Proportionality & Grasshoppers

Proportionality & Grasshoppers

 

What would it mean if students could jump proportionally as far grasshoppers? To find out, I brought in some grasshoppers.

 

First we measured the length of two grasshoppers to be approximately 1 inch. Next, we measured the distance of three jumps (in inches) from two grasshoppers I found in my backyard and took the average of all three jumps for an average of 43 inches.

 

Next, we measured the height of two students in inches and took the average for a result of 62 inches.

 

Finally we formed the proportion

 

1/43 = 62/x

 

x = 2,666 inches which is roughly 74 yards.

 

In essence, if students could jump proportional to grasshoppers we could nearly jump 3/4 of a football field.

 

How Matrices Can Help When You’re Dating On A Budget.

How Matrices Can Help When You’re Dating On A Budget.

The scenario was that each student was treating their partner out on a date for pizza with the only caveat being they were on a tight budget and needed to find the cheapest place to take their date.

I first had my student draw a picture of their dates!

 



(Eva didn't talk much)



The students were asked to skim through three restaurant take-out menus to find the price of a large pizza and placed the prices inside a 1 x 3 matrix (Matrix A).

 

Next, the students were asked to skim through three restaurant take-out menus to find the price of additional toppings for a large pizza and placed the prices inside another 1 x 3 matrix (Matrix B).

Next, I had each student ask their date how many toppings they wanted on their large pizza (I answered for their dates of course).

 

The students then multiplied matrix B by the number of toppings they wanted on their pizza and placed the prices inside another 1 x 3 matrix (Matrix C).

 

Finally, the students were asked to add Matrix A to Matrix C to find the total price at three restaurants for a large pizza with a specified number of toppings and choose the cheapest restaurant.

 

Estimating, Error Rates & Plotting

Estimating, Error Rates & Plotting

 

 

Take your class outside and designate a single starting point. From that point throw 5 or 6 objects at various distances. Next, ask your students to estimate how many feet each object is from the starting point. After they have estimated each object have them measure the length to the nearest foot and record their data in a table such as that below.

 

 

Next, have each student calculate their error rate using the formula (actual) – (estimate) / (actual) and change their decimal to a percent.

 

 

 

Finally, have the students plot the points on a coordinate (x,y) plane and form a scatter plot. It’s best to have them graph the equation y = x so that they can see their error rates.  

 

 

 

 

 

 

 

Scatter Plots With Ramps

Scatter plots move in two dimensions which allow students to see changes in slope as well as the relationship of the two data sets. The study of scatter plots lends to a lot of fun experiments and can also serve as a great segue to discussions on proportionality or the coordinate system.

Ramp Height & Distance Traveled.

We decided to build ramps and plot the height verses distance traveled. We increased the ramp in (approximately) one inch blocks and rolled a golf ball off the ramp to measure the distance traveled. See Below. To get better results we took the average of three rolls. Lots of FUN! 

 

What To DO With a Handful of Pennies? Measures of Central Tendency

 

 

 

A good icebreaker to use when introducing Measures of Central Tendency (Mean, Median, Mode, etc) is to grab a handful of pennies from your vehicle and lay them out on a table and have your students work in groups to place them in order of date from least to greatest (if you have a large class you may need multiple handfuls of pennies).  

 

Next, start collecting data.

 

Mode can easily be seen by the largest stack.

Median, Range, Q1, Q3, IQR can also easily be found

Mean is slightly tougher unless you allow your students access to a calculator

 

Next, have your students create a dot plot of the data

 

Finally, have your students pick 5 pennies for their homework. Tape the pennies to their worksheet so that they can read the date (see pic below).

 

Prime Number Challenge!

An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself.

Here is a chart detailing the all Primes from 1 - 100

We know via the proof-by-contradiction by Euclid that there are an infinite number of prime numbers, yet, this doesn't reveal them. Unlike a standard integer (whereupon whatever number you can come up with, for example n, i can surpass this number with the simple exercise of n+1), large prime numbers are incredible difficult to find. There is no formula for churning out prime numbers, they must be found :)

In 2008, a mathematician won $100,000 for finding the next highest prime number (the largest known to date)

The number is 2^43112609-1

Most likely you students won't be able to grasp how big this number really is, but, for intents and purposes, if you were to sum up all the atoms in the entire universe you would get a number roughly  10^80 (vastly smaller than the one shown here)

If you would like to see how big this number really is i suggest you download it from here http://prime.isthe.com/chongo/tech/math/prime/m43112609/prime-c.html 

