Grade 8: Geometry

Warm up with a few quick geometry warm-ups on the board while the class settles, so every child starts thinking about the skill.

This strand covers naming angle relationships made by parallel lines and a transversal, finding a polygon's interior angle sum from its number of sides, classifying quadrilaterals by their properties, and enlarging a shape by a scale factor. Model the method clearly, thinking aloud:

• Teach angles on a straight line (sum to 180) and at a point (sum to 360) first, since every other angle rule builds on these.
• Introduce corresponding and alternate angles as EQUAL pairs, and co-interior angles as a pair that adds to 180, using a labelled diagram every time.
• Derive the polygon angle-sum formula, (n - 2) x 180, by splitting a polygon into triangles from one vertex, rather than just stating it.
• Classify quadrilaterals (square, rectangle, rhombus, parallelogram, trapezium, kite) by their side and angle properties, not just their appearance.
• Teach enlargement as 'every length times the scale factor, every angle unchanged', using a scale factor greater than 1 before a fractional one.

Work this through step by step on the board, then have the class talk you through a second one.

• Find the sum of the interior angles of a hexagon (6 sides)
• (n - 2) x 180 = (6 - 2) x 180 = 4 x 180 = 720 degrees

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the practice worksheet independently while you circulate and support.

Circulate and look for these, they are the usual sticking points:

• Mixing up which angle pairs are equal (corresponding, alternate) versus which add to 180 (co-interior).
• Using the wrong value of n (number of sides) or forgetting to subtract 2 in the polygon angle-sum formula.
• Assuming a shape is a specific quadrilateral (e.g. a rhombus) from its appearance rather than checking its properties.
• Believing enlargement changes a shape's angles as well as its side lengths.

Pull the class back together. Ask one child to explain geometry in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.