Nucleus Learning - The Heart of Creative Education

A Great Online Teaching Program - Facile Learning

bogusia — Wed, 19 Nov 2008 14:09:23 +0000

In the school I teach, we use this online computer program for students doing sciences called: Facile Learning.

I like this program, and recommend it for anyone who wants to learn the science course material without a teacher. It is very visual, lots of animation, easy and fun to follow along. The program is very user friendly, and all you have to do is login and go. Choose a lesson, read through the lesson, look at the animation, and understand the concepts. After the lesson, you can take quizzes to test what you learned. The program records your results, so you can have a self evaluation instantly and recorded to see if you're improving.

It is geared specifically for the Quebec curriculum, but science is science, and the ideas are taught in all science classrooms all around the world. Therefore I think this program is awesome for any child that wants to learn science concepts wonline.

Yesterday, I used the program for teaching at the beginning of physics class, just as an intro to Forces. Some teachers, as I understand it, use this program in their classrooms regularly to explain concepts. Others assign the program to do for homework (most kids love it, as they go on the computer and have fun, instead of answering questions from a book). Last year I told the students at the beginning of the year that they have access to this fantastic program: Facile Learning. I gave them passwords and showed them a sample lesson online. Then, I reminded them of it before the first test, and some of them went on to review the concepts. Pleasantly surprised, they were hooked, and spread the word to the rest of the class. By the end of the year, I had probably 70% of the students going on Facile Learning regularly to study for their tests and even their final exam. It was such a symbiosis - teaching at school / students actually learning at home with the help of this great tool.

The main designer and programmer came to the school yesterday. She is fantastic, and very accomodating. She set me up with a password instantly, and I was online again. There is a fee for the passowrd, but very inexpensive, if you ask me... something like $30 - $40. For what you get, it is very reasonable. I would recommend this to anybody but especially for any homeschooler in Quebec, when trying to pass Physical Science 416 / 436 (the mandatory courses to graduate from high school in Quebec). Here is the site: Facile Learning. Enjoy.

Draw a Person Test (DAP) - a great way to tell a kid's intelligence

bogusia — Fri, 07 Nov 2008 17:12:47 +0000

Recently I went to the doctor for my son's yearly check-up. Our doctor is fantastic, and I am so lucky that I was fortunate enough to get him. Everytime we go, I learn something very interesting, this time was no exception.

The Doctor started asking standard medical questions: Was Jakub seriously ill this past year? Any ear infections? etc. Then he turned to his mental, social and physical development. And he asked me:

"Does Jakub know how to draw a person?"

I answered that probably yes, because he draws dinosaurs all the time, but I can't remember any people he drew recently... So the doctor gives Jakub (my 4 year old son) a piece of paper and asks him: "Draw a person". After a bit of shock and shyness, Jakub complies and draws a person. He started with a head, then a body, arms, legs, some eyes and mouth on the head - in their proper positions, and then also some hair. Nothing artistically pleasing, but just a stick figure (unfortunately I couldn't take the picture with me, as the doctor wanted to keep it in his records - the picture above is also Jakub's picture, from February 2008 - he was 3 years and 20 months old). The doctor said that was interesting, and started explaining the theory behind the "draw a person" test to me.

He said that at the test is very universal. Many studies show that the results are similar in all the corners of the earth. The way the kids draw the person determines at what mental developmental stage they are at. You can pretty much test for intelligence with a simple drawing. At the age of 3 kids start to draw circles and lines, but usually can't really make a stick figure look like a person. At the age of 4, they are supposed to start drawing people more like we're used to: head, arms, legs. But at the age of 4 (mental age of 4) most kids draw the arms and legs coming out of their heads - no body. Jakub didn't do this. His picture had a body. Even in the picture above - drawn when he was 4 months shy of four, Jakub drew a body. The doctor said that this was an indication that his mental development stage is more like a 5 year old rather than a 4 year old (I always knew my son was smart :)). At the age of 5, children start drawing bodies, arms and legs coming from the bodies. Then, between 5 and 5.5, kids start to draw more detail, including 3 fingers (not 5), clothes, etc. The doctor didn't go into more than this - figuring I'm not interested past my son's age anyway.

But when I got home, I wanted to know more about this cool non-invasive test: the Draw a Person test. I actually didn't know it was called that until I researched it online. Supposedly this test has been around for a whole century, and it's been used everywhere in the world, for children of many ages (up to 13 as I've seen in the few studies I read through), and by psychologists to analyze not only intelligence but also emotional stability of kids. It is the perfect test, because it is very simple and non-invasive, yet so telling of the child.

