Unit 1: Expressions

1. Unit 1: Expressions

2. Warm-Up • Please take a pretest from the stack at the front of the room. You have 10 minutes to complete it on your own. • This is not for a grade! It is to help me see where you are. Please do your best.

3. Metric and Customary Units of Measure • WHY do we have 2 systems of measure? It seems CONFUSING! • In the United States we use the customary system. • Most of the world uses the metric system • http://www.youtube.com/watch?v=DQPQ_q59xyw • 1988 – U.S. will use metric system for trade and commerce • Liberia and Burma are the only other countries that do not use the metric system!

4. Notes • Mass – amount of matter in an object • Weight – force experienced due to gravity • Metric – used in most of the world and science • Customary – commonly used in the United States

5. Notes Accuracy and Precision • Accuracy – closeness of a measurement to the correct measurement • Precision – level of detail an instrument can get; same result repeatedly

6. Practice On Your Own A benchmark is a reference that you can use for estimating measurements. For instance, a small paper clip is about an inch long , so the length of a small paper clip could be a benchmark for estimating length in inches.

7. Practice On Your Own • Use small paper clips to estimate the length of your pencil. Count the paper clips to estimate the length of the pencil in inches. • Check that your estimate is reasonable by using a ruler to measure the pencil to the nearest 16th of an inch. Each person should measure to make sure that you are being precise! • The mass of a small paper clip is a good benchmark for the mass of 1 gram. Hold your pencil in one hand. Pick up paper clips in your other hand until their mass feels about equal to the mass of the pencil. Count the paper clips to estimate the mass of the pencil in grams. • Check that your estimate is reasonable by using a metric scale or balance to measure the mass of the pencil to the nearest gram. Measure twice. • Give an example of a situation in which it would be useful to estimate measurements by using benchmarks • Measure the length of a small paper clip in inches. Are estimates made by using small paper clips as a benchmark for inches likely to be overestimates or underestimates? Explain.

8. Clean up room and present Mathbook profiles

9. Exit Ticket Suppose Miss Wheaton gets really stressed from teaching 8th graders and goes home and eats a lot of food to make herself feel better. By May she is 220 kg (about 500 lbs on Earth)! She decides the fastest way to lose weight is to go to the moon. When she goes to the moon and gets on a scale it still says 220 kg but she feels weightless. Explain in complete sentences why her idea was not a good one.

10. Warm-Up • In a complete sentence, explain the difference between accuracy and precision. • How would my mass change if I travelled to Jupiter? What about my weight? • Which scale would be most accurate? Why? • Draw a picture of a dartboard where someone threw 3 darts and was precise but not accurate.

11. Explain… • What is metric and customary? • What is the difference between weight and mass?

12. Notes • Fill in the rest of the table • Length • Area • Volume • Angle

13. Measure the length of a pencil to the nearest centimeter. • Count the small markings from the first line on the left to the line that shows 1 centimeter. How many are there? • Each line shows 1 millimeter. How long is the pencil in mm? • Measure the pencil to the nearest inch. • Count the small markings from the first line on the left to the line that shows 1 inch. How many are there? • Measure the pencil to the nearest sixteenth of an inch. • Name 5 items that would be appropriate to measure with a ruler. • Choose the most appropriate measure • Width of your smile: 2 ½ in or 2 ½ ft? • Thickness of your notebook: 3 mm or 3 cm? • Use a ruler to measure each object to the nearest sixteenth of an inch and to the nearest millimeter. a. Your thumb b. your desktop

14. Metric or Customary? • Inch • Millimeter • Acre • Newton • Pound • Gram • Centimeter • Mile • Meter • Yard • Degree • Pound

15. Notes In your notes make a chart. Fine one object for each category. Measure twice for metric and twice for customary (1x per person) so we can see how precise you were. How accurate will your tool allow you to be?

16. Homework Find objects you can measure for length, width, area, and volume. Create a table like the one in your notes. Take each measurement for metric and customary twice so you can see how precise you are. Label!

