5th Grade CCSS Math Vocabulary by Domain

In all my searching around the internet, I have had a difficult time finding vocabulary for Common Core listed by domain. So, with the help of some resources and my own notes from last year, I made the following list:

5th Grade CCSS Math Vocabulary by Domain

• .docx format
• .pdf format

Here is some great math vocabulary words in .pdf format that are word wall ready (my favorite list out there)

Full List of Words (for reference)
A-L word wall ready words
M-Z word wall ready words


More math vocab cards

PDF Listing of math vocabulary words

5th Grade Math Resources for CCSS 5.NBT.7

5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

UNPACKED EXPLANATION: Do computations with decimals in all four operations, being able to relate work to models or drawings, and utilize strategies based on place value, properties, and the inverse relationship of addition and subtraction. It's the culmination of the entire NBT strand.

WHAT THE PARCC WILL EXPECT: I've said it before and I'll say it again. The practice test hasn't, in my mind, done justice to how difficult the actual PARCC test is. So my advice is to make sure this standard, as all others, is taught to the letter of what's being asked. The practice questions are a straight forward .035 x 1.5 and 5.63  + 14.37, which aren't that difficult. So just go ahead and hit the depth of the entire standard, I think it's the best way to go.

RESOURCES:

• Math Worksheet Land Worksheets
• Mr. Maffesoli.com Worksheets on 5.NBT.7
• A couple of great word problem pdfs: Diminishing Return and Got Your Number.
• EngageNY full module: This huge document can be a little cumbersome, but if you do a search on the standard 5.NBT.7 then you'll find a few great problems and scoring rubrics here. 
• 5.NBT.7 games

5th Grade Math Resources for CCSS 5.NBT.6

5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

UNPACKED EXPLANATION: 4 digit by 2 digit division with strategies that involved an understanding of place value relationships (as in moving that decimal place to the left and right), understanding that division is the opposite of multiplication, and understanding the properties of the operations involved. Finally, students should have the ability to explain their calculation visually. 

WHAT THE PARCC WILL EXPECT: I'm not sure if many teachers out there have looked in depth at what the PARCC has to offer, but I have to say that I'm not very impressed in a lot of ways. If you look at this standard, it's really sophisticated in what it expects out of students. Not just the ability to divide, but the ability to elaborate on their calculation and process is important. Well, then there's the PARCC question, here's a screenshot of what the PARCC asked for 5th graders to do:

Yep, here it is. The point I'm trying to make here is if you go to the depth of understanding that 5.NBT.6 asks of you to go with your students, they'll have no trouble handling the low level, low quality type of question being asked of them on the PARCC assessment (I know that's a fairly brutal and straightforward critique, but that's how it is with this).

PARENT HELP: I discussed having parents help with basic multiplication and division practice at the beginning of the school year in my 5th Grade Math Resources for CCSS 5.NBT.5 post, and will elaborate on that here. 

If you set aside the initial.... six weeks or so of the school year for parents to help their children at home reinforcing basic multiplication and division facts, it can save you a lot of time in the classroom. I haven't met a 5th grade teacher in the all the world who doesn't lament the fact that a good percentage of their students don't walk through the door on the first day with fundamental math facts down, mainly multiplication facts and standard algorithm, as well as the ability to divide with the standard algorithm. So here's some resources that can be utilized for that purpose:

BASIC SKILL PRACTICE:

• ROCKET MATH: Rocket Math offers 1 minute timings (you can read more on that in my 5.NBT.5 post under basic skill practice). Here are some division sheets in ORIGINAL FORMAT and in NEW FORMAT. 
• GAMES:
• Fun 4 the Brain Division Games: A great listing with some pretty neat games that practice basic division facts. 
• Math Playground Division Games: Some neat games that will help kids in need of a little practice.
• WORKSHEETS: 
• Math aids.com listing: I like the offerings here, lots of great basic division practice. 
• Math drills.com listing: You can't go wrong here, there are tons of choices.
• Common Core Sheets listing: Again, tons of choices and variations available here. 

