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Day #1 Investigation 1.1 In exercise 1-2, find an equivalent fraction for each fraction. Find one fraction with denominator less than the one given. Find another fraction with a denominator greater the one given. 1. 4 12 2. 15 9 In exercise 3 4 insert <, >, or = to make a true statement. 3. 5 12 9 12 4. 15 35 12 20 5. Choose the correct statement. 5 11 3 300 a. b. 6 360 4 360 c. 1 90 3 33 d. 4 360 36 360 Add or subtract fractions with like denominators. 6. 4 8 9 7 7. 15 15 10 10 8. Evaluate 1 x for 8 5 x 8 Add or subtract mixed numbers with like denominators. 9. 2 6 7 5 10. 7 7 7 4 5 3 9 9 11. 5 7 3 12. 9 2 4 10 3 5 5 2
Day #2 Investigations 1.2-1.4 1. Decide whether each angle is closest to 30, 60, 90, 120, 150, 180, 270, or 360 without measuring. Then name the angle as acute, right, obtuse, or straight. For exercises #2 5, write an equation and find the measure of the angle labeled x, without measuring 2. 3. 4. 5. 3
For exercises #6 10, find the angle measures. Use the diagram of the protractor below. JVK and KVL are called adjacent angles because they have a common vertex and a common side. 6. m JVM 7. m KVL 8. m KVM 9. The complement of JVK 10. The supplement of JVK Day #3 Investigation 1.5 1. Draw an angle for each measure. Include and arc indicating the turn. If you need more space, use a clean sheet of paper and attach. a. 45 b. 25 c. 180 4
In exercises #2-3, draw the polygons described. If there is more than one (or no) shape you can draw, explain how you know that. If you need more space, use a clean sheet of paper and attach. 2. Draw a rectangle. Side lengths of 8 cm and 4 cm. 3. Draw a triangle. AB = 2 in. AC = 1 in. BAC = 75. Add or subtract fractions with unlike denominators. 4 3 11 5 4. 5. 5 4 12 6 1 3 6. Evaluate x for x. 7 4 7. The school track is 8 7 mile in length. Sherry ran 3 2 mile. How much farther does she have to go to get all the way around the track? 5
Day #4 Investigation 2.1 1. Without measuring, find the measure of the angle labeled x in each regular polygon. In exercises #3-4, draw the polygons described. If there is more than one (or no) shape you can draw, explain how you know that. If you need more space, use a clean sheet of paper and attach. 2. Draw a triangle. BAC = 75 3. Draw a trapezoid PQRS. QPS = 45. and ACB = 75. RQP = 40. PS = 1 in. PQ = 2 in. EXTENSION Find the value of x. 4. 5. 128 (3x + 5) (5x + 2) 40 6
Day #5 Investigation 2.2 For exercise #1 6, without using a protractor, find the measure of each angle labeled x. 1. 2. 3. 4. 5. This figure is a trapezoid. 6. This figure is a regular hexagon. EXTENSION 7. Kele claims that the angle sum of a polygon he has drawn is 1660. Can he be correct? Explain. 7
SPIRAL Subtract mixed numbers with unlike denominators. 9. 7 9 5 3 10. 8 10 3 6 8 7 4 7 Day #6 Investigation 2.4 1. What is the sum of the exterior angles of any polygon? 2. Find the measure of an interior angle of a regular heptagon.. 3. Find the measure of an exterior angle of a regular heptagon. 4. Find the indicated angle measure 5. Without using a protractor, find the measure of the missing angle in each triangle. a. b. c. 8
EXTENSION If doing extensions, you may skip #s 1, 2, 3. 6. An exterior angle of a regular polygon is 24. Find the number of sides of the polygon. 7. Write an equation to represent the situation and solve to find the size of the missing angle. SPIRAL Multiply fractions and mixed numbers. 9. 1 3 2 3 5 10. 2 2 5 5 4 6 11. A standard paper clip is paper clips be? 1 1 in. long. If you laid 75 paper clips end to end, how long would the line of 4 Day #7 Investigation 3.1 For exercises #1 4, use the given side lengths. If it is possible to make a triangle, explain why. If a triangle is not possible, explain why. 1. 5, 5, 3 2. 8, 8, 8 3. 7, 8, 15 4. 5, 6, 10 9
