In elementary school we are taught to add/subtract fractions in a way that, quite frankly, is a BAD WAY of adding/subtracting fractions! If you don't know what I'm talking about, here's a short review... We have a fraction, say (1/2). Let's add a third. We have (1/2) + (1/3). So, what's the first step? Well, in elementary school you were probably taught to cross multiply. Let's try it We first get (1)(3) = 3 and (1)(2) = 2 Adding these together gets us 3 + 2 = 5 Now we multiply the denominators, getting (2)(3) = 6 We can now put these two numbers together: (5/6) Though this method works, it's not the best way to go about adding two different fractions. First off, why the heck does this work?! Though it seems like magic, there's a method. First, we cross multiplied. Putting this in a way that shows the whole expression gives (3)(1) + (2)(1) = 3 + 2 (2) (3) 2 3 We... read more
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When working with fractions, I find it effective to require students to convert each fraction that we work with to its decimal equivalent, to convert that decimal equivalent back into the original fraction, to convert that decimal into its percentage equivalent, to work a simple percentage problem using that percentage and finally to work the same problem using the initial fraction. This comprehensive method helps students to see the relationships between fractions, decimals and percentages in a holistic way and to promote the necessary skills in each element.
Buckle up readers, it's Trig time! Trigonometry can be scary to many students, and in my opinion, a lot of that is because one of the most confusing concepts in trigonometry occurs right at the very beginning, in the form of the Unit Circle and Radians. Let's start at the beginning. Give yourself a circle with a radius of 1. Now center that circle on the origin of a coordinate plane, so that the line of the circle itself passes through the points (1,0) (0,1) (-1,0) and (0, -1). Got that? Now, this circle is referred to as the Unit Circle, because the radius is one unit and it is therefore easier for us to do various manipulations and calculations with it. Now choose any point on the circle (we'll call the coordinates of that point (x,y)), draw the radius to it (which will still be a length of 1), and drop a line back perpendicular to one of the axes. Do that and you'll have a right triangle with the radius as the hypotenuse,... read more
Yes, there is only one way. Let's say for example that we have a fraction of 2/3. Now, the bottom number is the denominator which means the number of equal parts into which a whole circle most specifically is divided. So the circle is divided into 3 equal parts. On the other hand, the top number is the numerator which means how many equal parts out of all of them are lightly shaded inside the circle. So 2 out of all 3 equal parts of the circle are lightly shaded. Now, the only way to change the number of equal parts without affecting the fraction value is to multiply it by any number you want which will also change the numerator. So let's say for example that in the fraction of 2/3, if you wanted to divide each of those 3 equal parts into 2 further equal parts, you will have a new number of equal parts which is 6 (3*2=6). This will affect the numerator 2 as well since this is included in the total number of equal parts, so each of the 2 equal parts that are lightly... read more
Mothers generally know this trick. It works especially well with food children do not want to eat, but must. Tell the child that he only has to eat 3 bites. Then let the child eat just that many bites, which you can count together if you like. Increase the number of bites as the child learns to count. Alter the exercise with how many peas can be left on the plate; how many bites can be exchanged for another food or desert, and other tricks. As the child learns fractions, work with eating (or leaving on the plate) 1/2 of the food, or 3/4, or other familiar fractions. Fill glasses 1/2 full of their favorite beverage and offer another 1/3 or 3/4 or so more when he drinks the first fractional amount. Conversations and expectations and games like this applied to food and drink, picking up toys, helping out around the house, etc., help children from ages 5-7 develop their number sense. These tricks can be used just about every day for a few minutes a day--longer only if... read more