ADDRESSING 5.NBT.6 WITH RIGOR, SYSTEMATICALLY: Once students have basic division facts down (fact families basically), and can function within the standard algorithm, it's time to start talking about how to handle those remainders. By 5th grade, they shouldn't just be putting an "r" and writing the remainder next to it, they should either take that remainder and make a fraction with remainder in the numerator and divisor in the denominator, or continue on by using a decimal in the quotient (I like my students to keep going to the thousandths place if necessary). 

Long division with the remainder as a fraction

Long division with decimal remainders

DIVISION WITH FRACTIONAL REMAINDERS:

• WORKSHEETS:
• Math aids.com: Why go elsewhere when it's right here.
• Dads worksheets.com: Tons of results here, there are many possible worksheets you can use.

DIVISION WITH DECIMAL REMAINDERS: (there are some options at the links immediately above this as well)

• Math is fun.com example: Kids can open this on an iPad or computer to get a very detailed example on how this works. 
• Khan Academy Dividing Completely to Get Decimal Remainder: I used this lesson in my class to some good results, it was a flipped lesson and students really understood what he was showing them.

5th Grade Math Resources for CCSS 5.NBT.5

5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

UNPACKED EXPLANATION: What more is there to say here? Multiply using the classic method known as the standard algorithm. The key here is the world "fluently," which means students need to be able to do this quickly and with skill. 

WHAT THE PARCC WILL EXPECT: The PARCC practice test that is currently out there has three problems that are 5.NBT.5. This is a 36 question test, so realizing that a full 8% of this test is based on this one standard, that should show us all that this is a HUGE standard. Of course, this shouldn't be a surprise. The ability to multiply fluently is a foundational math skill, and should be something students are practicing and reinforcing all year long.

The PARCC practice problems are: 

463 x 1,945 =

371 x 2,584 =

625 x 847 =

So, considering that this is a huge standard, let's discuss a few approaches: 

PARENT HELP: Multiplication and division with the standard algorithms are HUGE HUGE HUGE skills that can't be taught in a two or three week period. They need constant practice throughout the year. One way I like to do this is by involving parents. From the beginning of the school year, I send home multiplication and division practice as homework for the first few months. This gets parents involved, because even though many parents struggle to help their kids with the more rigorous CCSS based math stuff, they can provide support when it comes to multiplying and dividing. I also try to focus on basic skill checks through the first few months. Too many 5th graders don't have their basic multiplication facts down, so let's hit this standard from bottom to top.

BASIC SKILL PRACTICE:

• ROCKET MATH: If you don't know what Rocket Math is, it's 1 minute timings that students try to complete and move up a rocket chart. Teacher directions are HERE, and the timing sheets are HERE (the classic ones that I use because they're the ones my school has, and some newer ones that I don't like as much but they are out there HERE). These are good to send home, and have parents do the timings at night for practice, and then do some timings in class. I have a good system going with these and can do a full timing, and have everything put away within 3 minutes. It's good and quick practice for basic skills, which are necessary. Students can't multiply fluently if they're constantly doing multiplication on their fingers.
• Games: I could list literally thousands of different basic fact games, but instead, just go to Google and search for basic multiplication fact games and you'll see for yourself. I'm going to focus on a few of the best here. 
• Multiplication.com Games: A large collection of games that reinforce facts. I put this link up on my classroom webpage for students to use at home.
• Times Table Games: A decent listing of some basic facts games.
• Worksheets: Here's some basic facts worksheets to get you started.
• Tons of sheets in one pdf file.
• Create your own basic facts worksheets at The Math Worksheet Generator.
• Worksheet Works worksheet generator:  Good stuff here!

ADDRESSING 5.NBT.5 WITH RIGOR: Let's move beyond basic skills into mastering this skill and really starting to push students abilities with the standard algorithm.

