302A final exam review

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302A final exam review
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Final Exam

• Tuesday, May 12
• 11am 1pm
• In our usual classroom
• Review session
• Thurs, 5/7 _at_ 1230pm here.

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Some Answers to 6.1 homework

• 28) We need a constant ratio of men to women. 9
  men x men 4 women 360 womenSolve 9 360
  4x x 810 men now.
• If we want a ratio of 2 1, then we want 405
  women. We have 360 women, so we need 45 more
  women to make the ratio 2 1.

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• 31a) Lets draw a picture.Crew of 4 menIn 5
  days 1 buildingIn 10 days 2 buildingsIn 15
  days 3 buildingsIn 20 days 4 buildings
• So, a crew of 4 can build 4 buildings in 20 days.
  Two crews of 4 can build 8 buildings in 20 days.
  10 crews of 4 can build 40 buildings in 20 days,
  so 40 people altogether.

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Some Answers to 6.2 homework

• 1a 4 of 450. Think 1 of 450 is 4.5, so 4 of
  450 is 4 4.5, or 18.
• Or, 4 of 450 is close to 5 of 450. We know
  that 10of 450 is 45, and so 5 is half of 10,
  so half of 45 is 22.5.

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• 1h 30 is what percent of 35?
• Think part whole percent 100.
• So, 30/35 x/100? Well, 30/35 is close to
  30/36, or 5/6, which is about 83.
• Or, 30/35 is close to 35/40, or 7/8, which is
  87.5.

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• 1p What is 100 more than 35?
• 100 of 35 is 35, so 100 more is 35 35 70.

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8. Two dresses

• 119 with 40 off
• Pay 60
• 119 0.60 71.40

• 79.99 with 20 off
• Pay 80
• 79.99 0.80 63.99
• Second dress is cheaper.

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• 30. To find 0.5, we know that this means
  0.5/100. If we multiply numerator and
  denominator by 10, we get (0.5 10)/(100 10)
  5/1000, or 1/200.

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Exploration 6.7

• Do Part 1 1 with your group.

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What is on the final exam?

• From book 1.2, 1.3, 1.4, 1.7 2.3 3.1, 3.2,
  3.3, 3.4 4.2, 4.3 5.2, 5.3, 5.4 6.1, 6.2
• From Explorations 1.1, 1.4 2.8, 2.9 3.1, 3.3,
  3.6, 3.13, 3.15, 3.18, 3.19 4.2 5.8, 5.9, 5.10,
  5.12, 5.13, 5.14, 5.15 6.3, 6.5,
• From Class Notes Describe the strategies used
  by the students--dont need to know the names.

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Chapter 1

• A factory makes 3-legged stools and 4-legged
  tables. This month, the factory used 100 legs
  and built 3 more stools than tables. How many
  stools did the factory make?
• 16 stools, 13 tables

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A test 3 problem

• If 3/5, carefully draw 1/6.
• Two approaches

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Chapter 1

• Fred Flintstone always saysYABBADABBADO. If
  he writes this phrase over and over, what will
  the 246th letter be?
• D

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Chapter 2

• Explain why 32 in base 5 is not the same as 32 in
  base 6.
• 32 in base 5 means 3 fives and 2 ones, which is
  17 in base 10.
• 32 in base 6 means 3 sixes and 2 ones, which is
  20 in base 10. So, 32 in base 5 is smaller than
  32 in base 6.

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Chapter 2

• Why is it wrong to say 37 in base 5?
• In base 5, there are only the digits 0, 1, 2, 3,
  and 4. 7 in base 5 is written 12.

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Chapter 2

• What error is the student making? Three hundred
  fifty seven is written 300507.
• The student does not understand that the value of
  the digit is found in the place 300507 is
  actually 3 hundred-thousands plus 5 hundreds and
  7 ones. Three hundred fifty seven is written
  357--3 hundreds plus 5 tens plus 7 ones.

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Chapter 2

• True or false?
• 578 318 1008
• 24015 4325 gt 20005
• 139 lt 228 lt 417
• False 578 318 1108
• False 24015 4325 14145
• True 12 lt 18 lt 29

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Chapter 3

• List some common mistakes that children make in
  addition.
• Do not line up place values.
• Do not regroup properly.
• Do not account for 0s as place holders.

