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Answer Key for Grade 5 – Quarter #4

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Answer Key for Grade 5 – Quarter #4 Answer Key for Grade 5 – Quarter #4 (for both individual work and for group work) Notes for Parents: • This document is intended for parents and teachers – not for students. • This answer key doesn’t include all answers. Week 25 Individual Work: Triangular numbers: 1, 3, 6, 10, 15, 21,15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, etc. Sequences: 1) Add 6 to previous number: 9, 15, 21, 27, 33, 39, 45, 51, etc. 2) Multiply by 3: 7, 21, 63, 189, 567, 1701, etc. 3) Add previous two numbers: 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, etc. 4) Powers of Two. 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2,048, 4,096, 8,192, etc. Group Assignment: for Tuesday. 1) no 2) yes 3) yes 4) no 5) yes 6) no 7) yes 8) yes 9) 13 is a factor of 403. 403 is in the 13’s table. If you divide 403 by 13, there is no remainder. 10) 43 and 68 11) 4 and 45 for Thursday. Goldbach’s Conjecture: 36: 5+31; 7+29; 13+23; 17+19 54: 7+47; 11+43; 13+41; 17+37; 23+31 90: 7+83; 11+79; 17+73; 19+71; 23+67; 29+61; 31+59; 37+53; 43+47 120: 7+113; 11+109; 13+107; 17+103; 19+101; 23+97; 31+89; 37+83; 41+79; 47+73; 53+67; 59+61. Week 26 Individual Work: Powers of 11: 11, 121, 1331, 14,641, 161,051, 1,771,561, 19,487,171, 214,358,881, 2,357,947,691, etc. 5 17 47 1) 21 2) 66 3) 87.5 4) 11 5) 26 6) 90 4 10 7) 83 8) 233 7 9) 3205 11 Group Assignment: for Tuesday. 1) You get one of the Powers of Two: 2, 4, 8, 16, 32, etc. 2) You get the Fibonacci Sequence (adding the last two numbers): 1, 1, 2, 3, 5, 8, 13, 21, 34… 3) 13 weeks 4) $0.69 for Thursday. Powers of 11. The first four rows are obvious because each of the numbers in the row are single digits. After that it gets trickier because many of the numbers in the row are double digits. So then, we just carry the ten’s place to the left and add. Week 27 Individual Work: 1) 1 2) 6 3) 2 4) 5 5) 2 6) 4 7) 4 8) 0 9) 6 10) 0 11) 1745 ⅕ 12) 6642 ⅔ 13) 1,344 14) 40,281 Group Assignment: for Tuesday. 1) Cut the number in half, and the whole number above and below that value are the two numbers we square and subtract. Example: half of 19 is 9½. 10 x 10 – 9 x 9 = 100 – 81 = 19. 2) 9 = 25 – 16 13 = 49 – 36 15 = 16 – 1, 64 – 49 17 = 81 – 64 25 = 169 – 144 27 = 36 – 9, 196 – 169 31 = 256 - 225 33 = 49 – 16, 289 – 256 39 = 64 – 25, 400 – 361 47 = 576 – 529 55 = 64 – 9, 784 – 729 63 = 64 – 1, 144 – 81, 1024 – 961 4) “No prime number can be expressed at the difference of two squares in more than one way.” 5) 105 = 121 - 16; 169 - 64; 361 - 256; 2809 – 2704 for Thursday. Hexagonal numbers: 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703… Heptagonal numbers: 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783… Octagonal numbers: 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936… Icosagonal numbers: 1, 20, 57, 112, 185, 276, 385, 512, 657, 820 Week 28 Individual Work: 1) ⅖ 27 25 11) 275 15) 38,808 5) 40 8) 48 1 2) /7 12) 8,844 16) 678 ⅚ 6) 37 9) ⅔ 5 60 13) 26,322 3) /11 1 17) 35 2 10) 5 4) 1 /7 7) ¼ 10 14) 2,394 Group Assignment: for Tuesday. Magic squares 1) 34 2) The sum can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, the corner squares, the four outer numbers clockwise (or counterclockwise) from the corners (e.g., 3+8+14+9), the two sets of four symmetrical numbers (e.g., 2+8+9+15), and more! 3) The two numbers in the middle of the bottom row give the date of the engraving: 1514. for Thursday. 