• Mr. Maffesoli.com Listing: Mostly 2 x 2 multiplication worksheets in pdf format. 
• Internet for Classrooms.com Listing: Has 2 x 2, 2 x 3, 2 x 4, etc. 
• Mathaids.com Worksheet Builder: Build some algorithm based problems here and download as pdf. 
• Mathdrills.com Worksheet Listing: Many worksheets that address the standard algorithm. 
• CCSS Math Internet Resources: Worksheets, videos, interactives, etc.
• WORD PROBLEMS:
• Mr. Nussbaum Story Problems: 10 examples exist here. 
• A few rigorous multi-step multiplication word problems
•  Multi-step Multiplication word problems from superteacherworksheets.com: It's usually not a free site but this is a free pdf.
• Math-aids.com build your own two step multiplication problem pdf sheet.
• Helping with math.com listing: Some decent and challenging word problems exist here.
• Full module from engageny.org: Do a 5.NBT.5 search in this pdf and find a great listing of some highly rigorous problems, some warm ups, and even some rubrics and scoring samples.
• Lessons for Learning: A large pdf document provided by the Public Schools of North Carolina, I found some great and rigorous word problems here.

5th Grade Math Resources for CCSS 5.NBT.4

5.NBT.4: Use place value understanding to round decimals to any place.

UNPACKED EXPLANATION: Round decimals to either tenths, hundredths, or thousandths, although strategies and skilled learns should apply to any place.

WHAT THE PARCC WILL EXPECT: The PARCC Practice Tests question for 5.NBT.4 tests students ability to round decimals without a given context (without telling them "round to the tenths place," etc.). The actual problem is:

The PARCC does this quite a lot. There are 6 numbers that can be dragged, meaning that two numbers will be left behind, so the traditional test taking strategies, especially process of elimination, won't be as effective here (although it still helps). Students will need the ability to do exactly what's laid out above, to be able to match numbers to their rounded counterparts, and do it without context.

RESOURCES: I'll focus on resources that cover all the components of this skill. You'll likely want to start with doing a lot of rounding with context, and eventually move to the more rigorous side of this standard.

• ROUNDING WITH CONTEXT:
• Short explanation before some rounding of specified digits
• 4 page packet that rounds with context
• Mathworksheetland.com lesson outline: It's all context based rounding here. 
• Massive listing of worksheets from internet4classrooms.com: Tons and tons of context based rounding sheets, I mean TONS.
• Assessment for 5.NBT.1-4: Actually some decent problems here.
• GAMES
• Rounding decimals soccer
• Scooter Quest
• ROUNDING WITHOUT CONTEXT: There's not a lot out there for rounding decimals that leaves no context. My advice here is to look at the PARCC problem above and craft some problems that are similar to it, this ensures students are getting rigorous problems that make them problem solve and think. I highly recommend going to that level if possible,
• Performance assessment task from insidemathematics.com: Look through this document for a few rigorous problems with scoring rubrics. They could be used for practice or even incorporated into assessments. 
• Iowa released test items: Released items from the old NAEP test that are now aligned to CCSS (interstingly enough, a lot of these problems were originally meant for 7th and 8th graders). Search the document (ctrl+f) for 5.NBT.4.

5.NBT.4 VIDEO:

5th Grade Math Resources for CCSS 5.NBT.3

5.NBT.3:  Read, write, and compare decimals to the thousandths.

(a) Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

(b) Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

First of all, this standard has two parts. We will first focus on part (a) of the standard:

5.NBT.3a

UNPACKED EXPLANATION: To put it as simple as possible, this part of standard 3 asks students to write the expanded form of numbers, fractions included to represent tenths, hundredths, and thousandths. 

WHAT THE PARCC WILL EXPECT: Just like 5.NBT.2, there are no performance tasks for 5.NBT.3 (a or b). So, the best approach to take here is to use these standards to prepare students for the more rigorous work that lies ahead later on in the NBT domain. If your students can accurately write standard, word, and expanded form of numbers that go to thousandths, they'll be fine on this standard. It really is a simple one that can be tied to some other standards as well.

RESOURCES: Again, this will be fairly straight forward. If you teach in sequence (and there's really no reason you shouldn't with this domain, it's already laid out that way), then your students will already have a good understanding of place values in the base ten system, making this the next step.

