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Using the math formula chart for conversions and measurement

Using the math formula chart for conversions and measurement. Conversions & Measuring (part 1) SFHS 2008. Using the Math Formula Page. You have been handed a formula page on which to take notes. As we go over a formula, and what the parts represent, write down what the letters represent.

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Using the math formula chart for conversions and measurement

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  1. Using the math formula chart for conversions and measurement Conversions & Measuring (part 1) SFHS 2008

  2. Using the MathFormula Page • You have been handed a formula page on which to take notes. • As we go over a formula, and what the parts represent, write down what the letters represent. • Being able to use, and using the chart will improve your score.

  3. Let’s look at the Chart first . . . • This part of the chart gives you metric and customary length measurement units. • When an = sign is used, it means they can be interchanged so that all the units are the same. • These same units are useful to know for Science!

  4. The next part of the chart deals with volume, these are liquid volume measurements. Solid volume measurements are on the formula page side, and require cubic measurement units such as cm3 or ft3.

  5. Mass and weight are considered the same in Math, but not in Science. . .

  6. These are to help you with time conversions . . . • Remember, in a problem, units must be the same. • You can not calculate correctly if one unit is in days and another is in hours. • To change, use the factors given. • Don’t guess – LOOK!

  7. There are 60 minutes in every hour. 2.5 hours multiplied by 60 minutes per hour gives us a total time of 150 minutes. Example: Four friends took turns using the stationary bike at a health club. Huan used it three times as long as Melanie. Susie used it half as long as David, and David used it 15 minutes longer than Huan. The four friends used the stationary bike for a total of 2.5 hours. How long did Susie use the stationary bike? F 60 min G 45 min H 30 min J 15 min Who is the person that the problem names and yet doesn’t give you any hint about time? That is the person who has the “x” minutes for time. Huan Melanie x minutes Susie David Huan used it three times as long as Melanie so Huan 3x minutes Melanie x minutes Susie David Now, to attack the problem. There are four people named here. Write down all of their names in a list. Huan Melanie Susie David Read the rest of the problem again to fill in the other friends’ times based on Melanie’s time. David used it 15 minutes longer than Huan so Huan 3x minutes Melanie x minutes Susie David 3x + 15 minutes And finally, Susie used it half as long as David so: Huan3x minutes Melaniex minutes Susie (3x + 15)/2 minutes David (3x + 15) minutes This problem talks about minutes when speaking about individual times. However, total time is in hours. We need to convert hours to minutes so that we are working with the same unit of time.

  8. Example: Four friends took turns using the stationary bike at a health club. Huan used it three times as long as Melanie. Susie used it half as long as David, and David used it 15 minutes longer than Huan. The four friends used the stationary bike for a total of 2.5 hours. How long did Susie use the stationary bike? F 60 min G 45 min H 30 min J 15 min Do NOT jump the gun!!!! Did you say that J is the answer? Just because 15 minutes is option J does NOT mean that J is the answer. Do NOT mess around with this complicated equation!!! Type the left side of this equation into y= on your graphing calculator. y = 3x + x + (3x + 15)/2 + (3x + 15) Now, use the table feature to find the value of x when y = 150 minutes. As you scroll down the table, you find that x = 15 minutes when y = 150 minutes. Recall, just who used the bike for x minutes? Melanie. Who does the problem ask about? Susie If you immediately picked J without going back to see what you were looking for, you would have picked the wrong answer!!!! Since we know a total time for the four friends, we need to add all of their times together. Huan + Melanie + Susie + David = 150 minutes 3x + x + (3x + 15)/2 + (3x + 15) = 150 Quit the y= on your calculator to go back to the home screen. Now type in Susie’s time expression, using 15 in place of x. (3x15+15)/2 and then enter Susie’s time is 30 minutes so the correct answer is option H. Option F is David’s time and option G is Huan’s time.

  9. Let’s move onto the rulers that are on the formula chart. • Just about every TAKS test has required students to measure!

  10. There are two rulers on the Mathematics formula chart. • One is a centimeter ruler. • The other is an inch ruler.

  11. At various times, the TAKS test has asked you to measure with one or the other. The first year of TAKS, students were asked to measure with both rulers -- on the same test!

  12. Very rarely does a TAKS question stop just at measuring. Most questions ask you, after you find the necessary measurements, to: • Find the surface area • Find the composite area • Find the volume

  13. The figures that you are asked to measure vary. Usually you are given a net of a 3-dimensional figure. You need to figure out which part(s) are necessary for finding the value they want. Then, you are expected to correctly measure those parts and use the measurements to answer the question. The question almost always involves using some formula on the formula chart.

