Unit 1 Homework List

Name: ______________________ Block: ____ Date Assigned: 8/17, 8/18 DUE DATE: 8/22, 8/23 Title: Syllabus and Name Card Assignment

1. Get your syllabus signed 2. Finish your Name Card

Date Assigned: 8/22, 8/23 DUE DATE: 8/24, 8/25 Title: Reflection 1 Assignment

Respond to the following in a 1 page handwritten reflection. You may use pen on this. What did you learn about mathematical thinking today? Write some examples from the activity today that illustrate what you learned. Be specific and use proper grammar. Yes, grammar matters. *If you need more to write about, extend this to where you can see this type of thinking in your own life – do NOT just write “to solve math problems”. There is no right answer, so don’t write down what you think I’m looking for because you’re probably wrong on what you think I’m looking for anyway.

Date Assigned: 8/24, 8/25 DUE DATE: 8/29, 8/30 Title: Ancient Number Systems Assignment

Recall the number systems we analyzed in class. They’re in different bases depending on how people are counting. 1. Create your own number system that is either in base 10, 20, or 60; that is,

create symbols that represent numbers. 2. Indicate what base you’re using. 3. Write an explanation for what each symbol represents and why you used it.

Use complete sentences. *Next class, we will have our peers analyze our systems. Be creative, but don’t troll too hard.

Date Assigned: 8/29, 8/30 DUE DATE: 8/31, 9/1 Title: Analyzing Arithmetic Assignment

Respond in complete sentences in your own words: 1. What does it mean to add? 2. What does it mean to subtract? 3. What does it mean to multiply? 4. What does it mean to divide? 5. If you divide by 0, do you get 0 or undefined? Explain your reasoning using

at least 2 complete sentences. I want you to think on this. How can you make sure that you understand and remember if dividing by 0 is 0 or undefined?

Date Assigned: 8/31, 9/1 DUE DATE: 9/5, 9/6 Title: Applying Arithmetic Assignment

1. Scientific Notation You may or may not have heard of scientific notation from science classes in the past, but we’re going to analyze it here. To make sure we all understand it, scientific notation takes a number and puts it between 1 and 10, then moves the decimal. How much you move the decimal is indicated by multiplying that number by 10 to a power. This makes it so that we can easily compare orders of magnitude. See the illustrations below to refresh your memory.

Standard Form Scientific Notation 61500 6.15×10!

0.0000568 5.68×10!! 321 3.21×10!

In the following exercises, if it is in standard form, convert to scientific notation. If it is in scientific notation, convert to standard form. 1. 314159 2. 4.22715×10! 3. 1.09×10! 4. 3.078×10!! 5. 0.07085 6. 64,960,000 7. 9.004×10!! 8. 0.0941 9. 0.0004518 10. 5.1874×10! 11. 1.912×10!! 12. 147.89

2. Conceptual Questions. Respond in your own words in complete sentences. i. What does the exponent mean? Why does the decimal move to the right

when the exponent is positive and left when it’s negative?

ii. Make some observations: which one is bigger, 9.18×10! or 1.001×10!? How do you know? DO NOT just write “because the number is bigger” or anything along those lines. Dig deeper.

iii. Numbers in scientific notation are still numbers, so you can still add or

subtract them, right? What are ways you think you can do this? Test it below in #3.

iv. How about multiplying and dividing? What strategies can you use to

multiply and divide numbers in scientific notation? (Keep in mind that multiplication is commutative (order doesn’t matter) and the idea of cancelling things). Again, test it in #3.

3. Arithmetic with Scientific Notation

Add, subtract, multiply, or divide, then write in scientific notation. You may leave division as a fraction and reduce it. 1. 9.18×10! + 1.001×10! 2. 2.85×10! 3.16×10!! 3. !.!"×!"!

!.!×!"! 4. 7.085×10!! + 3.078×10!!

5. 1.5×10! 6.25×10!! 6. 1.09×10! + 4.22715×10! 7. !.!"×!"! !.!"×!"!!

!.!×!"! 8. !.!×!"! !.!×!"!

!.!×!"!

9. 5.1874×10! − 4.3174×10! 10. 1.98×10! − 2.08×10!

Date Assigned: 9/5, 9/6 DUE DATE: 9/7, 9/8 Title: Epic Fraction Practice Assignment

1. Drills, Part I Add, subtract, multiply, or divide to simplify.

1. !!+ !

!" 2. !

!∙ !! 3. !

!!− !

!

4. !!!! 5. !

!!+ !

! 6. !"

!∙ !!!

7. !!"+ !

! 8.

!!!!!

9. !!− !

!

10. !"!∙ !! 11. !

!− !

!" 12.

!!!!

