Area of Trapezoids made easy.

Area of Trapezoids made easy.

In the world of quadrilaterals, the formula to find area of Trapezoids is one of the most feared by middle school students. Perhaps it’s the use of parentheses. If you throw these bad boys into a problem it’s sure to create a certain level of anarchy. Possibly it’s the use of the numbers 1 and 2 written below and to the right of the two bases (b) in the parentheses.

Regardless of of the reason, the formula for Area of Trapezoids has caused many kids to surrender without so much as a fight.

The kicker is that the formula is not difficult to solve. In this blog we will look at a couple of the key terms, dissect the formula, give three examples of finding area and show you a three ways to model finding the area.

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Area of Squares, Rectangles, Rhombuses, & Parallelograms

If you ever google: "How to find the area of a Square? Rectangle? Rhombus? or Parallelogram?" You are going to find a bunch of different answers.

For a Square, the formula given will be the Side Squared. The Rectangle's formula given is Length x Width. To find the area of a Rhombus you are given two different formulas: Base x Height or Diagonal #1 x Diagonal #2 divided by 2.  Finally, the Parallelogram's formula for area is Base x Height.

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All of these formulas are obviously correct, but you can make your life much simpler (or at least your kids) just using one simple formula:

Base x Height.

How is this even possible? The reason it's possible is because all four objects are Parallelograms. For a lot of students, it doesn't make sense how a Square, Rectangle and Rhombus  are also Parallelograms. Below are the rules for an object to qualify as a Parallelogram. 

  • Must have 4 sides

  • All 4 sides must be straight

  • Opposite sides must be the same length

  • Opposite sides must be parallel (so there are two sets of parallel sides)

  • Opposite angles must be the same

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To the right we can see that the Square, Rhombus, and Rectangle each have a total of four sides and each of the sides are straight lines.

The blue and orange highlighted sides are parallel with each other. So each object has a total of two sets of parallel sides.

The green arcs (angles) are opposite of each other. These two angles are the same. In the Square and Rectangle all the angles are 90 degrees, but in the Rhombus the two opposite green angles are both acute angles (less than 90 degrees).

Opposite black arcs (angles) are also the same. In the Rhombus the opposite blacks arcs are each obtuse angles.

Because all 4 shapes (square, rectangle, rhombus & parallelogram) are parallelograms we can just use BASE x HEIGHT to find the area of all four of these shapes.

Modeling Area of Parallelograms

Squares and Rectangles are the two easiest shapes to model. Grid paper is a very easy way to show this to students.

On both of these images not only can you see the base and height but you can visualize the individual squares that make up the rectangle and square. So when we say the area of the rectangle is 10 cm squared we can see 10 squares that have sides that are each 1 cm

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Modeling with Cheez-its

An easy way to engage students is to use Cheez-its (or other square food items like Starburst) when modeling. It's a simple way to turn this into a hands on lesson and the kids like the payoff at the end.

Modeling a Rhombus or Parallelogram (non square/rectangle)

Modeling the area of a Rhombus or parallelogram is a bit harder with cheez-its (cutting up a cheez-its = pure mess). But it is fairly easy to model with grids. We can even turn the grids into a hands on lesson.

Below we have a Parallelogram (base of 8 with a height of 4) and cut it into two pieces by cutting on the height. We can rearrange the two sections to form a rectangle with a base of 8 and a height of 4 (same dimensions as before). By rearranging the Parallelogram we can visualize the 32 squares that make up the area

Below is another example of a parallelogram. We can take this parallelogram with a base of 10 and a height of 3 and cut into two parts by cutting on the height line. The two sections can be rearranged to form a rectangle with a base of 10 and a height of 3. By rearranging the Parallelogram we can visualize the 30 squares that make up the area.

We can model a Rhombus the exact same way by cutting into two parts (along the height) and then rearranging. 

Length x Width vs. Base x Height

Is Length x Height the same as Base x Height?

The answer is Yes (sort of). It all depends on your perspective. On the image below left we are looking down on the rectangle. So, we would refer to these dimensions as the length and the width.

On the image below right we have changed our perspective of the rectangle. We are now looking straight ahead, so our dimensions are now base and height.

So Base and Length and Height and Width are basically the same.

 When looking down on a rectangle we can see length and width.

When looking down on a rectangle we can see length and width.

 When the same rectangle is upright (like above) we can visualize the height and base.

When the same rectangle is upright (like above) we can visualize the height and base.

We hope you found this article helpful. You can follow us on:

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If you are looking for a more challenging activity for you kids check out "Finding Area of Unique Shapes" on Amazon.

This is a collection of 44 different shape combinations using rectangles, triangles, trapezoids, and circles.

The shapes progress in their difficulty.