5. From exercises #1-4, which sets of side lengths can make each of the following shapes? A. an equilateral triangle (all three sides are equal length) B. an isosceles triangle (two sides are equal length) C. a scalene triangle (no two sides are equal length) D. a triangle with at least two angles of the same measure. For exercises #6 and #7, draw the polygons described to help you answer the questions. 6. Suppose you want to build a triangle with three angles measuring 60. What do you think must be true of the side lengths? What kind of triangle is this? 7. Suppose you want to build a triangle with only two angles the same size. What do you think must be true of the side lengths? What kind of triangle is this? 8. Giraldo is building a tent. He has two 3-foot poles. He also has a 5-foot pole, a 6-foot pole, and a 7-foot pole. He wants to make a triangular-shaped doorframe for the tent using the 3-foot poles and one other pole. Which of the other poles could be used for the base of the door? 10
9. Which of the following shaded regions is not a representation of 12 4? A. B. C. D. EXTENSION 10. Which of these descriptions of a triangle ABC are directions that can be followed to draw exactly one shape? A. AB = 2.5 in., AC = 1 in., B = 40 C. AB = 2.5 in., B = 60, A = 40 B. AB = 2.5 in., AC = 1 in., A = 40 D. AB = 2.5 in., B = 60, A = 130 SPIRAL Divide fractions and mixed numbers. 11. 1 2 3 12. 4 5 3 5 3 2 4 6 13. Burger barn has ground beef? 2 1 46 pounds of ground beef. How many -pound burgers can be made using all the 3 3 11
Day #8 Investigation 3.3 For exercises #1 4, use the given side lengths. If it is possible to make a quadrilateral, explain why. If a quadrilateral is not possible, explain why. 1. 5, 5, 8, 8 2. 5, 5, 6, 14 3. 8, 8, 8, 8 4. 4, 3, 5, 14 5. From exercises #1-4, which sets of side lengths can make each of the following shapes? a. a square b. a quadrilateral with all angles the same size c. a parallelogram d. a quadrilateral that is not a parallelogram 6. A quadrilateral with four equal sides is called a rhombus. Which set(s) of side lengths from exercises #1 4 can make a rhombus? 7. A quadrilateral with just one pair of parallel sides is called a trapezoid. Which set(s) of side lengths from exercises #1 4 can make a trapezoid? 8. Compare the three quadrilaterals below. a. How are all three quadrilaterals alike? b. How does each quadrilateral differ from the other two? 12
EXTENSION 9. Think about your polystrip experiments with triangles and quadrilaterals. What explanations can you now give for the common use of triangular shapes in structures like bridges and towers for transmitting radio and television signals? 10. If you choose five numbers as side lengths, can you always build a pentagon? Explain. Day #9 Investigation 3.4 1. In the diagram below. Line T is a transversal to parallel lines L 1 and L 2. a. Find the degree measures of angles labeled a g. b. Name the pairs of opposite or vertical angles in the figure. 2. In the parallelogram, find the measure of each numbered angle. 13
3. Use the given drawing to answer the questions.. a. What are the measures of angles a, b, c, and d? 30 b. Explain how you found the missing angles. Evaluate. NO CALCULATOR 4. - 23 + 9 = 5. -19 + (-21) = 6. 1 + (-30) = 7. -10 (-9) = 8. 9 15 = 9. 22 (-8) = 10. 8-5 = 11. - 4 7 = 45 72 12. -6 (-3) = 13. -32 8 = 14. = 15. = 9 8 14