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Chapter 3

• Is this student correct? Explain.
• 347 59 add one to each number and get 348
  60 408.
• No 347 59 is the same as 346 60 because
• 346 1 60 ? 1 346 60 1 ? 1,
• and 1 ? 1 0.
• The answer is 406.

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Chapter 3

• Is this student correct?
• 497 ? 39 497 ? 40 ? 1 457 ? 1 456.
• No, the student is not correct because
• 497 ? 39 (497) ? (40 ? 1)
• (497) ? 40 1 458.
• An easier way to think about this is 499 ? 39
  460, and then subtract the 2 from 499, to get 458.

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Chapter 3

• Is this student correct?
• 390 ? 27 is the same as 300 90 ? 20 ? 7. So,
  300 70 ? 7 370 ?7 363.
• Yes, this student is correct.

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Chapter 3

• Multiply 39 12 using at least 5 different
  non-traditional strategies.
• Lattice Multiplication
• Rectangular Array/Area Model
• Egyptian Duplation
• Repeated Addition, Use a Benchmark
• 39 10 39 2
• 40 12 ? 1 12
• 30 10 9 10 30 2 9 2 (30
  9)(10 2)

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Chapter 3

• Divide 259 15 using at least 5 different
  strategies.
• Scaffold
• Repeated subtraction
• Repeated addition
• Use a benchmark
• Partition (Thomas strategy)

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Chapter 3

• Models for addition
• Put together, increase by, missing addend
• Models for subtraction
• Take away, compare, missing addend
• Models for multiplication
• Area, Cartesian Product, Repeated addition,
  measurement, missing factor/related facts
• Models for division
• Partition, Repeated subtraction, missing
  factor/related facts

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Chapter 3

• Vocabulary
• Addition addend addend sum
• Subtraction minuend ? subtrahend difference
• Multiplication multiplier factor product
• Division dividend divisor quotient
  remainder/divisor
• dividend quotient divisor
  remainder

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Chapter 4

• An odd number
• An even number

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Chapter 4

• Prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 2
  factors
• The number ONE is NOT PRIME.
• Composite numbers 4, 6, 8, 9, 10, 12, 14, 15,
  16, 18, at least 3 factors
• Square numbers 1, 4, 9, 16, 25, 36, 49, 64, 81,
  an odd number of factors

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Chapter 4

• Prime factorization many ways to get the
  factorization, but only one prime factorization
  for any number.
• Find the prime factorization of 84.
• 2 2 3 7, or 22 3 7

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Chapter 4

• Greatest Common Factor The greatest number that
  a factor of every number in a set of numbers.
• The GCF of 50 and 75 is 25.
• You try Find the GCF of 60, 80, and 200.
• 20
• 60 20 3,
• 80 20 4,
• 200 20 10.

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Chapter 4

• The Least Common Multiple is the smallest number
  that is divisible by a set of numbers.
• The LCM of 50 and 75 is 150.
• You try Find the LCM of 60, 80, and 200.
• 1200
• 60 20 1200,
• 80 15 1200,
• 200 6 1200.

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Chapter 4

• What is the largest square that can be used to
  fill a 6 x 10 rectangle?
• 2 x 2 You can draw it to see why. (Which is
  involved here, GCF or LCM?)

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Chapter 5

• Fractions modelsPart of a wholeRatioOperatorQ
  uotient
• Make up a real-world problem for each model above
  for 6/10.

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Chapter 5

• Name the model for each situation of 5/6.
• I have 5 sodas for 6 people--how much does each
  person get?
• Out of 6 grades, 5 were As.
• I had 36 gumballs, and I lost 5/6 of them. How
  many are left?
• In a room of students, 50 wore glasses and 10 did
  not wear glasses.
• Answers quotient (5/6 soda per person)
  part-whole (5/6 As) operator (5/6 of 36
  gumballs, or 30 are gone--6 remain) ratio (51)

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Chapter 5

• There are three ways to represent a fraction
  using a part of a whole modelpart-wholediscrete
  ,number line (measurement)
• Represent 5/8 and 11/8 using each of the
  pictorial models above.

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Chapter 5

• If represents 12/25, show what 2 will look
  like.