You can check a video preview of this product below.



A dozen ways to help your kids with math this summer. (Stopping the Summer Slide)

Teachers have a Love/Hate relationship with Summer. Sure the time off to relax and spend time with their family is neat. But there is a dark cloud looming on the horizon. I'm talking of course of the Summer Slide.

The Summer Slide is students amazing ability to forget everything that they just learned the previous 9 months. As teachers, we know its coming yet we are still stupefied by its reappearance each year.

As a parent, what can you do to stop the Summer Slide (or a least slow it down) and give your child an edge this upcoming school year? Glad you asked!

You could make your child sit down and do math worksheets, but that would be just pure misery for everyone involved. Instead, I have included a dozen low stress, easy ways you can engage your child in discussions about math this summer (without your kids realizing you are working on math).

#1 - "How Much Longer" Situations

We have all been there. You taking a long trip (a vacation, visiting Aunt Doris or going to the store) and the kids keep asking you "How much longer?," or "When will we be there?" This is a great time to work on unit rates, reasoning and estimation skills.

Let's say you are driving to Nashville, TN and you have another 150 miles until you arrive. Of course the brats (your kids not the food item - even though that might make the story more interesting. Also, I'm sure your kids are actually quite lovely and a joy to be around on a long road trip.) in the back seat start asking "How much longer?"

Instead of just telling them how much longer (It's not going to keep them quite any way) you can give them your numbers and discuss how much longer they think it will be. This gives you  chance to guide them through the process of thinking mathematically.

For example, let's say you are traveling 60 miles per hour and you have 150 miles to travel. How much longer. The answer is 2 hour and 1/2 hours (or 2 hours 30 minutes). The goal is not to necessarily get the right answer (It would be nice), but instead get your child to think about how to use the numbers to get the answer.

There are many ways to get this answer. For example, maybe your child realizes that if you travel 60 miles in 1 hour, you would travel 120 in 2 hours and 180 miles in 3 hours. 180 miles is farther than you are actually going so the time will be between 2 and 3 hours. Another way could be that your kid realizes that 1 mile = 1 minute so the trip will take 150 minutes and 150 minutes is the same as 2 hours with another 30 minutes.

You can then build on this by asking how long it would take if you were traveling 80 miles per hour (not including the quality time spent with a local police officer discussing speeding laws in the state of Tennessee).

This doesn't need to be limited to just driving and miles per hour. Let's say you are at a baseball game (For example a Lehigh Valley Iron Pigs minor league game) this summer and the first 2 innings take a total of 40 minutes. At this rate how long will the game take to complete?

#2 - Finding the cost of gas on a trip

Let's say you are once again heading out on vacation, this time from San Francisco to Bend, Oregon (sounds like you are having a great summer so far!!).  The distance you need to travel is 480 miles each way. Your family has two vehicles to select from: a mini-van which gets 20 miles per gallon or a sedan which gets 30 miles per gallon. 

First, you could have your child figure out how many gallons you will need for each. The mini van will need 24 gallons of gas one way or 48 gallons of gas round trip. The sedan will need 16 gallons one way or 32 total gallons. The process of getting these numbers (without a calculator or paper) can be done a variety of ways. For the mini van you child might realize that 5 gallons = 100 miles or that for the sedan 10 gallons = 300 miles.

Once your child realizes that it takes an additional 16 gallons of gas for the round trip with a mini van they can then calculate the cost. For example, if the cost for a gallon of gas is $3 it means that it will cost the family an additional $48 in gas. You could then have a discussion about the value of paying the extra $48 but having the extra room and comfort of a mini van.

You can even use this to find a common multiple of the numbers 20 and 30 (which is 60). For example, you would need 3 gallons of gas to travel 60 miles with a mini van and 2 gallons of gas with a sedan.

#3 - A visit to the Land of Unit Rates (aka the Grocery Store)

It doesn't matter if it's Piggly Wiggly, Wegmans, or Krogers (or any of the other fine grocery chains) there is no better place to see unit rates in action than the grocery store. 

Just buy two 1 pound packages and use the $1 you saved to get a snickers bar!

As you travel through the store you will see unit rates all around you (Don't be afraid). Grocery stores will often have signs like "5 melons for $10" or "3 boxes of Mac and Cheese for $5". In most cases you DON'T need to buy 5 melons or 3 boxes of Mac and Cheese. These are just ways to manipulate you into buying more items than you planned on buying. You can just buy one Melon or Mac and Cheese. But what is the cost?

If you take the cost ($) and divide it by the number of items (melons for example) you will find the cost for each melon. So $10 divided by 5 = 2 or $2 per melon. What if you divided the number of items (melons) by the cost ($)? You would find how many melons you can get for $1. In this example you would get 0.5 melons per dollar (As a general rule grocery stores frown on you ripping apart a melon and telling the cashier you just need a dollars worth). Not only can you discuss with you child how to find the cost for each item, but you can talk about which form of unit rate makes sense. 