1) 10, 1 2) 15, 18 3) 2, 18 4) 10, 4 5) 99 = 100 - 1; 324 - 225; 2500 - 2401 6) 23 = 144 - 121 7) 81 = 225 - 144 ; 1681 – 1600 8) 945 = 961 – 16; 1089 – 144; 1521 – 576; 3249 – 2304; 5041 – 4096; 9409 – 8464; 25,281 – 24,336; 223,729 – 222,784 Week 29 Individual Work: 3 28 5 21 1) /8 4) ⅖ 13) 591.66 16) 1.8738 20) 0.37 7) 55 10) 1 21 18) 50 5 23 2) ⅓ 5) /9 14) 22.935 21) 0.0007 8) ½ 11) 0.4 17) 1000 1 9 19) 2000 3) 1 ⅘ 6) 1 5 15) 0.08 22) 0.026 40 9) /9 12) 20.12 23) Common factors: 1, 2. Common multiples: 60, 120, 180, 240, 320, 380, 440, etc. 24) Common factors: 1, 2, 4, 8. Common multiples: 24, 48, 72, 96, 120, 144, 168, etc. 25) Common factors: 1, 2, 5, 10. Common multiples: 60, 120, 180, 240, 320, 380, 440, etc. 26) 483 ⅜ 27) 28 Group Assignment: for Tuesday. 2) The final column is always the product 1) The statement is false. of two numbers that are two apart. 3) The factors of 901 are 1, 17, 53, 901. Week #29 Group Assignment: for Thursday. 1) 0, 2, 4, 6, 8 2) 0, 5 3) 2, 6 4) 5 5) 2, 5, 8 6) 1 7) 2+2+31; 3+3+29; 3+13+19; 5+7+23; 5+11+19; 5+13+17; 7+11+17; 11+11+13 8) Sarah is 15 years old 9) Jimmy will be 25 years old Week 30 Individual Work: 1 7 69 21 2 8 1) ¼ 2) 1 /9 3) /10 4) 8 ⅔ 5) 70 6) 100 7) /15 8) 2 ½ 9) /33 10) Counting up by fourths: 7 3/4, 8, 8 ¼, 8 2/4 (which reduces to 8 ½) 11) Counting up by sevenths: 6 5/7, 6 6/7, 7, 7 1/7, 7 2/7. 12) Counting back by thirds: 8 1/3, 8, 7 2/3. 13) Counting back by ninths: 3 2/9, 3 1/9, 3, 2 8/9, 2 7/9, 2 6/9, 2 5/9, 2 4/9. 14) Counting down by tenths: 4, 3 9/10, 3 8/10, 3 7/10, 3 6/10, 3 5/10, 3 4/10, 3 3/10. 15) Counting down by fifths: 3, 2 4/5, 2 3/5, 2 2/5, 2 1/5. 16) 0.56 17) 767.106 18) 22.77 19) 2.9992 20) 0.21 (same as #6) 21) 0.000117 22) 13/1,000 23) 9/10,000 24) 0.003 25) 0.055 26) GCF = 1, LCM = 63 27) GCF = 6, LCM = 36 28) 325 5/12 29) 34 30) 15/44 31) GCF = 18, LCM = 108 32) 16 + 1089; 81 + 1024; 144 + 961; 529 + 576 33 a) 3,599 b) 159,999 c) $6.25; 625; 624 Group Assignment: for Tuesday. Triangle flipping: Move the two bottom outside coins up two rows, and move the top coin to just below the bottom row (but keep it in the center). for Thursday. Five Odd Numbers: 27, 29, 31, 33, 35. Week 31 Individual Work: 6 11 1) /11 5) /24 9) 6 13) 35.44 17) 0.00028 21) 0.173 25) 72 in 29) 3 gal 4 8 2 2) /7 6) /45 10) 3 /7 14) 760.049 18) 0.0805 22) 0.001 26) 4 ft 30) 24 pt 2 3 6 3) ⅔ 7) 1 11) 4 /9 15) 2.574 23) 712 /11 27) 105,600 ft 31) 48 oz 19) 1000 5 4) 2 ⅙ 8) /9 12) 6 ½ 16) 7.999 639 24) 81 28) 8 cups 32) 4 ton 20) 10000 Group Assignment: for Tuesday. Sum of Two Squares • 4225 is equal to the 39th square number plus the 52nd square number. • 4225 is equal to the 25th square number plus the 60th square number. • 4225 is equal to the 16th square number plus the 63rd square number. • 4225 is equal to the 33rd square number plus the 56th square number. Aliquot Sums • The aliquot sum of 15 is 9. • The aliquot sum of 18 is 21. • The aliquot sum of 19 is 1. • The aliquot sum of 1 is 0. • The aliquot sum of 700 is 1036. • The aliquot sum of 102 is 114. Puzzles! • Measuring a Brick. Twenty bricks would be 18’ 11 ½” long. • Lots of Pets. Together, they have 20 pets. for Thursday. Aliquot Sequences • The aliquot sequence for 39 is 39, 17, 1, 0. • The aliquot sequence for 37 is 37, 1, 0. • The aliquot sequence for 9 is 9, 4, 3, 1, 0. • The aliquot sequence for 15 is 15, 9, 4, 3, 1, 0. • The aliquot sequence for 16 is 16, 15, 9, 4, 3, 1, 0. • The aliquot sequence for 45 is 45, 33, 15, 9, 4, 3, 1, 0. • The aliquot sequence for 6 is 6. • The aliquot sequence for 25 is 25, 6.
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