  14. Now, we will deal with the inch ruler. In Part Two we will deal with the centimeter ruler. More of the TAKS questions that have been released involve centimeters (but not all, which is why we need to work with inches, too)

  15. 1 2 3 Let’s study the inch ruler. The longest line refers to the inch. The next longest line, half way between the “inches” is the half-inch. Half-way between the “halves” are the “fourths”. And, half-way between the “fourths” are the “eighths”.

  16. This problem was on the April 2006 Exit-level test. 20 Jackie made a rectangular prism to hold her earrings. The net of the rectangular prism is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the rectangular prism to the nearest ¼ inch. What is the volume of this rectangular prism to the nearest cubic inch? First, circle the phrase “volume of this rectangular prism”. You need to look at the chart and find appropriate formula. Since, you are given a net, you need to imagine what this figure looks like in 3-D. The “B” is area of the rectangular base. What is the formula for that area? For the entire prism? Write it on your paper/test booklet.

  17. This problem was on the April 2006 Exit-level test. 20 Jackie made a rectangular prism to hold her earrings. The net of the rectangular prism is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the rectangular prism to the nearest ¼ inch. What is the volume of this rectangular prism to the nearest cubic inch? Now, locate the inch ruler. Next, locate the slash that notes “fourths”. Now, determine the lengths that you need. Volume requires a length, a width, and a height.

  18. Now, use your inch ruler on your Mathematics chart to measure the length, width, and height of the prism. Write down your measurements as you go. Consult your paper again. We were asked to find the volume. What is the formula for finding the volume of a rectangular prism? Enter the measurements that you found and use the calculator to find the volume.

  19. Here are the answer choices. Which is closest to the volume of this rectangular prism? F 4 in.3 G 1.3 in.3 H 8.5 in.3 J 13.5 in.3 Hope you chose G.

  20. Okay---Now you do some problems on the back page for practice

  21. Checking: 42 The energy of a certain particle is 3.86 joules. If this particle loses 0.105 joule of energy every 30 seconds, what will its energy be after 8 minutes? F 2.18 joules G 1.68 joules H 3.02 joules J 2.29 joules One time unit is seconds; the other is minutes. We need the same unit. Since 1 minute = 60 seconds, 8 minutes = 8(60) = 480 seconds 480 seconds/ 30 seconds = 16 times that the particle loses 0.105 joule. 3.86 joules – 16(0.105 joule) = 2.18 joules

  22. Checking: 6 The world’s fastest flying insect is the dragonfly. It can fly 36 miles per hour. If a dragonfly flew in a straight path at this rate, what distance would it fly in 15 minutes? F 2 mi G 9 mi H 25 mi J 540 mi One time unit is hours; the other is minutes. We need the same unit. One hour is 60 minutes so 15 minutes is one-fourth ¼ of an hour. 36 mi/h( ¼ h) = 9 miles

  23. Checking Formula is S = 6s2. Measuring the length of a side, we got 1¼ inch (1.25) S = 6(1.25 in.)2 = 9.375 in2

  24. We’ll have more measurement problems to work on in part two . Don’t forget about Study Island

  25. Using the math formula chart for measurement Part 2 Applications

  26. In Part One , we spoke about conversions on the formula chart. We also spoke about the inch-ruler that was on the chart and did a problem requiring us to measure with that ruler. Now, we are going to concentrate on the centimeter ruler. More questions on the released TAKS tests have use metrics. In addition, only the metric ruler is on your science formula chart.

  27. 1 2 3 Let’s first talk about the centimeter ruler. The longest line refers to the centimeter. Since there are 10 millimeters in a centimeter, each centimeter is divided into ten equal-sized spaces. Each of those slash marks represents a tenth of a centimeter.

  28. Let’s use the centimeter ruler to do an actual TAKS problem. You have on your paper the same problem as shown here.

  29. This question was # 60 on the Feb 2006 Exit Level TAKS test. Use the ruler on the Mathematics Chart to measure the dimensions of the net of the rectangular prism shown below to the nearest tenth of a centimeter.

  30. Which of the following best represents the dimensions of the rectangular prism? F. 7.5 cm by 1.5 cm by 3.0 cm G. 10.5 cm by 1.5 cm by 9.0 cm H. 10.5 cm by 3.0 cm by 9.0 cm J. 7.5 cm by 3.0 cm by 3.0 cm

  31. You should find the centimeter ruler on the formula chart. Before you just start measuring everything, you need to figure out what this figure actually looks like when it is together. We would need to measure length. We would need to measure width. And we would need to measure height The figure is a rectangular prism. Its dimensions would have length, width, and height. Right now, measure the dimensions and record them on your paper.

