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  • Teaching Through Natural Inspiration
    student the natural joy and thirst for learning This natural thirst and joy for learning is present in children so obviously in the early years Though once introduced to the system of grading the child can subconsciously develop strategizing a subtle form of innocent manipulation to work at receiving that age old important authority parental teacher s acceptance Focusing on the importance of grades can breed memorizer students those who practice memory techniques to give back to a teacher what the student thinks the teacher wants rather than the optimal learner students Even though memorizing can be an effective study tool memorizing is not likely the quality learning result that a teacher truly wants for the student Where grading may be an important part of the educational system it is only effective if minimal importance of it is placed upon the psyche of the child Introducing games in the curriculum of a child s schooling reminds the child that learning is by its very own nature supposed to be fun Designing curriculum that regularly incorporates left brain right brain activities such as spatial functioning card games both encourages the child to desire learning again what was once a natural thing and while literally developing new healthy dendrites in the child s growing brain For an example on Teaching Through Inspiration here are some of our Fun Math Learning Games http www math lessons ca activities Geometry html http www math lessons ca activities OneEquals html http www math lessons ca activities equiv fractions bingo htm If you enjoyed this article subscribe to receive more great content just like it Subscribe via RSS Feed About the Author Comments 3 Trackback URL Comments RSS Feed Stella says April 30 2010 at 6 07 pm I am currently in a Master s teaching program in Maine and we have talked about this over and over in all of my classes One thing we discussed during our last class is that Maine might be changing their whole education system where everything is standards based The idea behind it is that grades will be eliminated and students will move to the next subject when they have mastered the content and reached the standard Grades can be a very difficult thing for students and for teachers because they don t always measure the actual knowledge As you said some students learn to memorize things and forget it after the test or assignment and don t actually learn the material I feel that all students want to learn and succeed in school but there is a stigma attached to doing well in school and getting good grades I am dreading giving A B C D F grades when I teach because I don t always feel that they are an accurate measure of the student s progress and hard work Vidal Aponte says June 25 2010 at 9 44 am You nailed it right on the head If we want our kids to improve in math or

    Original URL path: http://www.math-lessons.ca/teaching-through-natural-inspiration.html/ (2014-10-09)
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  • Golden Mean Ratio: Egyptian Scultpure
    and rhombi Alekseĭ Petrovich Stakho Mathematics of Harmony From Euclid to Contemporary Mathematics and Computer Science Scott Anthony Olsen Book English 2009 pp 57 59 Soroko believed that the Bust of Nefertiti was created based upon the Geometries of the Golden Mean Ratio and the Fibonacci Sequence A graphical image of Her Bust as was drawn by Soroko is shown in this link http www pinterest com pin 529454499915732124 Highly recommended to click on this link to have a finer and more detailed idea of the geometries that Thutmose is thought to have in mind when sculpting Her Bust One can appreciate in particular how the front top vertex of Her headdress is in perfect alignment with Her Heart and Breast Bone Depicted here the Golden Mean Ratio and in the geometries thought to be applied by Thutmose the Egyptian Court Sculptor in the creation of Nefertiti s Bust n is to m as m is to n m or algebraically n m m n m A more clear example of the pattern he believed Her Bust was created upon the Fibonacci Sequence can more easily be seen in examining nature s pattern in pine cones and seashells This ratio is also the most efficient mathematical equation for trees absorbing the most amount of sustenance from the sun s rays hence growing in a spiral In the same way today we can apply solar panels onto rooftops mimicking this pattern to most efficiently absorb the sun s rays For further discussion on Fibonacci Sequence visit here http www math lessons ca fibonacci sequence html See in the photo at the top the chamomile spiral as well as in this link on fibonacci sequence showing the pattern Adding two consecutive numbers from the sequence to equal the next one following the