• Adjective/Noun Theme: As someone who has been through a full round of Intel Math training, I fully believe in and utilize many of their strategies, including adjective/noun theme. The a/n theme has been around long before Intel, but is very conceptual and powerful when students learn to utilize it. HERE is a document that explains adjective/noun theme in the four operations. And HERE is another document on adjective/noun theme with decimals. The basic premise here is that numbers are adjectives that describe nouns. You can't add together two unlike nouns (you can't add together 4 dogs and 2 cats without some sort of combining of nouns). So if it's 45 hundredths + 8 tenths, we have to do some converting to get 45 hundredths + 80 hundredths, and then we add the adjectives to get 125 hundredths. It's a simple yet effective way of teaching this stuff that is conceptual and leads to long term retention of learning. 
• Some worksheets and pdfs:
• mrmaffesoli.com 5.NBT.3a worksheets: A listing of some great 5.NBT.3a worksheets, there's quite a few here.
• Common Core Sheets: There's a pretty large listing here.
• Internet 4 Classrooms 5.NBT.3a: Wow, there's TONS here. 
• GAMES:
• Mathman: A Sheppard Software game, very simple and straight forward Pacman style game that reinforced expanded form, although it might not go as far as decimals. It's good practice for kids struggling with their expanded form of numbers. 
• Fruit Shoot: Another Sheppard Software game. If you play the harder levels it's a spot on match for 5.NBT.3a.
• Walk the Plank: A game from mathforchildren, it's funny and kids enjoy it.

5.NBT.3a VIDEO: This is a Khan Academy video that discusses expanded form with multiplication, pretty much as stated in the CCSS. 

5.NBT.3b

UNPACKED EXPLANATION:  Compare two decimals to thousandths using inequalities (<, >, =). 

WHAT THE PARCC WILL EXPECT: Again, this standard is not included on PARCC practice exams. This is a pretty important standard for students to master, however, because it allows them to show mastery over comparing decimals, understanding place value, and even the ability to properly complete inequalities. So let's just go from there.

RESOURCES:This standard is almost identical to the inequalities standard that many states already had in place before the Common Core, so anything you, as a teacher, already have prior to CCSS (if you didn't trash it) would work great here. Here's a few online resources:

• orglib.com questions library for 5.NBT.3a and b: There's not a lot of questions here, but what they do have are to the point and would probably be what it would look like on PARCC. 
• Collection of lessons from mathworksheetland.com for 5.NBT.3b (some 3a stuff is in here as well).
• mrmaffesoli.com 5.NBT.3b worksheet resource page: Yet again, some great resources. Go ahead and bookmark this site, it's golden for everything CCSS.
• Common Core Sheets: Same as above for 3a. Good stuff, with many different versions of worksheets available. 

GAMES:

• Balloon Pop: A simple yet great game for ordering decimals. It's a challenge, but students are sure to enjoy it.
• AAA Math Comparing Decimals: It's more like an online practice test than a game, but it really works well. 

5.NBT.3B VIDEO:

Daily Math Challenge: Upping the Rigor in Mathematics Instruction

All teachers (should) follow lessons plans and unit plans in order to make their instruction cohesive and make sense. I'm not going to get into all the aspects of following scaffolded, developmentally appropriate lesson plans, but if you're "winging it" everyday in the classroom without a clear focus, don't expect a lot of learning to take place.

The point of this post is taking a little timeout in math everyday to let students think and work through challenging, rigorous problems without an immediately evident solution. I call this activity "daily brain work," and it takes 10 minutes. The intent here is to pose a problem to the class, and to step away and let them work through the problem on their own. Students should be able to elaborate and articulate how they reached their solution. Finally, go over the problem, have some students share their answers, and hopefully at least a few have the correct solution to share.

In order to get started, I needed some multi step story problems. Don't start too difficult, and make sure that everything you give students is developmentally appropriate for the majority of the class.

Here are some resources to find multi step word problems and other math puzzles / brain workouts:

Math Multi-Step Word Problems

• 25 Word Problems at IQ Study Activities: A good starting point to find some straight forward story problems appropriate for 5th graders.
• A Few Pages of Story Problems at about.com: Nothing fancy, just some more story problems.
• Helping With Math Word Problems Guide: A page with some information on how to help students approach open ended questions, and a bank of questions as well.
• Challenging Word Problems at Math Top 10: Good stuff here, there's a lot of them too.

Brain Teasers / Math Puzzles

• Houghton Mifflin Grade 5 Brain Teasers: A nice little collection of word problems and brain teasers already set into CCSS categories.
• Math Salamanders Printable Math Puzzles: The whole salamander theme is a little bizarre, but there's a lot of good puzzles here. 

