To solve word problems we have to create a system and solve it. To do this we first need to analyze the problem to create 2 equations, these are the steps to do this:

Steps:

1. Read carefully!: You should at least read 3 times, try to highlight all the important words of the problem.
2. Declare variables: This means that you have to recognize the variables you are using, and determine the letters you will be using.
3. Write the system: After gathering all the information, just write it as equations.
4. Solve & check: It is important to solve the system and check if the answer is right.
5. Answer: Write a sentence that answers what the original question is, make sure it makes sense.

Translating words into an equation

Some useful hints you can remember are these:

Equal sign will probably be represented as verb + is/ was/ will be. For example: The car’s speed WAS 75 km/h

Switch words:

It will be confusing because the words will not be matching your equation most of the time:

Than means subtraction

More means addition

From means subtraction as well

Difference also means subtraction

Sum means addition

Example:

*workbook page 483*

Another example:

*workbook page 481*

I hope this is useful for you to understand a little bit more about word problems.

If you want to know how to solve systems in more depth, you can check my last blog post where I explain the different ways you can solve them.

First of all:

What is a system?

A system is a set of equations that you solve together (at the same time), usually to find the solution.

What is a solution?

A solution is the point where two lines cross each other, (X, Y) is used to represent its coordinates. If you have a graph you can predict how many solutions it has.

For example:

Parallel lines never intercept each other, which means they do not have any solution. They have the same slope.

Coincident lines are exactly infront of each other, therefore they will have multiple or infinite number of solutions. They have same slope and same intercept.

Oblique lines or intercepting lines will only have one solution.

There are three ways of solving a system without a graphic:

The first way of solving a system is by substitution:

Substitution consists of  ‘substituting’ or replacing one equation into the the other.

Example:

The second way of solving a system is by inspection:

It consists of quick mental calculations that help to find the solution of a system without using algebra. Most problems will require to mentally eliminate one of the variables to be able to find the answer but if from the beginning you only have one variable it will be way easier.

Example:

The third way of solving a system is by elimination:

Elimination is a very useful tool for when all the variables have a coefficient and you want to avoid the usage of fractions. It consists of adding or subtracting the same variables, getting a zero pair and being able to use substitution afterwards (It is similar as the inspection method but the difference is that at least one of the variables have a coefficient with a value higher than 1). It is recommended to add to not have problems with the signs.

Example:

–Vocabulary————————————————————————————————————–

Zero pairs: A pair of numbers that when added the answer is equal to zero.

Equations: Two mathematical expressions united by an equal sign, stating that they are equals.

Variable: Something that does not have a fixed value.

My wonky Initials Project

Part 1.

For this project we had to draw our initials in desmos, creating equations, and properly using domain and range to shorten the line and get only the portion of line we needed.

First I used the template Ms. Burton provided to draw our initials on:

*All the points I drew are represented as the pink points in this image*

Then, I plotted the points for each letter in a table of values:

Part 2.

After doing all the planning, we had to write the table of values ​​in Desmos, an online graphing tool.

Now, I had to write an equation representing each line.

For letter A, I plotted the table of values in a piece of paper, and started finding the slope.  I used point-slope form to write the equation, this is the easier form to use when you have a slope and points, however, I rearrange the point-slope form to get either general form equations or slope intercept form and have some variation in the equations.

After getting all the equations, I wrote them in desmos.

For letter A, I used these equations:

I also wrote the proper domain to get the exact line section I needed.

For letter I, these equations and domain were used:

Finally, for letter P, I used these equations:

In this case, I used domain and range because there is a straight vertical line and because it has a slope of 0, there is no domain to write:

The final graphed project looks like this:

There are three ways of finding and writing the slope of a line when you only have the coordinates.

The first and the base formula is the ‘y-intercept form’, it is written as follows:

y=mx+b

m represents the slope, it is always accompanied by x

b represents the y-intercept (starting point)

How to:

The second way of writing slopes is the ‘point-slope form’, this form is usually used when there are ugly looking equations. The formula is written like this:

m=

How to:

The third way of writing slopes is the ‘general form’, this form is seen very often however it does not give you much information about the equation and you have to rearrange everything to find the slope and the coordinates. However it is a very simple equation that is very pretty visually.

Formula: ax+by+c=0

How to:

I hope these formulas help you save time when finding slopes without a graph.

This week’s blog post is about creating your own “slope treasure hunt”, you can do this activity if you want to review for a test or try to make your study a little bit funnier.

So,

What is a slope?

A slope is a number that describes the steepness of a line, it is the same as the tangent ratio.

It is calculated as “rise over run”

Slope=

Negative numbers in the rise part means it is going down, and negative numbers in the run part means it is going to the left.

Example:

Now that we have seen a little bit about how slopes work, let’s try to solve a treasure hunt using slope coordinates:

Answer key:

Now create your own treasure hunt, remember to use the right coordinates and solve it to see ir works properly.

Create your own treasure hunt:

Remember to share it with others and try to make your study session more fun.

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.

How do we factor polynomials?

Expanding a polynomial and simplifying it’s pretty simple, however, how can we find the original polynomial when it is already expanded?

To do this we can go back to 4th grade lessons, they made us find the perimeter of a geometric shape by having the area value:

Something similar happens when you want to find the “perimeter” of a polynomial:

To find the perimeter of a polynomial, you have to ask yourself three questions:

If the answer to number 1 is yes, the polynomial can be solved as follows:

*If it does not go to the question number 2*

If the answers to number 2 is yes, the polynomial have to have these requisites:

*If it does not go to the question number 3*

*If it does not meet the requirements but is a binomial is possible to be a tricky one that cannot be solved*

• Difference of squares: Both terms need to be a perfect square, same with the variables.

Example:

1, 4, 9, 16, 25, 36, etc.

The variable is usually

If it meets the requirements, solve as follows:

If the answers to number 3 is yes, the polynomial have to have these requisites:

• It has to be in , , # format

Solve as follows:

Make sure to look for tricky questions and to check if the answers are right.