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.
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.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.
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.
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:
Soooo, I don't want to freak anybody out, but if you live in:
Arizona
New Mexico
Colorado
Oklahoma
North Dakota
Arkansas
Louisiana
Mississippi
Alabama
Georgia
Florida
Tennessee
Kentucky
Illinois
Indiana
Ohio
Pennsylvania
New York
Massachusetts
New Jersey
Delaware
Maryland
Washington DC
You are only a year and a half away from a new state mandated test, called the Partnership for Assessment of Readiness for College and Careers (PARCC from here forward) assessment. That's right, your state testing is about to change, and the change will be dramatic.
What makes this test difference is, well, a few things. First of all, it's computer based. That's right, students will be taking the high stakes test online. Plus, now, when we want to compare data across states, we won't be comparing apples to oranges to bananas. We will be comparing states using the identical assessment. So for those 22 states and DC, greater accountability is at hand.
But don't freak out! It's good news (hopefully). When the PARCC Assessment goes live during the 2014-2015 school year, each of those listed states will be fully aligned to the Common Core (CCSS from here forward).
We're talking about an assessment that will be taken in grades 3-12 by over 25 million students (according to the website).
I highly recommend teachers from any one of those states listed above to go to the PARCC website (which I've linked to twice, you can click the logo or the other link... oh heck, HERE IT IS AGAIN). Start digging through it and see what's waiting for us all right around the bend. 2014 is a lot closer than you think, A LOT CLOSER!!!!
