Algebra and Other Stuff

Hey everybody!

So, tomorrow is our final quiz on this algebra unit for term 2! Hopefully everyone in FE8B has been studying hard - I know I have!
Some things that we have learned for the final quiz are doing 2 step equations, and then how to solve equations that have different terms in them. For example: when the variable is the numerator or denominator of a fraction, when there are variables on both sides of the equal sign, and when we have to break brackets with variables in them. Here are some examples of each.
When the variable is the numerator of a fraction:
x/2 + 3 = 7
x/2 + 3 - 3 = 7 - 3
x/2 = 4
2(x/2) = 4 (2)
x = 8
check:
(8)/2 + 3 = 7
4 + 3 = 7
7 = 7
-> In that equation, I first moved the whole integer (+3) from the left side to the right by undoing it on the left, then doing the same function to the right side. Then I multiplied the fraction by 2, as that was the denominator, and did the same to the other side. The two 2s cancel each other out, leaving me with x=8. Then, I checked and it worked out.

When the variable is the denominator:
4/x + 6 = 10
4/x +6 - 6 = 10 - 6
4/x = 4
x(4/x) = 4(x)
4 = 4x
4/4 = 4x/4
1 = x
check:
4/(1) + 6 = 10
4 + 6 = 10
10 = 10
-> In that equation, I did the same as in the previous. So in the 4th line I multiplied the 4/x by the denomitor (x) and did the same to the other side. The two x's cancel each other out on the left side, giving us 4=4x. Then we divide each side by 4 (the coefficient) so that we get 1=x.

When there are variables on both sides of the equation:
3x = 5 + 2x
3x - 2x = 5 + 2x - 2x
x = 5
check:
3(5) = 5 + 2(5)
15 = 5 + 10
15 = 15
-> In that, all we have to do is cancel the integer with the variable on one side, and do the same function to the other side. That's how we got 3x-2x on the left side.

Finally, when there are brackets to break:
2(3 + x) = 10
6 + 2x = 10
6 - 6 + 2x = 10 - 6
2x = 4
2x / 2 = 4 / 2
x = 2
check:
2(3 + 2) = 10
6 + 4 = 10
10 = 10
-> In that equation, to break brackets what you have to do is multiply the number outside the brackets by each of the ones inside the brackets separately. Then it is just like any of the equations above.

In Science we started a new unit on water systems. We learned about how most of our water on the earth is polluted, to deep to get, or is salt water. Did you know 97% of the Earth's water is salt water? I didn't know that before today. Anyways, I will report more on that next week as we get more into the unit.

Until next Wednesday,
-K

Hi everyone.
Well, since it was a loooong weekend and I was sick yesterday, I only have one day to report on (today). Luckily, we did lots of math today! And I didn't write about math last week so let's talk about math!
So we have been learning more about integers and algebra. We have gotten into solving equations with variables and simplifying expressions.
To solve and equation with a variable:
There are two methods.
The first is to add the opposite integer of the coefficient to each side of the equation.
ex: x+2=34
x+2-2=34-2
x=32
check
2+(32)=34
34=34
The second is to divide each side by the coefficient.
ex: 4x=24
4x/4=24/4
x=6
check
4(6)=24
24=24

To simplify an expression:
You put all the integers with the variable together and use distributive property.
ex: 3x+4y-5y+x-2x+7
=3x+x-2x+4y-5y+7
=2x-y+7
*In that expression you can't use distributive property, as none of the integers have a common factor. An example with distributive property:
2x+6y-4y-8x+10
=-6x+2y+10
=2(-3x+y+5)

That's all for now!
Until next Wednesday,
-K

How Do Scientific Equipment Help Students Achieve Academic Excellence?