The Mac and Cheese example is a bit more difficult than the Melon example because when you divide the cost ($5) by the number of items (3 boxes) you don't get a whole number, but instead a decimal. This is a great time to use your estimation skills. Most kids will realize that the boxes cost for than a dollar each. A few for more will realize that if a box was $2 each that would be $6 total which is $1 to much. The cost is $1.67 per box. You can guide you child to under stand the cost is closer to $2 a box than $1 a box.

Grocery stores love to create situations where you think you are getting the best deal but they are really tricking you. Generally, if buy a larger container of food there is usually a bit of discount on the unit rate (less per ounce, pound or doughnut) BUT not always! Because stores have trained us to thing bigger is the better deal people will blindly get the larger package. To the left is an example from my local Krogers. Of the 7 or 8 people that bought strawberries while I was there, all but one (yes it was me) bought the 2 pound container of strawberries. You can point out examples of this as you meander through the store.

#4 - Let's Play Ball (Sports and Math)

If you have a child that is interested in sports you have a natural connection to math. It's impossible to watch a game on TV (or on your phone or computer) and not notice all the stats used. Just the basic act of watching a game with your child (in person or on TV) and discussing  the meaning of different stats (ERA, WAR, OBP, Batting average, slugging percentage, strike to ball ratio and so many more!!!) and how they are calculated can help a child think about math.

You can use these stats to make arguments about which player you think is the best. Often times when I attempt to talk to kids about who they think is the better player (could be football, basketball or any sport) their argument is that your guy "sucks." By understanding statistics the kids can make better arguments using data to support their opinion (This will also make the Language Arts teachers happy).

Want to amp it up a bit and still have fun? You can join a fantasy league (ESPN, Fan Duel, Draft Kings for example), play the board game Strat-O-Matic (they have games for almost every sport), or even play baseball video games. When you are in a fantasy league or playing games you can use math to justify your decisions.

#5 - Running a Lemonade Stand

A great ways for kids to make the connect to math and business is to let them run their own Lemonade stand. I let my kids have a lemonade stand a couple of times a year (once when we have a garage sale) and it's a lot of fun, but more importantly there are a ton of lessons to be learned from this activity.

I have my kids keep track of all their expenses (cups, ice, lemonade packets/lemons etc.). At the end of the lemonade sale we talk about Gross Profit, expenses and Net Profit. We also talk about the cost to make a cup of lemonade (cup, ice, lemonade) and our profit per cup.

To help their bottom line I buy all their unused inventory (extra cups and unused ice). For example, if they spent $8 on cups but only used 1/4 of the cups we will use $2 as their cost for cups. But, I will discuss how this would impact their business if I didn't do this.

#6 - Become Bob the Builder - build something... anything!

One of the best things a kid can do to help their overall math skills is to just build something. A table, workbench, ramp, dog house it doesn't matter. The act of making something will help with their geometric and measuring skills.

The nice thing about building items is that it's messy, hands on and requires problem solving skills (This is nice IF your kids clean up their mess!). Usually, the first time your kid attempts to build something it will be a random collection of materials that will be nothing like they were hoping to build. This is a great chance to give a little guidance/advice about angles, measurements and sketching out a design before starting.

Please: Do NOT just turn you kids loose with power tools (drills, band saws etc.) unsupervised. You can give your kids freedom, BUT you need to make sure they are safe!

#7 How far away is the lightning (or Fireworks)?

An easy way to sneak in a little math during the 4th of July or one of the many summer storms is to calculate the distance of the firework's explosion or the lightning bolt. This gives you a chance to talk about the difference between the speed of light vs. the speed of sound (You are welcome Science teachers).

The speed of light is so fast that virtually no time elapses from when an event happens to the time you see it. The speed of sound is much slower (375 yards/1125 feet per second). For estimation purposes you can figure about 400 yards per or 1,200 feet per second. A mile is 1760 yards or 5280 feet. 

When you see a lightning bolt (or firework) time the number of seconds until you hear the sound. Every second = about 400 yards. So 4 seconds is just a little less than a mile away and 5 seconds is just about a mile.

#8 - Raise a Garden

If you live in downtown Chicago this might be a bit harder, but for the rest of you this is another way to mix in a little math (and get some tasty produce!). One of the keys to a successful garden is the planning and layout. What are the dimensions of your garden? What ways could you layout your garden to maximize your space.  

