Looking for Pythagoras- Math Reflection Questions Investigation 4

1. Give three examples of fractions with decimal representations that terminate:
A terminating decimal is a decimal that has digits that doesn't go on forever. A terminating decimal is the same thing as a rational number, and doesn't repeat forever. Three examples of fractions with decimal representations that terminate are 1/8,  2/10,  and 1/4. The decimal representation of 1/8 is equal to 0.125, which is terminating because the decimal values don't go on forever. The decimal representation of 2/10 is equal 0.2, which is terminating because the decimal values don't go on forever. The decimal representation of 1/4 is equal to 0.25, which is terminating because the decimal values don't go on forever. 

2. Give three examples of fractions with decimal representations that repeat:
A repeating decimal is when the decimal values of the number goes on forever, or infinitely. Three examples of fractions with decimal representations that repeat are 1/3, 1/11, and 2/9. The decimal representation of 1/3 is 0.3333333...... (3 repeating on forever). This is an example of a repeating decimal because the three goes on forever. The decimal representation of 1/11 is 0.090909...... (09 repeating on forever). This is an example of a repeating decimal because the three goes on forever. The decimal representation of 2/9 is 0.222222...... (2 repeating on forever). This is an example of a repeating decimal because the three goes on forever. Usually, repeating decimals are shown with a bar over the number or numbers that are getting repeated.

3. Give three examples of irrational numbers, including one irrational number greater than 5:
An irrational number is a number that cannot be expressed as a ratio or a fraction. Three examples of irrational numbers, including one that is greater than 5, are √27, √30, and √34. The square root of 27 is approximately (fraction estimate) 5.196. The square root of 30 is approximately 5.477. The square root of 34 is approximately 5.8309. But remember that these square roots have no ends and the answers that I gave were just estimates. 

4. How can you determinate whether you can write a given decimal as a fraction:
You can determine whether you can write a given decimal as a fraction by looking at it. You automatically know that a decimal can be represented as a fraction if it is either terminating or rational. You also know that if something irrational, that it CAN'T be written as a fraction. If a fraction neither repeats nor terminates, you automatically know that it can't be written as a fraction, which means that it is irrational. When looking at the terminating decimal, you can look at the place value in which the last number is in. For example, let's use 0.02. THe 2 is in the hundredths place, so the fraction is 2/100. You could also guess and check to make the decimal a fraction. 

Realistic Fiction Story

Looking for Pythagoras- Math Reflection Quesions Investigation 2

1. Describe how you would find the length of a line segment connecting two dots on dot paper. Be sure to consider horizontal, vertical, and tilted segments. 

          Horizontal: 

          Vertical:

          Titled: 

There are two strategies for this:

1. You could get a ruler and measure the line segment or you could count the units between the two dots that make up the line segment. This may be accurate in some instances, like when the line is perfectly straight and the measurement ends at a whole number, but sometimes this strategy is inaccurate and hard to get the exact answer with.  

2. You could use the "square method." So you would first have to picture that that line segment is one of the four side of a square. Then, you would draw in the other three sides of the square. To do this, you use the slop of the segment or also known as the "rise over run". After creating a square based off of the simple line segment you would find the area of this square. I have already answered how to find the area in my investigation 1 set of question, but as a quick reminder, you you cut  up the shape into smaller triangles or squares and then add their area's up, or you could draw a bigger square around the square and take away all the excesses pieces from the total area of the bigger square. After finding the area of the shape, all you have to do to find the length of the segment (which is one of the sides of the shape) is find the square root of the area of the shape. 

2. 

a) Explain what it means to find the square root of a number. 
          When you find the square root of a number, you are finding the number that when multiplied by itself, creates the number you are find the square root of. For example, suppose we are trying to figure out the square root of 25. Well, we know that 5*5= 25. So 5 is the square root of 25. As another example, suppose a square has the area of 16 units. Since a square has 4 equal sides, an integer of the length of on of the sides of the square multiplied by itself will come to the total area of the square. The length of the sides of the square is the square root of the area of the square. Coming back to our example, we find out that each of the sides of the square are 4 units long. And since there are four sides to the square which each 4 units long, we can add them all up: 4+4+4+4=16. This proves that the length of the sides of the square is 4 each, as the area adds up correctly. aThis brings us to our final conclusion that the square root of 16 is 4. 

b) Explain whether or not a number can have more than one square root. 
          Yes, a number can have more than one square root. Since, the square of a number is when you multiply  a number by itself to get the digit wanted. For example, take the number 36. The obvious square root is 6. I got my answer as when you multiply 6 by 6, you get 36. However, there is more than just one square root for the square root of 36. The second square root for 36 is -6. The logical behind this answer is that when you multiply two negative integers your answer will always positive. So, -6 multiplied by itself is 36 also. So when writing questions on finding the square root of a number you must specify if you want a negative or positive number. In conclusion, a number can have more than one square root. 

