Item Description - SRI Phi - Please note: any activity that is not completed during class time may be set for homework or undertaken at a later date.

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Item Description - SRI Phi - For the Teachers Please note: any activity that is not completed during class time may be set for homework or undertaken at a later date.

In the first unit, students are first asked to make a sketch of two limpets when given their dimensions.

2 Item Description - SRI Phi - For the Teachers Please note: any activity that is not completed during class time may be set for homework or undertaken at a later date. SRI Phi Rotation Lesson Activity Description: This lesson contains three Short Response Units comprised of questions testing the Phi Common Curriculum Elements. In the first unit, students are first asked to make a sketch of two limpets when given their dimensions. They are then required to find the slope of each shell and, from this information, determine which limpet would be more likely to be found in a more exposed region. Unit two asks students to identify the mistakes in two maths problems and mark them using the same format as the teacher, who marked the first problem. In the third unit, students have to calculate how much icing is left over after it is used on a fondant. Purpose of Activity: This lesson is designed to provide students with the opportunity to practise the Phi Curriculum Elements that are tested in the Short Response QCS Test. CCEs: Sketching/ drawing (π60) Calculating with or without calculators (Ф16) Estimating numerical magnitude (Ф17) Approximating a numerical value (Ф1) Substituting in formulae (Ф19) Applying a progression of steps to achieve the required answer (Ф37) Suggested Time Allocation: This rotation lesson is designed to take one hour to complete approximately 20 minutes per unit. Teaching Notes: Students will need to use a calculator in these units. After students have completed each section, go through the answers thoroughly with them to ensure they understand how to reach the correct answer. Encourage students to volunteer their own answers, and if possible, start a group discussion about different answers.

3 UNIT ONE ITEM 1 [ **** ] Grant is a biologist who is interested in studying the adaptations of limpets that allow them to survive in rocky environments which are constantly subjected to the turbulent action of waves. During a field trip to Hastings Point, Grant notices that the conically shaped shells of limpets living in more exposed areas seem to be flatter than those who inhabit more protected rocks. Grant wishes to collect some data of the slope of limpet shells in each area. He records the following data: Limpet in area 1: height: 1.6cm, diameter: 3.1cm Limpet in area 2: height: 2.4cm, diameter: 2.cm Make a quick sketch of each limpet. Next, make some calculations to determine the slope of each limpet s shell, remembering that the formula for slope = rise/run. If Grant s hypothesis is correct, that flatter Limpets seem to inhabit more exposed areas, which of the two Limpets would you expect to be found in the most exposed region of the environment? Sketches do not have to be drawn to scale. Label each diagram with measurements Explain your approach.

4 UNIT ONE ITEM 1 [ **** ] Grant is a biologist who is interested in studying the adaptations of limpets that allow them to survive in rocky environments which are constantly subjected to the turbulent action of waves. During a field trip to Hastings Point, Grant notices that the conically shaped shells of limpets living in more exposed areas seem to be flatter than those who inhabit more protected rocks. Grant wishes to collect some data of the slope of limpet shells in each area. He records the following data: Limpet in area 1: height: 1.6cm, diameter: 3.1cm Limpet in area 2: height: 2.4cm, diameter: 2.cm Make a quick sketch of each limpet. Next, make some calculations to determine the slope of each limpet s shell, remembering that the formula for slope = rise/run. If Grant s hypothesis is correct, that flatter Limpets seem to inhabit more exposed areas, which of the two Limpets would you expect to be found in the most exposed region of the environment? Limpet in area 1 Limpet in area 2 3.1cm 1.6cm 2.cm 2.4cm Sketches do not For Limpet 1: ½ base = 1.55 have to be drawn to scale. Slope = rise/run = 1.6/1.55 = 1.03 For Limpet 2: ½ base = 1.4 Label each diagram with measurements Slope = rise/run = 2.4/1.4 = 1.71 Therefore, Limpet 1 has a lesser slope than Limpet 2 and is most likely to inhabit the exposed area. Explain your approach.

