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Year 7 Spring 1 Lesson 6: Finding angles in special trianglesObjectiveTo find missing angles in isosceles, equilateral and right-angled triangles.AimThe use of the circles at the start is so that students can see that when radii are used to make a triangle, the sides will be the same length and therefore it will be isosceles. This will be useful when they move to circle theorems later in the school. The right angled triangles that can be found all have one side as a diameter – this is also useful later on in the school, but doesn’t need to be looked at in depth here.ResourcesPowerpointBlank circles sheetPrintout of slide 18Printout of slide 19 (for those who need it only)Key words: Triangle, isosceles, equilateral, circumference, radius, diameter, centre.Settler: Numeracy Ninjas (max 10 mins)Activity 1: Show students the circle and ask them to imagine a triangle that has been made by joining dots on the circumference or centre of the circle. They must try to explain how to draw it without using their hands or pointing. It could be useful to introduce words like circumference and centre at this point. On slide 2 they must describe them to their partner. Compare different descriptions here and ask the class to decide which descriptions they found the most useful here.Being able to describe the shapes will help them to classify them later on.Questions for progressionHow can you describe your triangle without pointing?Which words can be used to make your description more specific?Activity 2: Give students their blank circle sheets and ask them to draw as many distinct triangles as they can in the time given (five minutes would be sufficient)After the five minutes is up, they should classify the triangles using their own groups. Once they have done, ask them for their classifications, trying to get as many as possible –they may not have sorted them into different types of triangle, which is also fine at this stage.Questions for progressionThese two triangles are the same – how do you know?How many different triangles have you got? Is this all of them?How do you know?Activity 3: Show the classification on slide 5. Ask the students how they have been sorted. They should already know the different types of triangle.Quickly summarise the different types of triangle using slides 6-9.The word isosceles comes from the Greek ‘same legs’ which help students to visualise ‘same feet’ at the bottom of the ‘same legs’.The key question is on slide 10 Questions for progressionHow have these triangles been sorted?What types of triangle do you already know from Primary school?What properties do you remember about hem?How do you know that this is an isosceles triangle without measuring the sides or angles?Activity 4: No angles are given in the triangle on slide 11. How can they find the angle at the centre?Give students time to think about this or discuss with their partner. There are three possible methods on the slides, but the student may have a different way. Compare all the different ways.Using what they know about triangles and isosceles triangles, ask student in their pairs to find the other two angles in the triangle.Collect and compare responses from the class.Ask them to repeat with slide 16. No more than 5 minutes should be spent on this before bring the class together.Little progressDon’t know how to beginQuestions for progressionHow did we find the centre angle for the last question?Could you do something similar this time?What extra lines could you draw?Could you use the answer from last time? How?Some progressFind the centre angle, but can’t find the others.Questions for progressionWhat is the sum of interior angles in a triangle?What do you know about these two angles?Why is that?How does that help?Substantial progressFinds the angles very quicklyQuestions for progressionCan you find the centre angle in a different way?Activity 5: Students answer the questions one at a time on slide 17.The questions are intentionally different so that student have to think about how to answer each question rather than just using a method that they repeat.Students then answer the questions from slide 18 in their books.Bring class together as soon as first person has successfully completed the challenge questions. Mark the questions as a class, asking students how they got their answers.Finish off the lesson with the last two slides.Little progressDon’t know how to begin.Questions for progressionWhat type of triangle is this?How do you know?What do you know about angles in isosceles triangles?Which angles are the same?Some progressAnswers questions 1 – 7 but is confused by the extra line in question 8.Questions for progressionHow can you find angle q?How do you know?What do you know about angle q and angle s from a previous lesson?So how can you calculate angle s?Substantial progressFinishes the sheet with all correct.Questions for progressionGive our challenge questions from slide 19.Can you find use what you know to find the angles in these questions?-62865129540Acknowledgement:Triangle in circles activity taken from Japanese textbook0Acknowledgement:Triangle in circles activity taken from Japanese textbook ................
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