I will produce a tiny fraction of the full number for you here, but if you want the full thing, you must go to the prime site http://prime.isthe.com/chongo/tech/math/prime/m43112609/prime.html

three hundred sixteen quattuormilliamilliatrecensexviginmilliaunsexagintillion,
four hundred seventy quattuormilliamilliatrecensexviginmilliasexagintillion,
two hundred sixty nine quattuormilliamilliatrecensexviginmillianovemquinquagintillion,
three hundred thirty quattuormilliamilliatrecensexviginmilliaoctoquinquagintillion,
two hundred fifty five quattuormilliamilliatrecensexviginmilliaseptenquinquagintillion,
nine hundred twenty three quattuormilliamilliatrecensexviginmilliasexquinquagintillion,
one hundred forty three quattuormilliamilliatrecensexviginmilliaquinquinquagintillion,
four hundred fifty three quattuormilliamilliatrecensexviginmilliaquattuorquinquagintillion,
seven hundred twenty three quattuormilliamilliatrecensexviginmilliatrequinquagintillion,
nine hundred forty nine quattuormilliamilliatrecensexviginmilliadoquinquagintillion,
three hundred thirty seven quattuormilliamilliatrecensexviginmilliaunquinquagintillion,
five hundred sixteen quattuormilliamilliatrecensexviginmilliaquinquagintillion,
fifty four quattuormilliamilliatrecensexviginmillianovemquadragintillion,
one hundred six quattuormilliamilliatrecensexviginmilliaoctoquadragintillion,
one hundred eighty eight quattuormilliamilliatrecensexviginmilliaseptenquadragintillion,
four hundred seventy five quattuormilliamilliatrecensexviginmilliasexquadragintillion,
two hundred sixty four quattuormilliamilliatrecensexviginmilliaquinquadragintillion,
six hundred forty four quattuormilliamilliatrecensexviginmilliaquattuorquadragintillion,
one hundred forty quattuormilliamilliatrecensexviginmilliatrequadragintillion,
three hundred four quattuormilliamilliatrecensexviginmilliadoquadragintillion,
one hundred seventy six quattuormilliamilliatrecensexviginmilliaunquadragintillion,
seven hundred thirty two quattuormilliamilliatrecensexviginmilliaquadragintillion,
eight hundred eleven quattuormilliamilliatrecensexviginmillianovemtrigintillion,
two hundred forty seven quattuormilliamilliatrecensexviginmilliaoctotrigintillion,
four hundred ninety three quattuormilliamilliatrecensexviginmilliaseptentrigintillion,
sixty nine quattuormilliamilliatrecensexviginmilliasextrigintillion,
three hundred sixty eight quattuormilliamilliatrecensexviginmilliaquintrigintillion,
six hundred ninety two quattuormilliamilliatrecensexviginmilliaquattuortrigintillion,
forty three quattuormilliamilliatrecensexviginmilliatretrigintillion,
one hundred eighty five quattuormilliamilliatrecensexviginmilliadotrigintillion,
one hundred twenty one quattuormilliamilliatrecensexviginmilliauntrigintillion,
six hundred eleven quattuormilliamilliatrecensexviginmilliatrigintillion,
eight hundred thirty seven quattuormilliamilliatrecensexviginmillianovemvigintillion,
eight hundred fifty six quattuormilliamilliatrecensexviginmilliaoctovigintillion,
seven hundred twenty six quattuormilliamilliatrecensexviginmilliaseptenvigintillion,
eight hundred sixteen quattuormilliamilliatrecensexviginmilliasexvigintillion,
five hundred thirty nine quattuormilliamilliatrecensexviginmilliaquinvigintillion,
nine hundred eighty five quattuormilliamilliatrecensexviginmilliaquattuorvigintillion,
four hundred sixty five quattuormilliamilliatrecensexviginmilliatrevigintillion,
ninety seven quattuormilliamilliatrecensexviginmilliadovigintillion,
three hundred fifty six quattuormilliamilliatrecensexviginmilliaunvigintillion,
one hundred twenty three quattuormilliamilliatrecensexviginmilliavigintillion,
four hundred thirty two quattuormilliamilliatrecensexviginmillianovemdecillion,
six hundred forty five quattuormilliamilliatrecensexviginmilliaoctodecillion,
one hundred seventy nine quattuormilliamilliatrecensexviginmilliaseptendecillion,
six hundred seventy three quattuormilliamilliatrecensexviginmilliasexdecillion,
eight hundred fifty three quattuormilliamilliatrecensexviginmilliaquindecillion,
five hundred ninety quattuormilliamilliatrecensexviginmilliaquattuordecillion,
five hundred seventy seven quattuormilliamilliatrecensexviginmilliatredecillion,
two hundred thirty eight quattuormilliamilliatrecensexviginmilliadodecillion,
one hundred seventy nine quattuormilliamilliatrecensexviginmilliaundecillion,
three hundred fifty seven quattuormilliamilliatrecensexviginmilliadecillion,
nine hundred quattuormilliamilliatrecensexviginmillianovemtillion,
eight hundred seventy six quattuormilliamilliatrecensexviginmilliaoctotillion,
four hundred twenty six quattuormilliamilliatrecensexviginmilliaseptentillion,
one hundred three quattuormilliamilliatrecensexviginmilliasextillion,
nine hundred forty three quattuormilliamilliatrecensexviginmilliaquintillion,
seven hundred eighty two quattuormilliamilliatrecensexviginmilliaquattuortillion,
three hundred seventy six quattuormilliamilliatrecensexviginmilliatretillion,
four hundred ninety four quattuormilliamilliatrecensexviginmilliadotillion,
five hundred ninety one quattuormilliamilliatrecensexviginmilliauntillion,
seven hundred forty two quattuormilliamilliatrecensexviginmilliatillion,
nine hundred thirty four quattuormilliamilliatrecenquinviginmillianongennovemnonagintillion,
five hundred eighty eight quattuormilliamilliatrecenquinviginmillianongenoctononagintillion,
four hundred ninety seven quattuormilliamilliatrecenquinviginmillianongenseptennonagintillion,
one hundred seventeen quattuormilliamilliatrecenquinviginmillianongensexnonagintillion,
five hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquinnonagintillion,
one hundred forty six quattuormilliamilliatrecenquinviginmillianongenquattuornonagintillion,
nine hundred sixteen quattuormilliamilliatrecenquinviginmillianongentrenonagintillion,