5 Marking Scheme Unit One In this unit, students were given the dimensions of two limpets and asked to draw labelled sketches. They then had to calculate the slope of each limpet s shell in order to determine which one was more likely to inhabit a particular area. CCEs Present in Unit: 16 Calculating with or without calculators. 19 Substituting in formulae. 37 Applying a progression of steps to achieve the required answer. 60 Sketching/drawing. Unit One Item 1 A B C D E The student accurately drew two labelled diagrams and produced a comprehensively explained approach of how to calculate and compare the critical angle of both shells. The student s final answer was correct and made reference to which limpet was more likely to inhabit the exposed area. The student drew two diagrams, but failed to label them accurately or at all. The student produced a comprehensively explained approach of how to calculate and compare the critical angle of both shells. The student s final answer was correct and made reference to which limpet was more likely to inhabit the exposed area. OR The student accurately drew two labelled diagrams and explained most of the steps required to calculate and compare the critical angle of both shells. The student s final answer was correct and made reference to which limpet was more likely to inhabit the exposed area. The student drew two diagrams, but failed to label them accurately or at all. The student produced a comprehensively explained approach of how to calculate and compare the critical angle of both shells. The student s final answer made reference to which limpet was more likely to inhabit the exposed area, but was incorrect. OR The student accurately drew two labelled diagrams and explained some of the steps required to calculate and compare the critical angle of both shells. The student s final answer was correct and made reference to which limpet was more likely to inhabit the exposed area. The student drew two diagrams, but failed to label them accurately or at all. The student explained very few of the steps he/she took in calculating and comparing the critical angle of both shells. The student s final answer made reference to which limpet was more likely to inhabit the exposed areas, but was incorrect. The student did not draw any diagrams. The student explained very few of the steps he/she took in calculating and comparing the critical angle of both shells. The student s final answer was incorrect. OR The student drew two diagrams, but failed to label them accurately or at all. The student did not explain any of the steps he/she took in calculating and comparing the critical angle of both shells. The student s final answer was incorrect.

6 Marking Scheme Unit One N O Model Response: Response is unintelligible or does not satisfy the requirements for any other grade. No response has been made at any time. Limpet in area 1 Limpet in area 2 3.1cm 1.6cm 2.4cm For Limpet 1: ½ base = 1.55 Slope = rise/run = 1.6/1.55 = 1.03 For Limpet 2: ½ base = 1.4 Slope = rise/run = 2.4/1.4 = 1.71 Therefore, Limpet 1 has a lesser slope than Limpet 2 and is most likely to inhabit the exposed area.

7 UNIT TWO ITEM 2 [ *** ] Jacob has tried to solve three maths problems. The first has been marked by his tutor by circling the incorrect parts and writing in the corrections. Jacob s two other problems also have one error, so correct each problem in the same way as the tutor. 1) y = x 3 + 7x -2 4 If x = 2 y = = 1 2 = ) 3) -4(2x 4) + (4+x) = -x x = -7x -14 ( 3-1 ) = + =

8 UNIT TWO ITEM 2 [ *** ] Jacob has tried to solve three maths problems. The first has been marked by his tutor by circling the incorrect parts and writing in the corrections. Jacob s two other problems also have one error, so correct each problem in the same way as the tutor. 1) y = x 3 + 7x -2 4 If x = 2 y = = 1 2 = ) 3) -4(2x 4) + (4+x) + 16 = -x x + 20 = -7x -14 ( - ) + 2 = + =

9 Marking Scheme Unit Two In this unit, students were shown working by a student of three mathematical problems, and informed that each contained an error. The first problem was marked by the student s teacher, and acted as an example so that students followed the same approach in correcting the final two problems. CCEs Present in Unit: 16 Calculating with or without calculators. 37 Applying a progression of steps to achieve the required answer. Unit Two Item 2 A B C D E N O Model Response: The student accurately corrected each error in the two remaining problems in exactly the same sequential approach as the teacher did in his/her example. The student accurately corrected each error in the two remaining problem; however they disregarded the stem and failed to apply the same sequential approach as the teacher did in his/her example. The student accurately corrected one error in the two remaining problems but inaccurately corrected the other. The student applied the sequential approach as the teacher did in his/her example. The student corrected multiple errors for one or both problems, when in reality they each only contained one. The student applied exactly the same sequential approach as the teacher did in his/her example. The student corrected multiple errors for one or both problems, when in reality they each only contained one. Further, they disregarded the stem and failed to apply the same sequential approach as the teacher did in his/her example. Response is unintelligible or does not satisfy the requirements for any other grade. No response has been made at any time. Notes: 1. Decimals and equivalent fractions were acceptable, however evidence of students having worked backwards to find the initial error will not gain full credit.

