Adding and subtracting decimals

Most recently, I finished the sections on adding and subtracting decimals. This is for my book, How to Help Your Child with Fifth Grade Mathematics. That chapter on computing with decimals just keeps getting larger and larger.

I have already finished the section on multiplying decimals. Before the month is done, as part of Camp NaNoWriMo, I’d like to review what I wrote for multiplying decimals as a way to write the section on dividing decimals.

I also want to write a section for adding decimals that makes connections to adding fractions. And then I’ll do the same for subtracting decimals.

It has been my experience as a teacher that many students in fifth grade struggle with computing with decimals. Then we move on to other concepts in mathematics, like geometry, and then we come around to fractions. As we come back to decimals again, as I do to see how students have progressed, I find that the work we do with fractions influences and informs the work and studying we did previously in the year with decimals. But not every student makes those connections on their own. As a teacher, I encourage those students who have made those connections to share them with their classmates. I also make it explicit, looking at parallel problems in decimals and fractions at the same time, for those students who are still having a hard time making those connections. I want to reflect this in my book as well, because it is a strategy that will help children and parents. I’ve seen it firsthand myself dozens of times, and it’s an idea worth sharing.

An Introduction to the Mathematical Practice Standards

Release 1.7.1

For the past two weeks, I have been working on Chapter 0 An Introduction to the Mathematical Practice Standards.

Please look for the next release on Friday, September 13, 2013 or Saturday, September 14, 2013.

I didn’t write as much this past two weeks as I had hoped. First, I am now back at work full-time teaching. While that can serve as an inspiration, as it did in what chapter I decided to work on, it also uses up a lot of my energy, creative and otherwise. Also, my district has decided to focus on rolling out the Common Core State Standards for Language Arts first, not the standards for Mathematics.

I am puzzled by this, because my principal asked me to go to some professional development sessions sponsored by our district at the beginning of last year. I was trained on the new Common Core State Standards for Mathematics, and have since done some professional development with my colleagues at our school. It certainly seemed to me that the district was going to start with Mathematics first.

It’s only going to slow me down, not stop me. I am going to finish this book; I complete things that I start. However, I have to be honest in saying I was hoping I’d have more of a support system in my work as a teacher as I did the work of writing. Now, I have the challenge of teaching to the Common Core State Standards for Language Arts, while Mathematics is still in transition. And I’m attempting to write a book designed to help parents with the Common Core State Standards for Mathematics. More challenging than I thought it was going to be, but not impossible. A good percentage of the book is complete.

While my current students will not be graded using the new Common Core State Standards, I have already introduced the Mathematical Practice Standards in the classroom. While we have begun our first unit of study on prime factorization, we are simultaneously working on problem solving and mathematical reasoning. I have already referred to modeling with mathematics several times in class. I like these Mathematical Practice Standards. This year, for my current students and myself, it will be a blend of these new standards from the Common Core with the Mathematical Reasoning standards from the State of California’s standards.

Solve Problems by Multiplying Fractions and Mixed Numbers

Release Notes: 1.6.1

Chapter 18 Solve Problems by Multiplying Fractions and Mixed Numbers is now complete.

There are also some minor edits to chapter 14.

I estimate that How to Help Your Child with Fifth Grade Mathematics is now 63% complete.

Please look for the next release in two weeks, on August 30, 2013.

Multiplying fractions and multiplying decimals (Release 1.5.1)

Release Notes: 1.5.1

Chapter 16 Multiply Fractions is now complete.

The section in Chapter 11 Compute with Decimals titled Multiply with Decimals is nearly complete.

There are also some minor additions to the introduction.

I estimate that How to Help Your Child with Fifth Grade Mathematics is now 57% complete.

Please look for the next release in two weeks, on August 16, 2013.

Release 1.4.1

Release Notes: 1.4.1

Chapter 17 Interpret Multiplication as Scaling is now complete. It was partially complete in release 1.3.1.

Chapter 9 Multiply Whole Numbers and Chapter 23 Volume of Solid Figures are now complete.

I did some online research regarding the various state additions to the Common Core State Standards. Accordingly, I have updated those chapters.

Chapter 4 is partially done. It does address Algebraic Patterning, a topic addressed by Kansas in their standards. It does not yet address the standard added by California.

I also updated Chapter 26, adding some discussion of Probability & Statistics, also from Kansas.

Chapters 12 and 20 are still reserved. There are no state additions to those domains that I am yet aware of.

I have also added to the Introduction, some paragraphs on the the development of this book and some background information on the Common Core State Standards.

I have calculated that How to Help Your Child with Fifth Grade Mathematics is now 53% complete.

Please look for the next release in two weeks.

Two Positive Articles about the Common Core Standards

I just had to share these articles that I’ve read over the past few days.

The first is “Not Your Typical Summer School: A Summer Camp Fights Learning Loss Using the Common Core”.

The second is “Why our nation needs common standards”.

As I started writing How to Help Your Child with Fifth Grade Mathematics in April, I started doing some online research. I was specifically trying to find out how many states had added to the Common Core State Standards for Mathematics. I teach in California, and I knew California had added to the standards. If I was going to write a book based on the Common Core Standards for Mathematics, I had to know what other states had added to the standards and what those additions were.

However, I was finding a lot of articles that were critical of the Common Core State Standards. I was finding that there was a lot of misinformation about the Common Core State Standards. There was also just a lot of missing information. People were not informed about the standards and were making statements that showed their lack of information. It was disheartening.

So, moving forward, I think I will do the occasional post, like this one, sharing some good, positive news about the Common Core State Standards.

Rounding Decimals

I finished Chapter 8 on rounding decimals for the latest version of How to Help Your Child with Fifth Grade Mathematics that I uploaded on July 5th, 2013.