nine hundred seventy two quattuormilliamilliatrecenquinviginmillianongendononagintillion,
nine hundred eighty four quattuormilliamilliatrecenquinviginmillianongenunnonagintillion,
seven hundred sixty one quattuormilliamilliatrecenquinviginmillianongennonagintillion,
one hundred fifty nine quattuormilliamilliatrecenquinviginmillianongennovemoctogintillion,
sixty quattuormilliamilliatrecenquinviginmillianongenoctooctogintillion,
eight hundred seventy three quattuormilliamilliatrecenquinviginmillianongenseptenoctogintillion,
two hundred fifty quattuormilliamilliatrecenquinviginmillianongensexoctogintillion,
nine hundred thirty nine quattuormilliamilliatrecenquinviginmillianongenquinoctogintillion,
four hundred sixty two quattuormilliamilliatrecenquinviginmillianongenquattuoroctogintillion,
eighty five quattuormilliamilliatrecenquinviginmillianongentreoctogintillion,
five hundred seventy five quattuormilliamilliatrecenquinviginmillianongendooctogintillion,
seven hundred forty quattuormilliamilliatrecenquinviginmillianongenunoctogintillion,
seven hundred fifty four quattuormilliamilliatrecenquinviginmillianongenoctogintillion,
five hundred seventy seven quattuormilliamilliatrecenquinviginmillianongennovemseptuagintillion,
ninety eight quattuormilliamilliatrecenquinviginmillianongenoctoseptuagintillion,
six hundred twenty quattuormilliamilliatrecenquinviginmillianongenseptenseptuagintillion,
five hundred fifty eight quattuormilliamilliatrecenquinviginmillianongensexseptuagintillion,
eleven quattuormilliamilliatrecenquinviginmillianongenquinseptuagintillion,
seven hundred seventy nine quattuormilliamilliatrecenquinviginmillianongenquattuorseptuagintillion,
five hundred twenty nine quattuormilliamilliatrecenquinviginmillianongentreseptuagintillion,
eight hundred eighty four quattuormilliamilliatrecenquinviginmillianongendoseptuagintillion,
forty two quattuormilliamilliatrecenquinviginmillianongenunseptuagintillion,
one hundred ninety eight quattuormilliamilliatrecenquinviginmillianongenseptuagintillion,
two hundred eighty seven quattuormilliamilliatrecenquinviginmillianongennovemsexagintillion,
six hundred forty three quattuormilliamilliatrecenquinviginmillianongenoctosexagintillion,
three hundred nineteen quattuormilliamilliatrecenquinviginmillianongenseptensexagintillion,
three hundred thirty quattuormilliamilliatrecenquinviginmillianongensexsexagintillion,
four hundred sixty five quattuormilliamilliatrecenquinviginmillianongenquinsexagintillion,
sixty four quattuormilliamilliatrecenquinviginmillianongenquattuorsexagintillion,
four hundred fifty five quattuormilliamilliatrecenquinviginmillianongentresexagintillion,
two hundred thirty four quattuormilliamilliatrecenquinviginmillianongendosexagintillion,
nine hundred eighty eight quattuormilliamilliatrecenquinviginmillianongenunsexagintillion,
one hundred forty two quattuormilliamilliatrecenquinviginmillianongensexagintillion,
one hundred thirty nine quattuormilliamilliatrecenquinviginmillianongennovemquinquagintillion,
five hundred sixty five quattuormilliamilliatrecenquinviginmillianongenoctoquinquagintillion,
seven hundred eighty five quattuormilliamilliatrecenquinviginmillianongenseptenquinquagintillion,
four hundred forty seven quattuormilliamilliatrecenquinviginmillianongensexquinquagintillion,
four hundred seventy four quattuormilliamilliatrecenquinviginmillianongenquinquinquagintillion,
twenty three quattuormilliamilliatrecenquinviginmillianongenquattuorquinquagintillion,
five hundred forty six quattuormilliamilliatrecenquinviginmillianongentrequinquagintillion,
three hundred fifty three quattuormilliamilliatrecenquinviginmillianongendoquinquagintillion,
seven hundred fifty eight quattuormilliamilliatrecenquinviginmillianongenunquinquagintillion,
five hundred thirty seven quattuormilliamilliatrecenquinviginmillianongenquinquagintillion,
three hundred twenty four quattuormilliamilliatrecenquinviginmillianongennovemquadragintillion,
eight hundred one quattuormilliamilliatrecenquinviginmillianongenoctoquadragintillion,
eight hundred thirty eight quattuormilliamilliatrecenquinviginmillianongenseptenquadragintillion,
one hundred twenty quattuormilliamilliatrecenquinviginmillianongensexquadragintillion,
three hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquinquadragintillion,
six hundred quattuormilliamilliatrecenquinviginmillianongenquattuorquadragintillion,
eight hundred sixty eight quattuormilliamilliatrecenquinviginmillianongentrequadragintillion,
four hundred sixteen quattuormilliamilliatrecenquinviginmillianongendoquadragintillion,
five hundred twenty five quattuormilliamilliatrecenquinviginmillianongenunquadragintillion,
four hundred quattuormilliamilliatrecenquinviginmillianongenquadragintillion,
seven hundred ninety quattuormilliamilliatrecenquinviginmillianongennovemtrigintillion,
three hundred eighty one quattuormilliamilliatrecenquinviginmillianongenoctotrigintillion,
two hundred eighty five quattuormilliamilliatrecenquinviginmillianongenseptentrigintillion,
eight hundred eighty eight quattuormilliamilliatrecenquinviginmillianongensextrigintillion,
two hundred fifty six quattuormilliamilliatrecenquinviginmillianongenquintrigintillion,
six hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquattuortrigintillion,
eighty five quattuormilliamilliatrecenquinviginmillianongentretrigintillion,
eight hundred fifty five quattuormilliamilliatrecenquinviginmillianongendotrigintillion,
four hundred fifty six quattuormilliamilliatrecenquinviginmillianongenuntrigintillion,
two hundred thirty one quattuormilliamilliatrecenquinviginmillianongentrigintillion,
five hundred seventy seven quattuormilliamilliatrecenquinviginmillianongennovemvigintillion,
five hundred twenty seven quattuormilliamilliatrecenquinviginmillianongenoctovigintillion,