There are many ways hands-on activities can help middle school students with their learning’s! First of all, using equipment in class can help stimulate one’s brain. Instead of simply reading out of a seemingly boring textbook, students can now challenge themselves to higher academic levels by exciting their minds and by looking forward to new classes. These activities in science help students strive for excellence throughout their classes. Secondly, using equipment in class can help students with developing both physical and mental skills. For example: When tearing a triple beam balance, students are able t strengthen their eye coordination by noticing if the scale is set to zero. Thirdly, these activities can help students be more prepared for problems involving mixtures and pure substances in the future, even if the problem is small. For example: For breakfast one day you want to make a smoothie with water, but are worried that your smoothie powder will not make a homogeneous mixture, and instead will have lots of different properties! You could think back to experiments that were previously conducted and have the knowledge to identify whether the powder is soluble in the solute water. What if the powder has very large individual particles and appears to have a rough texture? This could make the powder difficult to attract itself to the water! All of this previous knowledge comes in handy. Lastly and most importantly, these skills that the students have developed can be applied to all different subjects throughout their academic career and follow through with them throughout their lives as well. To truly achieve academic excellence, one must be able make connections with previous knowledge to new knowledge. By having the ability to conduct experiments with scientific equipment, students are able to not only develop skills like problem solving and the ability to work as a team, but can take those skills and use them towards the future.

Students across the district should be very grateful for the opportunity to create a better academic future!

Ill blog soon!

Math And Science

Hello Everybody! I hope all is well! In Fe7B, I know for a fact that all is well because we have just started a new Unit in math! Patterning and Algebra. This great unit is a great challenge for the brain! Right now, we have been focusing on problem rules. For example: 1,2,3,4,5,6,7,8,9,10. This rule is: Start at one. Add one number to each term every time. Also, we have been trying to find patterns within terms of patterns to find the next term in that one pattern. Here is an example of what class Fe7B has been exposed to:
99 x 11= 1089
99 x 22= 2178
99 x 33= 3267 - Find the next 6 terms in the pattern.

In these terms, we can see that the thousands digits are increasing by one each time. We can see that the hundreds digits are increasing by one each time as well. Also, the tens digits are decreasing by one each time. Finally, the one's digits are decreasing by one each time as well. We can now figure out the next six terms in the pattern.
99 x 44= 4 3 5 6
-1 -1 +1 +1
99 x 55= 5 4 4 5
-1 -1 +1 +1
99 x 66= 6 5 3 4
-1 -1 +1 +1
99 x 77= 7 6 2 3
-1 -1 +1 +1
99 x 88= 8 7 1 2
-1 -1 +1 +1

As for science, class FE7B has been continuing with our experiments. But,have now recently have reported how our hypothesis were related to our observations. Here is an example of two powders that Fe7B experimented with:
With the unaided eye Powder Number 1 appeared to be consisted of thick and large individual particles. The attraction between the particles was very strong due to the size. When mixed with water, the powder particles were able to attract each other much easier causing the attraction of the water to be minimal. This then caused the strongly attracted powder to clump and become heavier than the water, sinking to the bottom of the test tube. Also, a new form of matter was formed by the trapping of air particles with the liquid. The mixture had three properties causing itself to be heterogeneous.
With the unaided eye Powder Number 2 appeared to be consisted of small, thin and smooth individual particles. The attraction of particles was very weak due to the size. When mixed with water, particles held no attraction to each other and quickly became attracted to the water. This caused the powder to separate evenly throughout the mixture and dissolve after one minute of shaking. The mixture had only one property causing itself to be a solution or a homogeneous mixture.
I'll blog soon!

A Short Post

Hello.

This post may be short because I just got home a few minutes ago and I have to go out again soon, so I'm sorry in advance.
Anyways.
In Science we did the testing of our Hydraulic/Pneumatic Transport System Things yesterday. Overall, it went pretty well. No one in my class made anything that did the entire task, but there were many intelligent and interesting concepts. It was a bit chaotic, but we learned a lot. And now, we get to go back, take what we learned, and redo our systems to (hopefully) work better a second time. I think that by doing this, we learn a lot more than we would be just reading a textbook and taking some notes. We got to see exactly how to use Simple Machines and Hydraulic/Pneumatic Systems to move a load from point A to point B. We put the theories we learn from the textbook into use. If we didn't do that, they would just stay as words on a page to us, not an actual concept that works and moves in real life. In my past years, Science has just been textbooks, notes, and tests. Doing Science this way, getting actively involved, is much more engaging and challenging. I don't know how I could survive Science any other way now that we have done it like this.