This is one of those standards that does confuse some fifth grade students. I have always connected it to our base ten number system, and try to make it really clear to students why we round the way that we do.

That said, I have long found it confusing, though, in how we talk about rounding “up” and rounding “down”.

For example, 0.43 rounded to the nearest tenth is 0.4. We describe that as rounding “down”, but we don’t round the 4 in the tenths place “down” to a 3. It remains as a 4.

On the other hand, if we round 0.47 to the nearest tenth, then we do round it “up” to 0.5. In this case, the 4 in the tenths place does move “up” to the next largest digit, a 5.

As I was writing the chapter, it occurred to me that if we think of the whole number, rather than just that relevant digit, then rounding “up” and rounding “down” makes more sense.

Let’s take the numbers from 0.40 to 0.49. If we round each of them to the nearest tenth, then half of them, five, will round down to 0.4, while the other half will round up to 0.5.

The numbers 0.40 to 0.44 will round down to 0.4, while 0.45 to 0.49 will round up to 0.5.

I’m glad I wrote this chapter, because in thinking more about rounding numbers and how to explain that procedure, I clarified for myself something that has confused me about the language we use. In one context, it could be confusing. And I will still address that possible confusion with my students. In another context, it makes sense that we talk about rounding up and rounding down.

Read, write, and compare decimals

Yesterday and today, I worked on chapter seven: Read, Write, and Compare Decimals of my current project, How to Help Your Child with Fifth Grade Mathematics.

I will publish this chapter in the next version on July 5, 2013.

In the meantime, I want to point out a couple of websites that you might find helpful.

I have already added this to to my blogroll, but it’s worth mentioning. It is called A Maths Dictionary for Kids. It does use Flash, so it doesn’t work on my iPad, but I use it all the time on my laptop.

Specifically, click where it says “Enter Dictionary Here”. From there, click on the letter “E”, which will show all the dictionary entries that begin with that letter. Then click on “expanded notation”.  In the entry itself, there is a box where you can type in whole numbers and it will show you what they look like in expanded notation. FYI: expanded notation is the same as expanded form.

It won’t work for decimals, which your child in fifth grade will have to do, but it’s still helpful.

The other page is called Convert numbers into words. It gives you many options, including:

  • Convert Dollars and Cents into words
  • Convert Cardinal Numbers (integers) into words
  • Convert Decimal Numbers into words
  • Convert Ordinal Numbers into words

These are all useful, but “Convert Decimal Numbers into words” is perfect for working with this Common Core Standard for Mathematics.

Sample of book is ready

Tomorrow, I will publish an updated version of my book, How to Help Your Child with Fifth Grade Mathematics. That version will include the new material I have written over the past two weeks, as well as some minor revisions.

In thinking about tomorrow’s post, I realized that I had finished one of my goals, which was to publish a good sample of my book. If you’re like me, and have an e-reader device or use apps for reading e-books, then you’ve probably downloaded a free sample of a book you were interested in. I have yet to be impressed by any of these samples.

I decided I would do a better job with my book. Somewhere on the Leanpub website – which I cannot locate at this time – I read something about their samples. This inspired me.

The samples of e-books that I have downloaded have been short. Too short to get a feel for the book. Often, too much of the sample is taken up with copyright info and a table of contents. For a fiction book, I want the first chapter. If you don’t have me hooked by then, I’m probably not going to read your book.  For a non-fiction book, I want to skip ahead, and look at different parts of the book.

That’s what I’ve done with my book. The sample PDF that I’m currently looking at on my iPad runs 131 pages. And the table of contents is just for the sample. This is a really smart thing that the Leanpub people have done. If you click on one of the chapter titles in the table of contents, you’ll be taken to that chapter in the sample. I’m not going to waste your time giving you info in the table of contents that you can’t actually sample.

On the other hand, I have included the Introduction. The introduction does include information on all five domains, as well as all the chapters. So, the sample PDF gives you the best of both worlds. The table of contents will take you to what is actually in the sample, while the introductory chapter is for the complete book.

Full disclosure: the Introduction is not yet complete. I have yet to write the basic introduction to the Common Core Standards, but I have completed the How to Use This Book part.

What’s a domain? Under the Common Core Standards for Mathematics, there are five domains that categorize the different areas of mathematics. They are:

  • Operations and Algebraic Thinking
  • Number and Operations in Base Ten
  • Number and Operations – Fractions
  • Measurement and Data
  • Geometry

Accordingly, I have divided (math humor) the book into five sections, one for each domain. Each domain has a small introduction, which I have included in the sample PDF. And I have included the first chapter for each domain in the sample.

The domain on Operations and Algebraic Thinking has chapter 1, titled Use Parentheses and Evaluate Expressions.

Chapter 5, titled Understand Place Value, begins the domain section for Number and Operations in Base Ten.

The domain, Number and Operations – Fractions, begins with chapter 13, titled Add and Subtract Fractions with Unlike Denominators.

Chapter 21, Convert Measurement Units, is the sample chapter for the Measurement and Data domain.

Finally, the Geometry domain is represented by chapter 27, titled Understand Coordinate Graphing.

I have also included the glossary, which is in the Appendix.

And, last but certainly not least, – (more math humor) – I have included Chapter 0, which is an introduction to the Standards for Mathematical Practice. These are eight standards that run throughout all mathematics and can be applied in all of the domains.

Full disclosure: the chapter on the Mathematical Practice standards is also incomplete. I have prepared an edited version of the standards, removing references to middle and high school, but I have yet to add my own comments on each of these standards. That is forthcoming.

I hope you will find the sample of my book more than satisfactory. It might not be as good as picking up an actual book and thumbing through it to decide whether or not you want to buy it, but as e-books go, I think this is an acceptable solution (yet more math humor).