nine hundred thirty nine quattuormilliamilliatrecenquinviginmillianongenseptenvigintillion,
three hundred five quattuormilliamilliatrecenquinviginmillianongensexvigintillion,
nine hundred twenty quattuormilliamilliatrecenquinviginmillianongenquinvigintillion,
eight hundred eleven quattuormilliamilliatrecenquinviginmillianongenquattuorvigintillion,
seven hundred sixty six quattuormilliamilliatrecenquinviginmillianongentrevigintillion,
five hundred eighty five quattuormilliamilliatrecenquinviginmillianongendovigintillion,
three hundred eight quattuormilliamilliatrecenquinviginmillianongenunvigintillion,
six hundred seventy quattuormilliamilliatrecenquinviginmillianongenvigintillion,
one hundred thirty two quattuormilliamilliatrecenquinviginmillianongennovemdecillion,
one hundred twenty nine quattuormilliamilliatrecenquinviginmillianongenoctodecillion,
one hundred fifty five quattuormilliamilliatrecenquinviginmillianongenseptendecillion,
two hundred twenty one quattuormilliamilliatrecenquinviginmillianongensexdecillion,
eight hundred four quattuormilliamilliatrecenquinviginmillianongenquindecillion,
three hundred eighty one quattuormilliamilliatrecenquinviginmillianongenquattuordecillion,
five hundred forty eight quattuormilliamilliatrecenquinviginmillianongentredecillion,
six hundred twenty five quattuormilliamilliatrecenquinviginmillianongendodecillion,
seven hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenundecillion,
nine hundred forty three quattuormilliamilliatrecenquinviginmillianongendecillion,
twenty quattuormilliamilliatrecenquinviginmillianongennovemtillion,
six hundred ninety four quattuormilliamilliatrecenquinviginmillianongenoctotillion,
five hundred twenty eight quattuormilliamilliatrecenquinviginmillianongenseptentillion,
fifteen quattuormilliamilliatrecenquinviginmillianongensextillion,
nine hundred ninety nine quattuormilliamilliatrecenquinviginmillianongenquintillion,
two hundred twenty one quattuormilliamilliatrecenquinviginmillianongenquattuortillion,
seven hundred eighteen quattuormilliamilliatrecenquinviginmillianongentretillion,
one hundred ninety one quattuormilliamilliatrecenquinviginmillianongendotillion,
five hundred fifty seven quattuormilliamilliatrecenquinviginmillianongenuntillion,
seven hundred sixty one quattuormilliamilliatrecenquinviginmillianongentillion,
seven hundred eighty nine quattuormilliamilliatrecenquinviginmilliaoctingennovemnonagintillion,
thirty eight quattuormilliamilliatrecenquinviginmilliaoctingenoctononagintillion,
five hundred thirty nine quattuormilliamilliatrecenquinviginmilliaoctingenseptennonagintillion,
five hundred twenty two quattuormilliamilliatrecenquinviginmilliaoctingensexnonagintillion,
three hundred forty nine quattuormilliamilliatrecenquinviginmilliaoctingenquinnonagintillion,
seven hundred forty six quattuormilliamilliatrecenquinviginmilliaoctingenquattuornonagintillion,
eight hundred eight quattuormilliamilliatrecenquinviginmilliaoctingentrenonagintillion,
seven hundred ninety seven quattuormilliamilliatrecenquinviginmilliaoctingendononagintillion,
four hundred seventy six quattuormilliamilliatrecenquinviginmilliaoctingenunnonagintillion,
nine hundred seven quattuormilliamilliatrecenquinviginmilliaoctingennonagintillion,
six hundred sixty four quattuormilliamilliatrecenquinviginmilliaoctingennovemoctogintillion,
fifty quattuormilliamilliatrecenquinviginmilliaoctingenoctooctogintillion,
six hundred one quattuormilliamilliatrecenquinviginmilliaoctingenseptenoctogintillion,
two hundred forty eight quattuormilliamilliatrecenquinviginmilliaoctingensexoctogintillion,
four hundred seventy three quattuormilliamilliatrecenquinviginmilliaoctingenquinoctogintillion,
two hundred six quattuormilliamilliatrecenquinviginmilliaoctingenquattuoroctogintillion,
eight hundred seventy four quattuormilliamilliatrecenquinviginmilliaoctingentreoctogintillion,
one hundred thirty three quattuormilliamilliatrecenquinviginmilliaoctingendooctogintillion,
one hundred ninety four quattuormilliamilliatrecenquinviginmilliaoctingenunoctogintillion,
six hundred sixty three quattuormilliamilliatrecenquinviginmilliaoctingenoctogintillion,
five hundred eighty five quattuormilliamilliatrecenquinviginmilliaoctingennovemseptuagintillion,
three hundred thirty four quattuormilliamilliatrecenquinviginmilliaoctingenoctoseptuagintillion,
nine hundred eighty three quattuormilliamilliatrecenquinviginmilliaoctingenseptenseptuagintillion,
eight hundred five quattuormilliamilliatrecenquinviginmilliaoctingensexseptuagintillion,
seven hundred thirty four quattuormilliamilliatrecenquinviginmilliaoctingenquinseptuagintillion,
eight hundred three quattuormilliamilliatrecenquinviginmilliaoctingenquattuorseptuagintillion,
six hundred twenty quattuormilliamilliatrecenquinviginmilliaoctingentreseptuagintillion,
seven hundred five quattuormilliamilliatrecenquinviginmilliaoctingendoseptuagintillion,
seven hundred seventy eight quattuormilliamilliatrecenquinviginmilliaoctingenunseptuagintillion,
two hundred seventy quattuormilliamilliatrecenquinviginmilliaoctingenseptuagintillion,
nine hundred ten quattuormilliamilliatrecenquinviginmilliaoctingennovemsexagintillion,
five hundred sixty one quattuormilliamilliatrecenquinviginmilliaoctingenoctosexagintillion,
seven hundred sixteen quattuormilliamilliatrecenquinviginmilliaoctingenseptensexagintillion,
seven hundred sixty seven quattuormilliamilliatrecenquinviginmilliaoctingensexsexagintillion,
six hundred eighty quattuormilliamilliatrecenquinviginmilliaoctingenquinsexagintillion,
nine hundred fifty four quattuormilliamilliatrecenquinviginmilliaoctingenquattuorsexagintillion,
eight hundred fourteen quattuormilliamilliatrecenquinviginmilliaoctingentresexagintillion,
four hundred fifteen quattuormilliamilliatrecenquinviginmilliaoctingendosexagintillion, 