As I understand it, the procedure to administer the test is to tell the child: "Draw a Person" with not much more explanation. After that, there is a series of points the psychologist can award, depending on the picture's details (is there a neck? clothing? proportions correct? size of picture? etc.). Then, based on the child's age and the points of the picture, a mental age equivalence can be given. Cool!

A few days after my appointement, after picking up Jakub from Pre-School, I found a picture of two stick figures in his school bag. The hands and legs were coming out of the head. I was shocked... Jakub drew this? Did he regress in just a few days? I asked him: "Did you draw this?" He said: "No, a Emily drew this picture for me." He was so proud that his friend drew a picture for him, and I was happy to see that the DAP test is for real.

If you want to see some real studies (not on my child but on a statistical level) on this DAP test, here are some good sites I found:

This one is based in Pakistan, but is in english and has many sample drawings of the children's drawings and the analysis of them. The author of this paper also links culture and mental stability into the DAP test. Very interesting: STANDARDIZATION OF DRAW-A-PERSON test

This one is an exerpt from a book. I think eventually I will purchase this book, because this stuff fascinates me, but for now, this will do: Using Drawings in Assessment and Therapy

Building Houses of Straw, Sticks and Bricks - The Three Little Pigs

bogusia — Fri, 07 Nov 2008 14:22:18 +0000

Keeping with the theme of building, my last workshop for the younger elementary students was about building structures of different materials. I first read the kids the classic tale of the Three Little Pigs. After that we discussed the different materials that were used to build the three houses. I asked for the kids to hypothesise wether the story is correct.

Then was the fun part: the challenge. Dividing the kids into three groups, they had to go and be the three little piggies - one group built a house of STRAWS, the next built a house of POPSICLE STICKS and the third had to build a house of STONES. After a half hour, I was the big bad wolf and came with a blow drier and tried to blow each house down. At the end, we discussed the results, and talked about the different materials used to build houses in general.

I thought that the straw and wood house would blow over, none of them did. The kids liked that the results were not what was expected. Also, we discussed how the masking tape was a huge help, and that without it, there would be no support. Also we compared the masking tape to the real world of building houses - what it would represent.

This was a great science activity, learning to hypothesise, to do an experiment, to test out the hypothesis, and of course to build scale models of real objects/houses. The students had a blast!

I'm attaching the "Challenge" outline, if you would like to do the same fun activity. Also, if you want to find other teaching activities with the "Three Little Piggies" story, I found an awesome site online with links galore - all about the Three Little Piggies: The Three Little Pigs Lesson Plans

Competition - is it a good tool to motivate kids?

bogusia — Thu, 30 Oct 2008 16:29:25 +0000

I always thought that competition is an excellent way to motivate kids. Many times, I made contests in the class, competitions, etc. I always found it that extra bit more fun when I was a student, if I had to compete against some other students. That's probably why I really like games. My friends always tell me that I am very competitive and some friends even tell me that I'm overly competitive. It's true. I make a game out of everything. Even with myself. With anything I do, I try to improve myself, get faster, get more efficient... win.

Just like my life, I run my classes as a place to improve, a place to get faster, to understand best, to get more efficient - and what better way than a friendly competition?!

Recently, however, I find that competition is not for everyone. Most students really enjoy the sense of play, the sense of fun in beating or trying to beat their opponent in a silly competition, but for some kids competition evokes the exact opposite effect. Some students just shut down - they don't see the point of playing when they have no chance of winning.

I decided to make a list of things I think are good and bad (my pros and cons) about competition in the class. And then accordingly, I would decide whether it's a good idea for a given situation or not such a great plan for the lesson.

Pros:

1. Most kids really enjoy the "game" aspect of a competition. Fun = good for learning.

2. This is a great way to get the students to actively participate in the class. They get really involved, and just from the involvement they learn more than they would have by sitting and just passively listening.

3. Great for the bright and fast kids. If they're usually on the border of boredom, a game / competition will get them motivated to start thinking again.

4. Lets students have a sense of success.

5. If done in groups, can really develope comradeship with the other team members.

6. Some students work best under pressure. Competition is the perfect source of pressure.

7. Works better for older kids. Younger kids seem to take things very personally, and cannot distinguish between playing a game and reality.

Cons:

1. Not so great for the weaker students. If a student finds himself among intellectual superiors, they will either not participate or else get frustrated with the competition and possibly the subject itself.