You can track your garden expenses (seeds, plants, fertilizer, etc) and your total harvest (we have a little weight scale we use) though out the summer. If you want to amp up your garden math you can compare your expenses to the amount of money you would have spent. Was their any kind of savings? Even if it was more expensive you can talk about the health benefits of raising you own produce.

If you want to take this to another level you can have your kids set up a small farmers stand (or go to a farmers market) to sell their produce. Just like with the Lemonade Stand, this is a good way to teach some business skills along with math skills. (As a side note: I actually did this when I was in high school. As part of a project for Future Farmers of America (no I'm not a farmer) I raised cantaloupe for 3 summers. Each morning I would harvest the muskmelon, weigh and price each one. I would put my produce in a wheelbarrow and put out by the road with a couple of signs. I would play basketball while waiting for customers to arrive. I would usually sell out of produce by lunch. I made nearly $1,000 each summer!)

#9 - Lawn Mowing Business - the side hustle

There was a time when it was common for kids to make a little pocket money by mowing the neighbors yards.  Maybe it's because of all the lawn mowing services that have popped up over the years, but there seems to be fewer kids mowing lawns today. But, I would argue that the time has never been better for a teen to start a small neighborhood mowing business. Because kids are usually just using a push mower, their expenses are much less than the larger lawn mowing companies (along with not worrying about employee benefits, accountant cost, marketing, etc.). As a result, the kids can charge a lot less and still make a good profit.

Also, there are a lot of adults that remember mowing lawns when they were a kid and respect a kid today willing to work hard. And with less kids to compete with, the market is all yours.

What about the Math? Alright already!

First, your child is going to need to determine what they will charge. Is it going to be by the hour? A set rate per yard/lot? Based on square footage? Most of the lots in our neighborhood are roughly the same size so my son charges a flat rate per yard (double if the yard is actually 2 lots). How often are you going to mow? Could you charge a one time fee for the entire summer? What would you charge for this one time fee (remember: it should include a savings for the customer)?

Once you know the rate you will charge (which is you gross income) you can calculate your gross income per hour. For example, my son charges $15 dollars per yard. It takes him about 45 minutes to mow a yard. When he was calculating what he makes per hour he figured that he was making $5 for every 15 minutes. There are 4 groups of 15 minutes in an hour so he is making $20 per hour.

You can have your kids estimate their gas expenses by finding out how much gas is needed to mow a yard. For example, if it takes a gallon of gas (let's say it's $3 per gallon) to mow two yards that means it cost $1.50 in gas to mow a yard. You can find your net profit by taking you gross income and subtracting the expenses. If you want to take the to another level you can charge a rental fee for use of the mower and maybe include the cost to maintain the mower.

Other things you could do: What will you make per month from a customer? How much will you make if you mow 5 lawns during the summer. How many lawns would you need to mow to make a certain amount of money such as $1,000 or $5,000? How many hours would it take to make your goal?

#10 - Estimating the Savings and Prices when Shopping

This is a great life long skill for kids to learn. This is easy to talk about in the flow of a conversation. You're shopping with you child and there is a sale! Let's say there is a 20% off sale on all lawn mowers at your local John Deere dealer. You are looking at a $2,000 mower (Apparently the lawn mowing business is working out quite well!). How much will you save? What is your cost? Many kids struggle with understanding how easy it is to find 10% of a number. In this example, 10% of $2,000 is $200. So, 20% savings would be $400 (double the 10% savings). If you are saving $400 that means that the sale price would be $1,600 (2,000 - 400 = 1,600). You can do this with any product (yes even toothpaste!).

You can then take this skill and apply this to calculating tips or taxes. For example, you are Red Lobster with your family. The bill is for $80 and you decide to leave a 15% tip. How much will you leave? If 10% = $8 then 5% = $4 so 15% = $12 tip (8 + 4 = 12).

#11 - Estimating the size of a crowd

You are at a concert, movie, baseball game or any place with a gathering of people. One simple thing to do is to estimate the size of the crowd. When you do this, don't just have your child randomly scream out a number. Have them explain how they got the number. For example, perhaps they noticed that their appears to be about 9 people in each row and since there is 100 rows the crowd is about 900 people. Maybe they count how many people are in a section and multiply that by the number of sections. You can also estimate what percent of the crowd is male or female or what percent of the crowd is rooting for a certain team.

You can do this with other things like how many Coins or M&Ms are in a jar. The correct answer is not important, the focus is on the process of trying to figure out the answer.  I remember reading about how one of the questions Google used to ask possible employees was "How long would it take to wash all the windows in Seattle?" Obviously, there is no way to determine exactly how long it would take. They are just trying to see how you would TRY to solve this problem.

#12 Being Bullish on the Stock Market

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One of the best things you can do as a parent is to introduce your child to how money works and more specifically how the stock market works. You don't need to be a stock picking guru or understand how Options work. Just by demystifying the world of money can help your child achieve financial freedom as an adult.

