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### Geometry in 3-D for Middle School Math Teachers: Measuring Solids- 0 views

• In a combined operation, the navy and airforce have a helicopter and submarine at the levels shown: Helicopter: 230 m above sea level Submarine: 80 m below the surface of the ocean, directly under the helicopter A parachutist from the helicopter has 76 m to fall before hitting the ocean. a How far is the parachutist from the submarine? b What distance from the helicopter is she? c How far apart are the helicopter and submarine?

### Interactives . 3D Shapes . Intro- 0 views

• Introduction We live in a three-dimensional world. Every object you can see or touch has three dimensions that can be measured: length, width, and height. The room you are sitting in can be described by these three dimensions. The monitor you're looking at has these three dimensions. Even you can be described by these three dimensions. In fact, the clothes you are wearing were made specifically for a person with your dimensions. In the world around us, there are many three-dimensional geometric shapes. In these lessons, you'll learn about some of them. You'll learn some of the terminology used to describe them, how to calculate their surface area and volume, as well as a lot about their mathematical properties.

### Math Activities- 0 views

• 2.&nbsp;&nbsp;&nbsp; Powers of Three &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; I first ran across the fraction 1/243 in one of the Rama series of books by Arthur C. Clarke. Now 243 is the fifth power of 3. The decimal equivalent forms a very curious pattern as I describe in the notes. I then created an Excel spreadsheet to calculate decimal equivalents of the reciprocals of different powers of three to help analyze the patterns ( the notes explain how to create this spreadsheet ). I then could extend the work to explore powers of other repeating decimals. The only limitation is the size of your spreadsheet and your imagination.
• 2.&nbsp;&nbsp;&nbsp; Powers of Three &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; I first ran across the fraction 1/243 in one of the Rama series of books by Arthur C. Clarke. Now 243 is the fifth power of 3. The decimal equivalent forms a very curious pattern as I describe in the notes. I then created an Excel spreadsheet to calculate decimal equivalents of the reciprocals of different powers of three to help analyze the patterns ( the notes explain how to create this spreadsheet ). I then could extend the work to explore powers of other repeating decimals. The only limitation is the size of your spreadsheet and your imagination.
• 2.&nbsp;&nbsp;&nbsp; Powers of Three &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; I first ran across the fraction 1/243 in one of the Rama series of books by Arthur C. Clarke. Now 243 is the fifth power of 3. The decimal equivalent forms a very curious pattern as I describe in the notes. I then created an Excel spreadsheet to calculate decimal equivalents of the reciprocals of different powers of three to help analyze the patterns ( the notes explain how to create this spreadsheet ). I then could extend the work to explore powers of other repeating decimals. The only limitation is the size of your spreadsheet and your imagination.
• ...10 more annotations...
• 2.&nbsp;&nbsp;&nbsp; Powers of Three &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; I first ran across the fraction 1/243 in one of the Rama series of books by Arthur C. Clarke. Now 243 is the fifth power of 3. The decimal equivalent forms a very curious pattern as I describe in the notes. I then created an Excel spreadsheet to calculate decimal equivalents of the reciprocals of different powers of three to help analyze the patterns ( the notes explain how to create this spreadsheet ). I then could extend the work to explore powers of other repeating decimals. The only limitation is the size of your spreadsheet and your imagination.
• 2.&nbsp;&nbsp;&nbsp; Powers of Three &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; I first ran across the fraction 1/243 in one of the Rama series of books by Arthur C. Clarke. Now 243 is the fifth power of 3. The decimal equivalent forms a very curious pattern as I describe in the notes. I then created an Excel spreadsheet to calculate decimal equivalents of the reciprocals of different powers of three to help analyze the patterns ( the notes explain how to create this spreadsheet ). I then could extend the work to explore powers of other repeating decimals. The only limitation is the size of your spreadsheet and your imagination.
• 3.&nbsp;&nbsp;&nbsp; Graphing Project &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; As part of an analytic geometry I would often assign as a project the creation of a picture, a picture constructed from the equations in the geometry section. In some courses this mean only linear relations, or linear and quadratic functions or, in senior courses, trig and conic sections functions. A typical assignment is included. I would create an example ( to save space I've omitted the picture for this example,- you're welcome to try and produce it from the equations ). I would hand out the instructions, with the example, a blank table and a piece of graph paper, and, of course, a due date . Any picture in good taste was acceptable - geometric designs, copies of logos, whatever. The majority of the marks were for the math but I always included a small part for creativity and neatness.&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Much along the same lines, I once had senior students, once we finished the section on ellipses, try to construct the Toyota symbol as a combination of three ellipses ( best done on a computer ).
