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!

Our Annual Mesilla Plaza Field Trip

If you teach in Las Cruces, hopefully you're aware of a fantastic historical opportunity right in our own backyard. I'm talking about Mesilla. Mesilla is a window into the past.

Its plaza quite literally takes you back into the 1800s, being more or less frozen in time. If you're like me, and you work close by, you can take free walking field trips over to the plaza area. There are many opportunities available there, including the San Albino Basilica, J. Paul Taylor Museum, and the Fountain Theater, not to mention opportunities like touring La Posta de Mesilla and the Double Eagle Restaurant. Each of these locations offers its own historical opportunities.

Each year, I take my grade level on a short walk from our school to the plaza. We are met on the plaza by Mr. Taylor and the people from the monument that will exist in his house eventually. Our students head off in groups to tour San Albino Basilica, and discuss its history (we strictly discuss the history of the building and the surrounding area, no mention of religion is made during this discussion). Students enter the house of Mr. Taylor, and are taken back through the many rooms of this vast home, which will be a state monument in due time. We also tour the Fountain Theater, the oldest movie theater in the state of New Mexico. Finally, we eat lunch at La Posta, discuss the history of its building, and complete a scavenger hunt on the plaza.

This day is one the kids remember, and one we prepare well for. In 5th grade, we study United States history, so the discussion of the Civil War era height of Mesilla, and the long and storied history of the buildings and happenings in this area fit right in with what we teach.

So this year we will make our way over there in late October. The weather is usually great that time of year.

I realize that this post and the attached document will mean little to 99% of the teachers who read it, but I am putting it on here regardless, even if it ends up being for my own future reference.

What I'm including here is a two page reading about the history of Mesilla, a pdf document you can access HERE, and a 4 page scavenger hunt of Mesilla Plaza, which you can access in pdf format HERE.

The Giver End of Book Collaborative Class Projects

The Giver, by Lois Lowry, is a book I have posted about before, in a book review I did in 2008, and just a few months ago on the pages of this blog, in a post shrewdly titled The Giver, by Lois Lowry: Some Great Ideas for Teachers. 

As of today, September 28th, my class is nearly done with the book. In fact, we will finish the story in just a few more days. When that time comes, I plan on having my class complete a series of projects. The big push in my school district right now is collaborative learning / cooperative learning (something I've always used consistently in my classroom). It is harder to find opportunities for collaboration in reading class, especially as it relates to literature, but I've come up with a little something that is appropriate for the 5th grade classroom, and I call it simply the end of book collaboration projects.

In this, there are five projects that students can participate in. There is a mega triorama display, a collection of art work based on the story, a classroom imagining of the book of rules, advertisements to visit the community we know as "sameness," and the opportunity to re-imagine the ending, or expand upon the ending of the book. 

These projects give students the opportunity to work in their strengths, be it art, writing, or simply thinking creatively. The pdf document that I have created for this project includes a self-check for students to use, and a scoring rubric.

One word of caution here, if your students haven't finished the book, do not show them this document, it includes spoilers that would ruin the ending. This also holds true for you, the teacher. If you're reading this book for the first time, stay away from the document until you're done, I'd hate to ruin the ending for anyone. 

OK, so now for what you came for. To download this document in pdf format, simply click HERE. 

Book Report Idea: Book Report Sandwiches

My students are learning to love to read. I say learning because like so many other students, they don't see the joy in reading when it's been reduced to worksheets, basal readers, and isolated skill work.

I focus on letting my students read silently every day for 20 minutes, and when I do this, I'm reminded of my all time favorite class, 7th grade Literature with Ms. Gossett. This class was very simple, she had hundreds and hundreds of books available. We were allowed to read anything we wanted as long as it was within a year of our level below or higher. That was the whole class, we read and read and read, and produced book reports in different formats when we were done. That was the class that I actually read a novel for the first time, and I was hooked.

It's just sad that I didn't have that experience until 7th grade, and this was an advanced level course. How many students never get this opportunity?

So, to make a long story short, I ask my students to read and find something they enjoy. Of course, it's important to tie this reading into something tangible, in our case, isolated skills taught within the literary experience.

When my students are done with a book, they must produce a book report of some sort. I recently come across a great format that my entire class is "eating up," and that is the book report sandwich. This gives you the different areas of the report as bread, lettuce, tomatoes, etc., and each different ingredient of the sandwich. As I said, I came across this and can take no credit for it. I found this idea on the website for Mystic Valley Regional Chart School, and you can access this great .pdf file, it is called Sandwich Book Report. The document contains the necessary papers you would copy to make the sandwich, in both color and black and white, a scoring rubric, and some rough draft pages with prompts. It's excellent stuff!

Completed 50 State Project State Strips

My class just finished their state projects, called State Strips. You can find the information on this great research project on two posts I've done, both Teaching the 50 States, and 5th Grade State Research Project: State Strips. You can access the project guidelines for this great research project here (pdf format or docx format). 

Now that the project is completed, students have also taken the time to present their posters in class. I had students prepare a 1-2 minute long speech in which they taught other students about their state. The exemplary posters were then posted in the hallway. My students love seeing their work in the hallway (and on this blog), so I'm going to show some of the great examples below. Click on any image to see a larger version.