But lets be honest, most of the information you will find about the stock market will be very dry and boring. You don't want to bore you kid to death (Unless this is some form of punishment for not cleaning up their room) so what can you do? Two words: Mad Money.

Mad Money is a television show hosted by Jim Cramer on CNBC at 6pm EST. The show is sort of a cross between the stock market and MTV (When is was still cool). It is a high energy, fast paced show with lots of flashy graphics. 

From a math stand point the show is packed with percentages, graphs/charts, ratios and all the different financial terms that you would expect. The show will have from time to time a chartologist to explain how they read and use different charts and graphs to make their stock picking decisions.  Mad Money will have on different business leaders to discuss the metrics that they feel are important to their businesses success.

It's a fun show to watch with your kids and an easy way to start discussions about investing and money.

Wrap Up

There you have it: A dozen different ways to keep your kids engaged with math during the summer without using a single worksheet. For me, I try not to get bogged down in working on basic skills (not that there is anything wrong with that) but instead try to focus on situations that require math as an adult.

If you are going to focus on your child's individual skills (which is a good thing) I would highly suggest finding games and puzzles (you can find some of these on our website) that make the experience a bit more fun for you kids.

Wishing you a happy and productive summer.





Cereal Box Project: A middle school math project

For over a decade the Cereal Box Project has  been a staple in our classroom. The idea is that a cereal box company is introducing a new cereal and they want a unique design for the cereal box to help gain extra attention.

Because the company wants something creative, a simple rectangular prism simply just won't do. The goal is for students to find ways to combine different shapes together to create this eye catching cereal box.

The following is a basic outline of the steps that we follow with this project. In addition, I'm including a few lessons from this years Cereal Box Project experience. 

Step 1 - Come up with an Idea

 The idea? A light bulb of course. How do you make a light bulb? Make a Hendecagon of naturally.

The idea? A light bulb of course. How do you make a light bulb? Make a Hendecagon of naturally.

Like baseball? Really into Star Wars? Love doughnuts?

When coming up with an idea I find it helps student engagement when the students can use a topic that they are interested in. For example, if a student is really into baseball/softball they can make their cereal box look like a glove, bat, baseball field, home plate etc. This year a lot of my students are into the video game Fortnite. As a result, a large amount of cereal boxes has a strong Fortnite theme.


Step 2 - Reverse Engineer

As a middle school or elementary student there are certain limitations that we must work around. Many of these limitations are related to curves. For example, If you are trying to make a basketball (sphere), Football (prolate spheroid), or perhaps a megaphone (truncated cone) you are going to dive into a lot of math that is above middle school math level. 

Have the students think about what they want to create and how they can arrange different shapes to make this object. For me, the fun and challenging part of the project is to create these difficult shapes by using the students current knowledge and skills. 

Step 3 - Sketch out the idea

Put it down on paper. Draw the different shapes you are going to combine together to create your shape. Include dimensions.

Step 4 - Build a Prototype

I have our students build their prototype the same size as their actual project. We use scrap paper and masking tape to build these prototypes. A lot of potential pitfalls can be avoided during this step. 

Step 5 - Cutting out individual Pieces

When you begin to build your actual Cereal Box the first thing I like for students to do is cut out the individual sides. We build our cereal boxes out of card stock which is a real thick paper similar to poster board. The thicker paper is nice because it is more stable.


Step 6 - Decorate the individual Pieces

Before the students begin to assemble their projects they should first decorate.  Every year I will have a small collection of students that will tape their entire box together then decide to color and design it.  This almost always leads to frustration and crushed cereal boxes.

Step 7 - Assemble the Cereal Box

We use scotch tape on the final project. We try to tape as much on the inside as possible. As a general rule: The less tape you see the better the project will look.

Step 8 - Complete the required paperwork

We usually have students calculate the surface area and volume of their projects. In addition we also have students draw (to scale) Nets and 3D designs of the project. 

Lessons Learned from this years Cereal Box Projects

We had another successful year with our cereal box project. Many of the projects were creative and well done. Most of the students were fully engaged in the project. But we did have a couple areas that I need to clean up before next year.

The Curse of the Circle

We had a few students this year build cereal boxes that were either cylinders or had a circle as part of the design.  In both of these cases many students just randomly made a circle and just wrapped a long stretch of paper around the circle. There was no thought given to diameter, radius, or circumference. Needless to say, this made for a mess when it came time to make the cereal box the same as its prototype and with calculating surface area and volume.  