10 UNIT THREE ITEM 3 [ ***** ] Kelsey has been contracted to make a snow man cake for a Winter Wonderland party. After she makes the cake, she buys fondant icing to cover the cake but isn t sure how much to buy. Luckily, she finds the following table in her recipe book. Fondant Required for a 10cm height cake Diameter of Cake (cm) Amount of Fondant (grams) If the top and sides of each cake are covered by a 1cm thick layer of fondant, how much icing will Kelsey have left over if she buys the specified amount of icing from the table. Use the diagram and formulas provided and assume 1cm 3 = 1 gram of icing. Round your answer to the nearest gram. 10cm 35cm BODY 20cm HEAD Circumference of a circle: π x D Area of a circle: π x r 2 Volume of a cylinder: π x r 2 x h Where D is the diameter, r is the radius (radius is ½ D) and h is the height 10cm

11 UNIT THREE Show your working here.

12 UNIT THREE ITEM 3 [ ***** ] Kelsey has been contracted to make a snow man cake for a Winter Wonderland party. After she makes the cake, she buys fondant icing to cover the cake but isn t sure how much to buy. Luckily, she finds the following table in her recipe book. Fondant Required for a 10cm height cake Diameter of Cake (cm) Amount of Fondant (grams) If the top and sides of each cake are covered by a 1cm thick layer of fondant, how much icing will Kelsey have left over if she buys the specified amount of icing from the table. Use the diagram and formulas provided and assume 1cm 3 = 1 gram of icing. Round your answer to the nearest gram. 10cm 35cm BODY 20cm HEAD Circumference of a circle: π x D Area of a circle: π x r 2 Volume of a cylinder: π x r 2 x h Where D is the diameter, r is the radius (radius is ½ D) and h is the height 10cm

13 UNIT THREE Show your working here. Total amount of icing bought = 2200g + 00g = 3000grams Icing required for body cake top: π x r 2 x h (radius is equal to ½ D = ½ x 35 = 17.5) π x x 1cm = cm 3 side: circumference of circle x height x thickness π x 35 x 10 x 1 = cm 3 top + side = cm 3 Icing required for head cake = grams top: π x r 2 x h (radius is equal to ½ D = ½ x 20 = 10) π x 10 2 x 1cm = cm 3 side: circumference of circle x height x thickness π x 20 x 10 x 1 = top + side = 62.32cm 3 = 62.32grams Total icing = body + head = g g = grams Icing left over = icing bought icing used = = Therefore, 310grams of icing would be left over.

14 Marking Scheme Unit Three In this unit, students were provided with a table instructing them of the amount of fondant needed to ice cylindrical cakes of various diameters. They were then given the dimensions of a multi-layered cake and a table of formulas, and asked how much fondant the baker would have left over if she purchased the recommended amount. CCEs Present in Unit: 16 Calculating with or without calculators. 19 Substituting in formulae. 37 Applying a progression of steps to achieve the required answer. Unit Three Item 3 A B C D E N O The student showed all working as they substituted the given dimensions of both the cake s top and bottom layer into the given formulas. The student accurately determined the total icing left over by subtracting the amount of icing used from the amount of icing purchased. The student showed all working as they substituted the given dimensions of both the cake s top and bottom layer into the given formulas. This working was accurate. The student made a calculation error in subtracting the amount of icing used from the amount of icing purchased, so their final answer was incorrect. OR The student showed most working as they substituted the given dimensions of both the cake s top and bottom layer into the given formulas. The student accurately determined the total icing left over by subtracting the amount of icing used from the amount of icing purchased. The student showed all working as they substituted the given dimensions of both the cake s top and bottom layer into the given formulas; however, some of this working was incorrect. Similarly, their final answer was incorrect. OR The student showed some working as they substituted the given dimensions of both the cake s top and bottom layer into the given formulas. This working was accurate. The student made a calculation error in subtracting the amount of icing used from the amount of icing purchased, so their final answer was incorrect. The student showed no working, but their final answer was correct. OR The student showed some working as they substituted the given dimensions of both the cake s top and bottom layer into the given formulas; however, this working was inaccurate. Similarly, their final answer was incorrect. The student showed little working, and their final answer was incorrect. Response is unintelligible or does not satisfy the requirements for any other grade. No response has been made at any time.

15 Marking Scheme Unit Three Model Response: Total amount of icing bought = 2200g + 00g = 3000grams Icing required for body cake top: π x r 2 x h (radius is equal to ½ D = ½ x 35 = 17.5) π x x 1cm = cm 3 side: circumference of circle x height x thickness π x 35 x 10 x 1 = cm 3 top + side = cm 3 = grams Icing required for head cake top: π x r 2 x h (radius is equal to ½ D = ½ x 20 = 10) π x 10 2 x 1cm = cm 3 side: circumference of circle x height x thickness π x 20 x 10 x 1 = top + side = 62.32cm 3 = 62.32grams Total icing = body + head = g g = grams Icing left over = icing bought icing used = = Therefore, 310grams of icing would be left over.

LHS Algebra Pre-Test

Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well