• 8.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Sloping Letters &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; This is the start of a simple grade 9 introduction to the difference between positive and negative slopes ( also the slopes of horizontal and vertical lines ). It can easily be extended by having the students make up their own phrase ( always something in good taste ) and the corresponding description using slopes.
• 9.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Lotteries &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; I used lotteries at the junior and senior levels. At the junior level it is fairly easy to explain the basis of probability. Then I can use the multiplication principle as an example of fraction multiplication. I've attached a PowerPoint slide show I created to illustrate the chance of winning a lottery - the last page is a worksheet the students would have in order to follow along with the slide show. At the senior level I've created a variety of assignments ( I changed the lotteries I used from year to year ) primarily based on calculating the expected value of a set of lotteries. ODDS SLOT MACHINE CRAPS THE EXPECTED VALUE OF A SEVEN-GAME PLAYOFF SERIES BACK TO THE TOP
• 11.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Pi in a Can &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; This is a simple grade 9 or 10 exercise that combines measurement skills , graphing skills and the concept of slope. You need a variety of different diameter cans. You might assign this as a take-home project in which each student had to find the different cans at home or you might have different cans brought into the class ( once the activity is done, the cans could be donated to the local food bank ). The students, working in groups of two, need to determine as accurately as possible the diameter and circumference of each type of can. If this is to done in class you would need rulers and string ( wrap the string around the can to get the circumference, then lay it out against a ruler ). Each group of students creates a table of circumference versus diameter, then plots a graph, with diameter along the horizontal axis. The points should fit a linear relation fairly closely. For analysis, depending on the students and the course, you could do one or more of the following : leave it there, simply as an exercise in making a table and graphing calculate the slope, showing that it equals pi do curve fitting with the TI-83 or in Excel discuss direct variation as the line should go through (0,0) do error analysis, suggesting ways to improve the results ( i.e. averaging group results )
• 14.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Stylometry &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Stylometry is the statistical study of written material. It turns out that the style of a particular author shows up in the distribution of word length, sentence length, in the repetition of certain words, etc. . There have been many books written on the subject ( a good starting point would be http://en.wikipedia.org/wiki/Stylometry ) . Stylometry is sometimes used to settle disputes of authorship ( from the bible to Shakespeare to the courtroom ). As an exercise in graphing and descriptive statistics I would have students read passages from different texts ( or passages from the same text but in different chapters or sections ) and do some or all of the following ( depending on time ) : graph the distribution of word length graph the distribution of sentence length find average word length and sentence length compare graphs to help identify which passages are from the same author for an author who writes under his or her own name but also under a pseudonym, determine if there is a change in style look at the different methods used to calculate a readability level ( see http://en.wikipedia.org/wiki/Readability ) A favourite of mine was to use the short story The Feeling of Power by Isaac Asimov ( http://en.wikipedia.org/wiki/The_Feeling_of_Power ). It is a story about a time in the future when all calculations are done by machine and a technician discovers ( or rediscovers ) how to do basic arithmetic calculations by hand. BACK TO THE TOP
• DRILL SET I
• DRILL SET II
• DRILL SET III

### TIMES Modules- 8 views

• These modules are prepared by AMSI as part of The Improving Mathematics Education in Schools (TIMES) Project. The modules are organised under the strand titles of the Australian Curriculum. Number and Algebra Measurement and Geometry Statistics and Probability The modules are written for teachers. Each module contains a discussion of a component of the mathematics curriculum from early primary up to the end of Year 10. There are exercises that teachers may wish to undertake – answers are given at the end of the module and often screencasts giving a solution are linked and indicated by an icon.
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