Struggles with Scissors and Straight lines

Normally I will take a day (or two) to show the students a few tips/tricks when making and cutting out the sides of their project.  Because of a time crunch this year, I thought I could save a little time and just give a brief talk and turn them lose. In the end this just created a lot more work for me and made it harder to help out as many students.




Interested in giving the Cereal Box Project a try?

This book will give you an in depth guide to how I use this project in my class.









45 Gift ideas for Math Teachers and Fans of Math

45 Gift ideas for Math Teachers and Fans of Math

So it's getting close to Christmas and your are still looking for gift ideas for that special Math teacher or math fanatic in your life. Don't fret, we got you covered with 45 different ideas for that special mathematical person in your life.

We have divided the gift ideas into 6 different categories: 1) Clothing & Accessories 2) For the Classroom 3) Books 4) Around the House 5) Math Fun 6) Productivity and 7) Stocking Stuffers

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How I'm starting the school Year.

How I'm starting the school Year.

I used to open up the school year with some nice get to know you activities. For example, I might randomly partner students together and have them interview each other. After the students asked each other a few questions, they would introduce their partner to the rest of the class. This was always a nice way to ease into the school year and get to learn a bit about the kids.

As much as I (and the kids) enjoyed these opening day activities I always felt something was lacking. There seemed to be this disconnect with these activities and math. (Also, it seemed like every teacher in the building was doing some variation of this. So the students were doing this all day long. The novelty was lost by the time many got to me.)

Last year I tweaked how opened the school year. 

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Huge fans of

There are tons of great math websites in the world of the internet. One that I really like is a nonprofit site called BYU's mathematical department is the muscle behind this site. The site attempts to help answer the question: "When will I use math."

The site is a very user friendly site that's loaded with a bunch of terrific information. The site is broken down into a home page and 6 key sections: Blog, Careers, How to succeed in Math,  Did You Know, Math Resources, and a store.


The BLOG is not the main strength of this site. The articles are very interesting, but the frequency is somewhat limited. In 2016 the site posted around 5 articles. If you are new to the site you have over 70 different BLOG post in the archives to pick from.


This is my favorite part of the site. This section looks at around 40 different careers (everything from Actuary to Urban Planner) that rely on math.

The first thing this section does is to highlight a person with this job. Second, the low, medium, & high salaries for the job are listed. Third, educational requirements for a degree in this field are discussed. Fourth, the site talks about when math is used with this particular job. Next, a list of potential employers is mentioned. Finally, this section will list any miscellaneous facts or citations.


There is a list of 7 different things/tips that can help increase students chances for success.


Is divided into "Math in Real Life" and "Math Tidbits. The "Math in Real Life" part is a collection of nice articles about math. The "Tidbits" sections is random trivial facts about math.


This is my second favorite part of the website. This section of the site includes free resources, list of math competitions, curriculum ideas, links to different math sites and links to math puzzles.


The store is a collection of shirts for sale. 


The CAREERS and MATH RESOURCES sections make this a great go to site for teachers and parents. 

Famous Mathematicians

So you need to write a report on a famous mathematician. Maybe you want to drop some historical math knowledge on your math teacher. Perhaps you just want to learn about legends of the mathematical world. Below are links to 4 sites that should help you learn about these titans of the mathematical world.

Clark University

Gift ideas for Math teachers (The baker's dozen)

Gift ideas for Math teachers (The baker's dozen)

The struggle is Real

It's that time of the year. It is time to find a gift for people that you have no idea what they want. If the person you are looking for likes math we can help.  Below is a baker's dozen random math gift ideas. Think of these items as "affordable mathematical luxuries." 

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Making 3D Shapes and Similar Objects using Scale Drawing

Making 3D Shapes and Similar Objects using Scale Drawing

Creating 3 Dimensional Drawings

One of my favorite activities each year is using scale factor to create three dimensional drawings. We do this activity when we are studying Unit Rates. There are a variety of reasons why this is one of my go to lessons.

Hands On

This activity gives students the chance to create something. The act of drawing, measuring, & designing is a nice change of pace from the usual worksheet avalanche. The actual act of creating this object allows students to see the relationship of sides all changing proportionally.


This lesson gives students the opportunity to showcase their creative/artistic side. We have some basic guidelines, but in general students are free to design what appeals to them.


Many students are visual learners. For some students it easy to see difference between an object drawn to scale and an object that does not have a constant proportionality.

Connections with other classes

Art, Social studies (maps), industrial tech, and computer science classes are some of the classes that we are able to show a connection with.  For example, our art classes use one point perspective drawings which share a ton of similarities with our scale drawings.


The activity allows you to increase (or decrease) the difficulty. For example, if you have a student that is struggling you can use a very simple shape such as the letter "L" or use a very easy scale factor such as 2.  If you want to increase the intensity you can have students measure everything in inches (not centimeters) or require a very unusual scale factor such as 3/8 or 1.75.