BUT, with all that (using about 150 lines) there were over  4,321,381 lines omitted ...

What a mouth full!!!!

So, here is the goal. Using a large fake check made out for $100,000 and a small bag of candy, pose the challenge to see who can come up with the largest prime number using only paper, pencil and calculator (don't let them cheat on their cell phones by Googling) 

The eBay Experiment (Math & Business)

The eBay Experiment (Math & Business)



This is the perfect project for the educator who is familiar with selling on eBay! Those educators who are not acquainted with selling on eBay can also use this project but they should either take precaution that the project goes smoothly and everything is accounted for or have their students go through the motions of the exercise without actually listing the items.





This project involves asking each student to pick one item from their home that they wish to sell on eBay. The student will snap their pictures, write their product description and calculate their profit. This experiment could easily reach across disciplines and act as a writing assignment in their English class. (It's a good idea to get a permission slip signed by their parents to allow them to sell this item).









What You Will Need



An eBay Account

Paypal Account

1 Product To Sell

Camera To Snap Pics of Product

Permission Slip From Parents to Sell Product

Activity Sheet (see below)



Overview



Students will bring in their product to sell. The teacher will help the student take a picture of the product from multiple angles, fill out a description of the product and calculate the profits based on the activity sheet below. Students will learn the basics of revenue and cost by selling an item, subtracting the shipping and fees (students will need to calculate these fees by using percentages). And finally, calculate their profit.



Steps



1) Setup an eBay and Paypal account (can use your own or set up one specific for this assignment).



2) Designate a camera to use for all pictures



3) Have students bring a product into class to sell (with permission slip signed to sell it)



4) Hand out the activity sheet below to each student while at their desk and have them fill it out while you walk around the room taking pictures of each product.



Note: You will have lots of pics in your phone, so you should have a system to categorize each product with each student.



5) Have students turn in their worksheets



6) Have students begin writing a description of their product on a piece of paper.



7) If available, have each student turn in their description paper to their English teacher to be edited.



