Wednesday, December 26, 2012

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.

Monday, December 24, 2012

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.

Friday, December 21, 2012

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.

Wednesday, December 19, 2012

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

Monday, December 17, 2012

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.

Friday, December 14, 2012

Measuring Repulsion & Attraction With A Ruler

I love magnets! Even as a kid I enjoyed carrying magnets with me everywhere I went. I still remember the first time I stuck a magnet up to my grandmothers TV (Opps!). Although the study of magnetic properties can be pretty involving, magnets themselves offer great ways to bring simple lessons to life. In this lesson we will measure the effects of repulsion & attraction when two magnets interact. We will measure their interaction with a ruler.

What You Will Need

• Rulers

• Various Size/shape magnets (preferably labeled A, B, C...)

• Activity Sheet

Overview

Students will use various magnets to measure repulsion and attraction. Using a ruler, students can use the same polarity to repel the other magnet and record the distance of that repulsion. Next, using the same two magnets, students can use opposite sides of polarity to measure the distance along the ruler from which two magnets attract one another (be careful with the fingers!)

Steps

Step 1: Create groups of partners and give each group a ruler, bag of magnets and activity sheet.

Step 2: Have groups spread out along the floor

Step 3: Have student pick two magnets and use a ruler to measure the distance upon which they attract, and repel.

Step 4: Filling in activity sheet

Activity Sheet

1) Magnet______ and Magnet_____

a) Attraction begins slightly at _______cm apart.

b) Repulsion begins slightly at _______cm apart

c) When set beside each other they repel ____cm distance

d) At ______cm the two magnet fully attract (snap together)

Wednesday, December 12, 2012

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.

$((((((((((((7x)-1)\cdot 13 + y +3)\cdot 11)-x -y)\div 10)+11)\div 100)$

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)

Monday, December 10, 2012

Firewood By The Truck-load: Volume & Per Unit Pricing

Let's assume you got behind on your firewood splitting and needed to purchase some firewood for a week till you get caught up. You check you local paper and see they have prices of $80 per truck-load. What can one expect from a truck-load of wood? How many units? How much is this per unit? We will be using some basic volume to get the number of units and use this number to get a per unit price. We could then decide how long it will last based on types of wood, etc (Note: The purpose of this activity is for the application more so than for the usefulness. As anyone whose ever split wood knows, quality has more to do with density and how well the wood is seasoned..see below) Measurements Used Full Size F-150 Long-bed Truck Length = 8ft Width = 6.5ft Height = 1.6ft Piece of Firewood (We will assume the average log length is 18inches and has a radius of 8 inches which will be cut into 8 pieces for firewood) Units of Firewood by Volume For the sake of ease, let us assume that a truckload of firewood will be neatly stacked but not higher than the sides of the truck. Volume of truck bed 8x6.5x1.6 = 83.2ft^3 Volume of Firewood Log Changing Our Units to feet length = 18 inches = 1.5ft radius = 8 inches = 0.66ft Volume of a cylinder equals V = (pi)(r^2)(h) V = (3.14)(0.44)(1.5) = 2.05ft^3 Volume of Firewood Piece (once split into 8 pieces) 2.05ft^3 / 8 = 0.26ft^3 Units of Firewood Per Truckload Now that we know the volume of both the truck-bed and for a piece of fire wood we can simply divide them to see how much firewood should stack neatly into the truck-bed 83.2 / 0.26 = 320 pieces of firewood Adjusting For The Odd Shapes Since the pieces of firewood are not cubic, they are circle-sections. They will not stack neatly together. There will be added spacing between them. The seller could compensate for this by stacking the firewood above the walls of their truck, but we will assume they didn't. This spacing could be compensated with a little optimization. But, from stacking wood I think it would be safe to say that four every 10 pieces you will loose one to spacing. Thus we will loose 1/10th of our total to spacing. 1/10 of 320 = 32 320 – 32 = 288pieces of firewood. Prices Per Unit At the rate of$80 per truck-load. We have $80 per 288 pieces of wood 80/288 =$0.28 per unit.
The Calculations Are Quite Arbitrary

These calculations are quite arbitrary in their usefulness. Most firewood comes in different sizes. A true calculation of how good the deal on firewood would to compare volume to density as well as how seasoned. The purpose of this posting was simply to serve as an application.

From Here We Could

From here we could ask questions like.

