Answer Keys for Calvert Math

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nswer Keys for Calvert Math Lessons 1 40 101 120 0613-0615

1 nswer Keys for Calvert Math Lessons CONTENTS Math Textbook...63 Math Workbook...69 Math Lesson Manual...72

3 nswer Keys Math Textbook Lessons Geometry asics Chapter 8 1 angle 2 ray 3 ray 4 line segment 1 4; rays CD, CG, CF, and CE 2 angles DCG, GCF, ECF, ECD 3 yes 4 rays CG and CD 5 nswers will vary. ny four of the following are correct: JLI, ILK, HLK, JLH, JLK, and HLI 6 rays LJ, LI, LK, and LH 7 nswers will vary. 8 a 9 b 10 $ , , R3 14 2,155 R R ngles 1 acute, 20 2 obtuse, c 2 b 3 c See student s work Solution: 1 /4 min = x /60 min 60 4 = 15 in one hour 13 right angle Cumulative Review 1 3,674; 3, ,800,000; 1,000, , , > 8 < 9 = 10 2, , $ $ , , , ,202 R R , , , Commutative Property shrubs 32 $ pints 8.3 Triangles 1 scalene, obtuse 2 isosceles, acute 3 scalene, right 4 equilateral, acute 1 60, 60, , 60, , 35, ; 180 divided by 3 equals weeks shelves 14 15, , Commutative Property 16 56, ssociative Property 17 1, Identity Property 18 0, Zero Property 19 3, Distributive Property 20 15, Commutative Property 8.4 Polygons 1 yes 2 yes 3 no 4 yes 5 no 6 yes 1 pentagon 2 hexagon 3 triangle 4 quadrilateral 5 triangles, quadrilaterals 6 four congruent sides and right angles; ll are regular. 7 8 See student s work. 9 nswers will vary. 8.5 Quadrilaterals 1 rectangle, square 2 square, rhombus 3 square and a rectangle are alike because both have right angles and two sets of congruent, parallel sides, and they are different because a square has four congruent sides. 1 trapezoid 2 square 3 quadrilateral 4 parallelogram or rectangle 5 yes 6 yes 7 no 8 yes 9 no 10 yes ft ft; a rectangle 63

4 Math Textbook nswer Key Lessons Problem-Solving Strategy: Make a Drawing 1 4 blocks north, 2 blocks east Solve 1 Tom, Judy, Lee 2 55 inches 3 Monday: tomato, Tuesday: vegetable, Wednesday: chicken noodle, Thursday: mushroom, Friday: broccoli 4 8 boxes 5 January 20 Mid-Chapter Review 1 3 See student s work. 4 isosceles, right 5 scalene, right 6 equilateral, acute 8.7 Circles 1 C 2 QR 3 ST or QR 4 CR, CQ 1 2 See student s work mm m 5 1/4 of a yd cm in cm ft 10 Double the radius. 11 Find 1/2 of the diameter. 12 Yes, because the diameter connects two points on the circle cuts 14 No. Two radii may form an angle of any degree. When the angle formed is 180º, then it is a diameter. 8.8 Congruence 1 d 2 b 3 c 1 b 2 a 3 c 4 Yes, because the keys are the same size and shape. 5 No, because they are not the same shape. 6 a and b 7 Yes, because both have the same radius, so they are the same size, and they are the same shape because both are circles. 8.9 Symmetry 1 M 2 3 D 4 T No, because a chord does not have to pass through the center like the diameter. 5 6 See student s work. There are 12 different pentominoes. Extension