3.

a) Explain what it means to find the cube root of a number.

          To find the cube root of a number is similar to finding the square root of a number. In math, to "cube" something means to times it to the power of the three. So to find the the cube root of a number, you multiply the number by itself three times.  For example to find the cube root of 2 you would perform this equation; 2*2*2=8, Therefore, the cube root of 8, is 2/ 2 cubed is 8.

b) Explain whether or not a number can have more than one cube root.

           A number cannot have more than one cube root. The reason I say this is because, you cannot have a negative number multiplied by itself three times and equal a positive number.  For example, the cube root of 8 is 2, but that doesn't mean the cube root of 8 is also negative 2.  Because -2*-2*-2, equals -8.  Therefore, you can only have one cube root per number.  

Looking for Pythagoras- Math Reflection Quesions Investigation 1

1. In the city of Euclid, how does the driving distance from one place to another compare to the flying distance?

          In most cases, the driving distance from one place to another is longer than the flying distance. When driving you have to drive on roads and you can't cut between land to take short cuts. But, when flying you can fly diagonally cutting across land and not following roads. In other cases the driving distance from one place to another compared to the flying distance are the same. This happens when there is one straight route where not matter what flying or driving, there is no difference in distance. Overall, the flying distance can never be more than the driving distance, it's either less than or equal to the driving distance. 

2. Suppose you know the coordinates of two landmarks in Euclid. How can you find the distance between those two landmarks?
          To find the distance between the coordinates of two landmarks in Euclid, you can subtract x1 from x2, and also subtract y1 from y2. Then you take the absolutes value of x1-x2 and y1-y2. Lastly, you add the two absolute values, which gets you to the distance between the coordinates of two landmarks in Euclid. 

3. What are some strategies for finding areas of figures drawn on a grid?

          There are a couple strategies for finding areas of figures drawn on a grid: 

                    1. If it's a regular shape with "full boxes" you can just count the boxes that make up the area of the figure on the grid. 

                    2. It it's an irregular shape, then you can deconstruct the shape into rectangles and triangles. Then calculate the area of each rectangle or triangle. Lastly, add all the areas of the deconstructed shape together and you have your answer.  

                    3. Enclose the figure on the grid in a larger rectangle/square. Then find out how much the area of the unwanted parts of the larger rectangle/square is. Lastly, subtract the areas of the unwanted parts from the area of the larger rectangle/square.

RLA Complex Sentences

What is a complex sentence?
Complex sentences are made up of two 'clauses' that are joined. A complex sentence is made up of an independent clause and one or more dependent clauses.
           Dependent clauses- is similar to an independent clause, or a complete sentence, but it lacks one of the elements that would make it a complete sentence.

What are the different parts that make up a complex sentence?
1. Subordinating conjunction + dependent clause + comma + independent clauses
2. Independent clauses + subordinating conjunction + dependent clause (NO COMMA NEEDED)

What are the differences between complex sentences and compound sentences?
Compound:
- Contains two independent clauses joined by a FANBOY and comma
- Contains two independent clauses joined by a semi colon.
- The two halves could stand alone as individual sentences.

Complex:
- Contains one independent clause and one or more dependent clauses.
- A dependent clause does not express a complete thought and can't stand alone.
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5 sentence paragraph that uses both compound and complex sentences:

When Mary handed in her homework, she forgot to give Mrs. Johnson the last page.
Mrs. Johnson returned the homework, after she noticed the error.
When the bell rang, Mary ran to pack her backpack.
After she got on the moving bus, Mary realized that she had swim practice.
Mary has bad grades, because she studies at the noisy candy shop where she can't concentrate.
Mary likes to eat chocolate ice cream, but her friend likes Strawberry ice cream.
Mary was doing her homework when her computer crashed, so she lost all of her work.

Aquatic Tank- Guppies

Introduction
The guppy also known as million fish and rainbow fish, is one of the world's most widely distributed tropical fish, and is one of the most popular fresh water aquarium fish species. It is a member of the Poecilidae family and, like all other members of the family, is live-bearing. They are highly adaptable and thrive in many different environmental and ecological conditions. Male guppies are smaller than female guppies.

Guppy Needs
- Food: If you don't feed a guppy the right food then they could die. Guppies should be feed once a day:
Algae
Tubifex worms
Flake food
Brine shrimp
Bloodworms, micro worms, fruit flies, mosquito larvae, Daphnia and chopped up earthworms
- Light: The light should be on for 8-12 hours a day (timers are helpful).
- Temperature: Keep the tank at 75 to 80 degrees Fahrenheit.
- Space: Guppies need enough room to move around comfortably. They are speedy swimmers and like to dart back and forth, so plenty of space is important to their happiness and overall success. Figure on giving your fish about 2 gallons of water each. 
- Water: Guppies need dechlorinated water, changing 25% of it each week. Treat any water added to tank with water conditioner. pH and ammonia tests should be regular.