2. Not suitable for younger kids. The younger the kid, the easier they get frustrated, and the competition won't work. Younger kids don't understand that sometimes you win and sometimes you lose, therefore losing is a very traumatic experience.

3. Some students don't do well under pressure at all. You must know your students well to know which students can succeed under pressure, and which will not. Usually the ones that do well win a stressful situation should enjoy a friendly competition. Those kids that blank out during tests will not enjoy the competition either.

I find that school is all about competition anyway. When we give grades or stickers, we compare the students amongst each other. Even if the students don't know what other students got on a test or report card, we give them an understanding that an A is the best (like winning) and F is that they lost completely.

I actually had the opportunity to take a whole degree (my education degree) where there were no grades - just a pass or fail. I thought this degree to be a joke. I no longer felt I had to do my best. I knew that even my worst would allow me to pass the courses and I would get my degree. I always blaimed my lack of enthusiasm for the courses on the silly "no mark" system. But sometimes I wonder if I was just programmed by my previous schools and my parents, that this reward system, this mark system, this competition in my blood, made me not care about learning how to teach, because there was no carrot at the end of the string.

I wonder if I am really reaching for what I want, or am I only programmed to reach for a reward?

I think I'll still use competition in some of my classes, but I will not resort to a competition style game all the time. There are other activities that are fun and don't necessarily include competition - these activities can be great for all students - not just top of the class.

Dealing With Frustration - The Spaghetti and Marshmallow Towers

bogusia — Tue, 21 Oct 2008 16:55:01 +0000

The key to success is never to give up!

Yesterday I gave a science workshop to my younger group of kids: 6 - 9 year olds. I am typically a high school teacher, but this school year I am trying a different thing: workshops for homeschooled kids. And yesterday was one of those workshops.

I have a really great group of 6 to 9 year olds. At first it was challenging to understand really how small these kids are, how little they know about the world, how easy it is to surprise them with the simplest science experiment. I taught kids, but never this young before. I had to revamp my whole way of thinking about the class, about the kids, about science!

Yesterday was no exception.

I decided to teach them about structures, how the rectangle is very useful, but not a very stable structure. How the triangle is so much better, so much stronger, and how we can make a rectangle into a stable structure by creating a support, transforming it into triangles. Easy concept, lots of applications, great!

In order to demonstrate this concept further, I thought we would build some 3-D structures out of Spaghetti and Marshmallows. This was supposed to be awesome fun, and I thought it would help the kids really understand this concept. I have never tried this before, but "how hard could it be" I thought.

Well, let me tell you: it was hard! The younger kids especially had a hard time with their dexterity, and needed a lot of help from me. One child didn't quite get that we were building in three dimensions. Another just asked me to help him all the time (do it for him), and then when I left to help other kids, he accidently broke his structure. After fooling around a bit, he found a cool way of attaching the marshmallows to the spaghetti, and really wanted to show me. Another child got really really frustrated and after building an awesome structure, destroyed it and almost started crying. However, I convinced him to start again, with shorter pieces of spaghetti. This worked well, unfortunately, there was not enough time for him to complete his tower - this was another source of his frustration.

The older kids wanted to build large structures, but didn't plan ahead. Initially they thought that their structures were the best, and boasted that for everybody to hear. After adding more complexity to their towers, some of the structures broke. These kids however seemed to learn from their mistakes, and didn't give up quite as easily. They just continued building even without my insistence.

I don't know if I would do this activity with such young students again. Probably 9 year olds are the youngest I would go for the "Spaghetti and Marshmallow Tower" project. For younger kids, I would definitely change it up a bit. Make them first follow a step by step procedure... following my lead. Then, after the initial practice, I might let them go free and try to build something on their own. Also, an hour was just not enough. This is at least a two hour project. Time restrictions just added to the frustration.

On a positive note, today I got an email from the young frustrated child's mother. She sent me pictures of her son's spaghetti and marshmallow "stable structures". Supposedly, the child woke up really early today and decided to try again. The frustrated kid overcame his frustration and tackled the project again: He build some awesome structures. He didn't give up, just had a bit of a temporary melt down. What an inspiration to all of us. Just try and try again! Never give up! Overcome your emotions, and then try again - until you succeed.

How to tell the climate of the dinosaur age?

bogusia — Thu, 16 Oct 2008 14:07:53 +0000

Climate changes all throughout the ages. But how do we know that? How can scientists be so sure it was hotter during the Jurassic or Cretaceous periods? How can paleontologists determine what the weather was like during the age of the dinosaurs?