  32. Here are your options, again. Which answer choice is best? Which of the following best represents the dimensions of the rectangular prism? F. 7.5 cm by 1.5 cm by 3.0 cm G. 10.5 cm by 1.5 cm by 9.0 cm H. 10.5 cm by 3.0 cm by 9.0 cm J. 7.5 cm by 3.0 cm by 3.0 cm Hopefully, you selected F as the best choice.

  33. Many of the questions requiring measurement have asked for volume or surface area. • You will need to look at the formula chart for the necessary formula as well as for the ruler.

  34. Apr ’04 #38 The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest tenth of a centimeter What is the total surface area of this cylinder to the nearest square centimeter? Give this one a try on your own, first.

  35. Apr ’04 #38 The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest tenth of a centimeter What is the total surface area of this cylinder to the nearest square centimeter? S = 2πr(h + r) First, circle the phrase that tells us what we are looking for---total surface area. Next, look on the chart for the corresponding formula for a cylinder. Copy that formula on your paper.

  36. Apr ’04 #38 The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest tenth of a centimeter What is the total surface area of this cylinder to the nearest square centimeter? Height S = 2πr(h + r) Now, find the radius (r) and the height of the cylinder (h) on the net. Mark them. The height of a cylinder will NEVER have the circles attached. The radius is easy on this one—it is already marked. Be careful on that height!!!!!

  37. Apr ’04 #38 The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest tenth of a centimeter What is the total surface area of this cylinder to the nearest square centimeter? So, do you have an answer? ☺

  38. Added problem. V = Bh The base is a circle so V = πr2h V = π(1.7 cm)2(7 cm) = 63.55 cm3 Which of the following best represents the volume of this cylinder? A 110 cm3 B 94 cm3 C 75 cm3 D 64 cm3

  39. Try the next two problems on your own. We’ll go over them in a few minutes—just to check that you worked them out correctly. Perfect practice makes perfect.

  40. 25 The net of a right triangular prism is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the right triangular prism to the nearest centimeter. Find the total surface area of this right triangular prism to the nearest square centimeter? TSA = Ph + 2B P is perimeter of Base, B is rt triangle—need measures of a 3 sides h is height of prism—triangles are NOT attached to height B is area of Base—Base is triangle—height of triangle times base of triangle (they form the right angle) divided by 2

  41. For the triangular base: h = 4 cm, b = 3 cm, hypotenuse = 5 cm (Pythagorean triple!), P = 12 cm, B = (4 cm)(3 cm)/2 = 6 cm2For the prism: h = 3 cm TSA = Ph + 2B = (12 cm)(3 cm) + 2(6cm2) = 48 cm2

  42. For the triangular base: h = 4 cm, b = 3 cm, hypotenuse = 5 cm (Pythagorean triple!), P = 12 cm, B = (4 cm)(3 cm)/2 = 6 cm2For the prism: h = 3 cm TSA = Ph + 2B = (12 cm)(3 cm) + 2(6cm2) = 48 cm2 ☺

  43. V = Bh Base is a triangle so V = (bhT /2)hP = ((3 cm)(4 cm)/2)(3cm) = 18 cm3 Added problem: Use the same net above. Which of the following best represents the volume of this right triangular prism? F 18 cm3 G 60 cm3 H 48 cm3 J 36 cm3 ☺

  44. Last one! That word indicates that all of the sides of the pyramid have the same length. This problem is a bit different. Did you see the word “regular”? We can now find the area of ONE triangle, multiply it by 4, and have the total area. A = (bh)/2 = ((3 cm)(2.7 cm))/2 = 4.05 cm2 ☺ TA = 4(4.05 cm2) = 16.2 cm2

  45. Remember to come on Tuesdays, Wednesdays, Thursdays, and Saturdays for the next 2 weeks.We will have something new each time! • Thursday, from 2:30 - 4:30 –April 16– Objective 9 • Saturday, April 18 from 9:00am – noon - EXIT Level Students ONLY • Objectives 1, 2, 3, and 4, • Tuesday, from 2:30 - 4:30 –April 21 – Objective 2 • Wednesday, April 22 from 2:30 – 4:00 - All Students • Calculator Review • Thursday, from 2:30 - 4:30 –April 23 – Objective 10 • Saturday, April 25 from 9:00- noon - EXIT Level Students ONLY • Objectives 6, 7, and 8 • Saturday, April 25 from 9:00-noon- All Students • 5, 9, and 10 • TESTING : The week of April 27 – May 1

  46. Thank you for coming today.AIM For TAKS SUCCESS!!!

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