# Lines and Angles

Development:

1. Identifying/exploring concept of angle

2. Comparing angles

3. Developing a stardard unit that can be used to measure angles

4. Observe and record relationships: to other angles, in shapes, to fractions.

Stage 1 - students identify angles as corners

Stage 2 - recognise angles as openings, slopes and turns

- desibe angles using everyday language and use the term 'right angle'

Stage 3 - classifying angles as right, acute, reflex, straight, or a revolution

- measure in degrees and construct angles using a protractor

Points to Remember

* A good way to introduce terms is to have students act it out with their body

* Students find using protractors quite difficult

*Children tend to focus on the lines, e.g. the same angle drawn with smaller 'arms' will be called smaller than the one with longer arms

* Angles are all about rotation

Teaching Ideas

* What lines can you make with your body?

* What lines can ou find around you?

* Take a line for a walk: "If you feet had ink on them, draw the line your partne made as they walk."

* Create a chart of types of lines

* Go on an angle hunt (could restrict it to a certain angle)

* Bounce/Roll a ball off the bottom of a wall and try and get it in a cup

* Make an angle tester: Cut out 2 different coloured circles, and cut a slit of 1 radius in each. Then slide them together.

* Make different sized angles using straws. Use 2 different lengthed straws  join them together with a pipe cleaner.

* Look for lines in Art

* Other cultures: Ancient Egyptians used their knowledge of angles to reflect light into their pyramids

# 2D SHAPE, SYMMETRY, TRANSFORMATIONAL GEOMETRY

Theory

van Hiele Framework

1. Visual - see similarities and differences between shapes based on appearance

2. Descriptive - able to describe similarities and differences based on properties

3. Informal Deduction - relationships can be described between shapes and objects, e.g. "Are all squares rectangles?"

ENRP (Vic)

1. Holistic recognition of shape

2. Classification of shapes, using visual

3. Identification of 'classes of shapes'

4. Definition osf shapes and properties

(include diagram showing shape classification)

Teaching points:

* Metalanguage: tesselate, slide, rotate

* Very important to show students shapes in different orientations and non-regular forms

* Introduce the language when talking, e.g. parallel, even if I dont put it in a test.

Teaching Activities

* Take a piece of string with its ends tied to make a circle. With a partner, use the string to construct a 4-sided shape. What is the geometric name of your shape? Make another, another,etc. What did you change? Students could sketch or photograph their shapes.

* Tesselations: Take a 2D shape. Trace it. Slide shape. "No gaps, no overlaps!"

* Have students visualise the shape and change them, stretch them, and add other shapes to make a picture

*Geoboards: partners - make same shapes but different sizes (to focus on properties)

* Celebrity heads with shapes

* 2D shape mystery bag: Have a variety of shapes cut out of the same coloured paper placed inside a 'mystery bag'. Pull shapes out a little bit at a time. What shape do you think this could be? Why?

* Look at the work of Escher

* Think about tesselations in real life and why we use them

* Symmetry: Use pictures from nature (e.g. flowers)

* Take a photo (or image) - cut it in half, paste on grid paper, draw the other half.

* Look at letters that have symmetry, e.g. A, B, C, D, E

* Use mira mirrors to do symmetry

Websites/Books

* "Think of a number" - information book about maths (good!)