17. Warm-Up Division Opposite operation Product Quotient Subtraction Sum Choose the best term to complete each sentence. • ____ is the _____ of addition. • In the statement 10÷2=5, the number 5 is the _____. • When you add two or more numbers, the result is the _____ of the numbers. • Multiplication and _______ are opposites. • The _____ of 6 and 7 is 42.

18. Notes Order of Operations What are operations? • +, -, x, ÷ • Also exponents and () Order of Ops = PEMDAS • Please Excuse My Dear Aunt Sally • Parentheses • Exponents • Mult/Div • Add/Sub Ex: 2 + 4 x 10 ÷ 5 – 6 Ex: 23 x (4 – 3)

19. Practice On Your Own

20. Notes Evaluating Expressions with a Variable Variable - letter that represents a number that can vary If videogames are $10 each, the price will vary based on how many your buy. So the price will be 10v. Coefficient - number multiplied by the variable Constant – number by itself; does not change Expression – 1 or more variables; no = sign

21. Examples • Evaluate x + 5 for x = 11 • Evaluate 2a + 3 for a = 4 • On your own: 4 (3 + n) – 2 for n = 0, 1, 2

22. If c is a temperature in degrees Celsius, then 1.8c + 32 can be used to find the temperature in degrees Fahrenheit. Convert each temperature from degrees Celsius to degrees Fahrenheit. The highest recorded temperture in the United States is 57 °C. What is that in °F?

23. PEMDAS Think of a different acronym for PEMDAS. Everyone decorate a sign that includes your acronym and pictures. This will be added to your notes.

24. 5th Warm-Up: • Study your metric and customary table silently for two minutes • Get out the sheet of paper you had planned to take the Opportunity for Points on (or make a new one if you lost it…)

25. Notes Square and Cube Roots When we see 42 we think “4 x 4 = what?” When we see √16 we think “what times itself = 16?” Ex: 1. √100 2. √25 3.√81

26. When we see 23 we think “2 x 2 x 2 = what?” What do we think when we see the cubed root of 8?

27. Properties

28. p. 16 #1-4 in notes

29. Homework: p. 16 #8-11, 15-20 Advanced: Write your own order of operations expression. It should be between 5 and 10 steps long and include all parts of PEMDAS. Simplify your expression.

30. Notes Counterexample – disproves a statement or shows that it is false. Write a counterexample to disprove “the associative property is true for division.”

31. Counterexamples • All fruits have seeds on the inside. • All birds can fly. • Humans are the only animal that speak English. • All American money pictures a US president. • The sum of two numbers is always greater than either number.

32. Notes Examples: Write an expression for each phrase • 1 more than the product of 12 and p. • 4 less than a number n divided by 2. 3. Write a word of phrase for the expression 4 – 7b

33. A company aired its 30-second commercial n times during the Super Bowl at a cost of $2.4 million each time. Write an expression to evaluate what the cost would be if the commercial had aired 2, 3, and 4 times.

34. 24 • Using only +, -, x, ÷, and () write an expression that simplifies to 24.

35. Homework p. 12 #23-27, 29-30 p. 16 #6-7, 21,31

36. Warm Up Complete each equation and tell what property is represented. • __ + 4 = 4 + 8 • 8(___) = 0 • 5 + ___ = 5 • 4(x + 6) = 4x + ___(6) • 125/5 (use long division) • Write an expression for the phrase “twice the sum of 3 and g.”

37. Evaluating Expressions OFP Show all work! 1. Evaluate 9a+7b for a = 7 and b = 12 2. Simplify 82-2+322+b 3. Write an algebraic expression for the phrase “twice the sum of k and 4.” 4. What property would you use to make 6×f look like f×6? 5. Simplify 36-8x+4×3 BONUS: Simplify (32+43-1+(25)2-8÷2+38)÷1

38. Mount Sharp has beckoned Curiosity since the NASA rover made its grand entrance on Mars exactly a year ago, dangling from nylon cables to a safe landing. If microbes ever existed on Mars, the mountain represents the best hope for preserving the chemical ingredients that are fundamental to all living things. After a poky but productive start, Curiosity recently pointed its wheels south, rolling toward the base of Mount Sharp in a journey that will last many months. Expect Curiosity to channel its inner tourist as it drives across the rock-strewn landscape, dodging bumps and taking in the scenery. "We do a lot of off-roading on a lot of little dirt roads," said mission manager Jennifer Trosper. Curiosity will unpack its toolkit once it arrives at its destination to hunt for the organic building blocks of life.