    Original URL path: http://www.math-lessons.ca/golden-ratio-egyptian-sculpture.html/ (2014-10-09)
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  • Torus Math – The Doughnut
    we find most interesting is just under the blue torus image and it is a mutable image of a ring torus turning itself into a horn torus and this is one of the images that mathematicians today are calculating that Earth is most closer to as a realistic geometric shape than was once thought Earth in this respect is today referred to as the tube torus a shape that occurs often in Nature If you click on the link you can see just to the right under the blue torus a better mental picture of our reference As the distance to the axis of revolution decreases the ring torus becomes a horn torus then a spindle torus and finally degenerates into a sphere www wikipedia org wiki torus http en wikipedia org wiki File Torus png There are several on line sources of the manifolds 3 of which quote the same information Joyce Wikipedia and Harmonic Resolution com all denoting that manifolds are today a major branch of geometric study a curved space of some dimension For example the surface of a sphere and the torus the surface of a doughnut are both 2 dimensional flat surface perceived manifolds The manifold itself is the background for some mathematical object defined upon it as a canvas is the background for an oil painting This kind of geometry although very abstract is closer to the real world than you might think Einstein s theory of General Relativity describes the Universe the whole of space and time as a 4 dimensional manifold Wikipedia has wonderful moving images of the manifold turning into the torus and back into a manifold flat surface again and is worth having a gander for a more picturesque idea of what these terms are in Math under the subtitle

    Original URL path: http://www.math-lessons.ca/torus-math-doughnut.html/ (2014-10-09)
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  • Perimeter
    Measuring tape White board and dry erase markers Note If your classroom is not perfectly square or rectangular consider drawing a classroom layout on the white board that is easy to calculate the perimeter For more advanced students challenge them to find the perimeter of their irregularly shaped classroom Instructions Have the students measure the dimensions of the classroom to the nearest foot drawing a diagram of the classroom As the students measure the classroom either have them recreate the classroom on paper or on the white board in the front of the classroom Explain to the class that they are calculating the perimeter of the classroom You may consider saying The perimeter are the edges of the classroom that we are measuring The perimeter tells you the distance around the outside of a shape The classroom is shaped like a rectangle or a square so when do you think it would be helpful to know the distance around the classroom Yes if we were going to decorate the classroom with a ribbon we would need to know the length of the sides of the classroom The perimeter is an easy calculation to find just by adding the length of each side together Have the students calculate the perimeter of the classroom using their diagrams You can extend this activity and encourage the students to measure a room in their home and determine the perimeter of the room This can also be done measuring the perimeter of the outside playground at the school or the perimeter of the school s desks For more ideas about how to teach young students about perimeter and distance of shapes visit http www scholastic com teachers top teaching 2012 12 10 hands strategies teaching area and perimeter and http www watchknowlearn org Video aspx

    Original URL path: http://www.math-lessons.ca/perimeter.html/ (2014-10-09)
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  • Probability
    students will learn how to calculate and interpret probability Materials Large bag of assorted color candy Small plastic bowls It is best if you know how many color of each candy is present in the bag If this is not possible estimate the approx numbers of each Instructions Assemble the class into small groups Give each group a small plastic bowl and 1 2 cups of candy in each group s bowl Have the students count the total number of candies the number of candies of each color and record the data on a piece of paper Explain to the students that the probability of something occurring is another way of saying what are the chances or the likelihood that an event will happen You may consider saying We are going to calculate the probability of you getting a red colored candy from your bowl if you picked the candy with your eyes closed The probability is a number that helps you determine if something is likely to happen or not likely to happen To find the probability of picking a red candy we need two numbers The number of red candies in your bowl and the total number of candies in the bowl In this group they have 2 red candies and 31 total candies So the probability would be 2 31 which is a very small number So if they were to close their eyes and choose a candy it would most likely not be red Invite students to calculate the probability of picking each color and allow time for them to pick candies at random to explore the concept of probability further For older students extend the activity by practicing how to reduce fractions for example a probability of 3 18 can be reduced to 1 6

