Warm-up Activity Involving Time

I love my Think Geek Math Clock! But even if you haven't purchased the clock yet, you can still implement the idea. Simply draw a circle on a piece of paper, add a problem and ask your students to draw the answer in time. As you can see in the problem below, the time is 4:00.

Water Project

More Real Number Extra Credit

Volume of a cylinder & The sum of Areas

“Why do we need to know this?” How often do we get these questions in the classroom? Sometimes in order for students to see the value in mathematics you must take it away from them.




Take for example the formula for the volume of a cylinder, V = (pi)(r^2)(h)

If you take away the (h) within the equation you are left with the equation for the area of a circle. Thus, as we know, a cylinder is simply a bunch of circles stacked over top of one another. But, do your students know this?

Here’s an exercise,

1) Bring in a printable worksheet with numerous circles of equal size

2) As your students to cut out each circle

3) Next, ask them to find the sum of all the areas of each circle they cut out

4) Next, ask them to stack all the circles and use a ruler to measure its height

5) Finally, ask them to find the volume of the cylinder using V = (pi)(r^2)(h)

6) Does it closely resemble the sum of areas they previously calculated?

7) Wasn’t it a lot faster?

Creating a Valuable Expression Game

Creating a Valuable Expression Game

You know the routine, 2x + 3z, evaluate the expression when x = 2, z =1


You see the disconnect here right? None of our students care what the solution is. Now, let’s create a new expression in which students value the solution.


You need

1) A tennis ball

2) Meter/Yard Stick

3) Stop watch

4) A football field/ or play ground

5) And an expression worth evaluating



Here’s the goal. Students will be given points based on two variables: hang time (t), distance (d).



New expression: 2t + 3d



1) Have your students line up at the goal-line of a football field

2) Designate a ball return person

3) Have each student throw the tennis ball as high and as far as they can and record the hang time and distance

4) When you return to the classroom, write the expression on the board and have each student evaluate their points to see who the winner is



Extra: Want to make it harder? Use decimals or fractions.

For example use the expression 2.1t + 3.2d or 2/3t + 3/4d

Real Number Beer Pong (Extra Credit)

**although not for public school consumption, this is a very neat activity by one of my college students**

More Real Number Extra Credit

I'm a sucker for the real number system :) I love offering extra credit for this topic. Here is a cute idea based on a theme I did many posts ago titled "Pin The Tail On The Real Number Donkey". A student of mine had the same idea and her donkey looks better than mine. The only flaw is that her 'irrational' circle is mixed with the other 'rational' circle. It's still a cute project though!

Making Use of Old Phone Books

Old phone books may still offer some mathematics educational value.

 

It has plenty of built in subtraction problems

Another project would be to weigh the phone book and calculate the approximate weight of all the phone books in your area. You could even assign an approx cost if you research materials.

But, of all these, the best exercise for authentic learning I can think of is to simply ask your students what we could do with all these phone books? How could they be used in education?

Math For Breakfast

Here's the scenario, it's Monday morning and your kids are sleepy. The last thing on their mind is learning math. The solution could be as simple as a box of Fruit Loops or Cocoa Puffs!

These yummy treats are packed with fun ways to teach math.

Area, circumference or circles or spheres
Ratio's and Probabilities involving of colors
Adding, Subtracting, Number Sense...the list goes on!

Number Sense For K-2 (Piggybank)

I love this idea offered by one of my previous students. 

Using a picture of a piggybank, seven pennies and construction paper, students may arrange the number seven in various ways showing the properties of equality. 

Using T-shirts To Teach Math Properties

(Be sure to ask your local stores for donations)

Geometric Angles & Putt Putt (Math Field Trips)

Why can't we have more math fieldtirps! Kick off the new year by requesting a field trip to learn angles! And what better place to earn various angles than a putt putt corse

(Mini Golf With My Son)

Compound and Simple Interest & Your First Home

Compound and Simple Interest & Your First Home

 

This is a neat activity if you need to teach compound or simple interest. Bring in one of your local real estate books (or print real estate pics online) and have your students choose which house they would like to live in. Next, have them calculate the total amount they will pay over the course of 30 years using both formulas (if you are teaching younger students who need not yet learn compound interest it may still be in the interest of the teacher to calculate the same home using the compound interest formula)



Playing Squares with Addition, Multiplication, Division & Subtraction

Playing Squares with Addition, Multiplication, Division & Subtraction

Here is another great resource from Mathwise. The game is played normally, like you would play squares (for an example click here) but once the students complete a square using lines they must answer the math question inside the square to get points. If they answer incorrectly, no one get the points.

Word Search Math: Another Wonderful Exercise From Mathwise

Mathwise offers some great exercises. This particular exercise involves a number grid and your choice of addition, multiplication, subtraction or division used with an equal symbol

Simply create, or print off, a number grid and give your students the rules of play

In the exercise below, the students may only use the multiplication symbol and the equal symbol

The students search for numbers that could be multiplied. Next they add the “X” and the “=” symbol and circle.