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Chapter 5

• If these rectangles represent 12 of something,
  then each rectangle represents 3 of something.
  One third of a rectangle represents the unit
  fraction.
• So, we need to show 50/25, which is 16 full
  rectangles, and 2/3 of another rectangle.

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Chapter 5

• Errors in comparing fractions 2/6 gt 1/2
• Look at the numerators 2 gt 1
• Two pieces is more than one piece.
• Look at the denominators 6 gt 2
• We need 6 to make a whole rather than 2.
• There are more pieces not shaded than shaded.
• If we look at what is not shaded, then there are
  more unshaded pieces.
• The pieces are smaller in sixths than in halves.

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Chapter 5

• Appropriate ways to compare fractions
• Rewrite decimal equivalents.
• Rewrite fractions with common denominators.
• Place fractions on the number line.
• Sketch parts of a whole, with the same size whole

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Chapter 5

• More ways to compare fractions
• Compare to a benchmark, like 1/2 or 3/4.
• Same numerators a/b gt a/(b 1) 2/3 gt 2/4
• Same denominators (a 1)/b gt a/b 5/7 gt 4/7
• Look at the part that is not shaded 5/9 lt 8/12
  because 4 out of 9 parts are not shaded compared
  with 4 out of 12 parts not shaded.
• Multiply by a form of 1.

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Chapter 5

• Compare these fractions without using decimals or
  common denominators.
• 37/81 and 51/90
• 691/4 and 791/7
• 200/213 and 199/214
• 7/19 and 14/39
• lt gt gt gt

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Chapter 5

• Remember how to compute with fractions. Explain
  the error
• 2/5 5/8 7/13
• 3 4/7 9/14 3 13/14
• 2 7/8 5 4/8 7 11/8 8 1/8
• 5 4/6 5/6 5 9/6 5 1/2

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Chapter 5

• Explain the error
• 3 ? 4/5 2 4/5
• 5 ? 2 1/7 3 6/7
• 3 7/8 ? 2 1/4 1 6/4 2 1/2
• 9 1/8 ? 7 3/4 9 2/8 ? 7 6/8 8 12/8 ?
  7 6/8 1 4/8 1 1/2

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Chapter 5

• Explain the error
• 3/7 4/9 7/16
• 2 1/4 3 1/2 6 1/8
• 7/12 4/5 35/48
• 4/7 3/5 20/35 21/35 420/1225 84/245
  12/35

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Chapter 5

• Explain the error
• 3/5 4/5 4/3
• 12 1/4 6 1/2 2 1/2

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Chapter 5

• Decimals
• Name a fraction and a decimal that is closer to
  4/9 than 5/11.
• 4/9 0.44 5/11 0.4545 ex 0.44445 is
  closer to 4/9 than 5/11
• Explain what is wrong
• 3.45 .05 0.0145928
• This is 0.5 3.45. If we divide by a number
  less than one, than our quotient is bigger than
  the dividend.

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Chapter 5

• True or false? Explain.
• 3.69/47 369/470
• 5.02/30.04 502/3004
• Multiply by 1, or n/n.3.69/47 36.9/470, not
  369/4705.02/30.04 502/3004.

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Chapter 5

• Order these decimals
• 3.95, 4.977, 3.957, 4.697, 3.097
• 3.097, 3.95, 3.957, 4.697, 4.977
• Round 4.976 to the nearest tenth. Explain in
  words, or use a picture.
• Is 4.976 closer to 4.9 or 5.0? Put on a number
  line, and see it is closer to 5.0.

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Chapter 6

• An employee making 24,000 was given a bonus of
  1000. What percent of his new take home pay was
  his bonus?
• 1000/25,000 x/100
• 100,000 25,000x x 4

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Chapter 6

• Which is faster?
• 11 miles in 16 minutes or 24 miles in 39
  minutes? Explain.
• Use the rate miles/minutes. Then11miles/16
  minutes compared to 24/39.0.6875 miles per
  minute gt 0.6153 miles per minute. So the first
  rate is faster, or more miles per minute.

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Chapter 6

• Ryan bought 45 cups for 3.15. 0.07! Thats a
  great rate!What rate does 0.07
  represent?Describe this situation with a
  different rate--and state what this different
  rate represents.
• 3.15/45 cups 0.07 per cup. Another rate
  would be 45/3.15 14.28 cups per dollar.

