Patterning and Algebra Math Journal - Emily

Please answer this question using words, numbers and pictures

In an experiment, everyday 30% of the total number of bacteria die, and the remaining bacteria doubles. If in the beginning there were 140 bacteria, how many bacteria are there after 5 days?

4+ given for creating an algebra formula to represent the pattern

Due Monday, February 13, 2012

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

__________________Algerbraic Formula________________________

b=the next day’s number of bacteria

a= number of yesterday’s bacteria

n= 2(a x .70)

Why? Because if 30% of bacteria dies, that means theres 70% left and when you convert 70% to a decimal, you get .70. Then you multiply it by yesterday’s amount to get today’s amount, because the thirty percent of bacteria died. You will get today’s amount of bacteria before it doubles. Then you multiply it by two to double it and you will get today’s amount of bacteria.

_______Test out the formula and find the answer for five days________

** I rounded the total amount of total bacetria because you can’t have for example, .16th of a bacteria.**

DAY 1:

starting amount: 140

140 x .70= 98

98 x 2= 196 total bacteria on day one.

DAY 2:

starting amount: 196

196 x .70= 137.2

137.2 x 2= 274.4

274 total bacteria on day two.

DAY 3:

starting amount: 274

274x .7= 192.08

192.08 x 2= 384.16

384 total bacteria on day three.

DAY 4:

starting amount: 384

384 x .7= 268.8

268.8 x2= 537.6

538 total bacteria on day 4.

DAY 5:

starting amount: 538

538 x .7= 376.6

376.6 x2= 753.2

753 total bactera on day 5.

In the end, on day 5, there will be 753 bacteria.

Math Journal # i lost count - exponents {Emily}

Create two word problems with exponents. Write solutions for your questions that demonstrate how to use exponents. Provide diagrams or an accompanying picture to help illustrate your question.

1. Bob is training for a burger eating festival. On day one, Bob eats 2 burgers, on day 2 bob eats 4 burgers.On day 5, how many burgers does Bob eat? The number of burgers bob eats a day doubles the next. Problem is not realistic.

Solution: Day 1: 2²=4

Day 2: 4²=16

Day 3: 16²=256

Day 4: 256²=65536

Day 5: 65536²=4294967296

Therefore, Bob eats 4294967296 burgers on the fifth day, and Bob must be really fat by now.

Kate is getting paid 2 dollars everyday and it triples everyday. How much money will Kate have on her 3rd day? Would she rather take that or a million dollars?THis is surprising answer.

Cube 2 up until the 3rd time and you will get: 134217728.

On the third day, Kate will get $134217728 .

134 217 728 > 1 000 000.

Kate should ask for the 2 dollars everyday doubled.

Pizza Math Journal, this time WITH connections, Mr. Li.

An extra large pizza has a radi

**An extra large pizza has a radius that is twice as large as a small pizza. Determine the circumference and area for each pizza and compare the differences. Are there any relationships or connections? Think and write about two ways that this information can be useful in helping to solve real world problems. Give examples with pictures to show your math.**

For example, I’d say that the radius of the extra large pizza is 40cm. That would mean the diameter of a small pizza is 20cm, and the radius of it is 10cm. (For further calculations)

Large Pizza:

C= pi x d

C= pi x 80 (40 x 2 is 80) (d = 2r)

C= 251.38cm

The circumference of a extra large pizza is 251.38cm.

Small Pizza:

C= pi x d

C= pi x 20

C= 62.83 cm

The circumference of the small pizza is 62.83 cm.

**Relationships and Connections.**

The relationship between the circumference of the small pizza and the extra large pizza is that the small pizza’s circumference is almost one quarter of the extra large’s. The difference is 0.6 cm.

They both are found out by using the circumference formula.

They both use pi. (Obviously)

I realized that the circumference’s difference is found when four of the diameters of a small pizza can be found in one radius of a extra large pizza.

**Real Life Situations**

**1. **A builder could use that information when building a circular pathway decoration on a driveway of a small house then a large house, which wants the same design but the outer rim 4 times larger.