This question never really hit me until I saw a TV show on digging for dinosaurs in the polar regions. The paleontologists had to build tunnels in the tundra using dynamite, digging through solid ice, going through gruelling conditions, extreme cold all the time. This was interesting in itself, but then when they started talking about their discoveries, I started paying attention even more. The dinosaur scientists were telling us how the dinosaurs ate all these plants, how they travelled in herds, how they enjoyed a tropical warm climate, etc. I think the reason for my instant curiosity was the juxtaposition of cold temperatures now versus warm temperatures during the age of the dinosaurs; the barren landscape of the tundra versus what the scientists were claiming the dinosaurs ate on a regular basis.

So then, right away I thought: Hey, wait a second, how do we actually know what the temperature was like during the time of the dinosaurs? How can anyone claim that they can even guess on the temperature of a past era? And of course, as if the TV show read my mind, and the scientists started examining this question right then and there.

Here is the synopsis:

In present day there is a very significant relationship between the types of leaves found in warm climates versus cold climates. More specifically, it is the leaf margins (the edges of the leaves) that give the relationship. In a colder climate it is more common to find leaves with ridges or rough edges (non-entire margins) and in warmer climates it is more common to find leaves with smooth edges (entire-margins). What some botanists have done is make a world wide chart of smooth-margin leaves versus the mean average temperature (MAT) of the area. The findings are very consistent all around the world. With such a great map of the world flora and a "formula" so to speak for finding a mean average temperature, scientists are able to predict the average temperature of an area just from the % of smooth margin leaves in the area.

This is huge! From this kind of data, assuming the trend is similar in prehistoric times, one can determine the approximate average temperature just from fossilized leaves, by counting the smooth-edged versus rough-edged leaves. What a powerful tool.

Right away I took a little field trip outside to see if we could find smooth-margined leaves (I live in Montreal, a pretty cold climate). Every leaf I picked up had ridges on the edges. How did I never notice this before? Then we went to a friend's house. They are into planting tropical fruits (banana, lime, lemon, mandarin, orange). All their mini trees had leaves with smooth edges! Wow.

Being a science teacher, I right away thought what a great idea this would be for a science class. Get the kids to go outside, get them to collect 5-10 different kinds of leaves. Back in the classroom, let them examine the leaves, especially focusing on the edges of the leaves. Then allow them either to look through books with tropical leaves, or looking at actual tropical (indoor) plants to inspect the edges of those leaves. Make them compare, contrast etc. They will not only develop a sense of observation, but also they will see how this could be used to determining the climate of the time of the dinosaurs. They can start seeing how all this evidence fits together to make a picture of the past. I love it!

I tried to find the sources online to read more about this fascinating correlation, but they are all very scientific and very "statistical" in nature - not really my type of fun time reading. But I found a few that were OK, if you want to get more info on this cool topic:

One thing I couldn't find is a good answer to why this is so? Why do leaves with rough edges seem to inhabit colder climates, and leaves with smooth-margins grow in warmer climates? I'll keep on searchng, but for now, I think this is news in itself.

Very Funny: "How To Fail a Test" examples

bogusia — Thu, 16 Oct 2008 12:29:58 +0000

I got an email today from a friend. This is one of those "how to fail" emails with examples of kids doing funny things on tests. I really liked some of them (I actually laughed out loud in an empty room for two of them), so I'm passing it on to you. Enjoy:

From funny pictures for nucleuslearning

The Great Ramp Race

bogusia — Fri, 10 Oct 2008 13:01:34 +0000

At my weekly science workshops, I was teaching the kids about simple machines. Last week we did a few experiments on levers. This week however, I wanted them to try out the Ramp Race. I tried it with my grade 8 class last year, and it worked like a charm. The idea behind it is to build a series of ramps with limited materials and limited time (1/2 hour works well) to make a marble take the longest rout to get from the top to the bottom of a big box. See the attached specification sheet for the Great Ramp Race if you want to replicate it at home or in your classroom.

I find that these types of activities are not only fun, but also build leadership and team-work, and make the students work from scratch, having to brainstorm on their own in their own groups without an adult, having to problem solve, having to create something with limited tool / supplies. It is a great exercise for kids, and on top of that, they will never forget that an inclined plane is a simple machine! These types of activities are the things kids will remember when they grow up!

A few notes about these particular teams, these particular machines. I was very impressed, as they went well beyond what my grade 8's did last year. Instead of putting the popsicle sticks on one side of the box, these kids decided to go all the way around, making it a 3-D piece of science. One team made it in almost 7 seconds, and the other had a huge 17 seconds time - best time so far from what I've seen. The students always seem to take this challenge seriously and this time was no exception! The competition really adds to the fun of it!

