Stage 3 Measurement and Geometry Angles 1

Stage 3 Measurement and Geometry –Angles 1

Term 1 Week 9 Outcome: Measures and constructs angles, and Content Area applies angle relationships to find unknown Estimate, measure and compare angles using angles MA3-16MG degrees Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles Background Information A circular protractor calibrated from 0° to 360° may be easier for students to use to measure reflex angles than a semicircular protractor calibrated from 0° to 180°. Students should be encouraged to give reasons when finding unknown angles.

Language Students should be able to communicate using the following language: angle, arm, vertex, protractor, degree. Students should be able to communicate using the following language: angle, right angle, straight angle, angles on a straight line, angle of revolution, angles at a point, vertically opposite angles. A pair of adjacent angles has a common vertex and a common arm.

Working Mathematically Outcome describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM

Students: Working Mathematically  identifying the arms and vertex of an angle where both  explain how a protractor is used to measure an angle arms are invisible, such as rotations and rebounds (Communicating)  recognising the need for a formal unit for the measurement of angles  explore and explain how to use a semicircular  using the symbol for degrees ( º ) protractor to measure a reflex angle (Communicating,  Measure angles of up to 360 using a protractor. Reasoning)

 Construct angles using a protractor(ACMMG112)  extend the arms of an angle where necessary to facilitate measurement of the angle using a protractor  construct angles of up to 360° using a protractor (Problem Solving)  identify that a right angle is 90°, a straight angle  use the words 'between', 'greater than' and 'less than' is 180° and an angle of revolution is 360° to describe angle size in degrees (Communicating)  identify and describe angle size in degrees for each of the classifications acute, obtuse and reflex

 compare the sizes of two or more angles in degrees, eg compare angles in different two- dimensional shapes

 estimate angles in degrees and check by measuring

 estimating and measuring angles in degrees

 classifying angles as right, acute, obtuse, reflex, straight or a revolution  identifying angle types at intersecting lines. Learning Experiences Week: Ball Games Comment / Date Students roll a wet tennis ball along the ground at an angle to the wall. Students observe the ball rolling to and rebounding from the wall. The wet lines form the arms of the angle and the point where the ball hits the wall is the vertex of the angle. Possible questions include: . Where is the ball rolled from to create the smallest angle? . Where is the ball rolled from to create the largest angle? . What is the smallest angle that can be made? . What is the largest angle that can be made? Extension: Students record results by measuring the angles produced.

Week: Protractors Comment / Date Students are shown how to use protractors to measure angles in degrees. The teacher ensures that students are aware of: . the scale around the edge . the point on the protractor to be aligned with the vertex of the angle to be measured . the reason for two sets of numbers . the largest angle that can be measured . the need to line up an arm of the angle being measured with the zero degree line on the protractor, not its bottom edge. In pairs, one student estimates the size of an angle and the other student checks the estimate by measuring with the protractor. Extension: Students replicate angles in the room using geostrips. They then copy the angles onto paper and estimate and measure the angles.

Week: Measuring Angles in Two-dimensional Shapes Comment / Date Students are provided with a variety of two-dimensional shapes. Using a protractor, they measure the angles within the shapes. Possible questions include: . How did you measure the angles? . Using your knowledge of angle properties of two dimensional shapes, what do you expect your measurements to show? . How can you record your measurements? . How can you classify the angles you have found? . How can you classify the shapes according to their angles? . How can you compare the shapes by their angles?

Week: Kicking a Goal Comment / Date A small goal is created on an asphalt area using witches’ hats. Students place a ball in front of the goal. They draw the angle created in chalk on the asphalt, using the ball as the vertex and the goal posts as the ends of the arms. They then measure and record the angle created, using the teacher’s protractor. Students try to score a goal from that position. Students repeat the activity from other positions in front of the goal, drawing, measuring and recording the angle created in each new position. Possible questions include: . Where were the angles smaller? Why? . How did the size of the angle affect the ease of scoring a goal? Why? . If you moved the ball closer or further away from the goal line, did it change the size of the angle? How? Why? . How would the presence of a goal-keeper affect the angles created? Results could be recorded in a table using a computer.

Week: Classifying Angles Comment / Date Students identify, record and classify angles in the environment using the terms ‘right’, ‘acute’, ‘obtuse’, ‘straight’, ‘reflex’ and ‘revolution’. In pairs, students describe the angles they have classified eg the angles are all obtuse because they are greater than 90º but smaller than 180º. Students draw each type of angle and label the vertex and arms. This activity could be extended so that students could estimate the size of each angle in the environment and then check by measuring. Possible questions include: . Were some of your estimations closer than others? . Why do you think this was?

Week: Constructing Angles Comment / Date In pairs, students draw ten different angles for each other. Students then measure, label and order their partner’s drawings.

Week: Boomerang- Investigating the angles. Comment / Date Students read information n how to make a boomerang, looking carefully for facts about the size of angles and dimensions on wings. http://www.boomerangs.com/howtomakebooms.html Students design a boomerang, clearly labelling all the critical angles and dimensions for a successful flight. Extension: Students use plywood to make a boomerang

Week: Angling Comment / Date In pairs, students take turns to nominate the size of an angle eg 50º. Both students estimate and draw an angle of the nominated size. Students use a protractor to measure their partner’s angle. The student whose angle is closer to the nominated measurement is the winner. Variation: Students create two sets of cards, one with a range of angles drawn on them and the other with the measured size of the angles. They play a concentration game with the cards.

Week: Angles in the Environment Comment / Date Students collect a variety of pictures that show various angles eg buildings, football fields, aerial views. They identify angles in the pictures, trace them onto overhead transparencies and then describe them. Possible questions include: . What strategies did you use to describe your angles? . Did you discover anything about the type of angles identified? Variation: Students measure the angles traced and record their findings.

Week: Angles with Invisible Arms Comment / Date Students go on a hunt to identify angles with invisible arms eg door opening, rotation of door handle, rebounds. Students share and explain their findings with the class. Students make a class list of the angles identified.

Week: Angles at Intersecting Lines Comment / Date The teacher identifies different angle types created by intersecting lines in the environment eg doorframes. Students then identify any other angles created by intersecting lines that they can see. Students draw intersecting lines on the computer and label the angle created.

Resources protractor, pencils, paper, two-dimensional shapes, soccer and tennis balls, witches’ hats

Links PDHPE

Assessment See attached assessment page.

Evaluation Student Name: Date: St 3 Outcome MA3-16MG Measures and constructs angles, and applies angle relationships to Record find unknown angles.

1. Label the following angles as acute, obtuse, reflex, straight, right or revolution.

(a) (b) (c)

(d) (e) (f)

2. Measure the following angles in degrees.

(a) (b) (c)

3. Use your protractor to construct the following angles.

(a) 50° (b) 125° (c) 210°