1) If we use 40 pieces of firewood per night, how long will this last us?
2) If you wanted to, you could make a step-function based on how cold it is outside.

At 40 degrees we use 10 pieces of firewood per night
At 30 degrees we use 30 pieces of firewood per night
etc.

3) Could recalculate based on the volume questions for different size truck-beds or different materials

Friday, December 7, 2012

The purpose of this activity is short but important. That is to help students NOT associate number of outcomes with probability of outcomes. One could probably teach this to their students faster than they can read this post.

The Problem:

Khan Academy (the wonderful, wonderful people they are) was asked by Lebron James what the chances of making 10 free throws in a row? I won't attempt to outdo Sal on this one

But I want to draw attention to what I find to be a more interesting problem. That is, why do students tend to associate the number of outcomes with the probability of outcomes? In other words, students tend to sometimes think of outcomes such as hit/miss, win/loose, yes/no, etc in terms of each result having a 50/50 chance. Or again, we tend to think that probabilities of outcomes are always distributed equally. This is a dangerous error to make in life, but the good news is that this is often more an academic mistake than a real-life mistake

For example, ask the following two questions to the same person and see what answers you get.

1) If you shoot a basketball, whats the chances of it going in?
2) If you shoot a full court shot, are you more likely to make it or miss it?

The Solution:

The good news is that you can quickly teach kids to be skeptical of this by taking them to a basketball hoop during activity time or gym class and asking the two questions above, then testing them.

Wednesday, December 5, 2012

Variation Of "Bowling For Facts" Integers Addition

I love the creativity of elementary teachers! One notable project I found was First Grader At Last

I will reproduce their idea below and then show you a variation of how it could be used for teaching higher level math.

Here is a recap of their project

Today during math stations, the kids went bowling for addition facts...without the real pins and bowling balls, but still pretty fun! This is a partner game, and each player gets a bowling mat and a handful of colorful chips (I call them mini bowling balls). The players take turns rolling 2 dice, then adding the sums of the numbers rolled. When one of the players rolls a number found on one of their pins, they "knock over" that pin with a chip. The first player to have all pins knocked over wins the game! “

Here is a variation of the game that would allow you to teach adding and subtracting integers.

Using red and white dice (red =negative numbers, white = positive numbers)

The new bowling mat would look something like

 New Bowling Answer Sheet For Integers

Example

Roll Both Dice
Red = 5
White = 2

-5 + 2 = -3

Monday, December 3, 2012

Need a fun way for students to learn different polygonal shapes? How about making some special polygonal glasses or masks? Notice the octogon shape lenses?

 (Hey, no laughing at my horrible artwork!)

Today were going to expand our attire…polygonal style! The purpose of this activity is for groups of students to make their own masks or glasses while using different shaped lenses.

Here is a link to some printouts.
http://www.firstpalette.com/tool_box/printables/superhero.html

Friday, November 30, 2012

Teaching Integer Addition & Multiplication Tables Using Corn-hole

Corn-hole has become all the craze for parties. I can think of a dozen different ways they could be used to teach math lessons. I will share two of these ideas below.

Using Corn-hole to Teach Multiplication Tables

This activity would be great for the whole class but I truly think it would be a wonderful tool for helping those students who are behind to catch-up. If I was still in the public schools, I would single out the students who still struggle with their multiplication tables and find time during activity period, study hall, etc for them to play this game.

Essentially, you will have two different colored bean-bags. Both colored bean-bags will be labeled 0 through 12 (this can be done with a black marker). The student will be given both sets of bean bags. They will choose two bags from both colors and toss them.

Rules of Play

1) If they make both colors in they will multiply them and add this number to their score

2) If they make one color but not the other, they multiply them but do not add them to their score

3) If they miss both of them, they multiply them and subtract the number from their score.

Examples Of Three Tosses:

Toss 1: Blue Bag 2, Red Bag 5

-I make both: I record my answer and my score is 10

Toss 2:Blue Bag 6, Red Bag 1

-I make one, but not the other: I record my answer but my score is still 10

Toss 3:Blue Bag 4, Red Bag 2

-I miss both: I record my answer and subtract 8 from my score (new score is 2)

Score Sheet:

A score sheet could be something simple like

Red Bag #_____ Blue Bag #_____

_____x _____ = _______

Circle One: Made Both Missed One Missed Both

Score______

Using Corn-hole to Teach Integer Addition & Subtraction

The setup is the same as above, two different colored bean-bags. Both colored bean-bags will be labeled 0 through 12 (this can be done with a black marker). The student will be given both sets of bean bags. They will choose two bags from both colors and toss them.

