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!

5th Grade Math Unit 4: Fractions, Decimals, and Percents

5th Grade Math Unit 4 is on Fractions, Decimals, and Percents. This unit is pivotal to the 5th graders future success, especially as this group of skills is seen as very important to their understanding of algebra in middle school.

This unit is placed within my static pages (the link is above). As always, I am placing that entire page here for convenience. I hope you find it helpful:

Math Unit 4 in my 5th grade class is focused mainly on fractions, decimals, and percents. In many conversations with 6th grade teachers, I am often told that if their incoming math students know only two things, it needs to be basic multiplication and division facts, and the ability to work with fractions. This is the unit that we start on coming back from Christmas break, and it carries for an entire month. Of course, the teaching of these skills begins early in the school year through daily math practice and consistent math homework as well.

This upcoming school year, we have drawn out the following schedule (our entire math schedule for the 2012-2013 school year can be accessed in .doc format HERE):


January 9 – January 18: Equivalent fractions, decimals, and percents
January 22 – January 30: Compare and order fractions
January 31 – February 8: Add and subtract fractions

When viewing the document for the entire school year, you can see that "unit 4" includes the data unit as well. This was done for our own purposes, but for the purposes of this blog, I have kept these two units separate.

Each one of the skills listed above constitutes what we call a "cycle," according to our Plan-Do-Study-Act (PDSA) format of data analysis and collection. I will list each cycle separately below, with the necessary documents, and some valuable resources and ideas:

Equivalent Fractions, Decimals, and Percents

At one time, as many teachers have, I tried teaching these three skills separately, and found that it was redundant. Fractions, decimals, and percents all go so nicely together, and should be taught together. The PDSA for this cycle is available HERE, as well as the Unit 4 Exam (a quick note, the exam for the entire unit is what I have linked to, the first two problems (the first and most of second page) are what constitutes the exam for this section. To save time, we normally take that portion in isolation, change out the numbers, and give the test). Our tests are in the format they are in because it closely resembles the New Mexico Standards Based Assessment. Here are the resources for this cycle:

• Fling Your Teacher: An online multiple choice review quiz that eventually lets the student fling the teacher in a trebuchet.
• Fractions Through Lines of Symmetry: A simple starter worksheet (pdf) that has students cut shapes into various fractions. It's a simple way to get started or give struggling students a chance to be a little more successful.
• Equivalent Squares: A very cool dominoes style game that students will enjoy. It plays right into the very point of this skill. It's a pdf document, it comes with very clear instructions and the squares ready to cut out. 
• Percentage Squares: Another great game, it's not the same as the one listed above, but is a very good, quick activity in pdf format. Since I've listed two resources from the same site, go ahead and check out Teaching Ideas, a great site from the UK with tons of printables. 
• Equivalent Fractions Memory: A matching game played in browser.
• Math Illuminations Equivalent Fractions Builder: If you use a Smartboard to teach, use this great interactive for whole class teaching.
• Equivalents Table: This is pretty much the backbone of this entire lesson.
• Worksheets: 
• Worksheet Works Equivalent Fractions Worksheet Builder, and the entire Worksheet Works Fraction Page
• Mathaids Worksheet Builder and the fractions page
• Equivalents Fill in Practice Worksheet: An easy to use worksheet that practices the skill exactly as it appears in the unit exam.
• Equivalents Packet: A few good activities, already ready for printing.
• Fraction Strips: This is a good activity. I have students make fraction strip books based on the strips in this worksheet. It's a great visual

Compare and Order Fractions

When looking at the Unit 4 Exam and the PDSA for this lesson, you'll see that this lesson involves putting fractions (and decimals) in the correct order, and comparing them using <,>,= statements. We go up to twelfths, and use like and unlike denominators:

• Math Playground Comparing Fractions, a simple starting point: A good place for the student that just needs more practice to get it online. I have students take a sheet of paper, and work out the problems as they go.
• Flower Power: An ordering decimals computer based game.
• Worksheets:
• Are You My Equal?: A packet with some decent activities, this whole thing is put together as a unit, with a summative assessment at the end. I'm partial to the fraction templates, equivalent fractions, and dare to compare worksheets included (which I have isolated into a separate pdf file HERE). 
• TONS of Blackline Masters: I'm surprised I hadn't ever come across this page. There's tons of pdf documents available that are age appropriate for 5th grade, including fraction strips, circles, and a Fraction Number Line. This is based exactly on a lesson done in Math Investigations (but a lot less costly, free always helps).
• Math Drills Worksheets: A lot of comparing decimals worksheets.

Add and Subtract Fractions

Here's the final part of the unit. The PDSA for this lesson and the Unit 4 Exam will both show that we teach adding and subtracting fractions with both like and unlike denominators. Once students have the hang of it, move on to having them add and subtract mixed numbers:

• Action Fraction: A fun online game at Fun School. I played it for a few minutes, by Level 3 it can get a little difficult, but it's fun and engaging.
• Math Playground Practice Activity: Another nice activity from Math Playground. It gives good practice in the web browser. Send a kid with some paper to work the problems, and they get instant feedback.
• Worksheet Works: Fraction Addition Sequence (I love this activity and will be using it). There's also a nice selection of Fraction Addition Skills and Fraction Subtraction Skills worksheets there. Everything they have on fractions can be seen HERE (I absolutely love this website). With all of these worksheets, have the struggling student use the Fraction Circles as a tool to help them along.