And now I have to go so...
Until next Wednesday,
-K

Integers

Hello everyone
In Math we have started a new unit on Algebra and Integers. We have just been working on Integers so far. But what are integers you may be wondering? Well, an integer is simply just any positive or negative number. It can be a fraction, decimal, or whole number. Some other key terms we have learned are opposite integers and a zero pair. Opposite integers means that they are the same distance from zero on a number line. For example, -3 and +3. Opposite integers are also zero pairs because when added together they equal zero.
We have learned so far how to add and subtract integers.
To add integers with the same sign, you just add the numbers together and keep the same sign.
ex: (+4) + (+6)
=(+10)
To add integers with a different sign, you subtract the smaller value number from the larger one and then take the sign from the larger value number.
ex: (+5) + (-13)
=(-8)
To subtract integers, you switch the second integer from negative to positive or vice versa and then add the two together. Then, you follow the same addition rules as I stated above.
ex: (+3) - (-7)
=(+3) + (+7)
=(+10)

(+8) - (+2)
=(+8) + (-2)
=(+6)
So, that is what we are doing in Math. Have a good week!
Until next Wednesday,
-K

Hey Everybody! I hope all is well, especially since Winter has hit a breakthrough!! It is now turning dark at 5:30, NOT 4:30!!! Hopefully, I am not the only one celebrating. Now, back on topic, I will talk about our new units in both math and science! For math, firstly, we have started a new unit in fractions and decimals. Learning great skill sets, class Fe7B is able to add, subtract, multiply and divide not only decimals, but fractions as well. You may think dividing and multiplying decimals is hard but, the process is really quite simple. When multiplying decimals, the easiest way to find your product is by making your decimals whole numbers. For example: 3.4 x 7.8 can be 34 x 78. Afterwards, when you find your product, you have to divide it by 100 since you moved over the decimals by two place value spots. This is the final step. 34 x 78= 2652 divided by 100 = 26.52. When dividing decimals, the process is similar to long division with regular numbers. The one difference is that the divisor has to be a whole number and whatever you apply to the divisor, has to be applied to the dividend as well. For example: 12.9 divided by 3.9. In this division question 3.9 has to be a whole number by shifting the decimal over to the right. This means that the same applies to 12. 9. The new question is: 129 divided by 39. Here is a picture of the long division work:

As you can see, the answer is 3.307 which can be rounded to 3.31. The decimal is put after the place value spot of the 9 in 129. This is just like any other long division problem.

As for science, we have really gotten into experimentations involving substances and mixtures. In class, FE7B has started an activity involving experimentation. How will four solutes react with the solvent water? We first made hypotheses for all four powders. Then, we were able to start conducting our experiment. There needed to be a list of materials.

• water
• glass rod
• experimental powders
• graduated cylinders
• test tubes
• Florence flask
• funnel
• Safety glasses
• Test tube rack
• triple beam balance

Procedure: What steps will you take to make an experiment that will give you results that support your hypothesis?

1. Put on safety glasses or goggles. Tie back hair, consider safety before anything else.
2. Gather materials and equipment.
3. Put four test tubes into test tube rack.
4. Measure 20 mL of water using the graduated cylinder and put it into one of the test tubes. Repeat this procedure with the other 3 tubes.
5. Using the triple beam balance, measure 2 grams of each substance and place into each test tube
6. Place thumb over top of test tube and shake for 1 minute.
7. Make observations. Look for not dissolved solute at the bottom of the test tube. Look for particles suspended throughout the mixture and any other reactions between the solutes and the solvent.
8. Clean up and put away your materials and apparatus.
9. Draw conclusions

That is basically all that FE7B has covered so far. I'll blog next week!