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Prang Power!

If you work at any school in America I sure you are well aware of the Box Tops for Education Program. It's a super program and provides a lot of great resources. At most school I've been to the Box Top program is done as a school wide fundraiser. This certainly makes sense, there is strength in numbers. 

But what if you are a teacher and you are looking for an easy way to earn free items for your class? You don't want to do the Box Tops for just your class because that would undermine your schools efforts. It would be nice to find something that the other teachers in your building are not doing. The answer: PRANG POWER

What is Prang Power? Prang Power is an educational program created by Dixon-Ticonderoga the pencil company (which includes all Dixon, Ticonderoga, Lyra, & Prang products). Very few teachers are even aware of this program (I am the only person at our district). So how does this program work?

Step 1 - Sign up for the program

Signing up is easy and free. Just go to and sign up for the program. The whole process takes less than 2 minutes.

Step 2 - Collect UPC Codes

This is real easy to do at the start of the school year. Many of your students are going to have brand new boxes of pencils. Simply ask them if you can have their UPC codes. Most students are glad to get rid of the boxes. 

Ask you fellow teachers. Just like the students, teachers are loading up on pencils, chalk and other school supplies at the start of the year. Make the rounds at your school. Again most of the teachers are happy to get rid of their boxes.

Check in with your administration (this includes the secretaries). Often your school will purchase large amounts of pencils for testing and general use. Just like the kids and teachers, they are happy to get rid of their boxes.

Bonus Points - You can earn bonus points from prang for different things such as mentioning Prang Products on your school supply list.

Step 3 - Mail in UPC codes

As you collect UPC codes you can mail them to the Prang Program. Each UPC code has a point value approximately equal to the suggest retail price. So a $5 box is worth about 5 points. Prang will keep track of your points as you send them in.

Once you have earned 300 points you can begin cashing in your points for pencils, art supplies and other items.

Step 4 - Cash in your points for free Product.

At the start of this school year we received nearly 500 free pencils as the result of this program and we are close to getting more!

Todd Hawk is a middle school math teacher and the Founder of the Land of Math LLC ( You can reach him at or follow him on twitter: @landofmath2.



8 Reasons why Teachers Pay Teachers (TPT) is creating a grassroots disruption in education.

If you are involved in education you probably have heard of Teachers Pay Teachers (TPT). If you have ever tried to pin something educational on Pinterest I know you are aware of TPT. TPT was started by Paul Edelman, a New York teacher, in 2006. Today Teacher Synergy (the company behind TPT) has evolved into a major disruptor in the world of education.

Teachers Pay Teachers is a marketplace for teachers to buy and sell different educational material. Initially, TPT was a really cool place for teachers to make some extra cash on the side but it has turned into a major game changer in the world of education.

Five years ago only one or two teachers at my school ever heard of Teachers Pay Teachers. Today, TPT is just part of normal conversation in the teacher lounge or during staff professional development. There have been multiple times that teachers will laugh when they realize that they downloaded the same product from TPT.

The Impact of Teachers Pay Teachers is far greater than simply making some money for selling a few worksheets. TPT is helping fuel major change in the world of education. Below are few of the ways.


Because of TPT, teachers are now building different products. The act of building gives teachers a deeper understanding of the content they are teaching. We are striving for students to improve their problem solving skill, but teachers also need to work on this skill.  As teachers try to create new products it gives them a feel for what their students are going through.


If you are going to sell things on TPT, you can not just create boring run of the mill worksheets. You need to think differently. You need to make products that are unique and get students (and teachers) excited. What can you do to make a fraction lesson fun and challenging? Can you transform a traditional lesson into a hands on lesson? What about a game?

The process of being creative forces you to make the ordinary extraordinary.

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Don't fall for the seduction of the 1 cent pencil

The summer is wrapping up and the school year is about ready to kick off in full force.  This is the time of the year that is filled with optimism and excitement. Everything starts over.  Students get to meet new teachers, teachers get a new batch of students and parents get a chance to regain their sanity.

Despite all these warm and cuddly feelings that surround the start of school I am dreading another yearly tradition: parents buying their kids crappy pencils.

Don’t get me wrong, I to have been seduced by the allure of the 1 cent pack of pencils at Staples (or Wal-Mart, Kmart, etc.). As a parent you feel good about making such a wise purchase. After all a pencil is just a pencil.

“No so fast my friend,” to quote Lee Corso, the legendary football analyst from College Game Day (and Director of Business Development for Dixon Ticonderoga pencil company).  Pencils are NOT all the same and it DOES make a difference.

