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 Numbers and Operations in Base Ten CCSS Strand

I have completed pages of resources for all of the 5.NBT standards, which I have linked to below. I hope you find some great things you can use in your classroom. Everything I list is freely available online, no cost stuff only!

• 5.NBT.1
• 5.NBT.2
• 5.NBT.3
• 5.NBT.4
• 5.NBT.5
• 5.NBT.6
• 5.NBT.7

You can also see these listed on my Math School Year Outline (CCSS aligned).

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:

5th Grade CCSS Math School Year Outline

The 5th Grade Common Core State Standards (CCSS) are laid out in the following sequence in my school district: (this is my main listing that will link to a page for each standard. Be on the lookout for assessments, which are grouped in 2 week blocks for the most part)

THIS PAGE IS UNDER MAJOR CONSTRUCTION, SO BOOKMARK IT AND CHECK BACK OFTEN!

1st 9 Weeks:

• 5.NBT.1
• 5.NBT.2
• 5.NBT.3
• 5.NBT.4
• 5.NBT.5
• 5.NBT.6
• 5.NBT.7

2nd 9 Weeks:

• 5.NF.1
• 5.NF.2
• 5.NF.3
• 5.NF.4
• 5.NF.5
• 5.NF.6
• 5.NF.7

3rd 9 Weeks:

• 5.OA.1
• 5.OA.2
• 5.OA.3
• 5.MD.1
• 5.MD.2
• 5.MD.3
• 5.MD.4
• 5.MD.5
• 5.G.1
• 5.G.2
• 5.G.3
• 5.G.4

4th 9 Weeks:

• 4th 9 weeks is set aside for review (the scope and sequence in my district was written so that all standards could be taught before the administration of the PARCC). 

5th Grade Math Resources for CCSS 5.NBT.2

5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

UNPACKED EXPLANATION:  This one is fairly straight forward. This standard is commonly known as "the powers of 10," so keep that in mind. It's all about base 10 and understanding that you're multiplying by ten each time you move to the next larger place value, with an understanding of the opposite function of adding a 0, which is removing a zero, while understanding conceptually that removing a 0 means the decimal point has moved a place to the left. Finally, exponents are a great way to have students denote these relationships, and starts building upon skills they'll use a lot further on down the road.

WHAT THE PARCC WILL EXPECT: The PARCC Practice Test site does not have specific problems for 5.NBT.2, but when looking closer at this standard, students will need to be familiar with problems that resemble the following:

• 34 x 10,000 =
• 90,000 ÷ 30 =
• 0.00034 x 10,000 =
• Check out this collection of videos from LeanZillion that explains the entire process of powers of 10.

RESOURCES

• First off, a lot of the things I referenced in my post for 5.NBT.1 are relevant to this standard as well. So check that out: 5th Grade Math Resources for CCSS 5.NBT.1.
• Some practice problems at Orglib.com: This is a great site where you can make an account, build tests from a bank of questions, and even track student results. It's one of the closer things I've found that can mimic the PARCC assessment. 
• Even though it's in my last post, this is a spot on activity for this standard:
• Place value cups (click the link for instructions): This simple activity is very concrete for kids, and if you keep a few handy, they're good for reference later in the year for students who didn't retain everything they learned during the teaching of 5.NBT.1.
• Powers of 10 Yahtzee: Although I linked to the Google Doc here, I'll go ahead and explain this game in my own words: 
• Power of 10 Yahtzee should be played in pairs. Students should already have an understanding of exponents and how to navigate a place value chart. Each player is going to roll the dice. Whatever number player A rolls they will put it as an exponent to the base number 10 (if they roll a 4, they will be finding the product of 10 to the power of 4, or 10,000). Then player B goes. They do this 5 times, and add up their totals, whoever has the highest total wins. A more rigorous extension of this game for the advanced student would be to have each student roll two dice (preferably different colored dice would work), and have one color be the base number and the second be the exponent). 
• IXL Listing of Problems that Fit the Standard
• The following listing is for worksheets:
• Mathworksheetland.com 5.NBT.2 Listing: A great starting point. Why make your own worksheets when there's already practice stuff out there. If you know how, you can send these right to an iPad and have kids do some practice there, or print them out.
• Mrmaffesoli.com Printables: I use these, good stuff for sure.

