Elementary level Math and calculators



In my opinion, calculators should not be allowed in lower level Math classes.  In most, if not all cases, calculators are preventing students from attempting to solve simple arithmetic operations simply because they become lazy and don't want to think. 

I`m not saying that calculators should be banned altogether.  They are great if they are used properly.  Meanwhile, young pupils must learn how to do mental Math, and that requires them to understand basic mathematical concepts.  I came to realize that many students don`t know how to use calculators.  When solving a problem, they try several operations and come up with the right solution by trial and error.  Hence, mental Math is extremely important.

For instance, imagine someone that a young individual knows is selling some product and claims that there is some sort of discount to whoever buys three or more.  Of course, the calculator cannot be used in such a situation because it would seem as if there is no trust.  In such a situation, only mental Math would help in figuring out if it's worth it to buy more than one of that product.

Another example would be if someone who cannot function without a calculator works at a busy store, and all of the sudden the cash register stops working, and no calculator happens to be around.  What would such a person do in this case?  Would it be acceptable for them to tell their manager that they need to close the store simply because they don't know how to add taxes??

This is a serious issue that needs to be looked at by Elementary teachers very soon.  I've read so many blog comments where college students are urging others not to rely on calculators.  I'm including a link as a sample:

http://www.homeschoolmath.net/teaching/calculator-use-math-teaching.php

It's my hope that we start teaching those young minds how to properly use a calculator.  It's time for us to start exercising our brains again!

Using knitting elastic band as a manipulative

 

It may be hard for some students to realize that there is a relationship between fractions and percentages.  Therefore, it is crucial for a teacher to illustrate that idea in an unforgettable manner. 

Of course, there is more than one technique that can be used in such a situation, but the simpler, the better.  I find that the simplest one would be for a teacher to bring a a whole bunch of knitting elastic bands that are 32 cm long to the class and give students few minutes to figure out how those could be used in Math.  If any student comes up with the idea of elastic meter manipulatives, he/she is asked to demonstrate it to the rest of them.  If not, the teacher illustrates the concept by marking a line at 1 cm from one end.  From that point, and with the students' help, he/she marks every 3 cm.  That would make 10 marks in total, with 1 cm being left at the end.    The teacher should make it clear that the two extra centimeters are left out only to provide a better way to hold and stretch the elastic meter.  Next, the teacher labels the marks starting at 10% at the first mark, and ending at 100%.  The other face of the elastic can now be designed by marking and labeling the most used fractions (i.e. 1/4, 1/3, 1/2, etc.).  By doing so, the students will be able to see the relationship by flipping the elastic band back and forth.  Some word problems or simple activities can also be done to make sure all students are confident with this concept.

I believe that it's important that we introduce to the students an item that is used in everyday's life as a manipulative, because that will simplify matters greatly for them.

 

How to simplify for students the idea of proportions

Many students get overwhelmed when finding out that their teacher is going to introduce the concept of proportions. 

I totally agree that there are some Mathematical concepts that could be very difficult to digest if the teacher is not creative.  I have recently learned in my Math Methodology course at University that, proportion, which is the ratio of one quantity to another can be illustrated in a very fun way.  So how does it work?

The teacher starts a survey in the class.  This survey may be about anything that the teacher finds suitable based on the students' interests.  For instance, if the students are interested in sports, he/she can ask how many of them prefer soccer, how many prefer basketball, etc.  Students that fit in the same category have to stand next to each other, and the first person in each category has to hold a ribbon.  After all students get involved, a circle should be formed.  The teacher then stands in the center of the circle and holds all ribbons together.  This way students are able to clearly see the proportions of one category to another.

In conclusion, it's true that some Math ideas are harder to explain than others, but with little creativity, all concepts can be introduced in a fun and easy way.

How much math do we encounter daily?

How many times have we heard something similar to this phrase: "why do I have to learn about math?  I'm not going to use it anyways!"  Such a comment shocks me, because math is everywhere.

Where might we encounter math on a normal day?

1) Patterns - believe it or not, as soon as you wake up in the morning, math greets you.  If you take a look in your own bedroom, I'm pretty sure you'd be able to find some patterns, whether they are on your tiles, carpet, wallpaper, patterns are everywhere.