The trouble begins moments after the first bell.  The students complain that they can’t get their pencil to sharpen. Why? Because the quality of wood and lead is inferior and it is next to impossible to get many of these pencils sharpened. Many pencils are never able to be sharpened because the lead just falls out as you sharpen it. In addition, students are constantly getting up because their lead keeps breaking because of the poor quality. 

Mechanical pencils are no better.  Most of the time students are asking around for specific lead sizes because they ran out.  The lead in the mechanical pencils is so thin it snaps off with the slightest pressure.

Last year our 7th grade math department spent some of our supply money on extra Ticonderoga pencils (the Language Arts teachers just mocked us).  We could tell the difference and so could the kids.  The pencils were easy to sharpen, kept their point longer and didn’t break off as often.

By the way, I am not affiliated with the Dixon Ticonderoga pencil company.  There are many other fine pencil companies such as Blackwing (my personal favorite is the Blackwing 602), General’s, Golden Bear and Prospector.  Many of these companies make their pencils in the United States.

I know it seems like such a small thing, but anytime you can reduce distractions you are greatly increasing the students chances for success.   Parents are always looking for ways to help their children.  The purchase of a quality pencil is an easy and affordable way to assist with your child’s success.

Todd Hawk is a middle school math teacher and the Founder of the Land of Math LLC ( You can reach him at or follow him on twitter: @landofmath2.

Creating a Successful Math Newsletter

One of the things we try to do each year is to create a math newsletter to share with parents, students and administration.  The main reason is to help develop better communication with parents.  The development of our newsletter is an ever evolving process, but we feel like we have hit on some key things that make our newsletter very effective.

     At the start of the year we focus on gathering the email addresses of different parents, students and any one else that might want the newsletter.  We have been able to get around 90% of our student's families to sign up.  When we send out the newsletter we just email a PDF to the different people on our email list.  We mail copies to families that did not sign up for email.  We also make extra copies and leave in the classroom for students that might not see the email version. In the past we sent out newsletters each month.  This year we are attempting to send out one a quarter.

    Above is a sample of one of our newsletters. The rest of this article will focus on the content, features and structure of the newsletter.

#1 Headline: The first thing we do on our newsletter is state what it is and for what time period.  In this case we call the newsletter the "7th grade math newsletter" (yes we know, verrrrry creative).  If we had newsletters for each individual teacher we might have use something like Mr. Mitchell's Math Class (also very boring) or perhaps something slightly more interesting such as Math Mania.

#2 Contact Information: This part of our newsletter includes information such as Names, email address, school phone, planning period times, website, etc.

#3 Quote: We like to have a quote about dealing with one of two topics: 1) Importance of math and/or 2) Motivational. 

#4 Greeting: We address this to the parents despite the fact that many of the readers of the newsletter are our students.

#5 Dates to Know: Just like it sounds. We focus on big events such as early releases, no school, end of grading period, parent - teacher conferences, etc.

#6 Classroom Activity:  In this section of the newsletter we highlight an activity that takes place in the classroom. For example, this newsletter mentions our "Fab 5" which is a basic skills review at the start of each class.  In this section we might mention a math program we are using, special projects, or discuss our invention program.

#7 Upcoming Topics:  In this section we list what we are currently working on in class and what parents can expect in the next few weeks.

#8 Math Careers: One of our goals is to let parents and students know about the many career options available in mathematics.  It seems obvious to us, but many students have no idea about the math needed in different careers.  A couple of weeks ago a student told me how he wanted to be an architect but was stunned to find out math was required math.

#9 Get to Know a Mathematician: Here we are Highlighting a person that has a career that uses math.  We like to focus on interesting jobs/people that are unique. In this newsletter we focused on Tinker Hatfield the person that worked on designing Air Jordan shoes.  We make a conscious effort to have an equal amount of men and women.

#10 Websites of the Month/Quarter:  We feature two or three sites that we feel could be helpful and sometimes interesting. In theory parents and students can use these sites for extra practice or assistance.

#11 Past Websites of the Month/Quarter: Instead of deleting our  past website selections we keep them as a running list.  As the school year progresses this turns into a nice collection of resources for the student, parent and even teacher.

#12 Math Programs: Our school is located just 30 minutes outside of Columbus, Ohio and just 45 minutes from The Ohio State University.  This location allows us to have access to a variety of math programs.  

    In each newsletter we try to promote local Science, Tech, Engineering, and Math (STEM) programs.  This is information that most parents are not aware of.  By listing these programs many of our families are able to find items that interest their kids.

#13 Tips on Being successful:  Finally we include some words of wisdom from top business leaders.  The theme of this section usually focuses on work ethic, goals, and perseverance.

Todd Hawk is a middle school math teacher and the Founder of the Land of Math LLC ( You can reach him at or follow him on twitter: @landofmath2.