2. Conceptual Questions. Answer all in complete sentences.

i. When you find a common denominator, what are you really doing? Why is it necessary? (If you write “because that’s the rule”, you get an automatic 0 on the entire assignment).

ii. Why is a common denominator necessary to add or subtract fractions?

iii. When you add and subtract fractions (that are numbers only), you get a common denominator. What happens if you have variables instead of numbers? If you believe it is different, explain why you think so and create a rule. If you believe it is the same, explain why you think so.

iv. Why does division of fractions work the way it works? Explain in your own words.

3. Drills, Part II Add, subtract, multiply, or divide to simplify. Remember, just because I’m not giving you x or y doesn’t mean you can’t do it. It literally works the same.

1. !!∙ !

!

! 2. !

!!!+ !

!!!! 3. !!!

!∙ !!!

4. !!!

!!!! 5. !!

!!− !!

! 6. !

!− !

!!

7. !!!+ !

!! 8.

!!!!!!!

9. !!!"!

∙ !!!

!!!

10. !"!!!!!

11. !!!!!

− !!!!

12. !!!!

+ !!!!

Date Assigned: 9/7, 9/8 DUE DATE: 9/12, 9/13 Title: The Golden Ratio Assignment

Research the significance of Φ in one of the following areas and do a 1-page write-up on your findings. • Nature

(plants/animals) • Astronomy • Geometry

• Math in general • Art, Architecture, Design

• Others (anything else interesting you find)

Some guiding questions to help you: • How does Φ relate to the area you chose? (Provide detailed examples) • What makes this relationship between Φ and your chosen area important? •

Cite at least 3 resources. Remember, I want analysis, NOT summary. The following link is a good resource to begin your journey with Φ. http://www.goldennumber.net/golden-ratio/

Date Assigned: 9/12, 9/13 DUE DATE: 9/14, 9/15 Title: Unit 1 Review Assignment

1. Review of History What is one of the most significant inventions from the Mayans? Why is this significant? Think about how this concept impacts us mathematically and socially. Write at least a paragraph. Yes, you may research, but you must cite your sources and do analysis on what you found, NOT just copy it down.

2. Arithmetic – Applications and Skill Building

(1) Let’s talk cooking. Let’s say you had a recipe originally for 4 people. What number would you need to multiply the original quantities by to adjust it for...

a. 1 person and why? b. 2 people and why? c. 3 people and why? d. 8 people and why? e. 6 people and why? f. 10 people and why? g. 5 people and why? h. 7 people and why?

(2) In the hit game Pokémon GO, there’s a game mechanic called eggs.

Each egg takes a certain number of km walked to hatch. Let’s say you end up getting an egg that takes 10 km to hatch. The first day you have the egg, you walk 1 km. Each day after that you walk an additional 0.5 km (so the previous day’s amount + 0.5 km). How many days will it take you to hatch the egg?* Derive your solution with at least 2 mathematical methods. If you do 3 or more and they work, then each will get you extra credit. *How many days until you find out if you got a rare Pokémon or an Eevee?

(3) Imagine you’re observing a culture of bacteria. Each hour, it doubles. Tell me a way you would figure out how many bacteria there are after

a. 5 hours. b. 20 hours. c. 1000 hours. d. Question: Do you need the initial amount to answer the

problem I asked you? Why or why not? ***NOTE: In complete sentences, explain why your method works.***

(4) Chemicals undergo a process called “radioactive decay”. Periodically,

the amount of the chemical will decrease by half of what’s left. This is called “half life”. So, given a random chemical with a half life of 5 days, how long will it take to get 1/64 of the original amount? Question: Do you need the initial amount to answer the problem I asked you? Why or why not?

(5) You’re designing an auditorium. You decide to be creative with the seat layout because…why not? Let’s say that you have a total of 15 rows. In each of the following situations: (i) Identify the pattern; AND (ii) Find a way to figure out how many total seats there are in the house. (“The house” means “auditorium” in theatre terms).

a. Row 1 has 20 seats, Row 2 has 21 seats, Row 3 has 22 seats, Row 4 has 23 seats, and the pattern continues like that.

b. Row 1 has 20 seats, Row 2 has 24 seats, Row 3 has 28 seats, Row 4 has 32 seats, and the pattern continues like that

c. Row 1 has 1 seat, Row 2 has 4 seats, Row 3 has 9 seats, Row 4

has 16 seats, and the pattern continues like that.

(6) The sum of the interior angles of a triangle is 180º, of a quadrilateral is 360º and of a pentagon is 540º. Assuming this pattern continues, find the sum of the interior angles of a dodecagon (12 sided). Explain your reasoning with complete sentences.

(7) This unit, we’ve been skill building, rather than me showing you “how to do” a whole bunch of “math problems”. The goal is for you to not just solve problems I’ve shown you, but rather building the skill of applying your knowledge to problems. Write a half page about strategies you can use to tackle problems you’ve never seen before. #YouDontNeedExamplesForEverything #ExamplesAreWantsNotNeeds