In mathematics, relations are a representation of the ‘relationship’ between two sets of numbers, usually showing a relationship between x and y.

Relations have more than one y-value.

Examples:

The price of a smartphone depends of how old the model is

Walking time depends of how long is the distance to a place

Relations can be represented in 6 different ways:

In words:

“The price of a watermelon (P) is related to its weight (W)”

Table of values:

Set of ordered pairs:

Mapping (arrow) diagram:

Equations:

Equations are usually relations when they have a square root (√) or squared ()

Graphs:

*Function notation is used to represent functions, a type of relation*

Functions are special relations, for a relation to be a function each input MUST only have ONE output (only one y-value (output) per one x-value (input)).

Functions can be represented in 7 different ways:

In words:

“Mrs. Smith has one son named James, and Mr. Campbell has one daughter named Lucy”

Table of values:

Set of ordered pairs:

Mapping (arrow) diagram:

Equations:

Graphs:

Function notation:

That is how  functions and relations represented, remember that the difference between functions and relations is that relations have multiple y-values for one x-value, and a function only have one y-value for each x-value.

Interesting points or intercepts are the points (coordinates) where a line or a curve crosses either the x-axis or the y-axis.

The y-intercept is where the line crosses the y-axis, and the x-intercept is where the line crosses the x-axis.

Example:

To find these intercepts when you have a  you have to use this rules:

To find the x-axis you have to write the y variable as 0 (y=0):

Examples:

Similar to before, to find the y-axis you have to write the x variable as 0 (x=0):

Examples:

When writing these coordinates you have to put the x-coordinate first and the y-coordinate after:

(x,y) is the how the coordinates are written. 

x-coordinate: (x, 0)

x-value first and y-value as 0.

y-coordinate: (0, y)

x-value as 0 and y-value second.

People usually talk about their study method and how it works for them, however people do not usually talk about learning styles. Today, I will tell you about learning styles and the importance of them in our daily life.

There are many study methods, you might have tried or heard about them already. However, there are also learning styles.

What are learning styles?

A learning style is the way a student learns, there are three main learning styles, these are: Visual (Spatial), auditory (Aural), and kinesthetic (Tactile).

Why is it important to know them?

It is very important to know your learning style because you can find  the study method that works for you, it can also help you getting to know more about yourself and maybe even discover the reasons of some things you might do, like making doodles, watching videos, or listening to podcasts.

Characteristics

Visual learner: They learn the best by seeing and observing, they like to visualize and think how something works. They usually enjoy reading, are good spellers, very neat people, speak quickly and might get distracted by noise.

Auditory learner: Noise is the main characteristic in this type of learning, they get and retain information by listening to others or themselves, they are known because they read out loud and always have background music while studying.

Kinesthetic learner: They learn by using their hands, most kinesthetic learners are good at sports, energetics, very coordinated and could be a little be messy.

Which study methods work for each one?

For visual learners it is recommended to have a study routine where you watch videos, make flashcards, use mind maps, use charts and graphs, turn your notes into images, and use a lot of color to highlight your notes.

For auditory learners using songs to memorize, recording themselves, studying in quiet places, watching videos, and listening to music is very helpful.

For kinesthetic learners building models, using gestures to memorize, studying outdoors, conducting experiments, and using role play; are useful study habits.

Remember that these learning styles can be combinated and people can be, visual-auditory learners, auditory-kinesthetic learners, visual-kinesthetic learners, among others.

Try to experiment with many study methods and I hope that knowing your learning style helps you with this.

How can we prepare ourselves for an important test? How can we predict our test mark?

In this week’s blog I will tell you a study method and some tips to prepare yourself for a test.

Brainstorming is very useful if you do not have many time to study, or if you want to verify that you are actually prepared and remember the test contents.

If it is a midterm test, or a test that has many topics, write down all the unit or topic names:

Then time yourself from 2-5 minutes for each topic, and write, draw, or explain everything you remember without looking at your notes.

After you finish, review your notes or talk to others and check if you are forgetting anything, if so write down the things you missed in a different color and review them. At the end of your study time, repeat the brainstorming and make sure you understand the things that you missed earlier. Make sure to repeat these at least 3 days prior to a test.

Brainstorming is an easy review and study method, now here are some tips to increase your possibilities of getting a good grade:

Some tips to get a good grade in a test are:

• Sleep well: It is super important to sleep well because if you are tired the day of the test you might find you making simple mistakes that could be avoided if you were energetic and watching out for errors.
• Eat well: Try to eat a good meal, avoid candies or junk food that could make you feel tired during the test.
• Do not study the night before: If you do not understand something the day before the test, it is not worth to stay up late to understand it, you will be tired and will not remember it at all.
• Be conscious of your learning style: There are many learning styles, make sure you know which one is suited for you, so you can try study methods that work for that type of learning.