Sample Space, Clothing and Outfits

Normally a discussion on probability or statistics begins with outcomes from an experiment, what we refer to as sample space


Taken From CNX.org

A sample space is a set or collection of outcome of a particular random experiment.
For example, imagine a dart board. You are trying to find the probability of getting a bullseye. The dart board is the sample space. The probability of a dart hitting the dart board is 1.0. For another example, imagine rolling a six sided die. The sample space is {1, 2, 3, 4, 5, 6}.

Examples of Sample Space.

• The tossing of a coin, sample space is {Heads, Tails}
• The roll of a die, sample space is {1, 2, 3, 4, 5, 6}
• The selection of a numbered ball (1-50) in an urn, sample space is {1, 2, 3, 4, 5, ...., 50}
• Percentage of calls dropped due to errors over a particular time period, sample space is {2%, 14%, 23%, ......}
• The time difference between two messages arriving at a message centre, sample space is {0, ...., infinity}
• The time difference between two different voice calls over a particular network, sample space is {0, ...., infinity}

Many educators use a tree diagram to help students understand outcomes which is a very handy tool. 

(Flipping a Coin and Rolling A Die)

Yet, even with a great tool like a tree diagram, there is still a disconnect between the teaching and the student. We need a better way to reach them!

I like this idea suggested by one of my statistics students!

How Many Outfits Can I Wear?

Using stickers of different clothing (shoes, hats, dresses, etc), let your students discover the amount of mixing and matching they can perform to create different outfits. 

Composite Functions and Almonds f(g(x))

Here's a tough concept for high school math students, composite functions (for more on functions click here)

Definition of Composition of Functions

• Composition of Functions is the process of combining two functions where one function is performed first and the result of which is substituted in place of each x in the other function. 

Yet, what does this actually mean? And how can a young student of math make sense out of such abstract definitions. Let's call upon an analogy using almonds.


Let our ultimate goal be to have roasted almonds mixed with other assorted nuts. Thus, we have two machines; one that roasts the almonds and one that adds other assorted nuts in with the roasted almonds.

But, loosely speaking, a machine is simply a function; it transfers inputs to outputs (or in the language of math it transfers domains to ranges)

Let us revisit our example

(Here is a picture of our process f(g(x))

(Let x, our input, be regular almonds)

(We feed our regular almonds in our first machine, call it our g machine, which roasts our almonds)

(Our g machine takes plain almonds and roasts them, thus, it takes almonds x and roasts them making them g(x). We then take our roasted almonds and use them as our input in the next machine) 

(Here is out next machine, our f machine. Our f machine takes roasted almonds and adds assorted nuts )

(Thus, our final output for our regular almonds after traveling through two machines is roasted almonds with assorted nuts; f(g(x))

(Here is how such a concept would look in a textbook)

Number Sense For PreK-Kindergarteners

This is a cute idea created by one my Hands on Math students who teaches kindergarden. 

The Idea is to have your students arrange the skittles on their card to match the one given to them. After each card the students count the number of skittles they have. The goal is to arrange, for example, six skittles in a variety of different ways on a 5 x 2 card so that students become accustomed with estimating.

Paperclip Division With Remainders

This is a clever idea one of my students came up with for teaching division with remainders.

The student may either place the remainder from their division in the middle page or the amount of times the number divides (not shown here). The student may then either place the remainder or the amount of times the number divides on the edges of the construction paper. This particular student decided to do clusters of paper clips around the edges in 25's.  

Extra Credit From My Statistics Students

Go Faith! Awesome Job With Your Extra Credit!

Rollout Math

This is a neat, cheap and quick idea for teaching basic arithmetic operations taken from the Hands on Math book MathWise. In the pictures I use the letter x, but the project would be neater if you used stickers. 

Paperclip Multiplication, Division, Addition and Subtraction

Here is a fun and cheap exercise for teaching Multiplication, Division, Addition and Subtraction. 

1) Notice how the number three is in the middle of index card

2) Have students use paper clips and each sign +, -, x, / to form a problem with the answer of three

(3 paper clips divided by one paper clip = 3)

This is a fun riddle (be careful it's not what you expect)

What is heavier a pound of feathers, or a pound of gold?..........................................................................................................................................It's actually feathers!


....................................................................................................................................................

.......................................................

Weights of feathers are given in Avoirdupois units whereas gold is given in Troy units. A Avoirdupois pound is 453.59 grams whereas a Troy pound is 373.24 grams

Enjoy Your Summer Everyone!!!!!

I will be posting sporadically this summer but will start back up full-time in August. Please contact me if you have any ideas or math subjects that you want me to post about. 