Measuring Capacity Resource: Gallon Man and Capacity Visual

First off, I apologize for the long delay in posts. It's been a busy last month or so. We had our state No Child Left Behind testing a few weeks ago, then we had Spring Break, and finally I'm back. It was a whirlwind, but it's done, and now we can get back to business.

Currently my 5th graders are studying measuring, including measuring tools, one step conversions, and the various categories of measurement. I'll be posting unit plans for the Measurement unit soon (in New Mexico Standards and Benchmarks format, Common Core units will be coming over the summer).

For today, I wanted to share a resource that has served me well when my students are learning about capacity, and this little pdf document includes two visuals for working with US unit capacity (volume), including the relationship between gallons, quarts, pints, and cups.

The document includes this little visual:

It also includes this one:

They're both ready for printing and use in the classroom.

This document comes thanks to The Teacher Website, and is hosted there:

MR. GALLON MAN PDF

Polygon Practice Mega .pdf Document of Great Practice Pages for 5th Graders

I recently published 5th grade math unit 3: Area, Perimeter, Volume, Prisms, Pyramids, Polygons, and Circles. It's a huge unit that involves a lot of vocabulary and targeted skill practice. You can see that unit listed in my Math 9 Week Plans, in its own Unit Page, and in the more popular post titled 5th Grade Math Unit: Area, Perimeter, Volume of Prisms and Pyramids, Polygons and Circles.

I scoured the internet over the last couple of evenings, downloading pdf documents of practice pages that could meet my students needs. Currently, we're working on getting the vocabulary up for unit 3, and it's a huge task that involves over 30 definitions that are necessary for understanding and success in these skills.

I took the best of what I found in freely available online pdf documents and created a mega document that is 49 pages long and 1.4 megabytes in size. It's the practice pages that I'm intending on using during these upcoming weeks, and I believe that it could be of service to any teacher teaching these skills.

To download the document, which is available through my Google Drive, click:

POLYGONS MEGA DOCUMENT DOWNLOAD (pdf)

5th Grade Math Unit: Area, Perimeter, Volume of Prisms and Pyramids, Polygons and Circles

5th grade math unit 3 (which you can see listed in my subject specific page for MATH) is a huge unit. It covers area and perimeter, the volume of rectangular prisms and pyramids, polygons up to ten sides, and circles. The main bits of this unit get down to the vocabulary, practical application of the necessary formulas, and conceptual understanding of each concept.

The unit is available at its own page HERE, and is also posted here in its entirety. So without further delay:

5th Grade Mathematics Unit 3 is all about 3-Dimensional Geometry, including Area, Perimeter, Volume, Attributes of Polygons up to 10 sides, Circles, and Parallel / Perpendicular Lines. It's a big unit, but we always manage to pull it off with pretty good results. So let's get right to it!

Unit 3 is split into three portions:

UNIT 3.1: AREA & PERIMETER

The first portion of this unit is very simple, it's all about area and perimeter. We spend the majority of the time doing area and perimeter of quadrilaterals (especially area), but it's also a good opportunity to refine measuring skills by going outside, in the hallway, or measuring the classroom.

The assessment that I use for this cycle of instruction is very simple, and can be found HERE.

The PDSA (again, it stands for Plan/Do/Study/Act, and is the current form of lesson planning that my school does) can be found HERE.

Now that the nuts and bolts are out of the way, I'm going to list some great online resources that could help any teacher out in the classroom when teaching area and perimeter:

First off, I have already done a fairly lengthy post on Area & Perimeter, titled Area & Perimeter Teacher Resources: Worksheets, Games, and Activities.

• Interactive Shape Explorer: A Java based activity that can range from very easy to quite difficult. 
• Area & Perimeter Formulas: I'm printing this out and will use it with my more advanced students to study formulas and their relation to geometry.
• PBS Kids Cyberchase Airline Builder: An interactive game involving area and perimeter. 

And to repeat some of what I've already posted:

BEGIN THE UNIT WITH AN EXPLANATION:

• Perimeter and Area Visual Explanation: An Adobe Shockwave presentation that introduces the unit. Smartboard friendly.