8) After receiving back their edited descriptions, have student type each description up and email them to you.



9) Use all the information to list each item. I would make this a classroom project. Using an overhead projector or smartboard, I would have each student come to the front of the class and fill out the eBay template to list their item. This will teach them the basics of eBay while also showing off what they are selling.



Note: There is no real rush here. You don't need to do auctions, you could opt for a fixed rate auction and use their study hall time to fill out these eBay forms. Additionally, you could have other projects going on while each student comes up individually to fill out their form. Just give it some thought on how to maximize your time.



10) After the product sells, each student should fill out a profit statement where they subtract their costs from their revenue (see form below)







Added Notes:



1) To make things simple, I would narrow the shipping options to Small, Medium or Large flat-rate boxes. The costs for these options can be found via the United States Post Offices website.



2) To make things simple, I would limit the size of each item to that it fits in the small, medium or large flat-rate boxes. To be sure of this, I would swing by my local post office and pick up some free priority flat-rate boxes so that they have an idea of size.



3) Although not as fun, it would be a lot easier if the students went through the motions of this exercise but didn't actually list the items





Listing Sheet:



Name of Item______________________________________________________

Category of Item______________________________________________________

Listing Prices______________________________________________________

Estimated Shipping______________________________________________________

Used/New______________________________________________________

If Used, Tell About The Condition_____________________________________________________________________________________________________________________________________________________________







Profit Sheet



Total Revenue:

Listing Price ________(A)



Total Cost:

Shipping Price ________(B)

Listing Fee (0.10) ________(C)

Final Value Fee (5% selling price) ________(D)

PayPal Fee (3% selling price) ________(E)

Misc Costs (Avg of tape, packagin, etc) ________(F)



Profit ________(A) minus ________(B-->F) = _________ (G)

Commutative, Associative and Distributive Comic Book

Commutative, Associative and Distributive


Math definitions rank up there with fractions as some of the most dreaded material for students to study. Here is a cute way to lighten up the classroom a bit.

Have students create their own super hero’s labeled Commutative Man, Associative Man and Distributive Man. The only catch is that the super powers must be related to the math properties. For example, Associative man may use parenthesis for force fields or since order doesn’t matter commutative man may be able to use his powers from both hands.

Teaching Percentages By Going On A Math-Class-Date

No need for elaborate drill and kill percentage worksheets. One good problem is worth 10 worksheets. The goal is for your students to be able to calculate a 15% tip in a real life scenario.

 

You need a menu, a candle.

 

Split up your classroom in groups of 5 students. two will be on a date the other will be the waitress.

 

Have each couple order from the menu. The waitress will add up the order by hand and bring them each couple the bill. The couple will then calculate a 15% tip.  

 

Bee Hives & Hexagonal Shapes

It's very neat to see how evolution discards waste. Here we have constraints on resources forcing bees to to create the "maximum amount of space with a minimal amount of material." The result is the use of hexagons. 

Scaling Models With Sabertooth Tiger Teeth.

Scaling Models With Sabertooth Tiger Teeth.

As many of you know I homeschool my two sons (nothing like doing math in your pajamas). I'm going to be posting some stuff that we do with my five-year old. It's basic but it may spark some ideas to use in your classroom.

In this lesson we talked about Sabertooth Tigers and how their two large teeth measured 12inches in length. I wanted to compare this to our teeth. So we measured and figured our that our teeth were about 7 tenths of an inch. The goal was to let him figure out what he would look like if he had sabertooth size teeth. This was the result. 

A Fancy Way of Adding Zero & The Additive Identity

I have a love/hate relationship with riddles. I love them when I can solve them quickly, hate them when they keep me up at night for something that is normally too obvious for me to notice.

Here is an older riddle, if I can call it that, which your students may love.

“Take any number. Now add 5 to it. Multiply that by 2. Subtract 6. Divide by 2 and finally subtract 2 and you back to your original number. Why does this work?”

1) Let your students try it first on a couple of different numbers

2) Now let them try to figure out why it works on their own.

3) Have them write down the whole operation, paying special attention to order of operations. (((((x + 5) * 2) – 6) / 2) – 2)

4) Again, let them try to figure out why it works on their own.

5) Ask them to go through the following operation ((((5 * 2) – 6) / 2) – 2) and see what number they get (zero is the answer)

6) Ask them to restate the Additive Identity

7) Thus, this whole problem is simply a fancy way of adding zero to your initial number.

In Pursuit of Perfection of Form

Our students often never understand how they misplaced a negative symbol or added instead of subtracting. They often think of this is a part of the math process, and it is, to an extent. Many times, to my own embarrassment, I've stood in front of a classroom and butchered a problem on the white board. My only self-medication for these "duh" moments was knowing that we deal in an unforgiving science.

But still, I often wonder why our students are so sloppy in their work. I once pulled a young man, who was an incredible basketball player, off to the side to ask how he perfected is form so well in the sport. His response was of course practice. If I would have thought about it at that time I would have paralleled his form in basketball with his form in my lecture hall, but I didn't.  I'm writing this now so that you may draw this parallel with your students.