Please Tell Me Your Schools Out For Summer

If anyone is looking for some last min ideas, feel free to check out Vi Harts website http://vihart.com/ for awesome videos

Working On A Detective Story To Teach Math Properties

[Door slams open and in walks a pretty, blond, number 1 with high heels]

Number 1: "You a detective"



Detective Number 4: "You askin, or are you tellin"



Number 1" What difference does it make"?



{Detective number four is staring out the window]



D4: "The difference is always in the maken tootse"



Number 1: Listen, i need help! Now, are you the detective i need to speak with or not?"



D4: "You don't need a detective love, you need muscle and muscle aint what i do ya see?"



D1: "How do you know what i need?"



[detective number 4 turns and looks her over]





D4: I know, cause them heels been talkin since you turned the corner on Elms street. Whose in trouble huh? Your husband, Your lover. What difference does it make...you need muscle and muscle ain't what i do.



[detective 4 turns and looks back out the window]



Number 1: It's my brother...x...he's got himself into some trouble and now he's got himself held up



D4: Whats this got to do with me heels?



Number 1: He needs your help detective...I, need, your, help [she gets closer to and puts hand on his arm]



D4: Let me get this straight, your baby brother shook some hands and bet on black when he should of bet on red and now that he wants to take someone elses money for a ride you volunteering my services? I think I'll pass sweetheart



D1: It's not that simple. He didn't just shake hands with anyone, he shook hands with the likes of "three eyes"



[detective number four turns and looks at her]



D4: "three eyes"?



Number 1: "yes, three-eyes and if i don't help him their not only going to hurt him, their going to hurt his wife and kids...two boys, both still fractions"



D4: "you got that right tootse, three eyes is gonna off him, his wife, his fractions and you". You want my advice, I'd grab them kids and take a one-way train out of this state"



Number 1: And tell his kids they don't have a father anymore



D4 "it's better than the alternative"



Number 1: "Listen, either your going to help me or i'm going by myself...i can take care of myself but i can't let anything happen to those little fractions"



[detective 4 starts daydreaming of those two little fractions]



D4: "Where's he held up at"



Number 1: "Downtown, in the old abandoned parenthesis...are you really going to help us? [big smile]



D4: "I didn't say i was going to help...but i'll make a few phone calls. Now you go on home and call me tomorrow, you hear?"



Inner monologue "i always was a softie when it came to blond hair and high heels"



[Shows detective standing outside of abandoned parenthesis, smoking with a top hat. A gloomy, cloudy night]



{detective peeks through the window and sees



(5x - 3)



x is the brother

3 is “three eyes

5 is a soldier

The minus symbol is a knife



[detective moves to the door of the parenthesis to knock but hears the conversation going on inside”



#3 “Listen...see...i’m tired of waiting for my money to appear. I told you you had 24 hours to get me my money and the times winding down. Tell me why i shouldn’t cut my losses if you know what i mean?”



x “Please, think of my kids, their only fractions”



#3 “It ain’t me who needs to be think of your kids x, it’s you”



x: “Please, i promise i can get it by this time next week”



#3: “You got to be kidden me, you know who i am? I’m done dealing with this guy...time for you talk to the worms”



[detective number four knows what he has to do, he breaks through the parenthesis door and “distributes punishment” to 5x and 3 like so



(4)(5x) - (4)(3)



20x - 12



Latter shows the grave of the detective, with the blond in heels over looking, holding the hands of the little fractions.



Number 1“this man combined his life to save you boys, you remember him in your thoughts ok?”



The End



Tips For Writing Your First Book

Here is a project i've been working on for a few months, see my math downloads section to download the e-book for free

Your Book Now PDF

Parabolas and Water Fountains

The term parabola is often associated with the quadratic equation but students often encounter parabolas much earlier in their studies. For many, a parabola is simply a “u” or an “n” shape; either the top half of a circle or the bottom half. Later, when students start transforming the graphs of functions they begin to notice that parabolas can be wide or narrow in addition to being the shape of a “u” or an “n”. It was Apollonius who gave the shape its name, but it was Galileo who showed that projectiles falling under uniform gravity follow parabolic paths.
We can find parabolas everywhere in nature including water fountains.

What better way to introduce parabolas to your students than to take them to the local park and view the water fountains (If travel is an obstacle, look to your hallway to investigate the drinking fountains).

Potential questions to ask your students:
-Is the shape positive or negative?

-Is it narrow or wider than the graph of x^2

-Where is the vertex?

-Where on the graph is its slope zero?

-Where on the graph is its slope positive?

-Where on the graph is its slope negative?


Extra credit type of questions:

-What is a way to determine the area under the parabola?

-Given two parabolas and two potential equations, which equation is probably the best fit for which graph?


More involved experiment:

-Have your students use yard sticks for your x and y axis and try to find the equation of the parabola.