MAE3270 Module 6 - Lecture 2: Geometry

Chapter 1: Geometric Reasoning

• Year 3:

  • Identify angles as measures of turn

  • Compare angle sizes in everyday situations

• Year 4:

  • Compare angles

  • Classify angles as equal to, greater than, or less than a right angle

• Year 5:

  • Estimate, measure, and compare angles using degrees

  • Construct angles using a protractor

• Year 6:

  • Investigate angles on a straight line, angles at a point, and vertically opposite angles

  • Use results to find unknown angles

Chapter 2: Angles

Using a protractor:

• Align the protractor on top of the angle to measure it

• Encourage students to think in terms of 90 degrees

• Use the appropriate section of the scale on the protractor to measure the angle

• Draw attention to the inside and outside scales of the protractor

The sum of angles in a triangle is 180 degrees.

The sum of angles in a quadrilateral is 360 degrees.

The base angles of an isosceles triangle are equal.

The angles opposite the longer side of a scalene triangle are the largest.

Opposite angles of a parallelogram are equal.

A polygon with more than 3 sides can have some equal sides without having equal angles.

Regular polygons have equal angles.

Angles in a straight line add up to 180 degrees.

If one side of a line is at 77 degrees, the other side would be 103 degrees to add up to 180 degrees.

Vertically Opposite Angles

Verticle angles are opposite each other when two lines intersect each other. Two pairs or opposite angles are equal to each other.

Chapter 4: Orientation Misconceptions

If polygons are alwats shown as regular shapes sitting on one side, then children’s conceptual understanding of these shapes may be limited. Presenting figures in different orientations will allow children to focus on the characteristics that are important when describing them.

• Misconceptions about triangles

  • Students may not recognize triangles presented in different orientations

  • They may think a triangle must have a base at the bottom

  • Height can be labeled outside the triangle

• Misconceptions about polygons

  • Students may only recognize regular polygons

  • Irregular polygons are still polygons

  • Concave polygons have an internal angle greater than 180 degrees

Chapter 5: Geometric Terminology

• Difficulties with geometric terminology

  • Difference between everyday meaning and geometric meaning of terms

  • Similar means the same in everyday English, congruent means the same in math

Chapter 6: Spatial reasoning

• Problems with spatial reasoning

  • Students need practical experience to visualize relationships in diagrams

  • Hands-on materials can help develop spatial awareness

Chapter 7: Angle misconceptions

• Angle misconceptions

  • Students may think the length of the arms of an angle determines its size

  • Distance between the rays determines the size of the angle

Chapter 8: Conclusion

• Geometry helps represent space and describe location, movement, and relationships

• Building visual skills and reasoning is important in geometry

• Transformation and symmetry can be used to solve problems

• Geometry is used to solve problems and appreciate the world around us