Analyzing this

May be the key to helping your students perform this 

Coffee Taste Test Using Same Filter (Blind Sampling & Data Collection)

A question occurred to me today. As normal, I need my afternoon coffee. However, feeling excessively lazy, instead of making a new pot of coffee, I decided to simply fill the coffee pot back up and use the same filter from earlier this morning. As you can imagine, it wasn't exactly indulgent. Yet, I began to wonder if the coffee I was drinking was actually weaker, or was it my anticipation of it being weaker that made it so. Project!

Have your students conduct a blind taste test with other faculty members being their dummies. I would even let your students call them dummies...at least for the day. The taste test will involve each faculty to sample 3 small cups of coffee and record their data without knowing which cup of coffee is which.

Cup 1: First pot of coffee.

Cup 2: Same filter, same coffee, 2nd pot of water

Cup 3: Same filter, same coffee, 3^rd pot of water

The survey should be something simple, but measurable. For example, have them rank each cup of coffee on a scale of 1-10 with 10 being the highest.

Things to account for

1. When ranking, will the dummy be comparing the tastes of one cup to the other cups only, or will they be comparing them to previous cups of coffee. For example, if the dummy loves a White Chocolate Mocha from Starbucks as their number 10, they may rank all three of your cups a 1's or 2's. Thus, to account for this, you may want to raise the ranking system from 1-10 to something like 1-100.
2. Will the cups be served black or with sweater and cream? If the latter, you shuld make sure that each cup receives nearly the same amount.

After Results:

Have each student calculate some descriptive statistics (mean, median, mode, standard deviation, etc) and draw some conclusions. Does using the same filter and same coffee really make the coffee noticeably weaker? Or is it in our imagination?

Finally, the most important part of the activity is the after-activity discussion. Why might the tests be inaccurate? Was are sample size appropriate? What could we have done better? How might a double-blind test affect the results? Why might companies use blind taste tests when comparing their product to their competitors

Have fun...send me some pics if you decide to do the project!   

Representation & Modeling: Getting Your Students To Draw A Math Picture

A simple picture can go along way in helping your students solve an application problem. This is as true in pre-algebra as it is in calculus, however, representing the problem with a picture or diagram is often an overlooked step by students. The goal of the blog post is to help students see the value.

Drawing a diagram or other type of visual representation is often a good starting point for solving all kinds of word problems. It is an intermediate step between language-as-text and the symbolic language of mathematics. By representing units of measurement and other objects visually, students can begin to think about the problem mathematically. Pictures and diagrams are also good ways of describing solutions to problems; therefore they are an important part of mathematical communication. From Teacher Vision

Activity:

Take one full class and introduce nothing but word problem with the emphasis on using pictures to capture the problem. Next, quiz students on this vary concept. Read aloud to them a word problem and have them represent it in a picture while at the same time labeling everything they know. Use some variation the following rubric when grading their work.


Quality of Representation 1 2 3 4 5

Proper Labeling of Parts 1 2 3 4 5

Unneeded Detail             1 2 3 4 5


Lets Call Upon Another Example From The Teacher Vision Article

Question: A frog is at the bottom of a 10-meter well. Each day he climbs up 3 meters. Each night he slides down 1 meter. On what day will he reach the top of the well and escape--From Teacher Vision

Here is a possible representation of this problem.

Using Geometric Formulas To Simplify Life.

Bring in a nicely wound cord or garden hose (see below)

Explain to your students that you want them to determine the length of the cord or garden hose with the only condition being that they cannot stretch it out; they must find another way to measure the length.



Notice that the wound cord or garden hose is simply a bunch of circles stacked on top of one another. What if we calculated the circumference of the top circle and multiplied it by how many circles are formed by the winding process? Certainly you will be dealing with a margin of error here but it will at least get you in the ball park.

Note: be careful not to count a circle more than one time.  

Area of Irregular Shapes Using Roman Tortoise Formation

Out of curiosity, I decided to estimate the how effective the Roman Tortoise Formation was against opposing archery fire. Having only a few minutes during my morning coffee, I decided to limit my estimation to simply the front of the Tortoise Formation. Such an exercise would be fun for a classroom as well. Here was my thought ‘quick-an-easy’ process, feel free to point-out something more scientific or any potential mistakes.



The Goal: To estimate the area prone to archery fire with the Tortoise Formation.

Given: Google tells me that the Roman shield Scutum had the following dimensions


Height of Shield: 42 inches

Width of Shield: 26 inches.

Average Height of Roman man was 5 feet, 6 inches

Converting to feet, here is a general idea of the shape from the reference point of an archer standing directly in front of the formation.

Noting the rectangular shape and multiplying the average height by the width of six Scutum shields gives us an approximate area of

5.5ft x 13ft = 71.5ft^2

A = 71.5ft^2

The obvious areas prone to archery attack are the legs below the shield and within the semi-ellipsis surrounding their heads. To estimate these areas we could subtract the height of the shield from the average height of the man (5.5ft – 3.5ft = 2ft) and multiply this by the width of the six Scutum shields.

2ft x 13ft = 26ft^2

L = 26ft^2

As for the area’s within the six semi-ellipsis surrounding their heads, we could use the width of the concave shields (2.17ft) as half the circumference of the ellipsis and approximate the height of the radius as .5 feet. This would give us an approximate area of 1.7 ft^2 per ellipse (multiplied by all six would yield 10.2ft^2).

