Exemplar for Internal Achievement Standard. Mathematics and Statistics Level 1

Transcription

1 9103 Exemplar for Internal Achievement Standard Mathematics and Statistics Level 1 This exemplar supports assessment against: Achievement Standard 9103 Apply right-angled triangles in solving measurement problems An annotated exemplar is an extract of student evidence, with a commentary, to explain key aspects of the standard. These will assist teachers to make assessment judgements at the grade boundaries. New Zealand Qualification Authority To support internal assessment from 014 NZQA 014

2 9103 Grade Boundary: Low Excellence 1. For Excellence, the student needs to apply right-angled triangles, using extended abstract thinking, in solving measurement problems. This involves one or more of: devising a strategy to investigate or solve a problem, identifying relevant concepts in context, developing a chain of logical reasoning or proof, forming a generalisation and also using correct mathematical statements or communicating mathematical insight. This student s evidence is a response to the TKI assessment resource What s the Angle? This student has devised a strategy to determine, the dimensions of the sail (1) and the minimum height of the van (). Correct mathematical statements have been used throughout the response. For a more secure Excellence, the student would need to correctly calculate the minimum length of the van. NZQA 014

3 Student 1: Low Excellence Anchor point A (AB) AB tan 0 = 9 9tan0 = AB AB = 3.8m Length of sail edge (AC) a + b = c AC = AC = AC = AC = 9.58m (dp) Length of sail edge (AD) The angle at which to cut the sail fabric at the corner (CDA) AD = tan D = AD = D = tan 1 3 AD = D = AD = 10.04m (dp) The sail is a right angled triangle with sides 3m, 9.58m and 10.04m. The angles are 90 o, and The length of the pole will be = 5.78m The minimum width of the van is.4m DC sin13 = 5.78 DC = 5.78sin 13 DC =1.30m Height = 130cm The minimum height of the van is 130cm AC cos13 = 5.78 AC = 5.78 cos13 = 5.63m BC = BC = BC = 6.1m The minimum length of the van is 6.1m

4 9103 Grade Boundary: High Merit. For Merit, the student needs to apply right-angled triangles, using relational thinking, in solving measurement problems. This involves one or more of: selecting and carrying out a logical sequence of steps, connecting different concepts and representations, demonstrating understanding of concepts, forming and using a model and also relating findings to a context, or communicating thinking using appropriate mathematical statements. This student s evidence is a response to the TKI assessment resource What s the Angle? This student has selected and carried out a logical sequence of steps to correctly determine most of the dimensions of the sail (1) and the minimum dimensions of the van without including the extra.5 m in the length of the pole (). Appropriate mathematical statements have been used throughout the response. To be awarded Excellence, the student would need to determine all dimensions of the sail, consider the extra.5 m in the length of the pole and identify the minimum dimensions of the van. NZQA 014

5 Student : High Merit 1. AB tan 3 = 8 AB = tan 3 x 8 AB = 3.4m (1dp). AC = CB + AB AC = AC = AC = 8.7m (1dp) tan E = 8.7 E = tan 1 E = (1dp) The Sail 1 x sin 13 = AB x = sin13 x 3.4 = 0.76m AD cos 13 = AB AD cos13 = 3.4 AD = cos13 x 3.4 = 3.31m (dp) y = AD AC y = ( ) y =.8m

6 9103 Grade Boundary: Low Merit 3. For Merit, the student needs to apply right-angled triangles, using relational thinking, in solving measurement problems. This involves one or more of: selecting and carrying out a logical sequence of steps, connecting different concepts and representations, demonstrating understanding of concepts, forming and using a model and also relating findings to a context, or communicating thinking using appropriate mathematical statements. This student s evidence is a response to the TKI assessment resource What s the Angle? This student has selected and carried out a logical sequence of steps in calculating the lengths of AB (1) and AC () correctly, but there is a transfer error in calculating the angle in the sail (3). The student has demonstrated relational thinking by considering the correct length of the pole in finding minimum dimensions for the van (4). For a more secure Merit, the student would need to calculate and clearly communicate the correct dimensions of the sail. NZQA 014

7 Student 3: Low Merit Calculate Sail dimensions x tan 0 = 9 x = tan0 = 9tan 0 = 3.8 x = 3.8m (pole height) 1 AC = ( AC = 9.58m (Sail side) ) tan x = = CEA x = ( ) tan 3 x = 7. 9 CEA = 7. 9 (Sail angle) 3 Length of pole = 5.78m x = sin x = 5.78sin13 = 1.3m y = ( ) = 5.63m ( ) = 5.1m (1dp Smallest van is 5.1m long 4

8 9103 Grade Boundary: High Achieved 4. For Achieved, the student needs to apply right-angled triangles in solving measurement problems. This involves selecting and using a range of methods, demonstrating knowledge of measurement and geometric concepts and terms and communicating solutions which would usually require only one or two steps. This student s evidence is a response to the TKI assessment resource What s the Angle? This student has measured at a level of precision appropriate to the task, calculated the height of the pole (1), the length of one side of the sail () and an angle in the sail (3). To reach Merit, the student would need to identify the shape and size of the sail and correctly link the length of the pole to the dimensions of the trailer. NZQA 014

9 Student 4: High Achieved O A O T C S A H H Height of pole AB = tan3x8 = 3.4m 1 Dimensions of sail AC = (8 = = 8.7m ) Triangle ACE 8.7 CEA = tan 1 ( ) = Triangle ABC x = tan x = 3.4 tan13 x = 0.78m

10 9103 Grade Boundary: Low Achieved 5. For Achieved, the student needs to apply right-angled triangles in solving measurement problems. This involves selecting and using a range of methods, demonstrating knowledge of measurement and geometric concepts and terms and communicating solutions which usually require only one or two steps. This student s evidence is a response to the TKI assessment resource What s the Angle? This student has measured at a level of precision appropriate to the task, calculated the height of the pole (1) and the length of one side of the sail (). For a more secure Achieved, the student would need to more clearly communicate what the second and third calculations represent. NZQA 014

11 Student 5: Low Achieved a) x tan 1 = 9 tan 1 9 = x 1 x = 3.45 = 3.45 The height of the pole is 3.45m b) a + b = c = c c = c = 9.6m = 9.6m c) 9 tan 1 ( ).1 = 76.9 = 76.9

12 9103 Grade Boundary: High Not Achieved 6. For Achieved, the student needs to apply right-angled triangles in solving measurement problems. This involves selecting and using a range of methods, demonstrating knowledge of measurement and geometric concepts and terms and communicating solutions which usually require only one or two steps. This student s evidence is a response to the TKI assessment resource What s the Angle? This student has taken some measurements at a level of precision appropriate to the task, and found the length of one edge of the sail (1). The student has not calculated the length of AB correctly. To reach Achieved, the student would need to provide evidence of selecting and using another method correctly in the solving of a problem. NZQA 014

13 Student 6: High Not Achieved O AB = sin 4 = H AB = sin 4 = AB AB = 3.05m(dp) AC = cos4 = A H A 7.5 = H H 7.5 = AC cos4 AC = 8.1m(dp) 1