5 Math Textbook nswer Key Lessons vertical line symmetry:, H, I, M, O, T, U, V, W, X, Y, words will vary; horizontal line symmetry:, C, D, E, H, I, K, O, X, words will vary 8.11 Three-Dimensional Figures 1 rectangular prism 2 sphere 3 cone 1 cube 2 rectangular prism 3 sphere 4 Three-Dimensional Figure Rectangular prism Cube Square pyramid Sphere Number of Faces Number of Edges Number of Vertices Transformations 1 translation 2 reflection 3 reflection 4 rotation 1 reflection 2 translation 3 translation 4 rotation reflection 9 rotation and translation 10 nswers will vary. Possible answer: rotation in figure skating. 5 7 See student s work. 8 See student s work; rectangular prism 9 See student s work; cylinder Test Prep 10 a 11 d 12 $ $1, cases miles ,287,217 newspapers 10 moves Chapter 8 Review Language and Concepts 1 ray 2 pentagon 3 protractor 4 polygons 5 translation 6 square 7 rhombus Skills and 8 line segment 9 angle 10 angle 11 ray 12 obtuse 13 acute 14 acute 15 isosceles, right 16 isosceles, obtuse 17 equilateral, acute octagon 20 pentagon 21 triangle ft m 24 yes 25 no 26 E 27 Y 28 V 29 H 30 math, English, history 31 See student s drawing; 5 faces, 8 edges 65

6 Math Textbook nswer Key Lessons Chapter 8 Test 1 lines HI and FG 2 15 angles, angles JLF, FLK, HNJ, HNK, KNI, HMG, GMI, FMI, KLG, HMF, JLG, FLG, JLK, IMH, JNI 3 3 lines, lines FG, JK, HI 4 7 See student s work. 8 obtuse, isosceles 9 obtuse, scalene 10 right, isosceles no 15 yes, trapezoid 16 no 17 no 18 yes rectangles; See student s work. 2(1) + 2(11) = 24 2(2) + 2(10) = 24 2(3) + 2(9) = 24 2(4) + 2(8) = 24 2(5) + 2(7) = 24 Change of Pace 1 yes; See student s work. 2 yes; See student s work. 3 no Cumulative Test 1 a 2 c 3 c 4 b 5 d 6 d 7 c 8 b 9 b 10 a 2(6) + 2(6) = 24 Mind uilder Rectangle perimeter is 18 units. Chapter Perimeter of Polygons 1 20 m in cm m 2 56 yd cm 4 3/4 mi m 6 34 in. 7 5 cm 5 cm 5 cm 5 cm 5 cm 9.2 Circumference 1 radius 4 ft, diameter 8 ft 2 radius 6 m, diameter 12 m 3 radius 1 1/2 in., diameter 3 in mi, 48 mi 2 22 m, 66 m cm, 546 cm ft, 37.2 ft ft cm mm cm ft m ft in. 13 The diameter of her table would be about 3 1/3 feet; See student s work

7 Math Textbook nswer Key Lessons rea of Rectangles cm /16 cm cm m cm in ft yd m cm ft yd 2 or 54 ft m m yd ,600 ft Perimeter and rea of Complex Figures 1 short side = 3 mm, long side = 8 mm 2 each side = 3 in. 1 = 141 cm 2, P = 52 cm 2 = 108 ft 2, P = 58 ft 3 = 133 cm 2, P = 48 cm 4 = km 2, P = 87 km 5 = 40 yd 2, P = 30 yd 6 = 89.5 mm 2, P = 75 mm Note: See the drawing below for more accurate labelling of the figure. 7 8 See student s work. Test Prep 9 b 9.5 Problem-Solving Strategy: Draw It 1 2 links 2 D C 9.6 rea of Parallelograms Exploration Exercise 2 approximately 15 square units 3 5 units 4 3 units 6 rectangle, 15 square units, yes 7 15 square units; Multiply the base by the height to find area square units 2 18 square units 3 15 square units 4 base = 9 in., height = 7 in., = 63 in. 2 5 base = 3.1 yd, height = 4 yd, = 12.4 yd 2 6 base = 18 m, height = 2 m, = 36 m cm mm m 2 4 height = 4 ft 4 ft 9 ft 5 1,674 ft 2 6 Cut a piece off the parallelogram to turn it into a rectangle. 7 Yes, the plywood is 32 ft 2 and the paint will cover 50 ft 2. 8 < 9 = 10 > , 0.9, , 1.46, 1.64 Room : Peg, Room : Justine, Room C: Margaret, Room D: Connie, Room E: Rosa, Room F: Yvonne 9.7 rea of Triangles Exploration Exercise 2 base = 5 units, height = 3 units, area = 15 square units 4 triangles square units; Each is half of the parallelogram. 1 base = 10 ft, height = 18 ft, area = 90 ft 2 2 base = 5 m, height = 4.2 m, area = 10.5 m 2 3 base = 7 cm, height = 2 1/2 cm, area = 8 3/4 cm km yd in. 2 4 See student s work; rea = 15 m 2. Solve 1 nswers will vary. 2 1/6 hour, 10 minutes 3 12 oz m 2 67

