1. Unit 1: Relationships Between Quantities and Expressions Accelerated Algebra 1 / Geometry A N.RN.2,3 Using properties of rational and irrational numbers N.Q.1,2,3 Reason quantitatively and use units to solve problems A.SSE.1a,b Interpret the structure of expressions A.APR.1 Perform arithmetic operations on polynomials

2. N.Q.1,2,3 Reason quantitatively and use units to solve problems Metric and Customary Conversions Accuracy and Precision

3. Tonight’s Homework Watch the first 6 minutes of this YouTube video https://www.youtube.com/watch? v=x0VLp4FSe24 You can find this link on the calendar on my webpage under August 13 – Homework Video

4. Conversion Notes Precision and Accuracy

5. Conversions Precision and Accuracy Unit 1 Notes

6. Rounding

7. Systems we should know Metric Standard English (Customary)

12. G-Man (Gallon-Man)

13. Warm Up Convert each measure. 1. 3210 mm to centimeters 2. 18 in. to feet 3. 52.5 kg to grams 4. 2.5 lbs to ounces 321 cm 52,500 g

14. Dimensional Analysis Using the Conversion Factor Objective: Make unit conversions

15. Unit conversion factor A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Fill in some of the common unit conversion factors below. You can also use the reciprocal of these. 1 ft ? in. 1 yd ? ft 1 mi ? ft 1lb ? oz 1 pt ? c 1 qt ? pt 1 gal ? qt 1 hr ? min 1 min ? s 1m ? cm 1km ? m Warm Up

16. Unit conversion factor A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.

18. Choose a unit conversion factor that… Introduces the unit you want in the answer Cancels out the original unit so that the one you want is all that is left.

19. “Canceling” out Words

20. Practice: Choose the appropriate conversion factor. Inches to feet Minutes to hours Meters to centimeters

21. Convert 8 yards to feet… Make a decision: What conversion factor will you use? Hint! Use the one that will cancel out the units you want to change Set up the problem: Multiply the measurement by the conversion factor. Solve the problem: Perform the multiplication

22. A bucket holds 16 quarts. How many gallons of water will fill the bucket? Use a unit conversion factor to convert the units. What are the two conversion factors comparing quarts and gallons? Which one will “cancel” quarts? 16 qt 

23. You Try it! One bag of apples weighs 64 ounces. How many pounds does it weigh? Darren drank 2 liters of water. How many milliliters of water did he drink ?

24. Making Rate Conversions Use a unit conversion to convert the units within each rate

25. Convert 80 miles per hour to feet per hour. Convert 63,360 feet per hour to miles per hour.

26. You Try it! Convert 32 feet per second to inches per second. A craft store charges $1.75 per foot for lace. How much per yard is this?

27. Word Problems The average American eats 23 pounds of pizza per year. Find the number of ounces the average American eats per year. The average American eats 368 ounces of pizza per year.

28. Multiple conversions https://www.youtube.com/watch?v=ZKAVCdvzBb4 Converting from feet per second to miles per hour

29. Word Problems… A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling? Hint: Set up the words first. How many seconds in an hour? The car traveled 44 feet per second.

30. Warm Up If you are driving at 65 mph, how many feet per second are you traveling? Sam eats one Big Mac every day for lunch. If each Big Mac contains 28 grams of fat, how many pounds of fat will he consume in his lifetime if he lives to be 74 years old and begins eating Big Macs from age 10? 1 lb = 453.592 g You can use 365 days per year. You do not need to account for leap years. Answers may vary between 1439 and 1442 depending how and when you rounded.

31. Precision and Accuracy

32. How can you use appropriate levels of precision and accuracy?

39. A. 0.8 km; 830.2 m A tenth of a meter is smaller than a tenth of a kilometer, so 830.2 m is more precise. Example 1: Comparing Precision of Measurements B. 2.45 in.; 2.5 in. Choose the more precise measurement in each pair. 0.8 km Nearest tenth of a kilometer 830.2 m Nearest tenth of a meter

40. Choose the more precise measurement in each pair. Example 1 1a. 2 lb; 17 oz. An ounce is smaller than a pound, so 17 oz is more precise. 1b. 7.85 m; 7.8 m. 2 lb 17 oz Nearest pound Nearest ounce

41. A. Which scale is the most precise? Ida works in a deli. She is testing the scales at the deli to make sure they are accurate. She uses a weight that is exactly 1 pound and gets the following results: Scale 1: 1.019 lb Scale 2: 1.01 lb Scale 3: 0.98 lb Scales 2 and 3 measure to the nearest hundredth of a pound. Scale 1 measures to the nearest thousandth of a pound. Example 2 : Comparing Precision and Accuracy

42. B. Which scale is the most accurate?. Because 0.01 < 0.019 < 0.02, Scale 2 is the most accurate. Example 2 : Continued For each scale, find the absolute value of the difference of the standard mass and the scale reading. Scale 1: |1.000 – 1.019| = 0.019 Scale 2: |1.000 – 1.01| = 0.01 Scale 3: |1.000 – 0.98| = 0.02

43. 1. Choose the more precise measurement: 2.4 km; 2430 m 2430 m Lesson Quiz : part-1 2. Jorge works in a mail room. To test the accuracy of the scales in the mail room, he uses a weight that is exactly 8 oz. and gets the following results: Scale 1: 8.02 oz Scale 2: 7.8988 oz Scale 3: 8.015 oz a. Which scale is the most precise? b. Which scale is the most accurate? 2 3

47. Bright Days Blinds makes window shades. The width of a 30-inch shade should be within 0.18 in. of 30 in. A batch of shades has the widths shown in the table. Example 3 : Using a Specified Tolerance x

48. Do all of the shades measure within the specified tolerance? If not, which shade(s) are not within the specified tolerance? No, Shade B measures 29.75 in., so it is not within the specified tolerance. Example 3 : Continued 30 – 0.18 = 29.82 30 in. ± 0.18 in. means that the shade must be 30 + 0.18 = 30.18 between 29.82 and 30.18 in. x

49. A. 12 lb ± 3% 11.64 lb–12.36 lb Example 4: Using Tolerance Expressed as a Percent Write the possible range of each measurement. Round to the nearest hundredth if necessary. 12(0.03) = 0.36 Find 3% of 12. 12 lb  0.36 lb Write the measurement and tolerance. Write the measurement as a range. x

50. 14.77 oz–15.23 oz Example 4: Continued B. 15 oz ± 1.5% C. 3 m ± 0.2% 15(0.15) = 0.225Find 1.5% of 15. 15 oz  0.23 oz Write the measurement and tolerance. Round to the nearest hundredth. Write the measurement as a range. 3(0.002) = 0.006Find 0.2% of 3. x

51. Check It Out! Example 4 Continued 84.57 mg–85.43 mg 85 mg  0.43 mg Write the measurement and tolerance. Round to the nearest hundredth. Write the measurement as a range. x

52. 3. Monique is cutting wooden slats that are to be 20 in. long. Three slats have the following lengths: B Lesson Quiz : Part-2 A: 19.96875 in. B: 19.875 in. C: 20.0625 in. a. Which slat(s), if any, do not fall within a tolerance of 0.0625 in.? b. Which slat(s), if any, do not fall within a tolerance of 0.5%? B x