5th Grade Math Unit 1: Factors, Multiples, 2x2 Multiplication, 3x2 Division

As I've evolved my thinking on this blog a little in the five weeks I've been at it, I've started to change my own purposes for doing it. As I planned out math Unit 1 (which will be starting up for us here in just a little over two weeks), I started to think about the resources that I use year after year. So, I decided to include the PDSA (Plan-Do-Study-Act) files, as well as all the exams we utilize in the unit.

This units is housed in one of my subject specific static pages (the math 9-week plans page), in a page titled 5th Grade Factors, Multiples, Multiplication, and Division Unit, but I will include the text of that page verbatim below. Thanks for viewing, I hope this is of some help:




This is a big moment in the short history of this blog. I finally was able to get my computers set up in my classroom, and download all of my PDSA files and math tests that are already put together. As always, I will provide you with these for free. If you'd like more information on PDSA, see my page titled What is PDSA?

Math instruction for Unit 1 is divided into three portions, factors & multiples, multiplication, and division. Each section has a test, except for the final section (in this case, division). To save time, we always include the last section on the unit final exam. My goal here is to provide you with the necessary documents, and some resources as well. I work with my colleagues to make the exams, and plan our instruction backwards from there. The backwards design approach ensures that we are teaching what needs to be taught in the most efficient manner possible. Let's get started:

Factors & Multiples

The factors & multiples unit is set by the PDSA for that cycle, and was planned using backwards design, beginning with the Unit 1.1 Factors & Multiples Exam. It is set to take 10 days to teach, with one day at the end for testing and discussion. When viewing the exam, you will see that the main concepts to be taught are factors, multiples, prime numbers, composite numbers, square numbers, and prime factorization. What follows are resources and ideas for teaching each concept:

• My blog already includes a post and a static page about factors & multiples. I don't want to completely re-hash those here, but there are five different computer based resources available there.
• Factor Trees: I start right from the beginning of the year teaching with factor trees. Here are some great factor tree resources:
• A short and simple pdf document explaining what factor trees are. 
• Factor Tree Worksheet Builder: A good tool to make your own printable worksheets. You can customize the level of difficulty before making a pdf that you can save and/or print.
• Math Lines at Cool Math: I love played Zuma on Xbox Live (I'm kind of a video game nerd). This is Zuma with a twist. You can select a number, it defaults to 12. You have to shoot balls into other balls to make the product of the numbers 12. Very fun, good math practice.

Multiplication

Allow me to be a little more precise. This section of the unit on multiplication is 2x2 digit multiplication, as you can see in the PDSA file. Again, instruction was planned beginning with the Unit 1.2 Two by Two Digit Multiplication Exam. We have 7 days plus 1 day for testing to teach this portion of the unit. Here are resources for this section:

• Here are links to two sections on the great Worksheet Works worksheet building tool (see my post on this tool HERE). First there is a nice page with many options for teachers called Multi-Digit Multiplication Skills. I LOVE the variety of options available here. For your students who may be struggling with the standard algorithm, they also have Lattice and Grid worksheets. And before I forget, they have 2x2 digit multiplication word problems as well. 
• My school uses FASTT Math (a computer tool purchased from Scholastic, kids enjoy learning multiplication facts by playing the games and earning different things). It's not cheap, but fear not, there are free alternatives out there with free teacher tracking. At Math Facts Pro, you can create an account and track student progress as they play simple math games, at Math Trainer, kids can play a neat challenging game with annoying music (that you can turn off), and finally Multiplication.com has some really fun and visually cool games that kids are sure to love. 
• If you need more information on the lattice and grid methods, check out these videos:

LATTICE METHOD

GRID METHOD

Division

To be more specific, we're talking about 3 x 2 division problems. The PDSA will help guide instruction for this 8 days (with 1 day at the end for end of unit testing), as well as the End of Unit 1 Exam (I also have an English only copy), which includes the three by two division problems in it. For our data collection purposes, we collect data for this portion of the unit from the two division problems on the unit 1 exam for calculation in this PDSA cycle, and it also counts towards the end of unit 1 score. This "double dipping" serves us well, because we get the information we want, and do it in a timely, efficient manner. Here are the 5th grade division resources:

• Right back to Worksheet Works for their Multi-Digit Division Skills Worksheets. 
• Kids Numbers Long Division Practice Interactive: The sounds are probably the most annoying thing I've ever heard, but that's easily fixed. It does offer some good practice for kids struggling with their long division.
• Fun 4 the Brain has numerous division games, including Flying High, my favorite of the bunch.
• Finally, I'll let Khan Academy explain the process of long division, using the Divide, Multiply, Subtract, Bring Down method: