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nd 2 Period Math Monday: Bell Work The boiling point of water is 212 degrees Fahrenheit (°F). Propane boils at about –44 °F. How much hotter is the boiling point of water than that of propane? 1) draw the problem out- be sure to correctly label it 2) write the correct equation 3) solve 1. Critique What does this word mean to you? Examples… This word actually means….. a detailed analysis and assessment of something: evaluate (a theory or practice) in a detailed and analytical way. Explain how you would use this word in math. Essential Question Scientific Notation Adding and Subtracting Here are the steps to adding or subtracting numbers in scientific notation : 1. Determine the number by which to increase the smaller exponent by so it is equal to the larger exponent. 2. Increase the smaller exponent by this number and move the decimal point of the number with the smaller exponent to the left the same number of places. (i.e. divide by the appropriate power of 10 .) 3. Add or subtract the new coefficients. 4. If the answer is not in scientific notation (i.e. if the coefficient is not between 1 and 10 ) convert it to scientific notation Example 1: 2.456×105 +6.0034×108 = ? 8 - 5 = 3. The smaller exponent must be increased by 3. 2.456×105 = 0.002456×108 0.002456×108 +6.0034×108 = 6.005856×108 6.005856×108 is in scientific notation. Multiplication To multiply two or more numbers in scientific notation: 1. multiply the coefficients 2. Add the exponents. Division To divide two or more numbers in scientific notation: 1. Divide the coefficients 2. Subtract the exponent of the denominator from the exponent of the numerator. ( The first exponent from the second) Try These: Exit Ticket • • • • • • • • • • • 1. (3 x 103) + (2 x 103) 2. (2 x 10-7 m) + (3 x 10-7 m) 3. (8 x 10-8 m2) – (3 x 10-8 m2) 4. (3.8 x 10-7 m2) – (2.8 x 10-7 m2) 5. (5.0 mm) + (2 x 10-4 m) 6. (6.2 km) – (3 x 102 m) 7. (2 x 105 m)(3 x 106 m) 8. (5 x 10-4 m)(4 x 10-2 m) 9. (1.50 x 10-7 m)(2.50 x 1015 m) 10. (9 x 108 kg)/(3 x l04 m2) 11. (2.4 x 105 kg)(3 x 104 m) / (4 x 10-2 s2) Tuesday: Bell Work The moon experiences many extremes in temperature because it has no atmosphere. For example, on the side of the moon that the sun is shining on, the temperature can reach 260 °F. On the dark side of the moon, it gets as cold as –280 °F. How much is the drop in temperature from day to night? 1) draw the problem out- be sure to correctly label it 2) write the correct equation 3) solve 2. Precision What does this word mean to you? Examples… This word actually means….. the degree to which the correctness of a quantity is expressed. Explain how you would use this word in math. Essential Question Calculator Practice • • • • • • • • • • • 1. (3 x 103) + (2 x 105) 2. (2 x 107 ) + (3 x 109) 3. (8 x 108) – (3 x 106) 4. (3.8 x 107) – (2.8 x 1013) 5. (5.0) + (2 x 104) 6. (6.2) – (3 x 102) 7. (2 x 105)(3 x 1024) 8. (5 x 104)(4 x 1015) 9. (1.50 x 107)/(2.50 x 1011) 10. (9 x 108)/(3 x l04) 11. (2.4 x 105)(3 x 104) / (4 x 107) Word Problems • http://www.regentsprep.org/regents/math/al gebra/AO2/PracScientific.htm Exit Ticket • Talk with your partner about why it is important to write in scientific notation. • Create examples of when you could use scientific notation in your everyday life. Wednesday: Bell Work *HW in basket On a recent glider flight, Lucy took a tow to 3000 feet above ground level. She found a good thermal and climbed 1800 feet. Then she hit big sink and lost 2200 feet. What was her altitude at that point? 1) draw the problem out- be sure to correctly label it 2) write the correct equation 3) solve 3. Transform What does this word mean to you? Examples… This word actually means….. to simplify or solve a mathematical problem Explain how you would use this word in math. Lesson solve real-world problems using rational numbers in any form, including those problems involving multiple steps? Exponents Exponents The exponent of a number says how many times to use the number in a multiplication. In 82 the "2" says to use 8 twice in a multiplication, So 82 = 8 × 8 = 64 In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared" Exponents Example: 53 = 5 × 5 × 5 = 125 In words: 53 could be called "5 to the third power", "5 to the power 3" or simply "5 cubed" Example: 24 = 2 × 2 × 2 × 2 = 16 In words: 24 could be called "2 to the fourth power" or "2 to the power 4" or simply "2 to the 4th" Why use exponents??? Exponents make it easier to write and use many multiplications Example: 96 is easier to write and read than 9 × 9×9×9×9×9 Exponents are commonly used by mathematicians and scientists. Exponent *special info Example: 2^4 is the same as 24 2^4 = 2 × 2 × 2 × 2 = 16 ** When you have a negative base, you must put it is parenthesis when using a calculator! -8 ^ 2 means (-8)^2 You will not get the correct answer if you do not do this. The calculator doesn't read the – sign and just adds it to the answer. Exit / Closure Solve these 10 scientific notation problems for a class work grade. * Place them into the red, yellow, or green tray based on how well you understand the concept of scientific notation. Thursday: Bell Work One day in July, the temperature at ground level at the airport was 90°. A pilot reported the temperature at 10,000 feet was 50°. How much did the temperature drop per 1000 feet? (Hint: find the amount of temperature change and set up a proportion.) 1) draw the problem out- be sure to correctly label it 2) write the correct equation to solve the distance 3) then solve to figure out the change 4. Computation What does this word mean to you? Examples… This word actually means….. using 4 basic operations (=, -, x, ÷) to solve a problem . Explain how you would use this word in math. Lesson ... use the commutative and associative properties to add and/or subtract linear expressions with rational coefficients? ... use the distributive property to factor or expand linear expressions with rational coefficients? Order of Operations How Do I Remember Which Order To Do The Problem? BODMAS ! B- Brackets first ( includes Parentheses () or Brackets [ ] ) O- Orders (includes Powers and Square Roots, etc.) DM- Division and Multiplication (left-to-right) AS- Addition and Subtraction (left-to-right) Order of Operations After you have done "B" and "O", just go from left to right doing any "D" or "M" as you find them. Then go from left to right doing any "A" or "S" as you find them. EXAMPLES Example: How do you work out 3 + 6 × 2 ? Multiplication before Addition: First 6 × 2 = 12 Then 3 + 12 = 15 Create your ice cream cone 3+6x2 3 + 12 15 EXAMPLES Example: How do you work out (3 + 6) × 2 ? Brackets first: First (3 + 6) = 9, then 9 × 2 = 18 (3 + 6) x 2 9x2 18 ***Only do one operation per line!! EXAMPLES Example: How do you work out 12 / 6 × 3 / 2 ? Multiplication and Division rank equally, so just go left to right: First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3 12 / 6 x 3 / 2 2x3/2 6/2 3 EXAMPLES Oh, yes, and what about 7 + (6 × 25 + 3) ? 7 + (6 × 25 + 3) 7 + (6 × 25 + 3) 7 + (150 + 3) 7 + (153) 7 + 153 160 Start inside Brackets, and then use “Orders" First Then Multiply Then Add Brackets completed, last operation is add DONE ! Order of Operations Reminders • As the problems become more complicated it is very important that you do one step at a time!! This will prevent many mistakes. • And as always.... YOU MUST SHOW YOUR WORK!!! Practice Time! Practice problems Exit/ Closure Solve the following (use an index card) 3.8n + 15 = 30.2 Show your work to justify your answer Friday: Bell Work *HW in basket 1. The cells of the bacteria E. Coli can double every 20 minutes. If you begin with a single cell, how many cells can there be after 4 hours? 2. The population of metropolitan Orlando, Florida, has doubled about every16 years since 1960. In 2000, the population was 1,644,561. At this doubling rate, what could the population be in 2048? 5. Additive Inverse What does this word mean to you? This word actually means….. the opposite of a number (+5, -5). Examples… Explain how you would use this word in math. Lesson ... use the commutative and associative properties to add and/or subtract linear expressions with rational coefficients? ... use the distributive property to factor or expand linear expressions with rational coefficients? Scavenger Hunt • We will now begin our Pirate Treasure Hunt! Good Luck! • 3 + (122 + 6) + 52 x 2 + 28 = Order of Operations Let's solve problems!!!! Site 1 Site 2 Order of Operations Check 1) You may write on the paper 2) You MUST show all work 3) A calculator may be used to check your work...... BUT your work must match your answer Exit / Closure Partner discussion with your neighbor(s) – Tell the order of operations and why it is important to follow them!!