8 Math Textbook nswer Key Lessons ,740 ft in. 2 ; Subtract the area of the triangle from the area of the square. 5 in. 5 in. Square: = = 100 in. 2 Triangle: = 1/2(10 10) = 50 in. 2 Square Triangle 10 in. 10 in. = = Unshaded area = 50 in in. 7 4 cm 8 The area of a triangle is half the area of a parallelogram; Examples will vary. Mid-Chapter Review 1 = yd 2, P = 26.6 yd 2 = 14 m 2, P = 18 m 3 = 18 ft 2, P = 20 ft yd ft in. Cumulative Review 1 55, $ , , , / / / / /2 19 3/4 20 7/ / /6 24 7/8 25 5/8 26 1/9 27 = 28 > 29 > 30 < 31 < 32 > in cm m 9.8 Problem-Solving Strategy: Using Venn Diagrams Solve cookies 7 5 melons 11 ham 7 3 cheese Test Prep 9 a Chapter 9 Review Language and Concepts 1 circumference 2 volume 3 square 4 triangle 5 pi 6 parallelogram Skills and cm 8 10 in mi in cm m yd cm m yd cm mm 2 19 triangular prism 20 cylinder 21 cube yd 2, 27 yd in. 2, 320 in /3 ft 2, 1/27 ft , m 2, 2,306.4 m cm, 225 cm m 3 28 fifteenth students Chapter 9 Test cm m 3 58 cm in cm yd 7 35 cm in m cm 2, 20 cm in. 2, 40 in ft 2, 180 ft ft students 3 $0.24, $ / shelves 6 8 eggs 7 15 cups 8 75 minutes 9.9 Three-Dimensional Figures and Nets 1 c 2 b 3 a 4 d 1 c 2 a 3 d 4 b

9 nswer Keys Math Workbook Lessons Chapter 8 15 ngle should be greater than 90 degrees. Practice 120 Geometry asics 1 6: E, C,, GD, GF, GH 2 8: E, EC, CG, G, GF, GH, HGD, DGF 3, D 4 E, C 5 C, FH 6 D 7 See student s work. Sample solution: H I J E C 1 11 large, 8 small 2 78 boxes G D (15 if you include the straight angles G, EGF, and CGD). In the sample solution, the other 12 angles are GE, GC, GF, GD, EGC, EG, EGD, CG, CGF, GF, GD, and FGD. Practice 121 ngles 1 greater than 2 greater than 3 greater than 4 less than 5 less than 6 greater than 7 obtuse 8 acute 9 right 10 right 11 acute 12 obtuse See student s work. Sample solutions given: 13 ngle should be less than 90 degrees. C 14 ngle should be exactly 90 degrees. F E G F Practice 122 Measuring and Drawing ngles 1 10 ctual measurements may vary slightly See student s work. Practice 123 Triangles 1 5 ctual measurements may vary slightly. 1 = 68, = 65, C = 47, = 3.2 cm, C = 4.2 cm, C = 4 cm; acute, scalene 2 D = 70, E = 70, F = 40, DE = 3 cm, EF = 4.5 cm, FD = 4.5 cm; acute, isosceles 3 G = 42, H = 35, I = 102, GH = 5.2 cm, HI = 3.6 cm, IG = 3.1 cm; obtuse, scalene 4 J = 120, K = 30, L = 30, JK = 2.5 cm, KL = 4.3 cm, LJ = 2.5 cm; obtuse, isosceles 5 M = 45, N = 90, O = 45, MN = 3 cm, NO = 3 cm, OM = 4.2 cm; right, isosceles 6 30, acute 7 20, obtuse 8 50, obtuse 9 90, right 10 75, acute 11 equilateral 12 scalene 13 isosceles Practice 124 Polygons 1 yes, triangle 2 yes, hexagon 3 yes, pentagon 4 no 5 no 6 no 7 yes, pentagon 8 no 9 no 10 yes, quadrilateral 11 See student s work , , ,082 Practice 125 Quadrilaterals 1 rectangle 2 trapezoid 3 parallelogram 4 parallelogram 5 square 6 rhombus 7 trapezoid 8 rectangle 9 15 cm 10 no, trapezoid Practice 126 Problem-Solving Strategy: Make a Drawing 1 Sail 48 miles west and 12 miles south. 2 highway to Mayville and boat to Ocean City or train to Smithville and plane to Ocean City 3 Take goose over, then take corn; bring goose back and take fox over. Then return for goose. 69

