Unit 6: Scale Factor and Measurement

1. Unit 6: Scale Factor and Measurement How will you measure up?

2. Measurement What am I Learning Today? How will I show that I learned it? Determine appropriate units of measure Measure length to the nearest half, fourth, eighth and sixteenth of an inch. Convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships.

3. Following Directions Lesson • Take out a clean sheet of notebook paper. • Place it in front of you on your desk. • Fold your paper in half long ways “hot dog style”.

4. Following Directions Lesson • Open your paper up and place it holes to the top on your desk. • Draw a line all the way down the crease on the paper with a marker.

5. Following Directions Lesson • Fold the paper in half the other way “hamburger style”.

6. Following Directions Lesson • Open the paper up with the holes to the top. • Draw a line from the center of the paper to the margin closest to you.

7. Following Directions Lesson • Fold the paper again “hamburger style”. • Then fold it over again in the same direction as you folded it last.

8. Following Directions Lesson • Open the paper up. • Draw a line on each of the creases half way to the bottom margin. • Then fold your paper back up like you last had it.

9. Following Directions Lesson • Fold the paper over one more time in the same direction as your last fold, making it even more slender.

10. Following Directions Lesson • Open the paper up. • Draw lines on the four creases half as long as the last lines you drew, or ¼ of the way to the bottom margin.

11. Following Directions Lesson • Draw small lines on our paper in between each of the lines already on your paper and the left and right edges. • Make the lines extend down and be half as long as the last lines drawn.

12. Following Directions Lesson • Next, draw lines on the left and right edges all the way down below the margin, half way between the margin and the bottom of the paper. • How many lines have you drawn? • What fraction represents the whole amount?

13. Reading A Ruler • You read each line as a fraction or portion of the total number 16. • Remember, all fractions should be expressed in simplest form. 1/16 3/16 7/16 9/16 11/16 13/16 15/16 5/16 2/16 14/16 6/16 10/16 4/16 12/16 8/16 0 16/16

14. 7 3 3 15 1 1 1 11 3 7 5 13 5 1 9 8 16 16 2 4 4 8 16 8 16 16 16 16 16 8 How do I read a ruler? This is a typical carpenter’s ruler. Label your ruler exactly like this one. Now let’s see if you can read one properly. 0 1

15. What is this measurement? 1. 6 9/16 inches

16. What is this measurement? 3 3/8 inches

17. What is this measurement? 5 3/4 inches

18. Turn to a partner and discuss… 1) What if there were no units for measuring length? How would lengths be described? 2) Why is it important to have a standard unit of measurement?

19. Customary equivalencies Fill in your organizer with the following equivalencies.

20. Questions Notes = 1 qt 4 c 3 qt x 3 quarts = 12 cups. Questions Answers How do I convert between customary units of measure? 1) Write a ratio using a conversion factor. 2) Create a proportion using a variable for the value you are trying to find and the measurement given. 3) Find the cross product and solve for the variable. What is a conversion factor? The standard equivalents between two given units. In other words, “How much for one?” For example, 12 inches equals 1 foot. Remember, the order of each ratio must be the same!! How do I convert 3 quarts to cups? 1 • x = 4•3 x = 12

21. 144 cups = gallons. = 1 gal 16 c x 144 c 144 cups = 9 gallons. Convert 144 cups to gallons. 1 gallon is 16 cups. Write a proportion. Use a variable for the value you are trying to find. The cross products are equal. 16 • x = 1•144 Divide both sides by 16 to undo multiplication. 16x = 144 x = 9

22. Customary Conversion Practice 1. Convert 5 yards to inches. 2. Convert 16 tons to pounds. 3. Convert 11 quarts to cups. 4. A project requires 288 inches of tape. How many yards is this? 180 inches 32,000 pounds 44 cups 8 yards

23. Questions Notes 1) Write out KHDBDCM. Put a dot over the prefix of the given unit. Put another dot over the prefix of the unit you are trying to find. 2) Notice the direction and number of “hops” you have to make to get from the original prefix to the other. 3) Move your decimal the same number of “hops” in the same direction to get your answer. Questions Answers What are the basic metric units? - Meter measures length or distance - Liter measures volume or capacity - Gram measures weight or mass What are the metric prefixes? Kilo Hecto Deca Base Deci Centi Milli King Henry Died By Drinking Chocolate Milk How do I convert between metric units of measure?

24. Convert metric measures simply by moving the decimal.

25. Converting between metric units is as easy as moving a decimal! kilo hecto deca deci centi milli

26. 1.75 m = cm. SportsApplication The high-jumper cleared a height of 1.75 m. How many centimeters is this height? A centimeter is 2 places to the right of a meter in the chart. 1 m = 100 cm. You are converting a bigger unit TO a smaller unit. Multiply by 100. 1.75 m = (1.75 • 100) cm Move the decimal point 2 places to the right. 1.75 m = 175 cm

27. Caution! Make sure you are multiplying or dividing by the correct power of ten. Using Powers of Ten to Convert Metric Units of Measurement Convert. The CD case is 14 cm wide. 14 cm = _____ m 100 cm = 1 m, smaller unit TO bigger unit, so divide by 100. 14 cm = (14 ÷ 100) m Move the decimal point 2 places to the left. 14 cm = 0.14 m

28. Metric Conversion Practice Convert. 1. A book is 24 cm long. 24 cm = ____ mm 2. The chain has a mass of 16 g. 16 g = _____ mg 3. The volume of the liquid was 12,000 mL. 12,000 mL = ____ L 4. Frank’s paper airplane glided 78.9 m. Sarah’s plane glided 85 m. How many more centimeters did Sarah’s plane glide? 240 16,000 12 610 cm