I very much liked the step from enactive to iconic to symbolic, and I can see the potential of this. Hopefully, when the students now encounter a symbolic representation of an angle in their textbook they will think back to how this is the same as the angle they constructed using paper, and that is the same as the angle they can depict using their own bodies.
Perhaps they will not do this at first, but I will try and remind them from time to time. I think I too often forget that knowing the meaning of symbols is not something we are born with and that needs to be learned. Angles play an important role in life. Yet somehow, students often do not see these angles around them or associate them with the angles that they work with in the classroom.
When the students do not notice the angles around them, they are less likely to understand the importance of angles or to figure out how two angles are related.
In the next activity you will ask your students to identify different angles, first in the classroom, then in the school grounds. The activity then asks them to think about the importance of the measurements of the angles, and what would happen if they were changed. When taking students to work in the school grounds you should always make sure your students are aware of safety hazards they might encounter such as moving vehicles or building works, and prepare for changes in the weather.
Arrange the students in groups of four or five. Give the students their instructions before taking them out to the school grounds. Tell each group to find at least three examples of each different type of angle, such as obtuse, acute or straight angles. Then ask them:. If your students have access to digital cameras or mobile phones with an integral camera, these could be used to take photographs of the angles that the students find when they are working out-of-the-classroom.
This would be an exciting alternative way for them to record their findings. Back in the classroom ask the groups to report back to the whole class on some of their findings — reporting back on all of their findings might take too long.
This unit has focused on developing the concept of angle and recognising their presence in real life through your teaching. You have seen how you can use outdoor spaces as a mathematical arena where ideas can be explored and links and relationships in mathematics can be established. In doing so you have considered how to help students understand that angles are all around us, and that measuring angles is an important everyday skill.
Helping students to work in this way can help them become independent learners, able to think through the ideas they have studied in the classroom and apply them outside. Identify three techniques or strategies you have learned in this unit that you might use in your own classroom. As a teacher, you will get the best out of your students if you attend to the four points above in every lesson. Thus assessment can be undertaken before, during and after instruction:.
When you decide what the students must learn in a lesson or series of lessons, you need to share this with them. Carefully distinguish what the students are expected to learn from what you are asking them to do. Ask an open question that gives you the chance to assess whether they have really understood.
For example:. Give the students a few seconds to think before they answer, or perhaps ask the students to first discuss their answers in pairs or small groups. When they tell you their answer, you will know whether they understand what it is they have to learn. In order to help your students improve, both you and they need to know the current state of their knowledge and understanding. Once you have shared the intended learning outcomes or goals, you could do the following:. Knowing where to start will mean that you can plan lessons that are relevant and constructive for your students.
It is also important that your students are able to assess how well they are learning so that both you and they know what they need to learn next. Providing opportunities for your students to take charge of their own learning will help to make them life-long learners.
When you talk to students about their current progress, make sure that they find your feedback both useful and constructive. Do this by:. You will also need to provide opportunities for students to improve their learning. This means that you may have to modify your lesson plans to close the gap between where your students are now in their learning and where you wish them to be.
In order to do this you might have to:. By slowing the pace of lessons down, very often you can actually speed up learning because you give students the time and confidence to think and understand what they need to do to improve. By letting students talk about their work among themselves, and reflect on where the gaps are and how they might close them, you are providing them with ways to assess themselves.
While teaching—learning is taking place and after setting a classwork or homework task, it is important to:. Every student learns differently, at their own pace and style, both inside and outside the school.
Therefore, you need to do two things while assessing students:. There are some simple ways of doing this that you may like to consider, such as:. Once information and evidence have been collected and recorded, it is important to interpret it in order to form an understanding of how each student is learning and progressing. This requires careful reflection and analysis.
You then need to act on your findings to improve learning, maybe through feedback to students or finding new resources, rearranging the groups, or repeating a learning point. Assessment can help you to provide meaningful learning opportunities to every student by establishing specific and differentiated learning activities, giving attention to the students who need more help and challenging the students who are more advanced. Every effort has been made to contact copyright owners.
If any have been inadvertently overlooked the publishers will be pleased to make the necessary arrangements at the first opportunity. Video including video stills : thanks are extended to the teacher educators, headteachers, teachers and students across India who worked with The Open University in the productions.
Printable page generated Sunday, 14 Nov , Use 'Print preview' to check the number of pages and printer settings. Print functionality varies between browsers. Printable page generated Sunday, 14 Nov , TI-AIE: Using embodiment, manipulatives and real-life examples: teaching about angles What this unit is about It would be difficult to envisage our lives without angles.
What you can learn in this unit How to use manipulatives to help students to understand angles. Some ideas to link school mathematics with real life, both inside and outside the classroom. How to use embodiment to help students to understand angles. Activity 1: Embodying angles Part 1: Using hands Ask your students to show the following angles using their two hands joined at the wrist: an angle of 90 degrees an angle of 0 degrees an angle of degrees an angle of 45 degrees an angle of degrees a straight angle an obtuse angle a right angle an acute angle.
Figure 1 Students attempting Part 1 of this activity. Part 2: Using one arm Repeat the questions from Part 1, now asking the students to use one arm, with their armpit acting as the centre of rotation of the angle. Figure 2 A teacher demonstrating Part 2 of this activity. Part 3: Using other parts of the body to depict angles Arrange the students into groups of four or five. The two scales make it easy for us to measure angles facing different ways.
To measure the size of angle ABC , place the protractor over the angle so that the centre of the protractor is directly over the angle's vertex, B; and the base line of the protractor is along the arm, BA , of the angle. We use the inner scale to measure the angle ABC , as the arm AB passes through the zero of the inner scale. So, the size of angle ABC is 60 degrees. We write this as follows:. To measure the size of angle PQR , place the protractor over the angle so that the centre of the protractor is directly over the angle's vertex, Q ; and the base line of the protractor is along the arm, PQ , of the angle.
We use the outer scale to measure the angle PQR , as the arm PQ passes through the zero of the outer scale. So, the size of angle PQR is degrees. All rights reserved. Australian Business Number 53 The angle of the rotation is highlighted in green. When two lines intersect, the opposite angles are equal. Our page An Introduction to Geometry introduces the concept of parallel lines: lines that go on forever side by side and never cross, like railway lines.
If two parallel lines A and B are intersected by a third straight line C , then the angle at which the intersecting line crosses will be the same for both parallel lines. Angle c, which you will realise from the previous section is identical to a, is said to be alternate with a.
A protractor is commonly used to measure angles. Protractors are usually circular or semi-circular and made of transparent plastic, so that they can be placed over shapes drawn on a piece of paper, allowing you to take a measurement of the angle.
This example demonstrates how to use a protractor to measure the three angles of a triangle, but the same method applies to other shapes or any angles that you want to measure.
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