2) Symmetry and GEOMETRY - as soon as you're fully awake, if you're the type that loves looking out the window, you'd be able to see lots of symmetry and geometry: trees, plants, birds, even the window have symmetry and shape.

3) Time - whether you're going to work, school, or just staying home doing nothing, I'm pretty sure you take a peak at the clock several times a day.  It's just human nature.

4) Measurement - this type of math is all around us.  Your house is full of things you can measure.  Even if you're just having a meal, the amount of food intake, the numbers of calories, how much fat and cholesterol are involved, just to give few examples.

5) Money - there is no way someone can tell me that a day have passed without using money or a least seeing money.  Even if you just want to buy a cup of coffee, you have to figure out the amount of change needed for that.

6) Decimals - in a previous blog, I have described that decimals are like our shadows.  They never leave us alone.  We even have some decimals in us (i.e. weight, height, etc.).

7) Problem Solving - you might think I'm kidding, but even if you just spend your day playing video games, there is problem solving involved to figure out how to win a game.

These are only few examples of how we use and see math every single day of our lives.  I'm pretty sure now there is much more.

 

Comparing Fractions

Comparing fractions with like denominators is pretty straight forward, but once the students are introduced to fractions with different denominators, lots of confusion arises.  It's very normal for them to get perplexed, because it is sometimes not so obvious which fraction is larger than the other one.  Usually the larger the numbers, the harder it becomes to figure out the answer.  Fortunately, there is a very simple way, which helps a teacher demonstrate to his/her students how to do that comparison.

To compare any two fractions, all we have to do is cross-multiply.  That is, we multiply the nominator of the first fraction with the denominator of the second fraction, and write the value on the same side as the first fraction.  Then, we multiply the nominator of the second fraction with the denominator of the first fraction, and write that value on the same side of the second fraction.  The side with the larger value turns out to be the larger fraction.

Surely, an example would help.  For instance, to find out which one of the fractions below is larger, I will demonstrate by following the above-mentioned steps:

8/17 ? 3/7

(8*7) ? (3*17)

56 > 51

Therefore 8/17 is larger than 3/7!

After introducing such a method to the students, I'm extremely positive that the majority of the students would feel way more comfortable in dealing with fractions.

Converting a fraction to a percent

Many students find it difficult to convert fractions to percentages, because sometimes it is not so obvious what the answer is. 

The easiest and quickest way to introduce this process is to teach students how to estimate the percentage.  First, make the students get used to the idea of changing the denominator to a 100.  In order to do so, the denominator must be multiplied by a certain number.  To keep the fraction the same, we have to multiply the nominator by that same number.  Obviously, since we're working with whole numbers in this technique, the number in question is only going to be an approximation, but it helps the students get really close to the answer.  For example, if we are trying to find the percent of 8/26, we know that to get 100 as a denominator, we have to multiply both 8 and 26 by a number a bit less than 4 (since 100/4 = 25), so the percent would be slightly less than 32%.

I believe that by teaching the conversion this way, there is a good chance that students would have a better understanding about the relationship between fraction and percentage.



Caculating Percentages Mentally

Knowing how to calculate percentages mentally is not only important for kids to know, but also for adults.  How many times do we face a situation where we go to a store to buy some clothes and find out that there is a discount of a certain percentage?  If we can calculate the new value right away, we'd be able to figure out how much extra money would be left after the discount and see if we want to buy some other items with that difference.

There is a very quick way to calculate any percentage in few seconds.  All you have to do is break the percentage into two more familiar percentages (i.e. 5%, 10%, 50%, 100%).  Those percentages are more familiar, because they are very simple to calculate.  For instance, to obtain 10% of any value, we just move the decimal place once to the left, and 5% is half of that value.  To get 50% of a number, we divide by 2.

I will give couple examples to make matters clearer,

40% of 200 = ?

40% = 50% - 10%

50% of 200 = 200/2 = 100

10% of 200 = 20.0

Hence, 40% of 200 = 100 - 20 = 80

98% of 260 = ?

98% = 100% - 2% (and 2% = 10% / 5)

100% of 260 = 260

2% of 260 = 26.0/5 = 5.2

So, 98% of 260 = 260 - 5.2 = 254.8

This technique demonstrates that percentages are very easy to calculate, so long as we keep things simple.