10 Math Workbook nswer Key Lessons Practice 127 Circles 1 center 2 diameter 3 radius 4 EF 5 radii 6 10 cm 7 10 in See student s work. Radius should go from the center of the circle to any point on the circle. Diameter should go through the center of the circle and end on opposite points on the circle R27 2 $53, , /6 5 7/ /4 Practice 128 Congruence 1 C 2 H 3 I 4 J 5 6 F 7 8 D 9 G 10 E Practice 129 Symmetry 1 yes 2 yes 3 no 4 yes 5 no 6 no flip 12 slide 13 turn = 3 in., CD = 7 in., EF = 2 in. 18 Z = 90, X = 50, Y = 40 Test 134 Chapter 8 Test Prep 1 a 2 a 3 b 4 b 5 a 6 b 7 c 8 a 9 c 10 b Chapter 9 Practice 135 Perimeter of Polygons 1 70 cm 2 32 in ft 4 30 yd in m 7 72 km 8 75 in. 9 5 yd 10 n = (13 1/ /2) 2; 62 ft 11 n = 15 (6 + 5); 4 m 12 n = (8 1/2 + 11) 2; 39 in. 13 n = ( ) 2; 212 yd 14 n = ( ) 2; 80 ft 15 n = ( ) 2; 346 yd , 3, Enrichment 130 Symmetry 1 yes 2 yes 3 no 4 no 5 yes 6 yes 7 8 Please note that H has two possible lines of symmetry and O has an infinite number of lines of symmetry. Practice 131 Transformations 1 rotation 2 reflection 3 translation 4 reflection 5 translation 6 translation or rotation 7 reflection R /8 Practice 132 Three-Dimensional Figures 1 rectangular prism or cube 2 triangular prism 3 cylinder 4 rectangular prism 5 square pyramid 6 sphere 7 cone 8 rectangular pyramid 9 sphere 10 cylinder 11 cube Review 133 Chapter 8 Review 1 4; E, EC, CED, DE 2 4; E, E, EC, ED E and CED 55º, DE and EC 125º 5 triangle 6 parallelogram 7 trapezoid 8 10 cm 9 25 m 10 Yes, they are the same size and the same shape. Practice 136 Circumference 1 r = 6 in., d = 12 in. 2 r = 9 ft, d = 18 ft 3 r = 2.5 ft, d = 5 ft 4 12 ft 5 48 cm 6 54 yd ft mm km ft km in in., 94.2 in. 14 d = 6 in., C = in. 15 d = 18 in., C = in. Enrichment 137 Finding Pi 1 3 See student s work. 4 3 times, 3 times 5 7 See student s work. 8 nswers round to 3. 9 nswers round to Pi is related to C d by the circumference being about 3 times the diameter, which is equal to about 3.14, the value of pi. 11 oth measure the distance around a shape; perimeter is the distance around a polygon, and circumference is the distance around a circle. 12 The circumference is about 18 yards because 2 3 = 6 (the diameter). Pi is approximately 3, so 3 6 = 18 yards ft 14 a Greek letter with a value of about 3.14; C d; to find circumference, radius, or diameter 15 4 in.; 2 in.; See student s work. The diameter is approximately equal to 12 3, since π = The radius would be half of the diameter. 16 See student s work. nswer should include measuring the approximate circumference of the Earth from satellite or space exploration data, and then dividing by pi times 70