Only now the blue color represents positive integers and the red bags represent negative integers.

After the toss, students will record the sum of the positive and negatives.

Examples Of Three Tosses:

Toss 1: Blue Bag 2, Red Bag 5

-I make both: I record my answer as positive 2 combined with negative 5 (2-5 = -3) and record my answer as a positive score. My score is 3

Toss 2:Blue Bag 6, Red Bag 1

-I make one, but not the other: I record my answer as positive 6 combined with negative 1 (6-1 = 5) but nothing is added to my score. My score is still 3

Toss 3:Blue Bag 4, Red Bag 2

-I miss both: I record my answer as positive 4 combined with negative 2 (4-2 = 2) and subtract this from my total score. My score is now 1.

Wednesday, November 28, 2012

Tips For Teaching Horizontal & Vertical Shifts

To help your students understand vertical and horizontal shifts in graphs they need to start thinking in terms of x/y-intercepts, not x/y values. We will label this the method the horizontal slide vs the vertical slide.

Horizontal vs Vertical Slides of Function Graphs

Here is the graph of f(x) = x^2

Here is the graph of x^2 with a Vertical shift of 2 units (f(x) = x^2 + 2)

Here is a graph of x^2 with a horizontal shift of 2 units f(x) = (x-2)^2

Students' Trouble In Understanding

Most students tend to understand vertical shifts. It seems intuitive to them that adding 2 to x^2 will shift the graph 2 units in the positive direction. However, students tend not to understand the horizontal shifts. It seems backwards to them. The reason for this is that students are concentrating on what is being done to the variables as opposed to the x/y-intercepts. The task of this activity is not mastery but to shift the students' focus to what's happening with the intercepts instead of the what is being done to the variable.

What You Will Need

• graph paper
• multiple color markers
• Activity Sheet

Steps:

Step 1: On blank (x,y) coordinate graphing paper have students plot the following graph by generating random points.

f(x) = x^2

Step 2: Have students analyze the graph and determine the x-intercept and the y-intercept.

Step 3: Ask them what would you need to do to the graph of x^2 to change the y-intercept.

Step 4: Have them redraw the graph of x^2 anywhere else they want on the y-axis as long at it doesn't shift to the left or right.

Step 5: Ask the question how many units did your graph shift upward or downward?

Step 6: Have them contemplate what their new function will look like. Will it be x^2 plus 2, minus 2, multiplied by 2, divided by 2, etc.

Step 7: Show them what the new function will look like

f(x) = x^2 + 2

Step 8: Have them determine what the function would like if their graph what shifted up 2 more units. What would it look like if it was shifted down 5 units?

Step 9: Have them draw the two new graphs and write the new functions beside them.

Step 10: Ask them what changed in the graph, what remained the same.

Repeat the process with Horizontal shifts, having them concentrate on the x-intercept as opposed to what is being done to the variable x

Tuesday, November 27, 2012

How Much Soda Do You Loose From Fizz When Pouring?

Intro:

You know the routine, you open of a 16 ounce bottle of Pepsi and start filling your glass. As you pour the soda you notice a fizz is starting to form causing you to stop and wait so the carbonated bubbles don't spill over the rim of your cup. While waiting you begin to wonder, how much soda am I loosing by pouring it? Maybe I should just drink it from the bottle, at least I wouldn't need to wait for the fizz. The purpose of this activity is to figure out how much, if any, soda you loose when pouring it.

What You Will Need:

• Multiple 16 ounce bottles of soda (one for each group)

• A measuring cup that measures 16 ounces (16 ounces = 2 cups)

• Activity Sheet (below)

• Paper Towels

• An intro speech about being careful to avoid spills
Outline of Activity

Students will split-up in groups. Each group will pour 16 ounces of soda into a measuring cup (WITHOUT SPILLS!). They will wait for the fizz to halt and continue pouring until all soda has been poured. Students will then estimate how much, if any, soda was lost during the pouring stage and then express this number a percentage loss. Note, there will certainly be a margin of error in this activity, as most measuring cups are not accurate and there will be some amount of soda left in the bottle. However, these will serve as great after-activity discussion questions.

