*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.

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1 Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle. Develop the concept of a constant number like pi Graph the relationship of circumference (y) to diameter(x). x y Ordered Pair C/d 1 cm 3.14cm (1, 3.14) 2 cm 6.28 cm (2, 6.28) 3 cm cm (3, 10.42) If you divide the circumference by the diameter what do you discover? What is the ratio of circumference to diameter? Why are all the points you graphed approximately on a straight line? How many segments x will fit on the circumference of the circle? ( FW) x 26

2 Know the formula for the circumference and area of a circle 2. Know common estimates of pi (3.14 or 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. Compare actual measurements with estimated value of pi Given the following information, calculate the circumference and area. r = 15 d = 5 r = 5 d= 10 Choose which approximation (3.14 or 22/7) is easier to use to find circumference. r = 7m d = 12m d = 21m To find area. r = 7 inches r = 16m d = 6cm Measure the diameter and circumference of several circular objects. Use these measurements to calculate pi. How do your measurements compare to the known approximate value of pi? If there is a difference, explain. 3. Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare and explain the similarity between these formulas and the formula for the volume of a rectangular solid. 27

3 Calculate the volume of a rectangular solid Calculate the volume of a triangular prism Given a length of 4 cm, width of 5 cm, and height of 6 cm, calculate the volume. What would happen if the width doubled? If the length doubled? The area of the triangle in a triangular prism is 35 cm 2. Find the volume if the height is 15 cm. Find the volume of a triangular prism with a height of 8 inches and a triangular base with these measurements Find the volume of the triangular prism. 9m 6 7m 5m 6m 28

4 Find the volumes (dimensions are cm). ( FW) Calculate the volume of a cylinder Given a radius of 2.5 cm and a height of 6 cm, find the volume of the cylinder. Given a diameter of 10 meters and a height of 8 meters, find the volume of the cylinder. Which increases the volume more, doubling its height or doubling its radius? Compare and explain the similarity between the volume of a cylinder, triangular prism, and a rectangular solid Using the formula V = Bh, compare and explain the similarities and differences in calculating the volume of a rectangular prism, triangular prism, and a cylinder. 29

5 Students: 2. Students identify and describe the properties of two-dimensional figures. 1. Identify angles as vertical, adjacent, complementary and/or supplementary and provide descriptions of these terms. Adjacent Are 1 and 2 adjacent? ABC and 1? A B 1 2 C Are angle 1 and angle 2 adjacent? 1 2 Vertical Name the vertical angles. Explain why they are called vertical. Name the adjacent angles

6 Supplementary Are these supplementary angles? Complementary Are these complementary angles? Line L is parallel to line M. Line P is perpendicular to L and M. Name the following. If none can be named, leave blank. ( FW) P a b c d L e g f M Complementary Supplementary Vertical Acute Right Obtuse 31

7 *2. Use the properties of complementary and supplementary angles and of the angles of a triangle to solve problems involving an unknown angle. Find the value of 1 in the following figures Line L is parallel to line M. Find the missing angles. ( FW) 65 b L d a c 100 M Find the missing angles. ( FW) a b d 3. Draw quadrilaterals and triangles given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle). Name the triangle and draw a picture given the following information. A triangle with all sides congruent. A triangle with no sides congruent. A triangle that contains 1 right angle. 32

8 A triangle with two congruent sides and at least one right angle. A triangle that contains 1 obtuse angle. A triangle that has all acute angles. Match the name of the quadrilateral with its description. Draw each quadrilateral. A quadrilateral having equal sides but not right angles. A quadrilateral with exactly one pair of parallel sides. A quadrilateral with 90 degree angles and congruent sides. A quadrilateral with two pairs of opposite parallel sides. A quadrilateral with four 90 degree angles and two pairs of opposite congruent sides. Square Rectangle Trapezoid Rhombus Parallelogram 33

9 34

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

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