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.

Addressing Our Probability Inefficiencies

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

LeBron Asks: What are the chances of making 10 free throws in a row?: LeBron James asks Sal how to determine the probability of making 10 free throws in a row

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.  

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.

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.

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

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.

Math For The Summer: How Long To Fill Up The Pool

End of the year classroom boredom? Take your kids to the town pool or buy a kids pool and calculate some math :)

This exercise is perfect for calculating volumes, adjusting units and calculating the amount of time to fill a volume

p.s. You could also use buckets

Archamendes and Math In The Sand Box

It is believed that Archamendes wrote in the sand before he wrote on paper (papyrus). I've even read that Archamendes carried with him a box of sand at all times offering him the ability to work on mathematics from anywhere. I believe there is merit in this method. I would encourage you to take your students outside before the school year is over, to the nearest sandbox (or my case, mud) and conduct class with a stick.

Graphs of Functions In Nature

For Algebra teachers we know there are certain "go-to" graphs of functions that tend to be most popular in our texts. Having the ability to recognize these graphs enables the student to anticipate the shape of the graph and any of its variations. Simply knowing its normal shape allows students to visualize any transitions or reflections in the graph.

The point of this exercise is to send your students on a scavenger hunt in nature for the graphs of functions. Such an exercise would make a great recess or study hall period activity as well as an end of the class exercise.  

Math Outside The Textbook (Acute Angles In Nature)

Educators, we know that there is math outside the worksheets and textbooks. Let's take our students to the math! This short vid asks us to look for angles in nature

Angles In Nature 2

The power point was taken from here 
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