Name. STAR CITY Math / Geometry / No work = No Credit!!!!! Teacher Period

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1 STAR CITY Math / Geometry / No work = No Credit!!!!! 1. Highway 270 from Hot Springs to Mena passes through the Ouachita National Forest. The National Park Service is creating signs like the one shown below. Name Teacher Period 2. Mrs. Phillips wants to decorate her bulletin board with various street signs for a lesson on highway safety. She has a square piece of poster board from which to cut her sign. These signs can be opened during the spring when deer crossing the highway becomes a danger to drivers. Each half of the sign is an isosceles right triangle with equal legs measuring 1 meter. What length hinge, rounded to the nearest tenth of a meter, will be needed for the signs? A. 1.0 m B. 1.4 m The largest stop sign that can be cut from the poster board is a regular octagon with sides that are each 2 feet long. Approximately how long are the sides of the poster board? A. 1.4 ft. B. 4.8 ft. C. 6.2 ft. D ft. C. 1.7 m D. 2.0 m 1

2 STAR CITY Math Geometry No work = No Credit!!!!! 3. The following are instructions for installing speakers in a family room. All speakers should be placed the same distance from the main seating position. Once your main seating position has been determined, draw an imaginary radius with your seat at the center point of the circle and your center channel speaker, CC, at the edge as shown below. 4. Samuel s swimming pool is in the shape of a 20 foot square. To the nearest foot, what is the greatest distance he can swim across the pool in one direction? A. 20 ft. B. 28 ft. C. 80 ft. D. 400 ft. Use the figure below to answer question 5. CC = Center Channel Left = Left Main Right = Right Main LSS = Left Surround RSS = Right Surround What is the approximate distance from the center channel speaker to the right surround sound speaker? A. 6.5 ft. B. 9.2 ft. C ft. 5. What is the approximate length of x? A. 8.5 cm B. 9.8 cm C cm D cm D. 13 ft. 2

3 STAR CITY Math Geometry No work = No Credit!!!!! Use the figure below to answer question The size of a television is the length of the diagonal of the square screen. If a salesman wants to sell Brian a 22" television, what are the length and width of the television screen rounded to a tenth of an inch? A in. by 11.0 in. B in. by 15.6 in. C in. by 19.0 in. D in. by 15.6 in. 6. ΔABC represents a triangular base. If AD = DC, what is the m A? A. 15 B Roxie wants to determine the diameter of a large heating duct. She places a carpenter s square up to the surface of the cylinder, and the length of each tangent segment is 10 inches. What is the diameter to the nearest hundredth of an inch? C. 45 D What length of pipe is needed for a diagonal irrigation line across a square field that is 250 ft. long on each side? A ft. B ft. C ft. D ft. A in. B in. C in. D in. 3

4 STAR CITY Math Geometry No work = No Credit!!!!! 10. Bethany has planted a small garden as shown below. She decides to put a fence around the garden. If the fence forms a right triangle, about how much fencing is needed? A. 2.8 feet B. 6.8 feet C. 7.5 feet D feet 4

5 STAR CITY Open-Response / Geometry / No work = No Credit!!!!! Name Teacher Period GEOMETRY OPEN-RESPONSE ITEM A A. Jamal will be asking the city to build a nature area between two parallel streets, Hillview Road and Thompson Avenue. The triangle in the figure below represents the nature area. Jamal needs to include more information in the plan he is presenting. 1. Jamal will need to know the measure of ABC. What is the measure of ABC? Show or explain all of your work even if you use mental math or a calculator. A gate will be placed 90 ft. from point B at point D. D is the midpoint of BE. Jamal also knows the distance from point E to point F is 80 ft. as shown in the figure above. 2. For his plans Jamal will need to determine the length of BC. Determine the length of BC. Show or explain all of your work even if you use mental math or a calculator. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 5

6 STAR CITY Student Answer Document / Geometry / No work = No Credit!!!!! Name Teacher Period A 6

7 GEOMETRY OPEN-RESPONSE ITEM A (T.2.G.5B) A. Jamal will be asking the city to build a nature area between two parallel streets, Hillview Road and Thompson Avenue. The triangle in the figure below represents the nature area. Jamal needs to include more information in the plan he is presenting. 1. Jamal will need to know the measure of ABC. What is the measure of ABC? Show or explain all of your work even if you use mental math or a calculator. A gate will be placed 90 ft. from point B at point D. D is the midpoint of BE. Jamal also knows the distance from point E to point F is 80 ft. as shown in the figure above. 2. For his plans Jamal will need to determine the length of BC. Determine the length of BC. Show or explain all of your work even if you use mental math or a calculator. BE SURE TO LABEL YOUR RESPONSES 1 AND 2.

