### Unit 5: Origami Geometry

Key Concept:

Form

Related Concepts:

Measurement, Space

Global Context:

Personal and cultural expression

Statement of Inquiry:

Creativity is enhanced through an understanding of form and unique use of space.

Factual Concept Questions:

What is an angle?
What classification of angles are there?
How many degrees are in quadrilaterals and triangles?

Conceptual Concept Questions:

How do angles in various triangles and quadrilaterals relate to each other?
Where do angles arise in other subjects?
What is the biggest angle?

Debatable Concept Questions:

How do we measure angles?
How accurate should an angle be measured/drawn to?
What is the biggest angle?

Unit Content:

•Know and use the terms: line, line segment, parallel, perpendicular, intersect, angle, vertex

•Naming line segments, angles with: one letter, three letters

•Be able to classify the following angles: revolution, right angle, straight, acute, obtuse, reflex

•Be able to estimate (to +/- 20º) and measure an angle (to +/- 2º)

•Construct angles using a protractor (to +/- 2 )

•Discover the following angles relationships vertically opposite, angles at a point, supplementary, complementary, angles in triangles and quadrilaterals.

•Determine unknown angles using those relationships, giving reasons

•Understand and perform the following Transformations: Reflections and Translations

•Explore Reflection

•Introduction to Cartesian plane and coordinates.

#### Robert Lang: The math and magic of Origami

1. Have fun making different origami figures.

2. Choose one of your figures to work with during this unit.

3. Make two more of your chosen figure.

(ensure your folds are as sharp as you can make them)

1. Take one of your figures and unfold it completely.

2. Using a ruler and a pencil draw lines over each fold.

3. Find and label one each of the following angles on your paper:

4. Copy the table below into your books.

 Angle type First estimation of angle size (in degrees) before looking at the protractor Second estimation of angle size (in degrees) after looking at a protractor Actual angle size (in degrees)using a protractor to measure right straight acute obtuse reflex

5. For each of the angles you have labelled, do the following recording the values in your table:

i. estimate the size of the angle before you pick up a protractor and record it on your table;

ii. take a protractor and look at how large different angles are. WITHOUT putting this protractor on your piece of paper, estimate for a second time the size of each angle;

iii. using the protractor, measure your angles.

6. Did you measure your right angle and straight angle?? Were they actually 90 and 180 degrees?

7. Which angle out of acute, obtuse and reflex were your estimations more acurate for?
Why do you think this was?

8. How many of each angle do you have on your paper? Count them and record this in your exercise book.

Extra challenge: Work out the "Percentage Error" between your first estimate for an angle and the actual measured angle size.

1. Find and label (using correct notation) two sets of parallel lines and two pairs of perpendicular lines on your unfolded origami figure (the one where you labelled angles).

2. In your exercise books, define the following:

line, line segment, intersection and vertex

3. Find and label on your unfolded origami paper one line segment, one intersection and one vertex.