Vocabulary

I'll list a few sites that have good 5.NBT.2 vocabulary. I can't really even begin to say how important it is to teach students not only what academic vocabulary words mean, but how to use them in context. There's a lot of power in having students state their reasoning academically that goes beyond testing and helps reinforce the ideas they're learning about.

• A great pdf at what's a great go to resource for vocabulary, duplinschools.net. 
• UEN.org resource file with vocabulary.

5.NBT.2 Video

The first two videos are of Khan Academy explaining both multiplying and dividing by powers of 10:

Multiplying by Powers of 10

Dividing by Powers of 10

Lastly, the STEM teacher in me can't resist putting up this video that explains what exponential growth is really all about in a scientific regard. I give to you now, Cosmic Voyage, narrated by Morgan Freeman:

5th Grade Math Resources for CCSS 5.NBT.1

5.NBT.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

UNPACKED EXPLANATION: We're basically talking about place value, with an explicit focus on what it means to move up a place and down a place. Within this domain, students will be expected to work with numbers from billions to thousandths. A big pitfall here is to start adding and subtracting these numbers together. The reality here is an understanding of the place value system, and what it means concretely to move between the place values.

WHAT THE PARCC WILL EXPECT: The PARCC samples are taken directly from the PARCC Practice Tests website.

The sample for 5.NBT.1 is as follows:

When you click on the drop down "Choose..." box, you're given something similar to the following:

Teaching Grit and Rigor in the Classroom: Validating Everything I Do

OK, well it's been a long hiatus from the blog (7 months actually), but I'm back. This year has been a difficult one, with implementing the Common Core, and dealing with a lot of changes in my school district, but I am happy to say that I'm finding more time to get back to my passions, one of them being this blog... So, with that being said, let's move on.

This morning on my way to work, I listened to a great piece on NPR called "Does Teaching Kids To Get 'Gritty' Help Them To Get Ahead?" The article goes on to explain that a child's grit (determination, the willingness to fight on and never give up) can actually be a better predictor of success than can IQ score or standardized test scores. But it also states that it can be hard to implement strategies to teach 'grit,' that it seems to be an inherent trait that certain kids have and certain kids don't.

Yet, I've been stuck thinking about this all day. Every teacher deals with the kids who give up easily. We've all heard the 'this is hard, I quit' mentality that plagues so many children in our world today. Actually, those kids have probably always been there, and it can be easy to see them not being successful as they get older. After all, what is college all about? More than anything else, college tests your ability to do something for many years, dealing with tons of ridiculous garbage, bureaucracy, and politics, and finally get a degree and a job. College is all about grit and self-drive.

In the article, Jason Baehr, a philosophy professor at Loyola Marymount University says the following:

"But I'll say from our experience in the school, I see [kids learning to be grittier] all the time. ... You can create a classroom culture in which struggle and risk-taking is valued more than just getting the right answer."

I made a challenge to myself this year, well a few actually, but what it came down to was creating a classroom focused on process and not product, struggle and rigor and not just right answers and policy. Overall, I feel validated, I feel that my students have shown a greater ability to problem solve, to persevere, and to challenge themselves than ever before in the past. Of course there are the exceptions, as with any class, but I feel that I'm finally coming into my own and creating a classroom culture that demands grit, and I want to grow that.

This article is spot on the way I feel about education at this point in my career. We can discuss hands on learning and investigative approaches, project based learning and strategies to instruct in literacy and math all day and never come to a consensus. But what we need to do is realize that not every child is going to persevere, especially in a subject they aren't passionate about. What we can do, however, is train kids to fight, and deal with their frustration in a constructive way. After all, school isn't supposed to be fun or easy. It's supposed to challenge students, to make them think, to make them frustrated, and to learn to think outside the box. Rigor, relevance, and a classroom focused on the active struggle is a great start. Please read or listen to the article, if you missed the link above, here it is again:

Does Teaching Kids To Get 'Gritty' Help Them To Get Ahead?