**2. **A baker who liked the idea of his old cake, but now needs to make the outside 4 times larger so it can feed more people, like making the cake almost 4 times larger.

3. A small ferris wheel in a portable carnival now wants the ferris wheel 4 TIMES LARGER IN CANADA’S WONDERLAND.

Math Journal #4- Pythagorean Theorem

Measure the length and width of your TV. Calculate the diagonal distance of your TV using the Pythagorean Theorem. How does it compare to the listed size of your TV?

Wow. That was hard measuring my tv. I left alot of fingerprints, but for the sake of math, I still did it.

The length of my tv was 45 inches, and the width was 25 inches. According to the Pythaforean Theorem, I should be able to find the diagonal distance using it’s formula.

a²+b²=c²

a = 45 in.

b= 25 in.

c= diagonal length

45²+25²=c²

45²+25²= 2650 (diagonal distance squared)

Square 2650 = 51.47

51.78=51.5

51.5=52

52 in. is indeed the listed size of my tv. :)

Examples

1. Measuring screens, because the electronic producers need to find the diagonal distance of that so they can use the pythagorean theorem.

2. Measuring carpets. Carpet makers can use it to find the lengths of the diagonal distance.

3. Measuring the hypotenuse of a square cake. The baker can find the hypotenuse.

4. Walls. Builders can measure walls using the pythagorean theorum.

During this process, tumblr shut down on me twice. And I forgot to save it every 5 minutes. Don’t worry, Mr. Li, I learned my lesson.

-Emily

Math Test Reflection

Even though the math test was extremely difficult and made me want to give up MANY COUNTLESS TIMES, there are some things that I’m proud of. (Even if I really had to rack my brain for that)

1. I was proud that I got the circle part right and I had the right idea generally for question 5. Even though I got the numbers wrong while calculating the square, I got the circle formula and answer correct.

2. I’m proud that I read the questions thoroughly because usually I would just skim through and miss a lot of information given including what the question wants me to answer.

3. I’m proud that I didn’t give up. Honestly, there were way too much times that I wanted to give up and just hand in the test without even trying to answer some parts of some question (like question 5), i persuaded myself not to give up and to try to write down my calculations, so i could get points for even THAT.

PLus, I’m impressed how I wasnt afraid to ask questions because usually I don’t ask questions and rely on whats on the sheet of paper.

3 Mistakes (out of the million I made)

1. APPARENTLY, I CANT COUNT TO TWENTY. I FORGOT THAT 28 DOES NOT COME AFTER 19. I rushed on making the diagram, then forgetting that the square pizza had 20 slices, NOT 28. I will NEVER forgive myself. The cause of that mistake is because I was careless, and did NOT check over my work that thoroughly.

2. I did not check over my calculations. I could of avoided MANY CARELESS MISTAKES WITH MY CALULATIONS IF I just checked over my work and not rushing it.

3. I often discouraged myself and telling myself that that test was impossible. I knew I should of encouraged myself instead of discouraged because I play an important part of urging myself to go on.

Those were the main mistakes I made. All of the mistakes were caused by rushing, discouragement BY SELF, and carelessness.

Lesson learned: Since I know tha Mr. Li wants us to learn a lesson from this test, here it is: Don’t discourage yourself, check over your work, AND 28 DOES NOT COME AFTER 19.

And Mr Li, thanks for laughing at us.

Emily

Math Jounral - Circles

**An extra large pizza has a radius that is twice as large as a small pizza. Determine the circumference and area for each pizza and compare the differences. Are there any relationships or connections? Think and write about two ways that this information can be useful in helping to solve real world problems. Give examples with pictures to show your math.**

I’m going to say that the radius of a large pizza is about 40 cm. If the radius is twice as large as a small pizza, then that means a small pizza’s diameter is 40 divided by 2. (40/2 is 20) so the diameter of each small pizza is 20 cm because the diameter is twice the length of the radius. The formula of finding the area of a circle is .

I will do the areas for both sized pizzas first.

Now I will do the Area of the extra large pizza.

Since the radius of an extra large pizza is about 40 cm, I will keep that in mind.

