5th Grade Math Unit 2: Place Value From Billions to Thousandths, Notations, Comparing, Ordering, Adding, and Subtracting Decimals

I recently finished and posted to my static pages Math Unit 2: Place Value, Notations, and Decimals. This unit is part of my years worth of math units, which can also be accessed from my Math 9 Week Plans page.

In the spirit of convenience, I will also include the exact text of this unit here as a post in the main posts page of my blog. I hope that you can find this helpful:



5th grade Math Unit 2 involves place value from thousandths to billions, comparing and ordering numbers from thousandths to billions, and finally, adding and subtracting decimals.

The all encompassing, end of unit assessment can be downloaded in .doc format HERE to get you started.

These concepts are important to future success in math, and are taught in three parts so that the concepts scaffold onto one another as we go. This unit comes after a large numbers and operations unit that we started the year with, one in which students identified factors and multiples, worked with prime factorization, and finally refined skills in multiplication and division.

The unit is split into its three parts here, with all necessary exams and paperwork attached:

Unit 2.1: PLACE VALUE FROM THOUSANDTHS TO BILLIONS

It's important that students have an understanding of very large and very small numbers in the 5th grade. So we start by working on place value. Place value is a good place to start because it comes down to practice, repetition, and memorization of the place values.

The PDSA that accompanies unit 2.1 can be downloaded HERE.
The Unit 2.1 Assessment can be downloaded HERE. (I should mention right here that most of the assessments I have are also available in Spanish. Just let me know if you're interested).

By applying backwards design to this portion of Unit 2, the assessment shows a need for knowledge in: expanded notation, written notation, standard notation, and place value.

Activities to meet these needs are listed below:

First, I highly recommend a great activity called Place Value Cups. I originally came across this activity on a blog titled Look+Listen=Learn. By making these cups, students are given multiple opportunities to practice place value and expanded notation at the same time. It's a great activity, and I'm excited to see the difference it can make with students who struggle with this concept.

Teaching place value and the different notations is actually quite different than a lot of mathematical concepts. By this age, it should be more refinement and scaffolding than outright teaching. Let's be honest, if a child reaches 5th grade and has no understanding of place value, they've probably never been instructed before, or had some flat out awful teachers in the past, because it's integral to 3rd and 4th grades. I've found that students benefit more from practice practice practice than anything else. So while using the place value cups, I also refine the concept of how to say numbers.

Saying numbers aloud, especially larger numbers and numbers with decimals in them, can be daunting for the struggling math student. When I say "saying numbers aloud," I'm also teaching expanded notation. I like to rely on comma naming to give students a chance to know how to say numbers possibly before they conceptually understand big numbers (millions and beyond).

I teach students that the first comma is called thousand, the second is called million, and the third is called billion. We practice this in class. Then, we practice saying numbers with comma names. The great thing about this is that students never have to actually say a number larger than hundreds. Here's an example:

324,783,013.... The student would first say three hundred twenty four. This is simple, it's a concept that has been mastered by the vast majority of 5th graders years ago. Then it's a matter of naming that comma. It's the third comma we're looking at, and its name is billion. So, three hundred twenty four billion... Then the student would continue on... seven hundred eighty three, this time it's the second comma, million... seven hundred eighty three mission... thirteen. And that's the end of that. It really helps students understand and be able to say numbers, which we then build on with expanded notation. Expanded notation is fairly straight forward. It will also be covered in the resources below:

Here's a few resources to get you started:

• Place Value Charts at Adrian Bruce's Math Stuff: I will be printing off the charts and hanging them up in the classroom to use as an example. They go up to quadrillions. I only need up through billions.
• A simple, colorful chart to help with place value and expanded notation: PDF document.
• Numerous worksheets from MathAids.com.
• A chart to help students write numbers and understand their place values.
• A pdf packet of worksheets on the subject. I especially like page 10.

Unit 2.2: COMPARING AND ORDERING DECIMALS

After we have taught place value to thousandths (and billions), we move on to ordering decimals, and comparing decimals with <,>,= statements.

The PDSA for Unit 2.2 can be accessed HERE.
The assessment for Unit 2.2 can be accessed HERE.

By using the same method of backwards design, starting with the 2.2 assessment, we see that in this particular cycle of the lesson, students will be learning how to apply less than, greater than, and equal to statements to decimals, and will learn how to order large numbers with decimals (and simply large numbers is also acceptable here) either from greatest to least or least to greatest. Finally, it's important to apply these skills to word problems. So here we go:

• Head off to Khan Academy for his lesson on Comparing Decimals. Khan Academy is great, because he teaches through video, and offers various practice problem sets. Plus, he's got TONS of stuff.
• Fruit Shoot Comparing Decimals Game: An interactive game for students to play.
• I like for my students to practice ordering numbers on hanging number lines. It's a simple concept involving string and folded pieces of paper (or note cards). 

• This document, titled Gap Closing, has some great activities to fit this unit of study, particularly comparing and ordering decimals. 
• This pdf document includes a small chart I have my students make so they can begin to understand conceptually how and why they compare numbers, and what it actually means, in terms of place value, when one number is larger than another.
• Finally, a refresher on inequality symbols (if your students don't know this, they need to know this!)

UNIT 2.3: ADDING AND SUBTRACTING DECIMALS

Finally we end this unit with a cycle on adding and subtracting decimals. The concept is straight forward, and quite simply involves lining up the numbers to be added or subtracted by the decimal point.

