UNIT 2: Using Measures and Equations

This is a picture of my group members playing Jeopardy in math class.

How are algebra and geometry related?

In this unit, we have explored many concepts such as algebra that are related to geometry. There are algebraic formulas that can be used to explore many different kinds of information in geometry such as angles, volume, interior angles, exterior angles, circumference, Pythagorean Theorem and others. In this unit, we have mainly focused on Pythagorean Theorem, circumference, volume, and interior angles. For the volume, there are algebraic formulas that can be used to find out how much space an object takes up. The formula is base * height * width. I will create an example similar to the one in the textbook. There is a rectangular prism with a base of 2x cm, height of 6y cm, and a width of 7 cm. To find out the volume of this prism, simply substitute the base, height, and the width by the numbers. So the answer would be 84xy cubed cm. For the Pythagorean Theorem, the algebraic formula for it is a^2 + b^2 = c^2. Here's an example to further explain my claim. Let's say a leg is 5 cm and the hypotenuse is 20cm. To find out the other leg, simply substitute a by 5 and c by 20. If you square them , it should be 25+ b^2=400. Then subtract both sides by 25, and then find the square root of 375. The answer should be approximately 19.36cm rounded. So the missing leg is 19.36cm rounded. To find the circumference of a circle, you have to use the algebraic formula 2* Pi*r (r=radius). Pretend there is a circle with a radius of 4cm. To find out the circumference, you simply again substitute r for 4cm and then you can find out the answer. The answer should be 25.12cm as 2* Pi (3.14) * 4=25.12cm. So these are some examples to show how algebra is related to geometry. To conclude, algebra and geometry have many relationships and are very similar to each other.

This is the Magnitude Project for Unit 2 where Vadin and I worked as partners.

This project demonstrates "reason critically" and "collaborate constructively" as my partner and I have spent lots of time and effort working through this by meeting after school, and to find exact calculations, we had to reason critically. In the beginning, Vadin and I decided to use video chat for the worksheet as we could talk about our calculations and see if each other's steps are right and that we are using the same comparisons. Vadin and I have collaborated constructively as we talked and used video chat to assign roles for what we have to do in order to create a good piece of work. We helped each other out when we needed and by through working after school with the visual presentation, we have fairly done a good job collaborating together effectively. For example, Vadin did the visual pictures and I have done the calculations and the work. I needed help doing the visual comparisons so Vadin helped me out by finding a great resource which shows how long the London Bridge was built, the Mona Lisa was painted, and so on. For reasoning critically, it is important and we have applied this SLR by our calculations, scientific notation, reflections, and so on. We had to reason critically especially on the math work as we had to go through every single step and see if it was right or wrong. If one calculation has a mistake, it could mislead the audience and make them feel confused so this SLR really stood out in the project. Vadin and I also were reasoning critically for our visual comparisons to see if this will have an effect on the audience. Vadin and I have really emphasized our visual comparisons to let the audience know that for one person, it takes a certain amount of KwH for something to be built like the London Bridge, and other examples. So in order to be successful at this project, Vadin and I have really demonstrated reasoning critically and collaborating constructively.

Since unit 1, my work habits and participation level had somewhat increased as I have demonstrated enthusiasm, and the core values in class and turned in most of the homework on time with good quality. Out of a scale of ten, I would rate myself eight as I had received homework slips due to not writing down the homework on my planner and forgetting about it so this interferes with my responsibility. I know that for homework, it's like a practice and tests your level of understanding so I value it a lot as it helps me to increase my level of knowledge and test myself. For the class participation, I have demonstrated enthusiasm not only in Jeopardy, but also in front of the SmartBoard. Writing a solution on the SmartBoard and participating actively in a game makes my mind get thinking so the participation level would have improved from the start of unit 1. When I have questions, I ask them to my teachers and my parents so that I can understand the math concept. I have an outside math tuition teacher with CY and we review the same concept as in class so when I am confused, my math tutor helps me out. For the quizzes and tests, I am already prepared for those kinds of class assessments as I am "bombarded" by lots of math problems similar at school and outside in a good way. My outside tuition teacher first reviews my schoolwork with him but he gathers all of the questions that I have gotten wrong and "retests" me. This is a good review for me as the questions also in the quizzes and tests are rather similar. So I think that I have been doing a decent job advocating my learning.

