BIGGEST EVER MATHS & SCIENCE LESSON GUINNESS WORLD RECORD ATTEMPT NOVEMBER 2015 Title: Powers of Ten Part 2 Introduction to Scientific Notation (Standard Form). Learning Objective: Development of number sense related to large and small numbers in the context of counting in powers of ten, volume and facts about DNA. Reinforcement of concepts of shape and volume. Understanding how very large and very small numbers in the context of DNA are written. Resources part 2 Twelve rolled up newspaper sticks, one metre long. Some 1 centimetre cubes. Calculators which may include simple 4 function calculators and cell phone apps. Lesson Suggestions Here are 3 activities, each to last about 10 minutes. Teachers can choose to do 2 or 3 activities. 1. If the class have not already seen the Powers of Ten Video then start by showing it. This video zooms out, by ten times the distance each time, from the Earth to Outer Space, and zooms in from a man’s hand to the atoms and electrons that make up all matter. It shows a cell in the human body and the DNA in that cell. https://www.youtube.com/watch?v=bhofN1xX6u0
2. How many I centimetre cubes fit into a 1 mete cube? Make a 1 metre by 1metre by 1 metre cube using sticks made from rolled up newspaper. Sticks made from rolled up newspaper or magazines provide a cost free resource that can be used for number work, measurement and making models. Roll the paper tightly with string inside leaving short lengths protruding to tie the sticks together. The best way to do this is to fold the newspaper in three before you start rolling so that the edges of the newspaper are inside the roll, measure carefully and adjust to the required length of 1 metre. Make the cube as shown in the diagram and complete it by tying the sticks at all 8 vertices. You will need to ask 2 learners to hold up the top because the model is not rigid. Though rigidity is not relevant to the Powers of Ten activity, you may want to discuss with the class its significance in building structures like bridges and the fact that triangular frameworks (as in the octahedron shown) are rigid and strong. Place some 1 centimetre cubes inside the metre cube and ask “How many centimetre cubes fit into the metre cube if it is filled completely?” The learners should work out that to cover the base they need 100 cubes across and 100 rows of 100 cubes making 100 x 100 centimetre cubes on the bottom layer. To fill the metre cube takes 100 layers each containing 100 x 100 centimetre cubes making 100 x 100 x 100 = 1 000 000 centimetre cubes, that is one million centimetre cubes. This is 102 x 102 x 102 = 106. If time allows you might like to see how many learners can fit into the metre cube. They would enjoy this. 3. The size of DNA. How long is it? How wide is it? The complete set of genes in each of your cells is 3.2 billion base pairs on the DNA ladder, that is 3.2 thousand million. Ask the class how they would write down the number 3.2 billion. When you have agreed on three thousand two hundred million written as 3 200 000 000 then give out a calculator to each group. They can be different models including cell phone apps. Ask the learners to enter 3.2 and multiply it by 10 again and again until they get to 3.2 billion keeping count of the number of times they multiply by 10. Here are two of the results on different calculators Write down on the board the different representations found by the class and ask for comments. Ask why the number 9 appears. At this point you can introduce the notation 3.2 x 109 and explain that this notation is used all over the world for writing down big numbers. Explain scientists call it Scientific Notation and that it is also called Standard Notation. Explain why it is important to have an agreed (or standard) way of writing numbers so that people can communicate information without getting confused. Here are some numbers. Ask the learners to write them down in Scientific Notation. Ten 10 One hundred 100 One thousand 1000 The number of seconds in a day 86400 One million 1 000 000 The number of seconds in a year 31 556 926 One billion 1 000 000 000 The estimated population of the Earth 736 000 000 000 The DNA in a human cell is split into 46 chromosomes of varying lengths. If you could take one cell, uncoil all the chromosomal DNA and put it on a line, you would have 204 cm of DNA, although it is never actually stretched out like that. DNA is around 2 nanometres (nm) in diameter. That's two billionths of a metre. It is a good thing it's so thin, or it wouldn't fit in a cell, let alone the nucleus of a cell. Now discuss with the class what a billionth means. Explain that we use negative powers of 10 to denote dividing by 10, for example. One tenth One thousandth One millionth Explain that a billion is 109 (1 multiplied by 10 nine times) and that a billionth is 10-­‐9 (1 divided by 10 nine times). Ask the learners to enter 2 into their calculators and divide by 10 again and again, nine times, to show the diameter of the DNA double helix which is 2 nanometres. Discuss the way this is written in Scientific Notation as 2 x 10-­‐9. How much does DNA need to be magnified to be seen with the human eye? Most people can see things that are a tenth of a millimetre wide, or 1x10-­‐4 m. So multiplying 2 x 10-­‐9 by 10 five times, that is by 105 = 10 x 10 x 10 x 10 x 10, you get 2 x 10-­‐4 You have to magnify DNA one hundred thousand times to see a single strand with the human eye. You can't do that with an ordinary light microscope. You need a transmission electron microscope or an atomic force microscope to see it.