The PDSA for cycle Unit 2.3 can be downloaded HERE.
The Unit 2.3 assessment can be downloaded HERE. If you like to save time, as my grade level team does, we don't use this assessment, instead, we simply score the final page (the adding and subtracting decimals page) twice, once as part of the unit score, and once for a unit 2.3 score.

• Here is a nice visual from Cool Math.com that pretty much explains it all. 
• Enchanted Learning also has a page about adding decimals, with some fun pdf worksheet games to go with it.
• My favorite worksheet building site, Worksheet Works, has pages of fully customizable and downloadable (in pdf) addition and subtraction of decimals worksheets.

Just remember, the concept of adding and subtracting decimals is quite simple. It all comes down to lining up the decimal, regardless of how huge one number might be and how small the other might be. Your students also might think about using zeros as placeholders when doing this!

A Final Day of Classroom Setup

Tomorrow I have a meeting, and on Friday, registration. It's always exciting to look at the room, set up and more clean and organized than it will ever look again this school year. The desks are ready, work for the first few days already run off, and now it's just a matter of time before the first day of school. My classroom set up was pretty straight forward this year. I didn't change anything really, other than getting a few computers out of the way (it was feeling a little cluttered).

My school district is using a new attendance and gradebook software called Synergy. I'm still not trained on it, but I got a good first impression. If you're out there looking for some gradebook software, there are a few options that I like.

First of all, there is the best in my opinion, TeacherEase. This great site offers full grade book software for something like $8 a month, but many schools will purchase a school license because it's great. If you want to make your life A LOT easier, I suggest this great teacher tool.

If you want grade book software, but you need something free, look at Engrade. It's not as intuitive or user friendly as TeacherEase, but it's a good free grade book.

Learnboost is another free grade book option. I like it, again, not as much as TeacherEase, but it works if you want to move to online grading.

If you haven't yet made the move to online grading, you should. It's great because you have complete control. In TeacherEase for example, you can set different categories within your subjects (e.g. tests, daily work, group work), and give each a weight as to how much of the final grade it is worth. The gradebook updates itself, you don't have to average grades. And, the best part is, parents get anytime access through a web browser. Many of these sites are putting out smartphone apps as well. TeacherEase doesn't have an app (although I hope they do), but their website still works great in my Android browser.

Real quickly, I wanted to add in some pictures of my classroom just to show off the hard work.

First is the back corner / sink area of the classroom. I have a science shelf there (my school is old and there isn't a lot of closet space, so we have to make do), along with the famous Aggie wall. GO AGGIES!

This photo is looking at my desk (behind the book cases), and what I refer to as "my office." 

Worksheet Works: A Great Worksheet Maker For Teachers (and it's Free)

I am constantly on the lookout for good printables. As much as I like to use technology in my classroom, and as bad of a rap as worksheets seem to get these days, they are still the backbone of many a lesson, and, if done right and used right, are a valuable resource unlike any other. I definitely am an advocate of mixing traditional, tried and true teaching practices with the newer tools.

But where do you find these worksheets? Sometimes you get lucky and have awesome curriculum, and over the years, almost all teachers collect resource books, which are shared and passed around under they literally fall to pieces. If you're looking online, there are a few guidelines. First of all, you never should have to pay for anything. There are thousands upon thousands of worksheets and resources out there in any subject, for any grade you can imagine. The best place is Google, obviously. But it can be daunting. No matter what you search for, you're bound to get tens or even hundreds of thousands, if not millions, of search results.

I came across Worksheet Works this morning while writing up some resources for a math unit. I like this site because it gives the teacher many options before building a worksheet that comes in pdf format and can be printed. I have been making worksheets and saving them in my Google Drive for the past few minutes, and they're good. I like the options, and will be showing this tool to colleagues and using it during the school year. I hope you find it helpful.

Google Drive: All the Storage You'll Ever Need

Over the course of my teaching career (seven years), I've gone from using blank cd's, jump drives, a laptop, my own email account, Dropbox and other cloud services, to Google Drive. I still use services like Dropbox on my phone to store photos and such, but for my work files, Google Drive is all I need.

From the start, Google Drive gives you 5 gigabytes of storage. Only stored files that are not in Google Doc format count against your 5 gigs. I have tons of files in pdf format, jpegs, docs, etc, and haven't even put a 1% dent in my 5 gigs. I love that I can use my Drive on my phone, I can drop files into it on my computer and they immediately sync, and I can control the sharing and search-ability of individual files.

Most files translate over to the Google Doc format without too much trouble. Occasionally I'll find a file that gets messed up a little in Google Docs, so those files I keep in their original format, and they count against my storage.

If you don't have a Google account, GET ONE! I use Google for my document storage and editing (when I'm away from home or work), I use Google + to store my photos (this doesn't count against my Drive), and Google offers so many services, not to mention how great Gmail is. I highly recommend Google Drive, the 5 GB for free is a great deal, and the deals on upgraded storage are awesome (25 GB for $2.50 a month is awesome).

Free Online Service For Editing PDF Documents: PDFescape

If you're at all like me, you're constantly coming across pdf documents that contain great resources you want to use in your classroom. The problem is, the rest of the information isn't always great.

Now, I'm not advocating taking someone else's work and editing it, then passing it off as your own. But sometimes, I want to isolate the good pages in a pdf document, and for that, I came across a great web service called PDFescape. It's completely free, and will let you delete pages from a pdf, erase portions of pages, make annotations, highlights, etc. You can then download the pdf you created. You can do all of this without an account, for free. I've used it dozens of times and am constantly going back. It's a great service for the teacher who uses pdf documents.