How will we meeting the guppies' needs
We will make sure that out tanks aren't too over crowded, and if they start to reproduce quickly then we will separate the guppies as sometimes the adult guppies eat the new borns. The diet of just tubifex worms does not allow full growth. Adults should be fed flake food and tubifex, and the young should be fed crushed up brine shrimp and flake food. We will also make sure that our pH and dissolved oxygen levels are regular and safe for the guppies to live in. We will also make sure that the guppies are fed once a day and have enough light (8-12) hours throughout the day. 

Guppies in its mini ecosystem
The main interaction is between the male and female guppies, they will be reproducing constantly creating a lot of fry (young guppies). The second interaction would be between the guppies and the tubifex worms-  guppies can feed off of tubifex worms. Other than this, there probably won't be much interaction with the guppies and the other factors in the tank (snails, elodea, duckweed, and gravel).  

How many guppies can I keep in my tank
When you're dealing with guppies, you should keep a proportion of three females per one male, or all one gender. I'm not sure how big our tank in school is, but the rule of thumb is one inch of fish per gallon. 

My Weekly Fitness Plan

MONDAY	TUESDAY	WEDNESDAY	THURSDAY	FRIDAY	SATURDAY	SUNDAY
Dance class in school from 9:08-9:51am/ 43 minutes. We made warmed up to Ms. M’s tough warm up, practiced the dance she taught us, and worked on our own group dances. Play squash at my condo from 6-6:30pm/30 minutes with my Dad.	Dance class in school from 9:08-9:51am/ 43 minutes. We made warmed up to Ms. M’s tough warm up, practiced the dance she taught us, and worked on our own group dances. P.E. class starting at 11:39-1:02 pm. I will play badminton in P.E. class for about 80 minutes.	Dance class in school from 9:08-9:51am/ 43 minutes. We made warmed up to Ms. M’s tough warm up, practiced the dance she taught us, and worked on our own group dances. Play squash at my condo from 6-6:30pm/ 30 minutes with my Dad.	Dance class in school from 9:08- 9:51am/ 43 minutes. We made warmed up to Ms. M’s tough warm up, practiced the dance she taught us, and worked on our own group dances. Play squash at my condo from 6-6:30pm/ 30 minutes with my Dad.	Dance class in school from 9:08- 9:51am/ 43 minutes. We made warmed up to Ms. M’s tough warm up, practiced the dance she taught us, and worked on our own group dances. P.E. class starting at 1:37-3:00 pm. I will play badminton in P.E. class for about 80 minutes. Walked home briskly from Great World City. Walk home after being dropped off by the after school D bus. This is a 10 minute walk.	I went to Anisha's Birthday party where we went kayaking, boogie boarding, and paddle boarding  at the Mana Mana Beach Club East Coast. We did water sports from 4:00-6:30 pm/ 150 minutes.	Play squash at my condo from 2-3pm/ 60 minutes with my Dad.
Total active time: 73 minutes	Total active time: 123 minutes	Total active time: 73 minutes	Total active time: 73 minutes	Total active time: 133 minutes	Total active time: 150 minutes	Total active time: 60 minutes

1. Do you think you are getting enough exercise? Why or why not?

I think that I AM getting enough exercise each week. I try to exercise everyday for one hour. But, sometimes I'm not able to workout for one hour a day because of homework. Therefore, I make sure to a least exercise for 30 minutes a day. When I exercise I really try hard and give it my all, so it's not like I'm just sitting there while time passes. If I exercise properly for about one hour everyday properly, then I believe that I will get fitter and healthier.  What I also realized is that this week I tried exceptionally hard to get in one hour everyday of physical activity. Usually I only do physical activity after I've finished all my work. But, what I learnt is that doing physical activity everyday has its many benefits and I should always try to get at least 30 minutes a day, at least. This has really taught me a lot and has also persuaded me to change my day to day life style and making it more active. 

2. Check out the benefits of fitness document we have shared with you. What benefits of fitness do you hope to improve through your weekly fitness plan? Please list 3-5 benefits of fitness

1. Increased strength and stamina- in squash you need to have lots of strength to hit the ball hard, and stamina to keep on running from front to back to right to left, etc.

2. Makes body more agile- in squash you also need to be very light on your feet so that you can run quickly and hit the shots that are hard to hit. Whether it's drop shots or volleys you really need to run to hit the shots.

3. Enhances coordination and balance- in squash you need to have coordination when serving the ball and you ned to have balance when hitting the ball using your feet to stabilize you.

4. Improves athletic performance- since I'm going to start play squash competitively in June I will need my athletic performance to improve, so that I can start winning championships.

5. Enhances quality of sleep- I usually don't get a good amount of sleep, because I'm always up late finishing my homework. Furthermore, exercising everyday could help me finish my homework faster because after exercising your brain works better.