5. Yes he is correct. Because the formula for the area of a circle is π r 2 , the radius is squared so any change in the length, which is the same as the radius, must be squared also. DRAWING CIRCLES 1. Check students’ drawings. The diameters of their circles should measure 5 cm. 2. Check students’ drawings. The diameters of their circles should measure 1 inch. 3. Check students’ drawings. The diameters of their circles should measure 8 cm. EXIT SLIP A. 1. 93 meters ÷ 2 = 46.5 meters 2. Area of a circle = π r 2 = 46.52 π = 2,162.25 π ≈ 6,792.9 meters 2 3. 6,792.9 meters 2 per turbine 5 91 turbines = 618,153.9 meters 2 B.
inches 2. 2(4 in. 5 16 in.) + 2(4 in. 5 16 in.) + 2(4 in. 5 4 in.) = 288 in. 2 3. Outer wall surface area: 2 π (32 in.)(4 5 4 in.) = 9,650.97 in. 2 Inner wall surface area: 2 π (28 in. )(4 5 4 in.) = 7,740.88 in. 2 Top surface area: π (32 in.) 2 – ( π (28 in.) 2 ) = 3,215.36 in. 2 – 2,461.36 in. 2 = 754 in. 2 Total surface area: 9,650.97 in. 2 + 7,740.88 in. 2 + 754 in. 2 = 18,145.85 in. 2 4. 2 π (1.5 in.)(18 in.) = 169.56 in. 2 5. Area of L-shaped piece: (4 in. 5 1 in.) + (3 in. 5 1 in.) = 7 in. 2 Area of outer sides: (4 in. 5 4 in.) = 16 in. 2 Area of inner sides: (3 in. 5 3 in.) = 9 in. 2 Total area: 3(7 in. 2 ) + 3(16 in. 2 ) + 3(9 in. 2 ) = 96 in. 2
comparing data and they are quick references. Some disadvantages include that they don’t show precise data or values and they are subject to interpretation.
Where Math Gets Real Answer Key (cont.)
*with white behind logo
PAGE 16 BY THE NUMBERS: THE SIERRA CLUB Use the order of operations to solve. 1. Divide 2,700,000 by 400,000. 2. Multiply 6.75 and 64. 3. Add 432 and 7. 2,700,000 ÷ 400,000 5 64 + 7 =
3. Blyth Offshore, Middelgrunden, Princess Amalia, Riffgat 4. 60 meters – 40 meters = 20 meters 5. Yes, he is correct. Because the formula for the area of a circle is πr 2 , the radius is squared so any change in the length, which is the same as the radius, must be squared also. 6.75 5 64 + 7 = 432 + 7 = 439 WIND POWER! SKILLS SHEETS AS THE TURBINE TURNS 1. See table below. 2. Blyth Offshore: 2 turbines 5 3,421 meters 2 per turbine = 6,842 meters 2 Middelgrunden: 20 turbines 5 4,536 meters 2 per turbine = 90,720 meters 2 1. Area of a circle = π r 2 5,333 meters 2 = 3.14r 2 1,698.4 meters 2 = r 2
FINDING SURFACE AREA WITH NETS Page 83: Bonus! Bison Use the order of operations to solve: 1. Add the numbers in parentheses. 2. Subtract the sum from 2,000. 2,000 – (61 + 20 + 6) = 2,000 – 87 = 1913 Sessions 29 & 30 Getting Into Character Page 85: Making a Budget See completed budget chart on page 60. 1a. Allowance: $10.00 x 4 = $40.00 1b. Tutoring: 2 x $7.50 = $15.00; $15.00 x 4 = $60.00 1c. Monthly Income: $40.00 + $60.00 = $100.00 2. Badges: $20.00 + $35.00 + $15.00 = $70.00 TREEMAP OF EXPORT VALUE OF CUT FLOWERS 5 cm 1. 10 cm 2. 3 cm 3 cm 3. 4. 4 cm 4 cm
Single Turbine Circumfer- ence
Single Tur- bine Blade Sweep Area
Number of Tur- bines
Single Turbine Radius
Offshore Wind Farm
Location
33 meters 38 meters 60 meters
3,421 meters 2 4,536 meters 2 11,310 meters 2
Blyth Offshore
U.K.
2
207 meters
Middelgrunden Denmark
20
239 meters
Riffgat
Germany
30
377 meters
Princess Amalia Windfarm
Nether- lands
40 meters
5,027 meters 2
60
251 meters
APRIL 10, 2017 • Answers Page 82: Exit Slips A. 1. 93 meters ÷ 2 = 46.5 meters 2. Area of a circle = πr 2 = 46.52π = 2,162.25π ≈ 6,792.9 meters 2 3. 6,792.9 meters 2 per turbine 5 91 turbines = 618,153.9 meters 2 B. 1. Area of a circle = π 2 r 5,333 meters 2 = 3.14r 2 1,698.4 meters 2 = r 2 r = 41.2 meters 2. 5,333 meters 2 per turbine 5 72 turbines = 383,976 meters 2 Region Page 81: Drawing Circles 1 . Check students’ drawings. The diameters of their circles should measure 5 cm. 2. Check students’ drawings. The diameters of their circles should measure 1 inch. 3. Check students’ drawings. The diameters of their circles should measure 8 cm. Value Percent Fraction Asia $563 6% 1 20 Africa $1,280 15% 3 20 Europe $4,640 53% 1 2 North America and Oceania $152 2% 1 50 South America $2,130 24% 1 4 World Total $8,765 100% 1 EXPORT VALUE OF CUT FLOWERS IN 2014 (in millions of dollars)
Asia, Green
Europe, Purple
South America, Blue
3. Autographs: 3 x $15.00 = $45.00 4. Costume: 2.5 x $25.00 = $62.50 $62.50 + $50.00 = $112.50
scholastic.com/math answers continued on page 3 5. 4-Months' Income: $100.00 x 4 = $400.00 Expenses: $70.00 + $45.00 + $50.00 $112.50 = $277.50 $400.00 – $277.50 = $122.50 Yes, you will have enough money. You will have an extra $122.50. Africa, Orange North America and Oceania, Yellow 6. Possible answers include: Don’t wear or reuse an old costume; don’t get as many signed autographs; don’t attend all three days of the convention.
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