After Activity Discussion:

How much soda did each team loose during the process?

Why do you think soda was lost when pouring?

Is this enough loss to avoid pouring?

Does anyone know what creates fizz—be sure to ask your science teacher?

How accurate do you think your estimates are?

What could be throwing off your results?

How much soda do you think is left in the bottle?

Homework:

Estimate how much soda your family looses per month from pouring soda?

Activity Questions:

1) How much soda﻿ is in the bottle?__________

2) How much soda, if any, was lost during the pouring?_____________

3) Express this loss as a percentage_____________

Monday, November 26, 2012

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.

Wednesday, November 21, 2012

How long would it take a ball to drop to the ground if you reached as far up as possible? Let's find out with some help from quadratics and the square root property.

What You Will Need

• Golf balls, tennis balls, etc
• Stopwatch
• Measuring tape
• Formula for acceleration due to gravity neglecting air resistance.
• Activity sheet

Overview and Goal of Activity

The goal of this exercise is for students to use algebra to solve a real-life application. Students will work in pairs (or groups depending on the amount of stop watches you have at your disposal) to calculate how long a small ball will take to fall from the tips of their toes, reaching as high as possible, to the ground. Students will first use algebra and then will test their answer by actually timing the fall

Steps:

Step 1: Using adhesive or tape, tape at least one tape-measure to the wall from the floor to the ceiling.
Step 2: Pair up students and give each group a stop watch and an activity sheet (below)
Step 3: Have students measure themselves in inches or centimeters and record their height—Make sure they are measuring from the tips of their toes to their finger tips while reaching to the ceiling.
Step 4: Next, using the formula s(t) = 16t^2, where t is their height in seconds have them plug in their height for s(t).
Step 5: Have students do their best to solve for t.
Step 6: Have the students record their answer
Step 7: Have students go back to their seats
Step 8: Explain the process of how to solve for t by using the square root property.
Step 9: Have them partner back up and solve for t and record their answer
Step 10: Have students test their answer by dropping a ball and timing it. Have them record their answer
Step 11: Back to their seats for after activity discussion

Example of Activity Sheet

1) How tall are you from your toes to your finger tips __________cm/inches

Formula for acceleration due to gravity is
s(t) = 16t^2

2) Plug in your height for s(t) and do you best to solve for t

t = ___________

4) Using your notes from above, plug in your height for s(t) and solve for t

s(t) = 16t^2

t = __________

5): Using your stop watch take turns dropping the ball from the tips of your toes and record you answer (do this at least twice).

Time for ball to hit the ground ___________seconds

After Activity Discussion:

Why do you think there might be a difference in the times?
What does the s(t) stand for in the equation?
What does the 16^2 stand for?
Why do you think the 16 is squared?
Do you think your time would be different if you dropped a heavy rock instead of the ball?
Do you think your time would be different if you dropped a leaf?
Why do we ignore the minus in our two answers?

Homework:

Actual Problem Worked Out

Height = 84inches

84 = 16t^2
84/16 = t^2
21/4 = t^2
+/-squar root (21/4) = t
t= +/-2.29 seconds
t = 2.29seconds

Monday, November 19, 2012

Student Lockers & Math

The purpose of this activity is to provide insight into the math behind a student’s locker. The main topic covered is that of permutations, however, we will refer to it as combination since this is what students refer to it as). Even if your students are not ready for permutations they will find the activity interesting and it may serve as a great introduction to other math topics.

Imagine that you wanted to steal a diary out of your best friend’s locker to see what she was writing about you. You don’t know her locker combination but you plan on guessing three times a day until you get in. Will you eventually get into it by the end of this school year?

Let’s assume her lock has 40 digits and her actual combination (PERMUTATION!) is 3 digits. Take a guess how many different possible combinations there are? Next, calculate how many guesses you will be able to make at three times per day within a school year (180 days x 3 = 540 guesses).

The actual number of possible combinations (PERMUTATION!) calculated is 64,000.

With this number in mind, calculate how many days you would need to ensure you guessed the right combination (64,000/3) =21,334 days)?

What percentage chance pre year is this (540/64,000= 0.8%)?

The math behind the number?

The following is know as a Permutation with repetitive numbers allowed

Each digit has a 1/40 chance of being correct. Thus, with a 3 digit combination possibilities are calculated as

40 x 40 x 40 = 64,000

Activity Sheet:

1) Will you eventually get in to her locker by guessing three times a day? _____

2) How many possible combinations there are?

