Developing A Diagnostic Assessment Instrument And Implementation Guide
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Guide For Implementation |
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SNO |
Topic |
Subtopic |
Instruction for implementation |
Resources |
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TRIGONOMETRY |
Prerequisites subtopic |
Topic: Number and algebra sub: Introduce Real numbers, direct proportion · simple relationship between graphs and equations in form of oral questions · Illlustrate on the board, fortify with a short video on the subtopics and load it with activities · Do practicals on identifying direct proportion in real life contexts · Take them through use of calculatorr Sub 2: Patterns and algebra · Introduce the index laws to variables · Discuss and demonstrate the distributive law in algebraic expression · Let them do short quiz on the subtopics so far covered · Sub3: Linear and nonlinear relations · Introduce the cartesian plane · Plotting points on the cartesian plane · Finding distances between two points on the cartesian plane by graphing softwares · Sketching linear graphs using two cordinates · Solve linear equations · Graph simple nonlinear equations · Solve simple nonlinear equations Topic2: Geometry sub1 · Develop geometric reasoning by demonstration using handmade models · Explore enlargement transfomation · Introduce the concept of similarity by beginning from the known · Discuss the condition for similarity · Discuss ratio and scale factors in similar figures · At this point show them a video on geometric reasoning sub 2: Pythagoras and trigonometry · Investigate pythagoras theorem by giving them a background information · Discuss how the theorem is used to find the sides of a right angled triangle · Stress that the longest side is the hypotenuse · Give them real life applications of the theorem · If okay with the subtopic, introduce trigonometry · Provide the meaning of trigonometry · Discuss the three basic trigonometric ratios, that is Sine, Cosine and Tangent · Relate trigonometry with pythagoras and show them how angles and sides of a right angled triangle relate · Stress on the constancy of the sine, cosine and tangent · Discuss how to solve problems using ratio and scale factors in similar figures · Apply trigonometry to solve right-angled triangle problems · Issue quiz after a subtopic is finished with, cats after a topic is done with and final test after completion of lesson 1 and 2 · Group activities are to be aligned with the activities in the video presentation |
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1 |
Trigonometry 1 |
Measurement and geometry 1 and 2-r |
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2 |
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3 |
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4 |
Trigonometry 2 |
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5 |
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6 |
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7 |
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Diagnostic Instrument |
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Evidence of Level classification |
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Subtopics |
Below average student |
Average student |
Above average student |
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· Shows rough idea about tangent ratios · Can identify mistakes in his/her work and provide correct alternatives · Can draw diagram showing information · Calculates each distances but doesnot find distances between two parts · Can find angle of inclination but cannot further in answwering related questions · Records angle of elevation and depression, own and diistances as measured · Unable to show calculations involving ratios or scale factors in similar figures · Can plot points and join them to form a line · Possesses a bit of mathematical reasoning · Understands algebraic expressions by identification but cannot work simple algebraic probems · Unable to use calculator in determining the trigonometric ratios · Is able to apply pythagoras theorem in finding distances in right angled triangle but is unabe to use same in real life situation · Can identify similar triangles but does not understand how to find angles given distances · The principle of constancy in the ratios is lacking in their comprehension · Doesnot understand the connection between trigonometry and algebra · Unable to sketch linear graphs |
· Shows average idea about tangent ratios but still unable to appreciate the differenece with Sine ratio · Can identify mistakes in his/her work and provide correct alternatives succintly · Can draw simple diagram showing information · Calculates each distances and finds distances between two points for simple problems · Can find angle of inclination and further answwering some related questions · Records angle of elevation and depression, own and distances as measured · Averagely shows calculations involving ratios or scale factors in similar figures · Can plot points and join them to form a line · Possesses average mathematical reasoning · Averagely understands algebraic expressions by identification and can work on both simple and complex algebraic problems · able to use calculator in determining the trigonometric ratios but finds problem with the settings · Is able to apply pythagoras theorem in finding distances in right angled triangle and is able to use same in real life situation for simple problems · Can identify similar triangles but still unable to understand how to find angles given distances · The principle of constancy in the ratios is averagely demonstrated in their work · Slightly understands the connection between trigonometry and algebra · Able to sketch simple linear graphs but still with challenges in interpretion |
· Shows great idea about tangent ratios · Can identify mistakes in his/her work and provide correct alternatives · Can draw diagram showing information · Calculates each distances and finds distances between two points · Can find angle of inclination and further answwering related questions · Records angle of elevation and depression, own and distances as measured · Greatly shows calculations involving ratios or scale factors in similar figures · Can plot points and join them to form a line · Possesses great mathematical reasoning with clear and logical steps exhibited · Greatly understands algebraic expressions by identification and can work on both simple and complex algebraic probems · able to use calculator in determining the trigonometric ratios · Is able to apply pythagoras theorem in finding distances in right angled triangle and is able to use same in real life situation · Can identify similar triangles and understands how to find angles given distances · The principle of constancy in the ratios is demonstrated in their work · Understands the connection between trigonometry and algebra · Able to sketch linear graphs and interpret them |
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Student Level classification |
Strategies outline (Evidence classification ) |
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Below average |
Cannot recognize sides and angles in a right angledtriangle Doesnot recognize that hypotenuse is the longest side Shows a rough idea |
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Average |
Above average must: competently capture the four essential skills in mathematics: Understanding, Fluency, Problem-solving and reasoning Under undestanding: Sufficiently comprehended the relationship between graphs and equations Algebraic expressions by simplying both complex and simple expressions Trigonometric ratios for right angled triangles In Fluency: Familiar with all calculations and the graphs including cartesian plane In problem solving : Must be able to excellently model practical scenarios Applying the laws and theorems appropriately Reasoning: Logically and clearly by showing all steps in arriving at the answer Clearly sketching graphs Developed mind to underscore real word problems and challenges Lesson 3: Trigonomery 2 |
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Lesson 3: Trigonomery 2 |
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GENERAL COMMUNICATION |
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In all the works done, check for the common challenges and misconception |