A lesson plan showing the innovative integration of technology:

Contents:1. Trigonometry Challenge “Survey the Site Unit Plan!”2. The Actual Challenge (web pages downloaded)

1. Trigonometry Challenge “Survey the Site Unit Plan!”

The entire unit has not been included but a sample is below:

Unit Name: Survey the Site Challenge

Generative Topic: Trigonometry

This unit supports the following Essential Learnings:

Communicating being numerate being information literate

Thinking Inquiry Reflective Thinking

Overarching Understanding Goals

Students will understand: how to solve problems using

trigonometric principles that trigonometry and its principles

is an efficient tool to use when solving particular problems

that trigonometric principles can be manipulated to solve a range of problems

that trigonometry is used in many fields and careers

Unit-long understanding goals

Students will understand:

Pythagoras’s theorem and how to manipulate it The trigonometric ratio’s and how to use them to solve problems

The sine rule and cosine rule? (extension)

Performances of Understanding:(opportunities for assessment)

What is the point of learning about trigonometry?

Students are introduced through the use of a real life scenario to the need for Trigonometry. They are given the job of a consultant surveyor who has been employed to assess a rundown playground that is under the control of a local council or shire. From their learning they are to recommend and design an improved, safe and interesting playground. To assist with their thinking, research and reflection students are provided with a document to prompt them called “Get Thinking”. They are required to draw using technology a scale diagram of the finished playground. Ideally it could be set up as a simple game so that once students arrive at the correct information the playground would appear before them (gamemaker?)

How do you find all the side lengths of a right angle triangle when only two side lengths are provided?Students are presented with the problem “We need a fence!”. The kite shaped playground needs re-fencing. They are only given the diagonal dimensions and from this need to work out the perimeter of the playground. Supporting worksheets and activities: Hypotenuse Hunt, Discover Pythagoras, Pythagoras Practice, Manipulate Pythagoras, How did Pythagoras Prove his theorem and Who was Pythagoras will guide students as to how to solve the problem.

What is the sine ratio?Students are presented with the dimensions of the two current slides and the Australian Standard for the angle of inclination for slides and using a simple ratio they are to check whether the slides comply – as such they are really using the sine ratio. They then practice checking these ratio’s through choosing appropriate slides from a series of 6 slides. Students are then reminded that the correct slides must be added to their scale diagram and as scale diagrams are drawn from above they will have to calculate the width of the slides in order to correctly produce them. In this learning students are supported through further tasks, namely: Field Trip, Field Trip Continued, Sine on the Calculator and Sine Investigation. They are encouraged to use the calculator provided under accessories to do their work.

2. The Actual Challenge (web pages downloaded)

Below are the web pages and supporting documents that students locate on the online course:

Get Thinking

What do I already know? (Describe the facts and knowledge you already have.)

27.5cm

15cm

27.5/2.5=1115/2.5= 6 17 x2 34 x74 $2516

27.5cm

15cm

27.5/2.5=1115/2.5= 6 17 x2 34 x74 $2516

27.5cm

15cm

27.5/2.5=1115/2.5= 6 17 x2 34 x74 $2516

What do I need to know? (Brainstorm any questions that you will need to find the answers to in order to solve the problem.)

How can I find the answers to this problem? (List all the resources you could use.)

Which letter represents the hypotenuse in the following:

What is the length of the hypotenuse in each of the following:

Aim: To find Pythagoras’s theorem about right angled triangles.

Equipment:A pencil A protractor A rulerPaper

Method: 1. Using your pencil, protractor and ruler, draw five right angle

triangles on your pieces of paper.2. Number the triangles (1, 2, 3, 4 and 5).3. Measure and label the sides of each triangle in centimetres. 4. Label the shortest side of each triangle with the letter A.5. Label the next shortest side of each triangle with the letter B.6. Label the longest side of each triangle with the letter C.

Results:1. Complete the following table:

Triangle : Length Side A Length Side B Length Side C

(e.g. Triangle 2)

9cm 12cm 15cm

2. Using the information from the table above complete the

following table:

Triangle : A² B² A² + B² C²(e.g. Triangle 2)

81 144 81 + 144 = 225 225

3. When you square the shorter two sides and add them together what do they equal?

4. Can you describe this in relation to the longest the side?

5. Try to write a mathematical rule for what is happening:

6. Now try to describe this in words:

7. Your friend Kim is making a jump so that she can practice her cross-country horse riding jumps. She wants two diagonal post across the middle of it. She knows that the width of the jump will need to be 2.3m long and the height of the jump will be 1.4m. She can’t seem to figure out how long the diagonal posts should be. What would you tell her to do?

CONCLUSION:Find a definition of Pythagoras’s theorem and write it here:

How similar was it to your answers in questions 5 & 6?

On a scale from 1 to 10 (with 10 being the best) how well do you think you understand Pythagoras’s theorem?

Do you think you fulfilled the aim of this activity: yes/no

Pythagoras’ theorem says that in any right angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

c

c² = a² + b² a c is the hypotenuse in this case. b

Try to find the value of the hypotenuse of the following triangles:

If 1 + 2 = 3 then can’t we also say that 3 – 2 =1 or 3 -1 = 2 or 2 = 3 – 1…

If a + b = c then can’t we also say that c – b = a or c – a = b …

So then if you take Pythagoras’ theorem which says

a² + b² = c² what can we say about this? What conclusions can you make about this?

What would a² = What would b² =

See if you can use the information you have discovered to find the length of the third side in each of the following triangles:

You will need:

A large piece or a couple of pieces of cardboard/paper

A pencil A ruler

An eraser A protractor

Scissors Glue

Instructions:

1. Before you use your protractor, ruler and pencil to draw a right-angle triangle remember to try to use measurements for the sides that are an exact centimetre measurement (e.g. use 5cm instead of 5.2cm). This will be hard to do for all the sides but it is not too hard for the two sides that are not the hypotenuse.

2. Label the sides of the triangle A, B and C with C being the hypotenuse.

3. Also label the sides with their length in centimetres.

4. Make three squares, one that has a length equal to side A, one that has a length equal to side B and one that has a length equal to side C.

Focus POINT:

In numerical terms what do these squares represent in relation to the lengths. E.g. the length of A in mine is 16cm so you could say A = 16.What would the square for the side A be? What is its area? How can this be written in terms of A?

Wouldn’t it be A²? The square for B would be equal to B² and the square for C would be equal to C².

Label the square for A as A², for B as B² and for C as C².

Challenge:Using your scissors, can you cut up the A² and B² squares in such a way that they fit exactly on the C²?

If you can make the two smaller squares fit onto the larger squareWhat can you conclude?

What must A² + B² =

An easy example is:

1 2X4

1 6 x 1 6

8 X4

1 2 x 4 4 X4

Find out what you can about Pythagoras, include:

Who was he?

When did he live?

Where did he live?

What did he do?

Why did he do it? (probably not a very easy question to find the answer to but you could take an educated guess)

How did he do it?

How did he prove his theorem about the hypotenuse?

Any other information that you find intriguing, useful or entertaining.