ACTIVITIES:

• Interactive Shape Explorer: A nice interactive where students find the perimeter and area of various, randomly generated regular and non-regular polygons on a grid. Optionally, the teacher can ask students to copy the shapes on graph paper and solve there.
• The most simple classroom activity is to have students measure the dimensions of the classroom, a chalkboard, the hallways, their desk, etc. Then use those dimensions to find perimeter and area (and later on, volume). 
• Everything You Wanted to Know About Perimeter and Area: Go to pretty much any resource listing on perimeter and area activities, and you'll probably find a link to this one. There's a reason for it, it's simple and effective. It's Smartboard/projector friendly for whole class, and teaches as it goes.

GAMES:

• Cyberchase Airline Builder: An online game where students must use the given amount of sticks to create different polygons. 
• Zoo Designer: I wasn't impressed with this game at first glance, but played it for a few minutes and actually see some value in using this in class. This one is also web based.
• Real Estate and Perimeter Game: I found that at the blog Homeschool Parent. It's a good idea for a very effective in class perimeter or area game. I'll be using this, my students always enjoy the partner games.

WORKSHEETS:

• A to Z Teacher Stuff Area & Perimeter Worksheets and Printables: Decent, but not very difficult, worksheets to use in class. A good starting point.
• The Grid Game: This is a 4 page printable, I will be using the last page (the grid game), and possibly the page before it (perimeter patterns).
• Worksheet Works.com Worksheet Designer: A nice, easy to use tool that gives you worksheets in pdf format based on your needs.
• Large Worksheet Packet: What I like about this packet is it has a table at the beginning that names many types of triangles and quadrilaterals. If anything, I'll be using that first page.
• Free Math Worksheets: A decent page with some good worksheets in a lot of different skills. 
• Measuring Perimeter & Area: An adapted worksheet packet that has some good skill building activities within a pdf document.
• Math-Aids Perimeter and Area Worksheets: A good site with various worksheets, fully customizable before printing.
• Illuminations site: There is a worksheet about finding perimeter and area, and an online geoboard.
• A full supplement pdf from Bridges for Mathematics. There's good information here if you have no curriculum to start with.

UNIT 3.2: VOLUME OF RECTANGULAR PRISMS & PYRAMIDS

I've always enjoyed teaching volume, because it just makes perfect sense right after teaching area, and it's fun and the students usually enjoy the process.

Let's get started with the assessment, which can be accessed HERE (you'll need to download it to see the attached images, they don't seem to show up in the Google Doc preview), and the PDSA, which can be accessed HERE.

First, I'm going to list some basic volume of rectangular prism (and just general volume) links:

• A great interactive lesson for volume: Has instant feedback, and it's very clean looking.
• Math Illuminations Interactive Cube Builder: I love this interactive because it lays the cubes out flat (something that I've seen referred to as a "net"), which is also how we practice this in class, by building boxes and filling them with cubes. 
• A simple pdf poster from Scholastic on volume
• Interactive Formula Teacher: It's good stuff

Now, my favorite volume activities include making cubic units. I usually have my class use rulers to make a cubic foot, yard sticks to make a cubic yard, etc. I'm not even going to show a picture here, because all you do is use the given unit to make a cube. It's pretty cool and effective.

It's also important that students know how to use the units. I count off if students don't label units, and don't use them appropriately. I teach my students very simply that for a unit to be squared, it has to involve 2 dimensions, cubed involves 3. Here's a simple visual:

I also think it's important to expand and reinforce these concepts when applicable. My students always enjoy the EXPONENTIAL GROWTH activity, where we build some cubes, starting with a 2x2x2, going to a 4x4x4, then an 8x8x8, it looks like this:

Now on to the more difficult volume of pyramids:

It's actually very simple to find the volume of a rectangular pyramid. First, take the three measurements (length, width, height), and multiply. Now here's the catch: divide your answer by 3. That's it. The majority of the work here is getting students to understanding this 3:1 relationship, and practice it.

• A pdf document of a pyramid you can have students cut out and use to show the 3:1 relationship.
• Simple Explanation of the v=(l x w x h) / 3 formula (aaamath.com).
• Worksheet Works customizable worksheets on volume, area & perimeter.
• Various worksheets on volume at mathworksheets4kids.com

In my opinion, these first two sections of the unit go hand in hand, and are fairly simple for 5th graders to get once they grasp the concept. And the concept is important, let them experiment with 3D shapes (make them out of paper and fill them up with sand or rice). These are more or less developmentally appropriate skills for the vast majority of kids at this age level. 