3) How many guesses will you make at three per day for a school year?

4) Based on this, with 540 guesses what percentage of chance do you have at guessing the right combination? ______%

5) Given the actual number of combinations, how many days would you need to ensure you guessed the right combination?________How many school years is this_______?

6) What is your actual percentage chance of guessing the right combination in a school year? ___________

Friday, November 16, 2012

10 Ways To Make Your Math Class More Fun

I often get emails from educators asking how they can make their math class more fun. My normal suggestion is relocate your class to Toys-R-Us, but, alas, if this option is not available, here are at least some suggestions.

1) Mini Lessons:

Divide the total number of minutes you are in class by 5; this is how many lessons you should aim for. Thus, a 60 minute class should have approximately 12 lessons. For example, a 12-part mini-lesson class about fractions may look something like this.

• Mini-Lesson 1: Warm-up by asking what the class would rather have 2/3 of a pizza or 6/7, why?

• Mini-Lesson 2: Draw two circles, one with three parts, one with seven parts, and shade them. Then ask the same question as before and see if their answers differ

• Mini-Lesson 3: Have students label each part of their circle 2/3 or 2/7 and cut out each piece

• Mini-Lesson 4: Pair-up and have one student give their partner 1/3 of one pizza and 4/7 of the other. Have the other student give their partner 2/3 of one pizza and 2/7 of the other and then have them compare who has more pizza

• Mini-Lesson 5: Have all students return to their seat and close their eyes. Read two fractions aloud and ask them to raise their hand for the one they think is larger. Tally up the results and place them on the board. Do it again for another two fractions.

• Mini-lesson 6: Using the previous examples, show why one is larger than the other

• Mini-lesson 7: Discuss how knowing this might help them in real life, ask for their input

• Mini-lesson 8: Have your class form a circle while holding hands with you in the middle. Show them how ½ a circle is different from 1/3, ¼, or 1/5 by standing in the middle and extending two tape measures

• Mini-lesson 9: While still holding hands, take turns asking the students to guess different fraction sizes by reading out each others names “1/3 would be from Julie to Charlie, ¼ From Julie to Jamie, etc”

• ---I could go on forever but you get the point
Keeping it short will hold your students attention.

2) Get Them Out Of Their Seat:

Sitting for an hour straight is hard for me and I'm a 32 year-old man. In kid-time that's even longer. Switch it up! Form a circle like you did for story time in elementary school. Let them spread out on the floor. Turn out the lights and give them flashlights to do their worksheets. Sound dumb? Not as dumb as the expectation of having kids be attentive while seated for an hour.

3) Art:

Using art is a great way to illustrate word-problems. In fact, have your students draw pictures before answering any problem and see how much more attentive they are to the solution. Example, asking 5 x 3? Ask them to draw 5 apples, then another 5 apples, then another 5 apples.

4) Legos:

Using just a few Lego pieces will allow you to teach almost any concept. You could calculate volume, area, build polygons, build irregular shapes, calculate ratios, probabilities of one color, etc, etc.

5) Posters:

Got some boring definitions you need your students to learn? Have them create a poster. Better yet, tell them they are opening up a store and their only item for sale is this definition and therefore they need a sales-poster!

6) Group Work:

Group work can be a great learning tool. However, it's often barely used or underused. You need to be specific about what you want each member of the group to contribute. Solving an equation? Assign each member a task. Person A can only combine like terms, person B can only add or subtract, etc.

7) Less Problems & More Mastery:

Two awesomely thought-out problems are worth more than an entire worksheet of drill. There may be a time for lots of problems, for example the multiplication tables, but these are few and far between. Using just two problems will allow you to create content. Make your students value to the solution by actually creating a problem they would want solved. For example, why would the death/kill ratio be a better indicator a players skill in Call of Duty than simply number of kills? Or, the most text messages ever sent in a day is ____ what would their cell phone bill be if they had to pay 0.03 per text? Lets create an equation and solve it.

