Bowling With Math: A Great Order of Operations (PEMDAS) Practice Activity

Awhile back I posted a simple document called "Bowling With Math" without a lot of explanation in a post titled Order of Operations Game: Bowling With Math. Well, I am going to revisit that document, and expand on it a little bit today.

The Bowling With Math activity page ( you can download in .doc or .pdf format) has 10 "frames," just like in a regular bowling game. This activity is great because it can be varied in difficulty. The point here is that the teacher either chooses a few numbers (or rolls dice like I do), and students have to manipulate those numbers to equal the 10 different "pins" in the "frame," marking that number out each time they do so.

In my classroom (5th grade), I roll three dice. So let's say I roll a 5, 4, and 1. Students have to manipulate those three numbers using the order of operations (PEMDAS) to equal each pin number.

For example, I can do the following:

5+4+1 = 10
(5-4) x 1 = 1
(5-4) + 1 = 2
5+4-1 = 8
1x4+5 = 9

So let's say that's all I came up with, so I'd mark out the pins for 1, 2, 8, 9, and 10 and I would score 5 points for that frame.

In my class, I would do two frames per day, with students keeping their score on the score card each day. At the end of each week, students add their scores and keep a running total. This is a great activity that, when done consistently, teacher the order of operations in a very meaningful, engaging, and differentiated way. You can do as little as two numbers, or as many as you'd like. You can also change the rolls. Some weeks I'd roll five numbers and tell students to choose any three. Other weeks I'd roll six and tell them they could use no more than 3, etc. You can do whatever you want.

For convenience, I've added all the files, as well as a poster if you want to make a bulletin board for this activity, all in this convenient pdf file: PEMDAS BOWLING WITH MATH PACKET

Enjoy!

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!

SKUNK: An Awesome Math Probability Game

Every year when I'm teaching data analysis and probability, I introduce the dice game SKUNK. Students love this game, that is part chance, part strategy, and all probability. The game is very simple:

You have two six sided dice, and each student has a sheet of paper labeled SKUNK across the top, with lines separating each letter.

Roll the two dice, and students take the total and write down the points they just got. Here's where it gets interesting. You will ask anyone if they're going to take the points and leave the round. Students who take the points are safe, and get the points they had. Then you keep rolling for the students who are still in. Here's the fun part. If you roll a 1 on either dice, any student still playing gets zero points for that round. If you roll snake eyes, anyone still in that round is out of the game with no points.

This is a great game that students love. They love to play the odds. I explain to them the odds of rolling a one each time, and we discuss the probabilities involved.

It's a fun game to play around high stakes testing time, because kids can play it for hours.

I was about to type out the rules and put them in my Google Drive, but, I lucked out. Math Illuminations already has this:

Math Illuminations SKUNK Lesson Plan

Math Illuminations SKUNK Game Sheet (pdf)

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:

Area and Perimeter Teacher Resources: Worksheets, Games, and Activities

In 5th grade, we teach a unit on geometry, that mainly discusses 3-dimensional geometry. We do spend a lesson on perimeter & area. I find that this lesson normally is easy to grasp, and the vast majority of students move through it quite easily. I have a page of resources (games, activities, and worksheets) that could be of service to the classroom or homeschool teacher. These resources would be great in mainly a 4th-6th grade classroom, or maybe to challenge the very bright 3rd grader. Again, with this concept being fairly straight forward, it can be picked up pretty quickly. The unit is listed under my Math 9 Week Plans, and is titled Area & Perimeter Classroom Resources. I'm getting in the habit of re-posting these lesson and unit pages here within blog postings, I've gotten positive feedback from this, it's more user friendly than having people click all over the place. Here is the exact posting that you would find if you clicked the above link:



My school district adopted Math Investigations for use at the beginning of the 2007-2008 school year, and are still in that adoption. My school saw that our math scores were stagnant, and decided last year to try our hand at only utilizing the Investigations materials as a resource. We planned each unit out together, came up with our own materials (and compiled the resources we had and could find), and taught like that. The unit order that we came up with is the same one you'll see on the Math 9 Week Plans page. The reason I mention this is that we no longer have a curriculum to use. So as I go through these math units and lessons, I am going to list activities, games, ideas, and worksheets, because this will be my own resource as well. So that's where I'm coming from. Now let's get started:

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.

Perimeter and Area are usually one of the more simple concepts that come up in 5th grade. This listing of resources should help anyone get started. I'll be utilizing these and sharing them with my grade level team during this unit. As always, it's just a start. There are literally thousands of sites and worksheets out there. If you have anything else that you swear by, please share it here so I can get it up on the page.

Working With Frequency Diagrams

Every classroom I've ever seen asks students to collect data in raw form, and then analyze that data in one form or another. The raw collection seems easy enough. But the reality is, while most students can collect their data, many don't know how to analyze it or interpret data already placed in a pie chart, pictograph, frequency diagram, or bar graph (just to name a few).

So, it's off to BBC we go to play a game called Frequency Diagrams with Dick and Dom. This is an interesting game that will ask the player to figure out some totals based on given data. 

Next up, staying at the KS2 Bitesize (BBC) website, take this quiz on frequency diagrams.

For teachers, I came across this great site called Math Worksheets 4 Kids. Specifically I have attached a link to a page that has worksheets for Statistics. Check out the tally worksheets they have there, it's simple but will give you a quick view as to whether or not your students understand. 

Order of Operations Game: Bowling With Math

This following worksheet is a great math practice sheet. In 5th grade, students work a lot with the order of operations:

Parenthesees
Exponents
Multiplication
Division
Addition
Subtraction

What many students struggle with is the fact that Multiplication and Division are considered to be a "tie," and when working from left to right, you do whatever is first. The same applies to Addition and Subtraction. Many kids to this day still use the pnemonic device "Please Excuse My Dear Aunt Sally" to learn the order of operations. However, using these is a whole different issue. I've included a great game here called "bowling with math" that teachers are sure to love.

For my class, wait for me to give you directions, for anyone else interested, go ahead and download the attached document and enjoy. DOWNLOAD BOWLING FOR MATH HERE

If you're struggling with the limited instructions provided, basically, you roll four dice, take the numbers from each, and then use them to create different equations that have answers ranging from 1-10. The player tries to create as many combinations to "knock down" as many pins as possible.

If you're in a lower grade level, this game could be easily adapted, just change the directions as you see fit.