11 Math Workbook nswer Key Lessons Practice 138 rea of Rectangles sq cm 2 12 sq in sq mi sq in. 5 8 sq km 6 24 sq m sq yd /8 sq in /2 sq in sq ft sq m sq km 13 13,000 sq yd sq yd sq yd 1 < 2 > 3 = 4 4 yd 5 1 yd 2 ft 6 4 d 4 h Practice 139 Perimeter and rea of Complex Figures 1 P = 38 cm; = 66 sq cm 2 P = 116 yd; = 651 sq yd 3 P = 38 mm; = 48 sq mm 4 P = 39 ft; = 78.5 sq ft 5 P = 42 m; = 62 sq m 6 P = 46 in.; = sq in. 7a 1,150 sq ft b 1,450 sq ft c 2,600 sq ft Practice 140 rea of Parallelograms 1 3, sq mm sq yd 4 72 sq ft 5 n = ; 2,500 sq ft 6 n = 84 12; 7 cm Practice 141 rea of Triangles 1 6, sq ft 3 1,488 sq km 4 48 sq yd sq in. 6 n = 1/ ; sq in = 1/2 10 h; 20 in. Practice 142 Problem-Solving Strategy: Using Venn Diagrams 1 27 swim only 2 15 just football 3 20 both 4 10 red and white flowers 1 1, 5, 7, 35 2 prime 3 1, 2, 4, 8, Practice 143 Three-Dimensional Figures and Nets Two Square Feet Review 148 Chapter 9 Review 1 20 ft yd m in m yd 7 2 sq mi 8 1,058 sq ft 9 56 sq km sq mm sq in sq m 13 3 cu cm 14 8 cu cm cu cm sq cm sq cm sq yd 19 cube 20 cone 21 5 cm students Test 149 Chapter 9 Test Prep 1 c 2 c 3 d 4 a 5 b 6 c 7 c 8 b 9 c 10 d 71

12 nswer Keys Math Lessons Lesson Manual LESSON 102 ray: an endpoint and all of the points that continue forever in a certain direction from that endpoint line: a straight path of two points that continues on forever in two directions line segment: a part of a line with two endpoints LESSON 103 acute angle: measure greater than 0 degrees but less than 90 degrees right angle: angle of 90 degrees obtuse angle: measure greater than 90 degrees but less than 180 degrees octagon 3 6 LESSON 105 LESSON 109 Skill Development Equilateral triangle has both. Regular pentagon has both. Rectangle has both. Parallelogram has rotational. Regular hexagon has both. Right triangle has neither. lock letters have rotational. Regular octagon has both. Circle has both. 3 lines of symmetry LESSON 110 LESSON 113 See p. 230, Calvert Math, for examples. LESSON perimeter: 44 cm; area: 112 cm 2 2 perimeter: 16.2 ft; area: 12.6 ft 2 LESSON 118 LESSON Skill Development 1 Soccer was the most popular sport. 2 Chocolate- Jelly covered C 72

Summer Solutions Problem Solving Level 4. Level 4. Problem Solving. Help Pages

Summer Solutions Problem Solving Level 4. Level 4. Problem Solving. Help Pages Level Problem Solving 6 General Terms acute angle an angle measuring less than 90 addend a number being added angle formed by two rays that share a common endpoint area the size of a surface; always expressed