a quilt to sell it

How much math do I need to know?

The answer to this question lies with you. How much do you want to know? How much knowledge and understanding of mathematics do you need to be a better quilter? Your decision, of course, depends on what kind of quilting you wish to do and how far you want to go with it.

This book supplies all the math you need for the cutting and planning that goes into designing, making, and pricing a quilt. Many tables are in Appendix 3 so that you can easily access the figures you need; find blank forms there as well. Read and use this book, as and when you need it. You need not master everything at once.

When will I use math for quilting?

When you want to change the size of a pattern from a magazine or book, you use math. You use math to plan and design quilts. If you calculate how much fabric to buy or how much the fabric will cost, you use math. If you design a block, you bring plane geometry into play. You use plane geometry every time you arrange a set of blocks to make a design. As a quilter, and especially as a quilt designer, you use mathematics all the time!

Must I have a calculator?

No. With basic knowledge of how to add, subtract, multiply and divide, you are well prepared to perform by hand all the calculations needed to produce fine quilts. However, having a calculator certainly reduces error and eases the work.

Luckily, most computers have calculator software programs. Check your program or application files to see if you have one. If you want to use a calculator and do not