E = 10.2ft^2

Thus, for an opposing archer standing in front of the Roman Tortoise Formation would have approximately

• Area Prone to Attack = Area below the shield (L) plus semicircle areas above their shield (E).
• Area Prone To Attack = L + E
• Area Prone To Attack = 26ft^2 + 10.2ft^2
• Area Prone To Attack = 36.2ft^2

Or, approximately 51% of their body is exposed.

**Note: This seems a little high so I might have made a wrong approximation in length somewhere. Also, the roman soldiers body does not encompass the entire exposed area, so one would need to account for that as well. Nevertheless, this was just for fun.

Incorporating Puzzles (Homeschooling Our Two Boys)

Puzzles are excellent brain training and co-ordination improvement tools and are quite fun! In particular, they develop your abilities to reason, analyze, sequence, deduce, logical thought processes and problem solving skills. These types of puzzles also improve hand-eye co-ordination and develop a good working sense of spatial arrangements. See Full Article

Exponential Pushups: How Many Can Your Students Do

The purpose of this exercise is twofold; first, to show exponential growth, second to serve as a fun way of testing your student’s knowledge of exponents.

• Ask you classroom who can do 2 push-ups? Have someone show you.

• Explain that this is the same as doing 2^1 pushups.

• Ask you classroom who can do 4 push-ups? Have someone show you.

• Explain that this is the same as doing 2^2 pushups

Continue this exercise until you get to 2^7, from here have them calculate and image doing that many pushups. Where you stop from here is up to you.

Next, pair up your students and give them a worksheet with exponent problems. The only catch is, they must show you what the answer is by doing pushups.



Example,

• 3^2 a student from the group must show you the answer is 9 by performing 9 pushups.

Which Letters Of The Alphabet Are Graphs of Polynomials?

This light exercise is to get your students thinking about polynomial graph behavior. You could extend this exercise to guess they degrees and signs of the leading coefficients if desired. Simply print out a worksheet of all the letters of the alphabet and ask your students which letters are graphs of polynomials based on the following distinctions

1. Polynomial graphs are continuous. You can draw them without lifting your pen
2. Polynomial graphs have no sharp corners or cusps, they are smooth (see pic below).
   
   
   
   
   
   

(From www.mathisfun.com)

See mathisfun.com for a great tutorial and pics.

Using Word Search For Learning Key Words

Let's assume you want your students to learn all the key words for addition, subtraction, division or multiplication. Try using a word search without telling them the words to search for.

The Power of Actually Counting Large Numbers

One Thousand Pennies

 

Most four-year olds are very inquisitive. Mine loves developing his number-sense. He loves to ask me “Daddy, which is bigger ___ or ___ “as if the two numbers were about to bout, with the larger being the victor. Without ever practicing counting, he has learned to count to roughly 100 with only a few mistakes. More interesting than this is his development of number placement. Whereas many younger children can count, say to 10, ask them to count backwards and they begin to struggle. Although not fast, my son tends to count backwards just as well as forwards and I think the reason for this is that he developed his sense of numbers slowly without being asked to chant “one, two, three, four…” out loud until he remembered it. With this in mind I want to show you where counting has much more power, with large numbers.

One day my son asked me why 1000 was larger than 100. As most would, I started by telling that it takes ten 100’s to make 1,000, etc, etc. But noticing the blank look I asked for his patience as I decided to count aloud to 100 and then continued onward to 1000. His bright eyes sold me! There was no doubt after about 15 minutes later that 1000 was bigger than 100. To this day he still remembers how big it was.

 

How To Use This In A Classroom

For a better appreciation of larger numbers from your students have them count them.

Take 15 mins of down time and have your students listen as you count aloud to 10, than 100 than 1000.  Have them time you (you will most likely average one number per second). Next, have them calculate how long it would take to count to 10,000 or 100,000 or 1 million.  Have them express this in terms of days or hours.  

One Million Pennies

One Billion Pennies

 

 

Purchasing Fictional Stocks For Math Class

The goal is for students to calculate values & percentage change of fictional stocks. One could easily have them graph results as well.

Getting students interested in investing and budgeting can start in your math class. Give each student $100 of play money and a copy of stock/commodity prices (easily found in Wall Street Journal or online). Have students scour the handout of stock prices and pick which stocks/commodities they would like to invest their $100 in. After doing so, have them calculate how many shares they purchased of each (round to the nearest tenth for ease).

Next, over the course of the next month, have them track their investment (either by you reproducing the pricing sheet or by them checking online). Each week have them recalculate their balance based on the change in stock price and the percentage change.

Example:

Change in Value:

$100 @ $25 per share = 4 shares.

If after 1 week the new price is $24 per share your investment is = $96 (4 x 24).

Percentage Change:

96 – 100 = - 4

- 4/100 = -.04 or – 4%

At the end of a designated time period, have students sell their shares and pay them back in pretend money.

**Differentiated Instruction: If you had some advanced students who really liked this exercise but wanted more, you could discuss short-term capital gains taxes and have students calculate their actual profit.