Developing A Diagnostic Assessment Instrument And Implementation Guide

Guide For Implementation

SNO

Topic

Subtopic

Instruction for implementation                     

Resources

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

1

Trigonometry 1

Measurement and geometry 1 and 2-r                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              

2

3

4

Trigonometry 2

5

6

7

Diagnostic Instrument

Evidence of Level classification                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  

Subtopics

Below average student

Average student                                                                                                                    

Above  average     student

· 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

Student Level classification

Strategies outline (Evidence classification )

Below average

Cannot recognize sides and angles in a right angledtriangle

Doesnot  recognize that hypotenuse is the longest side

Shows a rough idea                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         

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

Lesson 3: Trigonomery 2

GENERAL COMMUNICATION

In all the works done, check for the common                  challenges and  misconception