Driving Blind?

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.

The Ultimate B-Day Expression

The purpose of this activity is to have some fun doing expression work. Students will substitute information into an expression with the end result being their birthday. Feel free to use calculators to make this a quick exercise. Here is the expression.

X = Month Of Your Birthday


Y = Day Of The Month Of Your Birthday

Note the vast amount of grouping symbols the kids will need to keep track of.

Example: My birthday is November 21st

x = 11
y = 21

My Math is thus

7(11) = 77
77 - 1 = 76
76(13) = 988
988+ 21 + 3 = 1012
1012(11) = 11132
11132 -11 -21 = 11100
11100/10 = 1110
1110 + 11 = 1121
1121/100 = 11.21 (11.21 is my b-day)

Math O’clock

Whether you’re teaching addition, subtraction, multiplication, division or algebra, nothing is better on a Monday morning than getting your kids out of their seat to do math problems. I call this game Math O’clock.

Steps:

Step 1: Have 12 students form a circle like a clock with each student representing an hour, like so.

Step 2: Have the rest of the class form a line

Step 3: Using index cards with pre-chosen problems that yield answers between (0,12], hand each student in line a problem in the index card for them to solve.

Step 4: Students must demonstrate their solution by lying on the ground inside the circle-clock using their feet as the hour hand and their arms as the minute hand to demonstrate the solution to their index card, like so.

Step 5: Make sure you have a rotation schedule so that all your students get to play.

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)

Buy The Play Doh Algebra Math Packet

After much demand, and personal sweat, i have finally put together the Play Doh Algebra Math Packet. You can purchase the packet for $2.99 by clicking the pics above or the link below.


Here is a product description 
"The following packet offers an awesome hands on way for teaching algebra. Each lesson has pictures, a detailed lesson plan, after activity worksheet, powerpoint and homework assignment.

Your students will have a blast learning equations with this activity. Everything is included (except the Play Doh :)"

Equation Sandwich Anyone? How to eat Algebra

I credit this idea to something similar in The Creative Teacher
<------------------------------------ One of the best books for Classroom Creativity




One of the great mysteries of the math teacher is how to get your students to show their steps!  Here is something that might help. Have them create an Equation Sandwich!





First you need bread(2), mustard, tomatoes, mayonnaise,  ham, cheese and lettuce like so

(bread(2), mustard, tomatoes, mayonnaise,  ham, cheese and lettuce)

Each piece represents a step of your algebra problem

2x + 3 + 6x - (-1) = 20 (Bread)

(2x + 6x) + (3 + 1) = 20 (Mustard) 

8x + 4 = 20 (Tomatos)

8x + 4 - 4 = 20 - 4 = (Mayo)

8x = 16 = 16 (Cheese)

8x/8 = 16/8 (Ham)

x = 2 (Lettuce) 

Showing Work (Bread) 

(You Get An Equation Sandwich)

(Eat The Knowledge!)

Solving Equations Using Weigh Scales

The following is a hand drawn experiment, however, i believe it would best be received if the educators actually used a scale and a real doggy-bowl(or a paper bag) on both sides to represent the variable as well as actually manipulated the experiment so as to show how the scale must balance. Thus, i'm well aware that the hand drawn experiment here is flawed...but i think you'll get the idea :)

How Many Bones Are In The Dog Bowl

Use Algebra To Solve

Now look in the dog bowl to see if you are correct?