    Original URL path: http://www.math-lessons.ca/probability.html/ (2014-10-09)
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  • Writing Mathematical Ratios
    everyday items In this activity students will learn how to calculate and write a ratio Materials 5 sealable bags red blue green marbles or unit blocks 20 of each color white board dry erase markers This is best done as a group activity with no more than 4 students per group Prior to the activity place a different amount of each marble color in each sealable bag For example Bag 1 may have 3 green 4 blue and 5 red Label each bag with a number to better keep track of the bags and marbles used Instructions Assemble the class into small groups Give each group a labeled bag of marbles Have the students count the total number of marbles in the bag and the number of marbles of each color and record the data on a piece of paper Have the groups rotate bags so that each group gets a new sealable bag and repeat steps 2 and 3 Ask the students What did you notice about the number of marbles in each bag What about the number of each color Explain to the students that the number of each color marble can be written as a ratio or a comparison You may consider saying A ratio is a number that compares to items together For example in Bag 1 there were 3 blue marbles and 5 red marbles so we could compare or write a ratio of blue marbles to red marbles by writing 3 5 For older students consider extending the activity by providing them with word problems involving ratios Have them explore how ratios can be maintained by doubling or halving quantities For example you might ask if the marbles are to stay in a 3 1 ratio how many marbles of each color would you

    Original URL path: http://www.math-lessons.ca/writing-mathematical-ratios.html/ (2014-10-09)
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  • Order of Operations
    Several clothing items coat shirt socks hat sunglasses gloves Whiteboard and dry erase markers Instructions Invite a volunteer to come to the front of the classroom Provide them with the various clothing items and explain to the class that even in everyday tasks like getting dressed there is a particular order or rules that we follow Ask the student to put the items on over top of their clothes to simulate getting dressed As the student does so point out what item went first then next Acknowledge that the order of the hat and sunglasses did not matter One could either put the sunglasses on first and then the hat or vice versa Explain how this relates to Math and the order of operations You may consider saying Just like with getting dressed Math has a special order to it We do operations that are in parentheses first then those that may involve exponents then multiplication and division then finally addition and subtraction However sometimes the order does not matter like with the sunglasses and hat When you are only left with addition and subtraction or multiplication and division you do the operations as they appear from left to right Write the following problem on the board 3 x 5 60 10 7 and walk students through the order of what has to be done first then next then last If time permits write additional problems on the whiteboard and have students work through the order of operations Additional Order of Operation Resources As students graduate to more advanced math it is essential that they be able to accurately manipulate and calculate values This is especially true with solving equations or problem solving For more interactive ways to introduce and practice the order of operations visit http www foundationsofalgebra com

    Original URL path: http://www.math-lessons.ca/order-operations.html/ (2014-10-09)
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  • Enjoy Making Bar Graphs
    students will explore the how to collect and graph discrete data Materials Chart Paper Markers Instructions In the classroom section off 4 distinct areas Using corners of the classroom is the easiest way to do this Ask the students What is your favorite dessert If you like cake go to Corner 1 if you like cookies go to Corner 2 if you like ice cream go to Corner 3 if you like candy go to Corner 4 Allow time for students to decide which dessert they prefer and then record the number of students in each corner On the chart paper have 4 columns one for each dessert option Write the number of students in the corresponding column Explain to the class that they just collected data on the type of dessert their classmates like You may consider saying Data can be in the form of numbers or words and in this case we determined how many of you like each type of dessert Next we are going to do a graph which is similar to a picture showing the data we just collected Create the axis of the graph labeling the number of students on the vertical axis y axis and the type of dessert on the horizontal axis x axis Mark the y axis according to provide enough numbers to represent the numbers of students in each category Draw in the bars to the corresponding number for each dessert type For younger students consider using stickers to represent the bars of the graph and have each student place a sticker in the dessert column they prefer Additional Graphing Resources Graphing is essential to building scientific knowledge and understanding as well as Math comprehension For more interesting graphing activities visit http classroom jc schools net basic math graph html

    Original URL path: http://www.math-lessons.ca/enjoy-making-bar-graphs.html/ (2014-10-09)
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