8) Homework Should Be Short and Sweet:

I hate the idea of homework. I hate the idea of taking time away from family and friends to do busy work. If you must use homework make it something really fun. Have them explain to their parents over dinner how a mathematician won \$100,000 for finding the next largest prime number and if their parents can't remember a prime number have them explain it to them. Have them research the largest number they can find and bring it back with them the next day for you to write in scientific notation. Give them an equation to solve and ask them to draw a picture of a guy drawing a picture of a guy solving it...I don't know! Just give them something fun

I know our establishment is anti-calculator but I assure you this, my two home-schooled boys will not be doing silly math problems by hand, I don't even care if they know their multiplication tables. I will put a calculator in their pocket and we will go outside and shoot bottle rockets to discuss math. My suggestion is thus, let the calculator do more of the tedious work and use your skill as an educator to concentrate on the why questions.

10) Use Math Stories, Math Trivia or Riddles

We all love a good story or a good riddle. Take some time to discuss how math is used today or how battles were won due to a generals mastery of mathematics, etc. Post weekly riddles or obscure equations on your walls. Tell them stories about quirky mathematical geniuses of the past. Find ways to peak their interest in the subject.

Wednesday, November 14, 2012

Using A Two-Column Proof To Argue With Parents

I've always enjoyed books on logic. As opposed to pulling my hair out while studying it in college, I once attended an online seminar with David Gordon of the Mises Institute titled “How To Think: An Introduction To Logic”. I can't recall the text we used for the course but it was a fun class. Anyone suffering through an elementary geometry class has, at some point, witnessed a two column proof in which the left hand side is used to denote a proposition while the right hand is either an axiom or something that can be derived from a former proposition (sometimes a hypothesis as well). Like so,

The purpose of this exercise is nothing more than introducing the two-column proof by allowing students to create a method for arguing with their parents. My advice would be to hook the class by asking, "what is something your parents won't let you do? Has anyone tried arguing with their parents? I mean really arguing with them and showing the flaw in their statement? Let me teach you"

NOTE: The outline below is nothing more than a fun, informal introduction. It's merely an attempt of playing with the process of creating a proof, the arguments presented below will be like that of a young child.

The argument presented is as follows. You want a cell phone but your parents claim you can't have one because you don't have enough money to pay the bill and you might run-up their bill (you could also use you are not old enough). How are you going to prove to them that this statement is not true. Or in essence, how can you prove that you do, in fact, have enough money for a cell phone.

Monday, November 12, 2012

Mathematics & Eyesight: Part 1 Field of Vision

I've always loved learning about social-biology and the effects evolution plays on development. One area of particular interest is the eye. More specifically, why do some animals have eyes sight that allots them a larger field-of-view than others? Why can some animals see farther or more acutely but have less peripheral vision? This activity incorporates degrees of a circle for better understanding. It would be great to couple this lesson with a biology teacher on your team. Note: The degrees used here are rough estimates and may be subject to “Google Error”. Feel free to double check the suggestions and send me corrections. The activity will still work the same.

What You Will Need

• Paper & pencil

• A 360 degree protractor

• Activity sheet (see below)

Overview and Goal of Activity

The activity will involve students looking at pictures of different animals and guessing their field-of-view. Students will then be told their field-of-view and trace the degrees of vision using a 360-degree protractor. After sketching the degrees of vision students will take guesses as to why this would help the animal survive.

Steps:

Step 1: Hand each student a 360-degree protractor and activity sheet (see below).

Step 2: Our first animal is the horse

Step 3: Have students guess at the degrees of vision of a horse

Step 4: Provide them the actual degrees of vision of a horse and have them sketch where they think the blind spot is (see below).

Step 5: Provide them with the actual information of a horses blind spot (see below).
Step 6: Have students guess to why such vision would be beneficial to a horse.

Example of Activity Sheet

1) Take a guess at the degrees of vision of a horse ____________degrees

2) Why do you think this? ______________________________________________________________________________________________________________________________________________________________________

3) The actual degrees of vision of a horse is near _350___degrees

4) Using your protractor, trace 350 degrees and where you think the blind spot is.

 (Notice the blind spot in the front)

5) Why do you think horses developed this form of eyesight?

Continued Activity

Step 7: Repeat the same steps for each of other animals you wish to study

Examples
Human Field-of-view = nearly 180 degrees

Owls Field-of-view = 110 degrees

Dogs view =250 degrees

After Activity Discussion:

Why do you think animal have different degrees of vision? Why do most hunter have a more narrow, forward degree of vision whereas most non-hunters have more peripheral view?

Homework Question:

What would life be like if your degree of vision was like that of a horse?