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Chapter 6

• Which ratio is not equivalent to the others?(a)
  42 49 (b) 12 21(c) 50.4 58.8 (d) 294
  343
• (b)

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Chapter 6

• Write each rational number as a decimal and a
  percent.3 4/5 1/11 2 1/3
• 3 3.0 (or 3), 3004/5 0.8, 801/11
  0.09, 9.092 1/3 2.3, 233.3

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Chapter 6

• Write each decimal as a fraction in simplest form
  and a percent.4.9 3.005 0.073
• 4.9 4 9/10 4903.005 3 5/1000
  3 1/200 300.50.073 73/1000 7.3

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Chapter 6

• Write each percent as a fraction and a
  decimal.48 39.8 2 1/2 0.841
• 48 48/100 12/25 0.4839.8 39.8/100
  398/1000 199/500 0.3982 1/2 2.5/100
  25/1000 1/40 0.0250.841 841/100000
  0.00841

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Chapter 6

• A car travels 60 mph, and a plane travels 15
  miles per minute. How far does the car travel
  while the plane travels 600 miles?
• (Hint you can set up one proportion, two
  proportions, or skip the proportions entirely!)
• Answer is the car travels 40 miles--the car
  travels 1 miles for each 15 miles the plane
  travels. 1/15 x/600.

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Chapter 6

• DO NOT set up a proportion and solve use
  estimation instead.
• (a) Find 9 of 360.
• (b) Find 5 of 297.
• (c) Find 400 of 35.
• (d) Find 45 of 784.

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Chapter 6

• DO NOT set up a proportion and solve use
  estimation instead.
• (e) What percent of 80 is 39?(f) What percent
  of 120 is 31?(g) 27 is what percent of 36?(h)
  87 is 20 of what number?
• Now, go back and set up proportions to find the
  exact values of (a) - (h). Were you close?

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Chapter 6

• Iga Tahavit has 150 mg of fools gold. Find the
  new amount if
• She loses 30?
• She increases her original amount by 90?
• She decreases her originalamount by 40?
• 105 mg 285 mg 90 mg

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Percent Proportion Questions

• In Giant World, a giant tube of toothpaste holds
  one gallon. If a normal tube of toothpaste holds
  4.6 ounces and costs 2.49, how much should the
  giant tube cost?
• One gallon is 128 ounces.
• Ounces 4.6 128 Dollars
  2.49 x4.6x 128 2.49 About 69.29

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Estimate

• In Giant World, a giant tube of toothpaste holds
  one gallon. If a normal tube of toothpaste holds
  4.6 ounces and costs 2.49, how much should the
  giant tube cost?
• If we round, we can think 4 ounces is about
  2.50. Since we want to know how much 128 ounces
  is, think 4 32 128, so 2.50 times 32 is
  80. (or, 2.50 30 75)

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Try this one

• The admissions department currently accepts
  students at a 7 3 male/female ratio. If they
  have about 1000 students in the class, how many
  more females would they need to reduce the ratio
  to 2 1?
• Currently 7x 3x 1000, so x 100 700 males
  and 300 females.
• To keep 1000 students in class, they want 2y 1y
  1000, so y 333 666 males and 333 females.
  They need to accept 333 - 300 33 more females
  to achieve this ratio.
• OR, with 700 males, they need 350 females, or 50
  more.

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Try this one

• Lees gross pay is 1840 per paycheck, but 370
  is deducted. Her take-home pay is what percent
  of her gross pay?
• Part percent 370 x Whole
  100 1840 100
• 370 100 1840x About 20 is taken out, so
  about 80 for take-home pay.
• Could also do 1840 - 370 1470 1470
  x 1840 100

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Last one

• Estimate in your head
• 16 of 450
• 10 of 450 45 5 22.5, about 67.5
• OR 10 of 450 45 1 of 450 4.5, or about 5
  6 1 6 5 30 30 45 75.
• 123 is approximately what percent of 185?
• Approximate 120 is approximately what percent
  of 200 120/200 60/100, so about 60.

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Good Luck!

• Remember to bring pencil, eraser and calculator
  to the exam.
• Study hard!
• Show up on time!
• 1100 am 100 pm Tuesday, May 12 (here)