This is my group getting a question right in a game of Jeopardy.

Yearlong Project October Update

THE PLAN-

The family project that I will use is to when we are sleeping, we can set a timer for the fan so that the fan won't be on until next morning when we get unconscious, to turn off any electronics that is left on when we're going on a trip, being sure to unplug machines as they have stand-by functions that consume energy even though they are turned off, keeping doors or windows shut when the air conditioner is on, turning off the water when I am brushing my teeth because it will not only save water but it will also save the electricity it takes to pump and heat the water, and so on. By setting a timer for the fan around 3 hours, it can save electricity by automatically turning it self off. Although our family uses the fans at full maximum power, we can save time so that we can cut down on our energy consumption. According to the manager of my apartment, our apartment has around 200<x<300 air conditioners (x is the amount of air conditioners there are but the management is not so sure)... The air conditioners are used around 5 times a week with more than 50hours. They are not used at night in all of the bedrooms, as there are more fans than air conditioners in our apartment.

Reflecting on my electricity monthly table, my family has been doing great at decreasing the amount of Kwh and meeting the goals listed above. For the first month, I had 636kwh but on the next month, my electricity bill was 550kwh, which is a decrease of 86kwh. For September to October, my electricity consumption has decreased from 550kwh to 507kwh, which is a decrease of 43kwh. I think that the reason for this decrease is because one of my "family" members went back to Cambodia last month (my maid). My maid also consumes electricity so since she is gone, I am not surprised that my monthly electricity consumption had decreased. My family also has done many ways that have mentioned above. Due to this project, our family had saved both the amount of energy used and our economic finances. Before this project, my family was doing a decent job on having a stable low energy consumption as we didn't use air conditioners at night, and other ways that didn't consume that much electricity. We used to have a maid living in our house until the first week of October, she decided to quit her job and fly back to Cambodia to visit her sick dad. This had even more decreased my family consumption as my maid who used fans, mobile chargers, and other electronic devices left. According to the management office, they say that there are approximately 223 air conditioners in this apartment (including the office). The temperature that my family sets is various although the most common temperature that we use is 23 degrees Celsius. For my family, we roughly use 2 hours on an average day although the air conditioners are mostly used to keep the teachers comfortable. Our family uses the air conditioners to make the air in the room cooler than with the fan as it helps to keep a cool temperature for my saxophone to protect it from humidity, and to make the air cooler than a fan. Recently, I have asked the management office and they stated that the total amount of hours the whole apartment consumes is around 34 hours. My family only uses 6% rounded for the total hours of air conditioners used in my apartment, which means that we aren't using that much electricity for the air conditioners. Not only does our family uses air conditioners, but we also use electricity for TV's. In our family, we have 2 TV's in total and we use them about 4 hours a day. The management doesn't know the real amount of televisions in my apartment although in the last two years, they did a survey to all the people in the apartment. The amount of TV's listed on the survey was 98. In a day, they said that 22 hours is the amount of hours the whole apartment uses. My family only uses about 9% rounded out of the total amount of hours used for the television per day. To talk more about my family habits, my family doesn't watch that much TV these days as before as the only thing that our family uses it is to watch news and sports and the amount of homework that my brother and I have collides this too. My mom and dad are starting to not watch the TV but use their Samsung Galaxy Tabs and phones to watch documentaries on their tablets, which I can say is conserving electricity and the TV usage. To conclude, this data table above shows me that my family is doing decent job on decreasing the amount of energy used although I can't guarantee that it will keep on decreasing even more.