A= x 40 x 40

A= x 1600

A= 5027cm squared.

**The area of a extra large pizza is about 5027 cm squared.**

Since the diameter of a small pizza is about 20 cm, that means that the radius of a small pizza is 10 (20/2= 10)

A= x 10 x 10

A= x 100

A= 314 cm squared

**The area of a small pizza is 314 cm squared.**

**Comparing the two areas.**

**1. Both Areas can be used to find the radius using the formula of Area/pi = pi x r x r/ pi.**

**2. Both Areas are found by using the formula A= pi x r x r**

Circumference. Circumference is found by the formula (C= pi x d or C= 2 x pi x r)

Circumference of a extra large pizza

Radius: 40 cm

C= x 40 x 2

C=251 cm

The circumference of a extra large pizza is 126cm.

Circumference of a small pizza

Radius: 10 cm

C= x 10 x 2

C= 63 cm

The Circumference of a small pizza is 31cm.

**Comparing the Circumferences**

**1. Both circumferences are found using the formula C= x r x 2 **

**Real Life Situations**

**Cake.** When a client wants they’re cake 4 times larger than the small sized cake they had last time.

**Health, if someone is pregnant or maybe their bones are too weak, they can use the circumference to figure out if they are healthy.**

Landscaping, many people want stone driveways with circular patterns. The landscapers can figure out the circumference to figure out how much stone do they have to order for that circle.

That was long :) -Emily

Math Journal - Emily

1 a) You can physically measure a circle in two ways. Placing a piece of string around the outside of the circle then measuring the string, or you can do it mathematically. By doing it mathematically, you can measure the diameter ( the distance of a circle from one side to another) or measure the radius ( half of the diameter; half of the distance between the sides of a circle) By using diameter to measure a circle, ou use the formula pi x d. If you use the radius to measure a circle you use the formula pi x 2 x r. By finding the distance around a circle it is called finding the circumference of a circle.

b) The definition of perimeter is “The distance around a two-dimensional shape or figure.” The definition of circumference is “The distance around a circle” A circle is a two dimensional shape,and by finding circumference, you are finding the distance around the outside of it, so basically the “perimeter of a circle” is called circumference.

2 a)If you increase the diameter of a circle, you will make the circle bigger, so you are making the circumference of the circle a larger number. Since the diameter of a circle is the same for ALL the distances between a circle, the whole circle becomes larger and when the circle becomes larger, its distance around it also becomes larger. So, if you increase the diameter of a circle, the circumference becomes a larger number.

b) The ratio of the circumference and the diameter stays the same though. If the circumference becomes a larger number and the dimater also becomes a larger number, they both will increase at the same rate, therefore, the ratio, which can be simplified to around the amount of pi, will be the same.

That was a really long journal using words i really do not usually use in my vocabulary. -Emily

A World Without Math

The world would be pretty clueless without math. Everything would be so confusing and no one would know how to count. We could never accomplish the things we accomplished today. Without numbers, we could never reach the moon or go into space. We could never know how to calculate how much materials we needed to build a house. We wouldn’t go to school because there would BE no school. There would be no villages or cities and we would all just be really un-up-to-date.

We would have no technology, and without technology, what would we do? We rely on technology a lot these days. We would have no electronic entertainment, for example tv, video games, or any cell phones. We all need numbers to make technology because we needed to calculate how much materials are needed to make the machine, and how much batteries are needed in order for the phone to work. Point is, the world needs math.

Money is also a big problem. Would everything be free and every one would just go anywhere and take whatever they liked? Probably not, because there would be nothing to steal. Anyways, we would never have machines to have plastic, all the food would go bad. For meat, who would clean the animals manually? Not me.

The world would be very uncivilized and everything would be much harder. People would struggle to stay in health too, all the equipment in the hospitals are electronic, and how would we know there was electricity if we don’t have math? People would be helpless if there weren’t equipment to help save lives. We need math to find out what medicine can help what diseases.

Face it, we need math.

A World Without Math

Wow how would we even get jobs? I think the point of this assignment is to make us think the world needs math. :) I get it the world needs math. I’ll try to like math haha :D