39. Scientists have been eager for a peek of Mount Sharp since Curiosity, the size of a small SUV, touched down in an ancient crater near the Martian equator on the night of Aug. 5, 2012. The world wondered whether Curiosity would nail its landing, which involved an acrobatic plunge through the thin atmosphere that ended with it being gently lowered to the ground with cables. Engineers had to invent new tricks since Curiosity was too massive to bounce to a landing cocooned in airbags – the preferred choice for previous rovers Spirit and Opportunity. After seven terrifying minutes, a voice echoed through mission control at the NASA Jet Propulsion Laboratory. "Touchdown confirmed," said engineer Allen Chen. "We're safe on Mars.” Scientists and engineers clad in matching sky-blue polo shirts erupted in cheers. Some were so excited that they overshot their high-fives.

40. Curiosity became a pop sensation. Several of Curiosity's handlers including Bobak "Mohawk Guy" Ferdowsi became science rock stars. The technical prowess required to pull off such a landing has "captured the imagination of a whole new generation of prospective explorers," said American University space policy professor Howard McCurdy, who has closely followed the $2.5 billion mission. Mission scientist SushilAtreya of the University of Michigan remained calm until the last ten seconds. "Then it hit me – it's crazy! It was an unbelievable feeling of relief when the first picture from the rover came down," Atreya said. Mike Malin, who operates Curiosity's cameras, ticked off two of his favorite pictures from the mission so far: A view of the rover's heat shield falling away right before landing and a color portrait of Mount Sharp. "That looks so much like Utah that it felt very familiar," said Malin, who heads Malin Space Science Systems.

41. Once the euphoria of landing wore off, the six-wheel, nuclear-powered rover went to work, spending two months testing its instruments and systems. The health checks took longer than expected because Curiosity was a complex machine. To celebrate the landing anniversary, engineers commanded one of Curiosity's instruments to play "Happy Birthday" as the rover took a break from driving.

42. NOTES How do NASA scientists know how far it is to Mars and how long it will take to get there? d = rt Distance = rate x time d, r, and t are variables because theyvary in different situations Rate – ratio compares 2 different kinds of numbers mph $/lb often “per” or “/” implies rate

43. Curiosity travelled 350,000,000 miles at 1,405, 622 miles/day. How long did it take Curiosity to get to Mars?

44. Example: 1. r = 50 ft/sec t = 300 sec What is distance? 2. d = 1 mile r = 6 mph What is t? p. 242 # 7

45. FUN with OPERATIONS • Find a partner. • Grab a sheet of paper and some colored pencils. • Pick a slip of paper out of the Ziploc bag. • Draw a picture/cartoon/interpretation that will help us associate the term with the operation it implies. • Share picture with class. • Tape picture to wall. *DISCLAIMER: Everything must be school appropriate.

46. Homework p. 228 # 3-10 p. 34 # 2, 4, 5

47. Warm Up • Evaluate 26-2x for x = 10 • What is the difference between weight and mass? Write an expression for each statement: 3. 1/3 of the sum of y and 2 4. 6 less than the product of 32 and x

48. Expressions OFP 5. Simplify √25 – 4x + 3(2)

49. PROPERTIES • Commutative • Associative • Distributive • Identity • Zero

50. Warm Up • 526/2 (use long division – no calculator!) • d = 10 meters, r = 5 meters/min, t = ? • Mrs. Ransfer is performing an experiment that goes terribly wrong. The beaker explodes covering Mrs. Ransfer in chemicals! She runs to the bathroom sink at a rate of 20 feet per second and gets there in 3 seconds. How far is the bathroom from Mrs. Ransfer’s room?