8 Score RUBRIC FOR GEOMETRY OPEN-RESPONSE ITEM A (T.2.G.5B) Description 4 Student earns 5 points. Part 1 answer of 135 contains the correct label of degrees. Part 2 answer of etc. is labeled in Ft. Response contains no incorrect work. 3 Student earns 4 points. 2 Student earns 2 ½ - 3 points or Student earns 2 points if 1 point is from Part 1 and 1 point is from Part 2 or Student earns 2 points if both points are from Part 2. 1 Student earns 2 points if both points are from Part 1 or Student earns ½ - 1 ½ points or Some minimal understanding of is shown. Ex: = 260 only Ex: Triangle CBF is a triangle only. 0 Student earns 0 points. No understanding is shown.. Ex: 260 with no support only B No response. A score of B will be reported as NA (No Attempt Zero Score). Note: Correct labels are an issue only at the 4 level.

9 Solution and Scoring Part Points 1 2 points possible 1 point: Correct Answer: 135 (degrees) AND Note: Do not give credit if an incorrect procedure is evident. 1 point: Correct procedure shown or explained: Note:Work may contain a calculation or copy error. Explanation may or may not contain the fact that the lines are parallel or the names of the types of angles involved Give credit for the following or equivalent: Ex: Since the lines are parallel, alternate interior angles are congruent. Therefore m CBD = m C = 45. Since ABC and CBD are supplementary, m ABC = (180 45) degrees. Ex: Angle C and angle ABC are same side interior angles, and they add up to 180. So since angle C is 45, angle ABC must be 135. Ex: CBD and ABC are supplementary, so m ABC = 135 degrees. Ex: Since angle CBF and angle ABC are a linear pair, angle ABC is 135 degrees. Ex: = m ABC. Ex: = 135. (the measure of an exterior angle of a triangle = sum of other 2 angle measures) 2 3 points possible 1 point: Correct Answer:260 2 or (ft.) AND Note:Do not give credit if there is evidence of incorrect procedure used to find the answer. Also, answer may be rounded, and decimal will depend upon method used. Do not give credit if rounding is done incorrectly. 2 points: Correct and complete procedure shown or explained: Note: Work may contain a calculation or copy error. Give credit for the following or equivalent: Uses properties of triangles: Ex: BF = = 260. Triangle BCF is a Triangle, so if one of the legs is 260, the hypotenuse is Uses the Pythagorean theorem: Ex: 2(90) + 80 = 260. BCF is an isosceles right triangle. (260)² + (260)² = (BC)² = (BC)² = (BC)² = BC

10 Or Uses Trigonometry functions: (cos 45 =.7071 = 260/BC, sin 45 =.7071 = 260/BC) Ex: BE is 180 since D is the midpoint, so the length of a side of the triangle is = 260. m CBD = 45 cos 45 = 260/BC.7071 = 260/BC BC = point: Work is incomplete (with answer correct or incorrect due to a calculation error). Or Procedures are correct: Ex: = 260 with answer of ½ point: Answer incorrect due to 1 procedural error. Some correct procedure shown or explained. Note: Work must get beyond = 260 only or only. Ex: BF = = 170 (procedural error omitting a segment) Triangle, so the hypotenuse is (2 correct procedures).

11 STAR CITY Math / Geometry / No work = No Credit!!!!! Answer Key and Alignment Answer Source SLE 1. B TLI T.2.G.5b 2. B TLI T.2.G.5b 3. B TLI T.2.G.5b 4. B TLI T.2.G.5b 5. C TLI T.2.G.5b 6. C TLI T.2.G.5b 7. C TLI T.2.G.5b 8. D TLI T.2.G.5b 9. A TLI T.2.G.5b 10. B TLI T.2.G.5b