Teaching the Hydraulics and Pneumatics Unit to Children

bogusia — Thu, 09 Oct 2008 16:14:05 +0000

Hydraulics and Pneumatics are great topics to teach children. First of all both words sound very impressive and when the children learn these words they will sound very important and knowledgeble if they use them. Also, hydraulics and pneumatics are used in many machines and in many everyday applications, therefore it is easy to show the importance of understanding these topics. One can easily show and explain the difference between hydraulics and pneumatics - a great "Compare and Contrast" analysis. Thirdly, there are many fun and impressive experiments that can be done with hydraulics and pneumatics in a very inexpensive way, with very accessible materials. And finally, since hydraulics and pneumatics is so useful, there can be multiple projects that children can actually build themselves. Thus weaker students and stronger science students can both do projects, yet with differing complexity.

Here are some of the techniques I use in order to teach hydraulics and pneumatics to children:

1. FLUID PRESSURE: Hydraulics and Pneumatics for me is a culmination of a study of Fluids. Therefore, before I talk about hydraulics and pneumatics, I must talk about Fluid Pressure.

I start with a discussion of Pressure in general, it's formula, the units.

Pressure: The measure of the force acting perpendicular to a unit area.

(Here I demonstrate pushing with finger compared to pushing with a whole hand against a wall, book, child volunteer from the class, with the same force. Since the children already have a good understanding of force, they can see that pressure is very similar to force, but spread out over an area - therefore the smaller the area it's spread out, the more concentrated the force is, and vice versa.)

Formula: P = F/A

(Even though children might not be ready to understand formulas yet, I like to introduce formulas to even the youngest children, so they start to see the relevance of math, and formulas in science.
I explain that the formula pretty much means the same thing as the definition above - Force spread over an area. This is useless for the weaker students, but will get the stronger science students thinking about the relationship between formulas and definitions... excellent for planting the seed for future physicists and engineers.)

Units: (from the formula N/m2) or Pa (pascals), kPa (kilopascals), 1kPa = 1000Pa

(I definitely talk about units whenever I introduce a new concept. I talk about where the units come from - starting with the formula: Force over area, force is measured in Newtons, area is measured in m squared. This is a great way to engage students, asking them for answers, leading them to the solution. Then I mention that instead of using two units, scientists decided to invent one unit to denote this relationship: Pa - after a well known scientist Pascal. And another great discussion point comes up when I talk about kPa and how it's related, just like g and kg or m and km. Lots of stuff to talk about here. Sometimes I even get the students to do research on who Pascal was, and why the pressure unit was named after him).

If force increases --> pressure increases

If area increases --> pressure decreases

(These statements are critical to mention and discuss in detail. This can be explained again with the pushing of a student with a whole hand compared to a finger. Or even talking about or demonstrating walking barefoot on a plank of 100 nails compared to walking onto one nail. Making such a plank of wood with many nails sticking out of it and keeping it for future classes is a good idea and when used to demonstrate this concept is very visual as well as dramatic - a good way to keep students engaged and to remember this concept. You can also use the example and demonstrate walking on many eggs at once compared to walking on just one egg. If you have access to an lcd projector in the classroom, there are many YouTube videos showing people walking on eggs, and not breaking them (here's a link to a good one: http://www.youtube.com/watch?v=LszleCrvFyQ )If you don't want to spend a whole class on this concept, you can just quickly talk about some of these examples, getting some input from students, and continue.)

Next I talk about pressure of fluids (fluids, by the way, are materials that flow like liquids and gases)

Fluid Pressure: Exerted in all directions equally

(I make sure to use many diagrams and as few words as possible in my notes. Students learn, understand and remember pictures so much better than a sentence.)

Confined Fluids: - any fluid in a closed system

- the fluids can move around within the system, but cannot leave or enter the system

examples: - blood moving through the body

- air moving in an air matterass

(A discussion of confined fluids is essential before starting a discussion of hydraulics and pneumatics. Also as many examples as possible makes the concepts applicable and less foreign to the children. Examples taken from the students themselves are even better, as the learning is less passive and more active at this point.)