Now, we move on to the final portion of this section on volume of pyramids, where we discuss the attributes of three-dimensional shapes, including vertices, faces, and edges. 

We're basically talking about vocabulary for this final section, so that's how I approach it. Let's move right into it:

• Geometry attribute vocabulary cards at Quizlet: A great starting place to get ideas or have kids practice for reinforcement.
• A great online resource that is clickable and shows the vocabulary: Good for Smartboards.
• A GREAT resource at Teaching Ideas: Posters for the shapes and attributes, and great downloadable resources. 
• Primary Resources has this page of TONS of great resources, including this properties page I'll be using.

So now we come to the finale of this lengthy unit, a set of lessons on polygons (up to 10 sides), and circles. The circles part especially tends to rock the kids around for a bit. 

UNIT 3.3: POLYGONS UP TO TEN SIDES & CIRCLES

Here we go, let's get started with the assessment HERE and the PDSA HERE.

First we'll deal with the polygons, because again, it comes down to vocabulary and practice (i.e. memorization and matching):

• A page with enough information about polygons to get any teacher started. Go here and grab the definitions you need to move forward. 
• Polygon Names: It is what it says it is.
• Polygons: Regular vs. Irregular.
• Some decent naming polygons worksheets (with some other stuff that would be review at this point).
• Another worksheet, this one about regular vs. irregular polygons.

OK, now we finally come full... circle (haha... nevermind). Anyways, students will learn radius, diameter, circumference (and all applicable formulas), as well as the value of pi to two places. 

The pi part again comes down to repetition and memorization. So, I came up with the now irreverent "PI MONKEY," a mainstay in my classroom. He hangs up near the front door, beckoning to the students each time they walk out the door:

Now that pi monkey has done his job, it's time to teach some circles!:

• Definitions at Coolmath.com: You need these, they get it all started. Students can review right here on the page.
• A great PowerPoint from Mr. Lovett on Wikispaces about circles.
• Some Visual Aides at Mathworksheetsgo.com.

Remember that circumference is simply pi multiplied by the diameter (or pi multiplied by the radius x 2): It looks like: C= pi x d  OR C= pi x (r x 2). It's fairly straight forward. 

OK, we've reached the end, FINALLY. Now that we're here, it's time for the big unit test. You can grab that HERE.

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 Great Collection of Simple Online Fraction Games (GCF and LCM Included)

Of the 80 blog posts I've done, it's not even close, the most popular post is 5th Grade Math Unit 4: Fractions, Decimals, and Percents (as well as its standalone counterpart). It's obvious that fractions, decimals, and percents are a major skill of great importance in the 4th and 5th grades.

This evening, in my web browsing, I came across a collection of 11 fraction games on a website called Jamit, which does software for use on most SmartBoards (since there are so many variations out there, like Prometheans, Mimios, etc.).

The games are simple, but the premise is the same. They help with fraction skills, from basic skills to multiplying and dividing fractions. My current use, as I'm in Unit 1: Factors, Multiples, Multiplication, and Division, is the game on GCF and LCM (Greatest Common Factor and Least Common Multiple).

I recommend the collection of fraction games on Jamit because they're simple, they work on a SmartBoard or similar device, and they reinforce the content effectively. Give it a look!

Illustrative Mathematics: A Great Resource To Help in the Transition to Common Core Standards

In my most recent web surfing, on Richard Byrne's Free Technology for Teachers blog, I came across a post  called Illustrative Mathematics. After looking into Illustrative Mathematics (this link goes to that site) a little more, I really like what I see. For each grade, K-12, you can see illustrations of what each common core standard is all about and how to utilize it. The image below shows the menu that comes up when you click on K-8 Standards at the main page, with a box around 5th grade. Any standard that lines up below fifth grade is clickable for more information. It's really a great resource if you're transitioning to the common core. In the state of New Mexico, we still have one more year in 4th and 5th grades before we move to the common core, but we're already hard at work aligning our content to make our work easier come this time next year.