APPENDIX B Lesson One

Day 1

Objectives

1. Recognize angles as geometric shapes that are formed whenever two line segments share a common endpoint.

2. Identify angles in a real-world setting.

Van Hiele-Geldof Instructional Phases  Initial Inquiry

 Direct Orientation

Van Hiele Level Indicators for the Topic of Angle (Scally, 1990)

I expect that students will be working at level one as they identify angles based on their appearance as a whole using standard and non-standard language. Students will often use irrelevant properties or relationships when describing angles.

Materials and Equipment

 Computer and projector (angles can also be drawn onto poster paper).

 Image of various angles

 Cardboard tubes

 Small students whiteboards and pens

Prior Knowledge

As the first lesson in this sequence, students are expected to already have some knowledge about geometry and measurement. In geometry, students should be able to identify vertices in shapes and be able to understand the terms line segment and endpoint. However, if students do not use this language early in this lesson they should not be asked to do so. It is important

that the students initially use their own language to describe the figures. Geometrical terms will be introduced at the end of the introductory activity.

In measurement, students should already be able to: recognize length as an attribute, compare lengths, recognize the need for units of equal length, measure by using multiple identical units, and measure by using a single iterative unit. Students will be expected to have these skills for linear measure before moving onto angle measure.

Learning Environment

The activities in this lesson will take place both inside and outside the classroom. When selecting a place outside the classroom, steer the students towards man-made artifacts that have straight lines, e.g., climbing frames. During the lesson, students are asked to work in pairs. Where possible, students should be able to select their partners. This will allow students to work with someone they feel comfortable sharing with. During the discussion, students will be asked to use the talk moves of adding on, revoicing, and wait time. Adding on is where the teacher prompts the students for further participation in asking them to add on to what one student has said. In the revoicing move, the teacher repeats what the student has said and asks the student if this is correct. This move is useful if the students’ initial response is not fully clear. Wait time is used to allow students time to think: the teacher will tell the student to take his/her time in answering the question.

Teaching Notes

One of the main objectives of this lesson is for children to recognize angles as geometric shapes that are formed whenever two line segments share a common endpoint. However, this lesson follows a constructivist approach in that children must come to this understanding themselves through the carefully planned activities. The teacher is a facilitator throughout this lesson and only teaches directly at certain points which have been identified in the plan. For example, in the initial activity, various angles are displayed for students to see, it is imperative that the teacher does not teach at this point in the lesson, students should describe what they observe and do so using their own language. One the students have identified what an angle is, it is then appropriate to use the formal mathematical terminology.

Before Phase

 Students will be introduced to the concept of angle via a computer projected image of a collection of different examples of angles. The teacher will introduce the shapes as figures at this time and not use the term angle/s. Write the word figure on the board so students are clear of the word.

The angles are intentionally portrayed in different orientations with sides of different lengths, to avoid the misconception that orientation and length of sides are salient attributes of angle.

 Students will initially work in pairs to answer the questions:

o What can you tell me about these figures from what you have noticed?

o What do all these figures have in common?

Have the students imagine that they have to explain to a kindergarten student what they see in simple terms. At this point visual observations such as lines, a point, and two lines in different directions are expected. If students are able to use the terms line segment and endpoint these should be accepted, but other language such as lines should also be included if this is the language used by the students. If students use the word angle, this will not be ignored, but it will not be discussed further at this point in the lesson. It is

important for the students to recognize what constitutes an angle before giving the figure a name.

 The whole class will come back together to answer the question:

o What do all these figures have in common?

Pairs will share their ideas and the students’ descriptions will be written onto chart paper, using the language the students used. During the discussion, students will be asked to use the talk moves of revoicing, adding on, and wait time.

 Following the discussion, the term angle will be formally introduced by the teacher. It will be written on the board and the teacher will model using the term and connecting this back to the attributes identified at this time from the language the students used.

 The teacher will then recap on prior teaching of the terms ray, line segment and endpoint. The words will be posted on the classroom wall for students to see. These terms will then be matched to the angles from this activity.

During Phase

 Students go out into the area surrounding the school to identify angles in the real-world setting. They will be specifically asked:

o “As you look around our environment (clarify meaning of environment), can you see any angles?” They will be asked to look and not to answer at this time. Some difficulties can be expected as students may struggle to see angles in a different context than the paper and pencil angles observed earlier.

 The teacher will support the

VOCABULARY CHECK