Gases Liquids

- are very compressible - are not compressible

- because the gas particles are very spread out - the particles in a liquid are not as spread out as in a gas

(Here I would call on a demonstration or experiment of this. You could do many things; some examples: take a syringe, fill it with air, and then cover the open end with your finger. Show that the air can be compressed by pushing down on the plunger. Let the students do this, so that they see it is not some sort of trick. Then fill in the syringe with water.
Again covering the end with your finger, show that now you cannot compress the water with all your might. Try very very hard to make sure they see your effort. Get students to replicate this. This also makes for a great whole class experiment / activity. Make sure you think of some interesting questions and then get the students to experiment / fool around with syringes filled with air and water. Watch out, because when I did this, lots of the time, the students ended up having a water fight with the syringes - not really a big deal if contained to the classroom though)

Examples of questions for a lab:

If you fill in the syringe with 20mL of air, to what volume can you compress it?

If you fill in the syringe with 20mL of water, to what volume can you compress it?

What is the difference between compressing air and water?

Attach two syringes with some tubing with air in the confined system. What happens when you press on the plunger?
Attach two syringes with some tubing with water in the confined system. What happens when you press on the plunger?

Attach three syringes (two of the same size, and one larger) with some tubing and a T valve. What happens when you press on one plunger?

Attach three syringes with some tubing and a one way valve. What happens when you press on one plunger?

(Lots of things happening here. The students start getting a feel for hydraulics and pneumatics. They realize that in hydraulics there is no delay, and the force is passed on instantly to the other syringe, while in pneumatics there is a delay of action because of the compressiblity of gases. Then you can introduce the valves - T intersection, one way valve, etc.
This shows the children different ways of controlling the flow of fluids. Make sure you relate the valves to something they are familiar with, like a tap in a bathtub, etc.)

2. HYDRAULICS AND PNEUMATICS: Once the children understand pressure and get their feet wet with syringes and pressure of fluids (gases compared with liquids, etc.) they are ready for hydraulics and pneumatics.

I jump right in by making a huge table, comparing Hydraulics to Pneumatics:

(As I write this table, and get the children to copy it, I have a class discussion every step of the way, along with demonstrations of

hydraulics: the two syringes with water inside them- when you push on one plunger, the other plunger moves... this can be used to lift an object - the basic principle of hydraulics!

and pneumatics: two syringes joined together with some tubing, with air inside them. When press down on one syringe, the other piston lifts.

By this point, student really start to understand what hydraulics and pneumatics is about and how it can be used.)

3. HYDRAULICS LIFT: This is an important part of hydraulics. There is many explanations online of the hydraulics lift, how it works and pictures of it, so I won't get into that (check out http://hyperphysics.phy-astr.gsu.edu/Hbase/pasc.html).
But it is important to explain to the children that a small force can be used to lift a large object (such as a car) - of course there is a trade-off: the large object goes up just a very small distance, while the force acting on the smaller piston, using a smaller force, has to go through a larger distance. This is why hydraulics is so useful. I would spend at least a class, if not two to go over this concept and do some experiments with it (two syringes, one small, one large connected with some tubing, along with some weights, small and large, etc.

4. PROJECT: I then jump in here with a project, where the students must build a hydraulic or pneumatic model of a machine. See the attached outline and some of the resulting possible projects: http://www.nucleuslearning.com/content/hydraulics-and-pneumatics-projects.

Wasted Time is Very Tough to Make Up

MathMentor — Tue, 30 Sep 2008 19:28:38 +0000

I’m an amateur long distance runner and I’ve always found it surprising just how long it takes me to catch the slowpokes!

Here is an example: If I run twice as quickly as someone else and I give them a five minute head start, in my mind I expect to catch them in a few minutes. I am running twice as quickly as they are, after all, like a rabbit versus a tortoise! In fact, I will only catch them after running full speed for an additional five minutes.

What if I run 110% as quickly as someone else and I give them a five minute head start? Being 10% faster is very quick indeed. In a marathon I might finish 25 minutes earlier. However, to make up that small lead would take me an eternal 50 minutes. Even though I’m so much faster, I won’t pass my competitor for an hour!

How to calculate it:

Let v be the relative speed of the faster runner. So if the faster runner was 10% faster, v would be 0.1. d is the distance it takes for the two runners to be even, and t is the time for the same.

Then:

d/(1+v) = t and d/1 = t+5

d=t+vt and d = t+5

vt=5

t=5/v

In the case of a 10% faster runner, v=0.1, which makes t = 5/0.1 = 50. It would take me 50 minutes to catch him. If I was running at 10km/hr, it would take me over 8.3km to catch him, even though his lead was never more than about 750m: the distance he could run in five minutes.

In the real world this translates into a strong lesson. It means that wasted time is very tough to make up even if you are very talented.