Another Math Puzzle... YAY!

Hungry Horace=50kg

Curly Kate=35kg

Tiny Tim=25kg

 

Please do scroll down to see my work and check... 

( I apologize if it is TOO long). To find out the weight of the individuals, I have done this:

I have marked Hungry Horace as H.
I have marked Curly Kate as C.
I have marked Tiny Tim as T.

Here is the equation for the first statement: Hungry Horace and Curly Kate put the 10c in and got on the scales: The dial showed 85kg:

H+C=85

Since I have found what Hungry Horace is (scroll down to see the weight of Hungry Horace), I have substituted H for 50.

50+C=85
-50        -50

C=35

Curly Kate has a weight of 35kg.

CHECK:

50+35=85

85=85
 :)

Here is the equation for the second statement: Tiny Tim got on and Curly Kate got off. The dial went down to 75kg:

H+T=75

We can use the equation T=25 in the bottom of the page to substitute the variable "T"

H+25=75
     -25  -25

H=50

Hungry Horace has a weight of 50kg.

We can conclude that C=T+10 because due to the fact that Tiny Tim got on, the weight has decreased 10kg which is my evidence.

CHECK:

50+25=75
75=75
:)

Here is the equation for the third statement: Curly Kate got back on and Hungry Horace got off. The dial went down to 60 kg:

C+T=60

If we substitute C with the equation above, here it is:

T+10+T=60
2T+10=60
       -10  -10
2T/2=50/2

T=25

Tiny Tim weighs 25kg.

CHECK:

35+25=60
60=60
:-)

Perfect Square/Cube

 

Which number (after 64) is the next number that is BOTH a perfect square and a perfect cube?  64 = 8 squared and 64 = 4 cubed  

 

The answer is :729

Here is my work:

The next fifth cube number is 125 because 5x5x5=125

But it can't be a perfect square and a perfect cube although 125=5 cubed.

The next sixth cube number is 216 because 6x6x6=216

But it can't be a perfect square and a perfect cube although 216=6 cubed. 

The next seventh cube number is 343 because 7x7x7=343

But it can't be a perfect square and a perfect cube although 343=7 cubed

The next eighth cube number is 512 because 8x8x8=512

But it can't be a perfect square and a perfect cube although 512=8 cubed

The next ninth cube number is 729 because 9x9x9=729

But it CAN be a perfect square and a perfect cube although 729=9 cubed

729= 27 squared and 729=9 cubed.

Algebra Puzzle 2

VALUE OF POPSICLE: 12

                   Ladybug: 13

                    Flower: 24

 SCROLL DOWN TO SEE MY EPIC WORK:

      

                           Find the value of each object in the puzzle. The numbers given represent the sum
                            of the objects in each row or column. You must look for relationships among the objects.

                     Show your work and how you figured it out when you post an answer!

Here is my work:

I realized that I could make some equations to prove what each symbol stands for. Here is my work:

 Flower + 2 ladybugs=50

2Flower + 2 ladybugs =74.

From this, I can tell that one flower is equal to 24 because by adding a flower to "flower + 2 ladybugs", it turns out to be 74. 

Since the flower is equal to 24, we can create equations with variables:

(I have used ladybugs as the "x" variable sign"

24+2x=50

-24         -24

2x=26

/2     /2

x=13                     So to conclude this, a ladybug is equal to 13

To check, you can use the other equation (the horizontal equation)

2(24) + 2( 13)=74

48+26=74

So it is right after all.

To find the value of the Popsicle, I used the equation which is equal to 60.

(Ice cream is "y" variable for the next two equations)

Equation:

2(24) + y=60

48+y=60

-48      -48

y=12             So the value of the Popsicle is 12. 

To check, I have used the other equation which the sum is 61. 

24+2y+13=61

37+2y=61

-37        -37

2y=24

/2     /2

y=12