Thurs Dec 16th More Constructions

LEARNING OBJECTIVE: To practise drawing skills using straight edge, pencil and ruler make accurate Constructions

SUCCES CRITERIA: You will be able to accurately construct the following

Triangles

• Copy a triangle
  
• Isosceles triangle, given base and side
  
• Isosceles triangle, given base and altitude
  
• Equilateral triangle
  
• Triangle medians
  
• 30-60-90 triangle, given the hypotenuse
  
• Triangle, given 3 sides (sss)
  
• Triangle, given one side and adjacent angles (asa)
  
• Triangle, given two sides and included angle (sas)
  
• Incircle of a triangle
  
• Circumcircle of a triangle
  

Triangle Centers

• Triangle incentre
  
• Triangle circumcentre
  
• Triangle orthocentre
  
• Triangle centroid
  

Circles, Arcs and Ellipses

• Finding the centre of a circle
  
• Circle given 3 points
  
• Tangent at a point on the circle
  
• Tangents through an external point
  
• Focus points of a given ellipse
  

LESSON: Work through the constructions by demonstrating them and then given students a chance to have a go at them

PLENARY: Checking answers walking around room / supporting students who are struggling.

Exam Questions: Use these questions with 25 mins to go as a 'test' to be handed ion an marked.

Tues Dec 13th / Weds Dec 14th - Constructions

LEARNING OBJECTIVE: To practise drawing skills using straight edge, pencil and ruler make accurate Constructions

SUCCES CRITERIA: You will be able to accurately construct the following

• Perpendicular bisector of a line segment
  
• Perpendicular from a line at a point
  
• Perpendicular from a line through a point
  
• Perpendicular from endpoint of a ray
  
• Divide a segment into n equal parts
  
• Parallel line through a point (angle copy method)
  
• Parallel line through a point (rhombus method) Angles
  
• Bisecting an angle
  
• Copy an angle
  
• Construct a 30° angle
  
• Construct a 45° angle
  
• Construct a 60° angle
  
• Construct a 90° angle (right angle)
  
• Constructing 75° 105° 120° 135° 150° angles and more
  

   
   

DEFINITION

Constructions: The drawing of various shapes using only a compass and straightedge or ruler. No measurement of lengths or angles is allowed.

STARTER: Can you draw a hexagon using just a compass and a ruler – NO MEASURING OF ANY KIND ALLOWED

Watch this Video for an Answer

LESSON: Work through the list of constructions above, show how to do the construction on the IWB< Get students to follow step by step then give them a few minutes to practise. Repeat with as many constructions as possible within the lesson.

Table of Contents

EXTENSION: If anyone is very good and needs some extension material get them to draw the inscribed and/or circumscribed circle for any triangle

Using Scale Drawings and bearings to solve problems

LEARNING OBJECTIVE: To use scale drawings of real situations to solve problems

SUCCESS CRITERIA: You will be able to construct a scale drawing of a journey; including bearings and then using measuring equipment (Protractor and ruler) solve problems

STARTER: To be completed on a piece of A4 paper

A plane flies 250 kms on a bearing of 155° then flies a further 350kms on a bearing of 85°. Draw a scale drawing of this journey and then use a ruler and protractor to answer the following questions:

1. What is the best scale to use to fit this on a piece of A4 paper
   
2. How far is the direct journey from the start to the finishing point?
   
3. What is the bearing of the direct journey
   
4. What is the bearing of the direct journey from the finishing point back to the starting point
   

LESSON:

Continue to work through Ex 12N on page 297 of Higher Text Book

EXTENSION QUESTION: A captain makes a 2° error when working out the bearing he needs before setting off across the Atlantic from new York on his way to Lisbon in Portugal (a distance of 5500 kms) he set off on a bearing of 132° instead of a bearing of 134°. Work out how far away from his destination he will end up.

PLENARY: Checking answers around the room, discussions as a class, feedback on confidence, exam question

Weds – Using Scale Drawings and bearings to solve problems

LEARNING OBJECTIVE: To use scale drawings of real situations to solve problems

SUCCESS CRITERIA: You will be able to construct a scale drawing of a journey, including bearings and then using measuring equipment (Protractor and ruler) solve problems

STARTER: Here is an aerial view of Heathrow airport, what is the bearing of the runway shown? What is the runaway number if this runway is seen from the other end.

Repeat for runway at Gatwick

LESSON:

Question 1

A ship sets off from Bridlington on the east coast of Yorkshire and travels in a straight line on a bearing of 065° for 80 kms.

How far due north has it gone from Bridlington, How far East has it gone from Bridlington.

Show how to draw an accurate scale drawing of the situation and then use a ruler to solve it

QUESTION 2

A plane flies 250 kms on a bearing of 155° then flies a further 350kms on a bearing of 85°. Draw a scale drawing of this journey and then use a ruler and protractor to answer the following questions:

1. How far is the direct journey from the start to the finishing point?
   
2. What is the bearing of the direct journey
   
3. What is the bearing of the direct journey from the finishing point back to the starting point
   

Work through Ex 12N on page 297 of Higher Text Book

PLENARY: Checking answers around the room, discussions as a class, feedback on confidence, exam question

Tue 6th Dec – more practice with bearings

LEARNING OBJECTIVE: To understand and use bearings

SUCCESS CRITERIA: You will understand how to find a bearing from one place to another

STARTER: Watch this Video on finding a bearing

LESSON: Reminder of 180° rule on IWB. Use lighthouse being seen from a ship problem.

Work through Questions on page 23 of Higher text book (worksheet)

PLENARY: Checking Answers Look at a Past Exam Paper

Mon Dec 5th – Bearings

LEARNING OBJECTIVE: To understand and use bearings

SUCCESS CRITERIA: You will understand how to find a bearing from one place to another

STARTER: Play Angler game on IWB

LESSON: Work through the lesson on Bearings. Not the last screen.

Worksheet (section 33 – Bearings),

PLENARY: Check Answers

Then work thorough Questions on page 23 of Higher text book (worksheet)

PLENARY: Checking Answers, Look at a Past Exam Paper