Answer questions 1-10:

Exploration 1: Introduction to the Geoboard Name: 50pts A geoboard is a manipulative commonly used in the elementary grades. Any geoboard, no matter its size, is simply a grid of pegs each of which represents a point. Any number of shapes can be made by wrapping rubber bands around the pegs. In this on-line format, it is difficult to provide everyone with a geoboard, so instead we will model a geoboard with a square grid of dots. For instance a representation of a 6 X 6 geoboard is shown below. Several copies of these grids are provided at the end of the exploration. Part A: Points. 1. (6 pts) How many different points can be represented in a 1.4 x4 grid of pegs? ii. 5 X 5 grid of pegs? iii. 6 X 6 grid of pegs? iv. 77 grid of pegs? v. If you had a geoboard with dimensions of nx#n, how many points could be represented? 2. (6 pts) Pick a peg near the center of the grid to be your reference \"point.\" If the grid did not have edges, how many \"points\" would be within... i. one peg either horizontally or vertically? ii. two pegs either horizontally or vertically? iii. three pegs either horizontally or vertically? iv. four pegs either horizontally or vertically? v. If you had a geoboard of large enough size and you picked a peg in the middle, how many points would be within n pegs either horizontally or vertically? 3. (6 pts) Below are several shapes that can be created on a geoboard. If you were to make the shape, how many pegs would be needed to make each shape? Write your answer inside each shape below. (Hint: The size of the shape does not matter. Also, not every \"peg\" inside the shape is needed to make the shape.\" Part B: Segments. Consider only a 6 X 6 grid of pegs to answer the following questions. 4. (4 pts) On the diagram below, draw two segments one that is parallel to AB but is twice as long and another that is parallel to CD but is half as long. 5. (4 pts) On the diagram below, draw two segments one that is parallel to EFand another that is perpendicular to EF. 6. (4 pts) Draw a segment that is a perpendicular bisector of GH 7. (4 pts) Select the peg in the upper left hand comer of the grid. From this peg, how many line segments of different lengths can be made? Three example lengths are shown. (Hint: A horizontal segment of one unit will be the same length as a vertical segment of one unit, which will not be the same length as a diagonal segment of \"one\" unit.) Total possible number of different segment lengths = Part C: Angles. Consider only a 6 X 6 grid of pegs to answer the following questions. 8. (4 pts) Consider segmentAB. Draw segments and label the angles with vertices so that ))mZBAC=45 ii)ym/BAD=90 iii)mZBAE=135 iv)mZBAF=180 9. (4 pts) Consider segment AB. Draw segments and label the angles with vertices so that iy mBAC = 45 il) mBAD =90 iii) mBAE = 135 iv) mBAF = 180 10. (8 pts) On the bottom row, make a segment AB. Using AB as one side of the angle and point A as the vertex, form as many different angles as you can.Three examples are shown. Use what you see to answer each question. A= B i. How many angles of different measures can be made? ii. How many of the angles are acute? iii. How many of the angles are obtuse? iv. How many angles are neither acute nor obtuse? \f